Formability and failure of polymeric sheets: experimental assessment and medical applications

Doctoral Thesis Formability and failure of polymeric sheets: Experimental assessment and medical applications Ana Rosa Sainz Supervisors: Dr. Gabriel Centeno Báez Professor of Manufacturing, University of Seville Dra. Maria Beatriz Cipriano de Jesus Silva Associate Professor of Manufacturing, University of Lisbon Dpto. de Ingeniería Mecánica y Fabricación Escuela Técnica Superior de Ingeniería Avda. de los Descubrimientos s/n. 41092 Universidad de Sevilla Sevilla, 2023 i Agradecimientos Me gustaría dar mi más sincero agradecimiento a aquellas personas que me han ayudado durante estos años en este camino, que desde luego me ha ayudado a crecer enormemente no solo de forma académica sino también personal. En primer lugar, me gustaría agradecer a mis directores de tesis, gracias a los cuales ha sido posible desarrollar todo este trabajo. A Gabriel Centeno, por haber confiado en mí desde el primer minuto y por haberme brindado innumerables posibilidades de mejorar en el trabajo y como persona, por nuestras grandes charlas camino a Lisboa y por haberme enseñado a siempre relativizar cuando las cosas se ponen difíciles. Gracias por haberme pegado ese “hacer las cosas especialmente bien” que te caracteriza. A Beatriz Silva, por haberme dado la oportunidad de trabajar contigo, por haberme enseñado y por haber tenido paciencia. Gracias por abrirme las puertas de tu casa y compartir conmigo tus anécdotas y experiencias de vida, porque gracias a eso también me llevo a una amiga. La siguiente frase aplica para ambos: “La enseñanza es más que impartir conocimiento, es inspirar el cambio. El aprendizaje es más que absorber hechos, es adquirir entendimiento.” William Arthur Ward. Mi eterna gratitud al Doctor Andrés Martínez, o profesor Martínez para mí, gracias por haber tenido siempre tiempo para mis dudas y preguntas, por haberme animado y apoyado cuando lo necesitaba y por estar siempre dispuesto a tomarte un café conmigo. También quiero agradecer al Profesor Carpóforo Vallellano, por haberme ayudado cada vez que lo he necesitado y por haberse preocupado siempre de que me fuera bien. Mi reconocimiento a la profesoras María Luisa e Inés por haberme acogido en Girona, por haberme ayudado y enseñado tanto, por vuestras ganas y disponibilidad siempre, gracias porque ambas sois un gran referente para mí. Espero que podamos seguir colaborando juntas mucho tiempo, porque ha sido un verdadero placer cruzarme con vosotras. Mi agradecimiento al Doctor Marcos Borrego, cuyo entusiasmo por aprender y mejorar en la vida se me pegó desde el primer día, gracias por haberme brindado siempre ayuda con amabilidad y ganas. Agradezco al Doctor Domingo Morales, cuyas charlas siempre me han dado ánimos y ganas de seguir adelante, y por estar siempre dispuesto a echarme una mano. A David Palomo, o “Pigeon” para mí, amigo con el que no he podido reírme más durante estos años, gracias por ayudarme y por haber tenido siempre unas palabras buenas para mí. Del doctorado también se sale con amigos. ii Al Doctor Andrés López, mis estancias en Lisboa siempre serán recordadas contigo, gracias por las grandes conversaciones (siempre o casi siempre cerveza en mano) que hemos tenido, y por haberme ayudado siempre que lo he necesitado. A Carlos Suntaxi, gracias por ser un gran ejemplo para todos. Al maestro de mecanizado Manuel Sánchez, persona que durante 4 años me ha recibido siempre con una sonrisa, pese a necesitar innumerables probetas. Gracias por todas tus enseñanzas Manuel. Al maestro de mecanizado Antonio Guillén, cuánto me has enseñado en tan poco tiempo y cuánto te agradezco, gracias Antonio por tu apoyo y por tu ayuda siempre. A Manuel y Antonio, siempre seréis un gran ejemplo para mí. Al Doctor João Magrinho, por ayudarme siempre que lo he necesitado y haber sido un referente, tanto como persona como investigador, espero que podamos seguir haciendo cosas juntos. A mis amigos María y Víctor, que me han acompañado durante esta travesía tanto en mis buenos como malos momentos, gracias por ser claramente la definición de amigos. A mi amigo Luis, que me conoce desde hace más tiempo que yo a mí misma, gracias por nuestras risas y por poder seguir compartiendo tanto. A mi amigo Joan, nunca encontraré las suficientes palabras como para describir la gran suerte que he tenido al cruzarme contigo, gracias por ser como eres. A Laly y Javier, mi familia, gracias porque me habéis visto crecer desde hace muchos años, por haberme dado vuestro apoyo y amor siempre y haberme ayudado desde todas las posibilidades que se puede ayudar a alguien. Siempre os estaré eternamente agradecida. Por último, me gustaría agradecer a la persona más importante de mi vida, a ti Javi, mi compañero de camino, gracias por haber sido incondicionalmente mi apoyo durante todos estos años, por seguir riéndonos juntos y cuidándonos, por sentirme la más afortunada del mundo. iii List of publications The following list contains the resulting publications of this doctoral thesis. JCR Journals: Paper 1: Rosa-Sainz, A., Centeno, G., Silva, M.B., López-Fernández, J.A., Martínez-Donaire, A.J., Vallellano, C. (2020). On the Determination of Forming Limits in Polycarbonate Sheets. Materials, 13(4), 1–17. https://doi.org/10.3390/ma13040928 Cites: 5 (WOS), 6 (SCOPUS), 8 (Google scholar) Category Name Impact factor Position Quartile JCR METALLURGY & METALLURGICAL ENGINEERING 3,623 17/80 Q1 Paper 2: Rosa-Sainz, A., Centeno, G., Silva, M.B., Vallellano, C. (2021). Experimental failure analysis in polycarbonate sheet deformed by spif. Journal of Manufacturing Processes, 64, 1153– 1168. https://doi.org/10.1016/j.jmapro.2021.01.047 Cites: 5 (WOS), 5 (SCOPUS), 8 (Google scholar) Category Name Impact factor Position Quartile JCR ENGINEERING, MANUFACTURING 5,684 15/51 Q2/T1 Paper 3: Rosa-Sainz, A., García-Romeu, M. L., Ferrer, I., Silva, M. B., Centeno, G. (2023). On the effective peek application for customized cranio-maxillofacial prostheses: An experimental formability analysis. Journal of Manufacturing Processes, 86, 66–84. https://doi.org/10.1016/J.JMAPRO.2022.12.044 Category Name Impact factor Position Quartile JCR ENGINEERING, MANUFACTURING 5,684 15/51 Q2/T1 iv Paper 4: Rosa-Sainz, A., Centeno, G., Silva, M.B., Vallellano, C. (2021). Experimental Investigation of Polycarbonate Sheets Deformed by SPIF: Formability, Micro-mechanisms of Failure and Temperature Analysis. Journal of Materials Research and Technology (in review). Category Name Impact factor Position Quartile JCR METALLURGY & METALLURGICAL ENGINEERING 6,267 8/79 Q1/T1 International Conferences: Paper 1: Rosa-Sainz, A., Magrinho, J., Silva, M. B., Centeno, G., Martínez-Donaire, A. J., Vallellano, C. (2021). Experimental research of formability limits in different thicknesses of polycarbonate sheets. International Deep-Drawing Research Group Conference (IDDRG 2021). Paper 2: Rosa-Sainz, A., Centeno, G., Silva, M.B., Vallellano, C. (2021). On the determination of the forming limits 1 by necking and fracture of polycarbonate sheet 13th International Conference on the Technology of Plasticity (ICTP 2021). Paper 3: Rosa-Sainz A., Centeno G., Silva M.B.,Vaz M.F., Vallellano C. On the assessment of formability and failure of polycarbonate sheet deformed by spif Manufacturing Engenieering Society International Conference (MESIC 2021) . Paper 4: Garcia-Romeu, M. L., Ferrer, I., Pasotti, C., Coma, J., Rosa-Sainz, A., Centeno, G. (2022). Preliminary study on the use of 3D printed biodegradable polymeric sheet for the manufacturing of medical prostheses by SPIF. Conference on Biomanufacturing 2022. Paper 5: Rosa-Sainz, A., Centeno, G., Silva, M.B., Vallellano, C. (2023). On the assessment of the forming limit diagram at necking and fracture for polymer sheets 14th International Conference on the Technology of Plasticity 2023 (ICTP 2023) (provisional acceptance). Paper 6: Rosa-Sainz, A., Ferrer, I., García-Romeu, M. L., Silva, M.B., Centeno, G. (2023). An experimental investigation of a cranial prosthesis using SPIF 14th International Conference on the Technology of Plasticity 2023 (ICTP 2023) (provisional acceptance). Paper 7: Rosa-Sainz, A., Centeno, G., Silva, M.B., Vallellano, C. (2021). On the assessment of the failure strains in conventional and incremental forming of polymer sheets Manufacturing Engenieering Society International Conference (2023) (MESIC 2023) (accepted). Paper 8: Rosa-Sainz, A., Ferrer, I., García-Romeu, M. L., Silva, M.B., Centeno, G. On the manufacturing of a cranial PEEK implant using SPIF Manufacturing Engenieering Society International Conference (MESIC 2023) (accepted). v Resumen Durante las últimas décadas, el paradigma de la Industria 4.0, que se dirige hacía procesos flexibles, de baja-media producción, y orientados hacía la personalización del producto, ha provocado grandes cambios en los procesos de fabricación, ejemplo de esta evolución es el avance que ha tenido la fabricación aditiva en los últimos años. Otro claro ejemplo de esta evolución se ha visto en el proceso denominado conformado incremental monopunto o SPIF (por sus siglas en inglés), que permite gran flexibilidad de proceso, ahorro de utillaje y permite la fabricación de productos customizados. Recientemente, la aplicación de SPIF a materiales poliméricos se ha visto incrementada, debido a que además de las ventajas del proceso mencionadas anteriormente, se han realizado verificaciones experimentales de que las deformaciones alcanzadas mediante SPIF se encuentran por encima de la curva límite de conformado por estricción o FLC (por sus siglas en inglés), sin fallo. Sin embargo, cabe señalar que en el caso de las láminas poliméricas no existe un procedimiento sistemático para construir el diagrama límite de conformado o FLD como está bien definido para chapa metálica. En este contexto, la primera parte de esta tesis doctoral tiene el objetivo de proporcionar procedimientos para obtener la curva límite de conformado por estricción (FLC por sus siglas en inglés) y por fractura en modo I de mecánica de fractura (FFL por su siglas en inglés), y con ello, obtener el diagrama límite de conformado (FLD) de materiales poliméricos. Las láminas poliméricas escogidas fueron tres polímeros termoplásticos ampliamente utilizados: policarbonato (PC por sus siglas en inglés), polietileno de alto peso molecular (UHMWPE por sus siglas en inglés) y polieteretercetona (PEEK por sus siglas en inglés). Por otro lado, esta tesis doctoral establece un marco de estudio de distintos parámetros de proceso en SPIF, con el objetivo de asentar una base experimental sobre la afectabilidad de estos parámetros de proceso a los tres materiales poliméricos mencionados anteriormente. El estudio se realiza en términos de deformaciones dentro del diagrama límite de conformado de cada material polimérico obtenido independientemente mediante procesos convencionales. La tercera parte de esta tesis aborda la fabricación de aplicaciones médicas mediante los dos polímeros biocompatibles, UHMWPE and PEEK, con el objetivo de demostrar factibilidad de fabricar mediante SPIF implantes médicos a temperatura ambiente. vi vii Abstract During the last decades, the Industry 4.0 paradigm, which is directed towards flexible, low-medium production processes, and oriented towards product customization, has caused great changes in manufacturing processes. An example of this evolution is the advance that additive manufacturing has had in recent years. Another clear example of this evolution has been observed in the sheet manufacturing process called incremental sheet forming (ISF), specifically in its simpler and dieless type known as single point incremental forming (SPIF). This method offers process flexibility, saves on tool costs, and enables the production of customized products. Recently, the application of SPIF to polymeric materials has increased, since, in addition to the advantages of the process mentioned above, experimental verifications have shown that the strains achieved by SPIF are above the forming limit curve or FLC, without failure. However, it should be noted that in the case of polymeric sheets, there is no systematic procedure to construct the forming limit diagram or FLD as is well-defined for sheet metal forming. In this context, the first part of this doctoral thesis is aimed at providing procedures to obtain the FLC and the FFL (Fracture Forming Limit Line) in mode I of fracture mechanics, and with that, obtain the forming limit diagram (FLD) of polymeric sheet materials. The polymeric sheets chosen were three widely used thermoplastic polymers: polycarbonate (PC), high molecular weight polyethylene (UHMWPE) and polyether ether ketone (PEEK). On the other hand, this thesis establishes a framework for studying the different process parameters in SPIF, to establish an experimental basis on the affectability of these process parameters on the three polymeric materials mentioned. The analysis is carried out in terms of strains within the forming limit diagram of each polymeric material obtained independently through conventional processes. The third part of this thesis deals with the manufacture of medical applications using the two biocompatible polymers, UHMWPE and PEEK, to demonstrate the feasibility of manufacturing medical implants at room temperature using SPIF. xiv Figure 2.14. Schematic representation of (a) the Incremental Backward Bulge process in a conventional CNC milling machine (Jeswiet, 2000) and (b) Incremental Stretch Expanding process (Kitazawa and Nakane, 1997). .................................................................................................................................... 28 Figure 2.15. Experimental equipment for ISF (Filice et al., 2002). ............................................................ 29 Figure 2.16. (a) Classifications of the ISF process and (b) process flow for manufacturing a part using ISF. ............................................................................................................................................................ 30 Figure 2.17. Schematic representation of a cross-sectional view of the rotationally symmetric SPIF process (Silva et al., 2008). ............................................................................................................................. 31 Figure 2.18. TPIF process variants: a) negative full die, b) positive full die and (c) positive partial die (Allwood et al., 2010). ........................................................................................................................ 32 Figure 2.19. DSIF with forming-tools carrying out simultaneous forming (Ajay and Mittal, 2020)........... 33 Figure 2.20. Operation principle of the hybrid process (a) first stage: stretch forming and (b) second stage: ISF process (Ajay and Mittal, 2020). ................................................................................................. 33 Figure 2.21. Schematic process of the (a) deformation of conical element and (b) single stage incremental forming (Ajay and Mittal, 2020). ....................................................................................................... 34 Figure 2.22. Schematic representation of multi-stage incremental forming (Bambach, 2004). ................... 36 Figure 2.23. Representation of the forming tools: (a) hemispherical-end (b) flat-end and (c) roller-ball end (McAnulty et al., 2017). ..................................................................................................................... 36 Figure 2.24. (a) CNC milling machine (Kurra et al., 2015).(b) Experimental set-up of roboforming (Meier et al., 2009). ........................................................................................................................................ 37 Figure 2.25. Purpose built Incremental Forming machines: (a) AMINO (Amino et al., 2014) (b) Designed Incremental Forming machine (Allwood et al., 2005). ....................................................................... 38 Figure 2.26. Polymeric failure modes in SPIF: (a) circumferential crack, (b) twisting and (c) oblique crack observed in the work by Martins et al. (2009). .................................................................................. 39 Figure 2.27. (a) Experimental strains in a truncated conical and pyramidal benchmark SPIF (Marques et al., 2012). (b) Principal strains on the outer surface within the principal strain space and fracture strains defining the FFL (Centeno et al., 2017). ................................................................................ 40 Figure 2.28. (a) Schematic representation of the local contact area (shell element) between the tool and sheet placed immediately ahead. (b) Instantaneous deformation zones and evidence of the extreme modes of deformation obtained from CGA technique (Silva et al., 2010). ......................................... 41 Figure 2.29. Membrane analysis of SPIF : (a) Schematic representation of the local contact area between the tool and sheet placed immediately ahead. (b) Approximation of the local contact area by a shell element. (c) Cross-section view showing the acting stresses in meridional, circumferential and thickness directions (Silva et al., 2010). ............................................................................................................. 42 xv Figure 2.30. (a)Triaxiality ratio as a function of sheet thickness calculated from the theoretical framework. (b) Experimental strains obtained in SPIF of truncated conical parts with 3 mm thickness using an initial drawing angle 30° for PC with tool radius of 4, 5 and 6 mm (Marques et al., 2012). ............. 48 Figure 2.31. Stress strain curve for PVC: (a) under different testing speeds at room temperature and (b) at 50 mm/min at room temperature, 40°C and 60°C (Bagudanch et al., 2017). .................................... 49 Figure 2.32. (a) Formability as a function of the initial drawing angle for sheet blanks with 2 mm thickness (Franzen et al., 2008). (b) PET sheet blanks with 2 mm thickness and initial drawing angles Ψ0 of 30°, 45° and 60° (Marques et al., 2012). ............................................................................................. 49 Figure 2.33. Variability of shapes manufactured by ISF with metals to demonstrate the feasibility of the process (Jeswiet et al., 2005). ............................................................................................................. 51 Figure 2.34. Geometry of a truncated conical with (a) fixed wall angle (Davarpanah et al., 2015) and (b) with variable wall angle (Durante et al., 2018). Truncated geometry of a pyramidal with (c) fixed wall angle (Durante et al., 2018) and (d) with variable wall angle (Bagudanch et al., 2017). .................. 51 Figure 2.35. Representation of (a) profile tool path and (b) helical tool path (Ajay and Mittal, 2020). (c) Constant step down (Attanasio et al., 2006) (d) Constant scallop height (Callegari et al., 2006) and (e) constant angular increment (Fiorentino et al., 2009). .................................................................. 52 Figure 2.36. Representation of (a) unidirectional tool path and (b) bidirectional tool path (Ajay and Mittal, 2020). .................................................................................................................................................. 53 Figure 2.37. Potential geometric errors in the SPIF process (Nasulea and Oancea, 2021). ........................ 55 Figure 2.38. (a) The individual components of a total hip replacement and (b) the components merged into an implant (Hospital Padmaja, 2022). ............................................................................................... 58 Figure 2.39. Processing steps in the manufacture of UHMWPE implants (Kurtz, 2016). .......................... 59 Figure 2.40. (a) Temperature-high laser build of cranial implants manufactured at several orientations with respect to the building direction and (b) location of the cranial implant (Berretta et al., 2018). ..... 60 Figure 2.41. (a) CAD model and final part of the ankle support (Ambrogio et al., 2005). (b) Uncompensated Titanium cranial implant (Duflou et al., 2013). ................................................................................. 61 Figure 2.42. (a) Designed produced and mounted clavicle implant on a generic synthetic bone (Vanhove et al., 2017). (b) Cheekbone area for obtaining the CAD model and cheekbones produced by SPIF (Guglielmi et al., 2021). ...................................................................................................................... 62 Figure 2.43. (a) The production of a palate die utilizing the SLS process. (b) The manufacturing of a PCL palate prosthesis utilizing ISF. ........................................................................................................... 63 Figure 2.44. Sequence to follow to manufacture a prosthesis by SPIF adapted from Bagudanch et al. (2018). ............................................................................................................................................................ 64 Figure 2.45. (a) Front view showing the manufactured implant required (left) and adjustment of the UHMWPE customized implant to the biomodel. (b) Geometric deviation (in mm) for the cranial implant manufactured using SPIF at a free spindle speed (Bagudanch et al., 2018). ........................ 64 xvi Figure 2.46. (a) PC manufactured cranial prosthesis over the zone to be replaced and (b) Principal strains of the cranial prosthesis within the forming zone by SPIF (Centeno et al., 2017). ........................... 65 Figure 3.1. Schematic representation of the polymeric Nakajima test specimens: (a) tensile strain (TS), (b) plane strain (PS), (c) biaxial strain (BS) and (d) equibiaxial strain (EBS). ..................................... 68 Figure 3.2. Schematic representation of the universal sheet testing machine indicating the main components. ............................................................................................................................................................ 69 Figure 3.3. Schematic representation of (a) major strain distribution of a TS specimen in the Nakajima specimen indicating the points considered, (b) evolution of major strains with time for the necking region, (c) time‐dependent approach application. .............................................................................. 71 Figure 3.4. Schematic representation of (a) a section perpendicular to the failure area of a Nakajima test for a TS specimen, (b) Temporary evolution of the Z displacement over the X position for instants before, after, and at the onset of necking, and (c) its spatial derivative on a section normal to the failure area. ......................................................................................................................................... 72 Figure 3.5. Schematic representation of the TS Nakajima specimen (a) during the test, depicting the necking propagation and the transition zone and (b) after fracture, depicting the thickness at fracture. ...... 73 Figure 3.6. Schematic representation of the SPIF process performed on a CNC milling machine for a truncated conical geometry indicating the main components. ........................................................... 75 Figure 3.7. Schematic view of the utilization of the ARGUS® system for a (a) truncated conical and (b) pyramidal geometries. ......................................................................................................................... 76 Figure 3.8. The final conical and pyramidal spifed specimens depicting the sections of analysis and the resulting strains within the FLD material. ......................................................................................... 77 Figure 3.9. View of the setup used along with the backing plate dimensions in mm for (a) truncated conical and (b) pyramidal geometries with fixed wall angles in CNC EMCO® and, (c) truncated pyramidal geometry with a variable wall angle in CNC Kondia®. ...................................................................... 78 Figure 3.10. Forming tools grouped by CNC milling: (a) 10, 12 and 20 mm diameter on CNC milling EMCO® (b) 4 and 6 mm diameter on CNC milling Kondia® HS1000. ............................................... 79 Figure 3.11. Equipment used in the SPIF tests: (a) FLIRTM T430sc and (b) SEM microscope JEOLTM JSM7001F. .......................................................................................................................................... 80 Figure 3.12. Equipment used in the SPIF tests: (a) camera IRBIS® Image IR13300 (b) CMM Mitutoyo® Crysta-Apex C544 and (c) Mitutoyo® Surftest SV2000. .................................................................... 81 Figure 3.13. Schematic representation of the considered trajectories (a) the unidirectional and, (b) the bidirectional trajectories. .................................................................................................................... 82 Figure 3.14. (a) Schematic diagram of a total hip replacement, depicting the different components. (b) Assembly of the artificial hip prosthesis into a pelvis. ....................................................................... 90 xvii Figure 3.15. (a) 3D printed backing plate in the SPIF setup along with dimensions in mm (b) 3D model printed using CURA software and, (c) PLA 3D printed backing plate mount in SPIF setup. ......... 92 Figure 3.16. 3D cranial model indicating the cranial bones and the planned reconstruction for (a) a zygomatic bone defect (cheekbone implant) and, (b) a temporary and parietal defect (cranial implant). ............................................................................................................................................................ 93 Figure 4.1. Application of the methodologies to obtain the onset of necking strains for a TS Nakajima specimen of PC with 1 mm of thickness. (a) Major strain (left) and surface shape (right) of the specimen’s failure area obtained by the DIC system. (b) Experimental time evolution of the major strain along the points of the selected section. (c) Time‐dependent approach application. (d) Z‐ displacement along the selected section. (e) The spatial derivative of Z‐displacement along the selected section. ................................................................................................................................................ 97 Figure 4.2. Application of the methodologies to obtain the onset of necking strains for a BS Nakajima specimen of PC with 1 mm of thickness. (a) Major strain (left) and surface shape (right) of the specimen’s failure area obtained by the DIC system. (b) Experimental time evolution of the major strain along the points of the selected section. (c) Time‐dependent approach application. (d) Z‐ displacement along the selected section. (e) The spatial derivative of Z‐displacement along the selected section. ................................................................................................................................................ 99 Figure 4.3. Application of the methodologies to obtain the onset of necking strains for an EBS Nakajima specimen of PC with 1 mm of thickness. (a) Major strain (left) and surface shape (right) of the specimen’s failure area obtained by the DIC system. (b) Experimental time evolution of the major strain along the points of the selected section. (c) Time‐dependent approach application. (d) Z‐ displacement along the selected section. (e) The spatial derivative of Z‐displacement along the selected section. ............................................................................................................................................... 100 Figure 4.4. Application of the methodologies to obtain the onset of necking strains for a TS Nakajima specimen of PC with 2 mm of thickness. (a) Major strain (left) and surface shape (right) of the specimen’s failure area obtained by the DIC system. (b) Experimental time evolution of the major strain along the points of the selected section. (c) Time‐dependent approach application. (d) Z‐ displacement along the selected section. (e) The spatial derivative of Z‐displacement along the selected section. ............................................................................................................................................... 103 Figure 4.5. Fractography of a TS Nakajima specimen showing the magnification of the fracture zone, the transition zone and the necking propagation for (a) 1 mm and (b) 2 mm thickness of PC sheets. .. 105 Figure 4.6. Formability limits by necking (FLC) and by Fracture (FFL) obtained for TS, PS, BS and EBS Nakajima specimens for (a) 1 mm and (b) 2 mm thickness PC sheets. ............................................ 106 xviii Figure 4.7. Application of the methodologies to obtain the onset of necking strains for a TS Nakajima specimen of UHMWPE with 2 mm of thickness. (a) Major strain (left) and surface shape (right) of the specimen’s failure area obtained by the DIC system. (b) Experimental time evolution of the major strain along the points of the selected section. (c) Time‐dependent approach application. .............. 108 Figure 4.8. Application of the time-dependent to the (a) BS and (b) EBS specimens of UHMWPE with 2 mm thickness. (c) Major strain distribution and fracture specimen of BS (above) and EBS (below) and ..................................................................................................................................................... 109 Figure 4.9. Fractography of the UHMWPE TS specimen. ........................................................................ 111 Figure 4.10. Formability limits by necking (FLC) and by fracture (FFL) obtained by means of tensile, plane, biaxial and equibiaxial Nakajima specimens in UHMWPE with 2 mm thickness. ................. 111 Figure 4.11. Application of the methodologies to obtain the onset of necking strains for a TS Nakajima specimen of PEEK with 2 mm of thickness. (a) Major strain (left) and surface shape (right) of the specimen’s failure area obtained by the DIC system. (b) Experimental time evolution of the major strain along the points of the selected section. (c) Time‐dependent approach application. .............. 113 Figure 4.12. Application of the time-dependent to the (a) BS and (b) EBS specimens of PEEK with 2 mm thickness. (c) Major strain distribution and fracture specimen of BS (above) and EBS (below) and (d) force-displacement for PEEK Nakajima specimens. .......................................................................... 114 Figure 4.13. Fractography of a TS Nakajima specimen showing the magnification of the fracture zone, the transition zone and the necking propagation for 2 mm thickness PEEK sheet. ............................... 115 Figure 4.14. Formability limits by necking (FLC) and by fracture (FFL) obtained by means of tensile, biaxial and equibiaxial Nakajima specimens for PEEK with 2 mm thickness. ................................. 116 Figure 4.15. Modes of failure of 2 mm thickness PC sheets deformed by SPIF in the conical geometry: . 120 Figure 4.16. FLDs depicting the experimental results obtained in SPIF for the truncated conical geometry with 2 mm thickness PC sheet. (a) Truncated conical geometry for performing the principal strain measurement using ARGUS® for the reference test and, analysis of the influence of the: (b) step down, (c) tool diameter (d) spindle speed, and (e) feed rate. ...................................................................... 122 Figure 4.17. Modes of failure of 2 mm thickness PC sheets deformed by SPIF in the pyramidal geometry: (a) fracture, (b) twisting and (c) fracture and crazing. ..................................................................... 124 Figure 4.18. FLDs along with the contour of major principal strain on the final specimen tested for each of the SPIF testing conditions considered. (a) Truncated pyramidal geometry for performing the principal strain measurement using ARGUS® with the reference test and, for changing in (b) and (c) step down, (d) and (e) in tool diameter, (f) and (g) in spindle speed, (h) and, (i) in feed rate. ......................... 126 Figure 4.19. FLDs with the maximum strains at fracture for the SPIF tests varying the step down from 0.1 to 0.5 mm, the tool diameter from 20 to 10 mm, the spindle speed from 20 to 1000 rpm, and the feed rate from 1000 to 250 mm/min in the truncated (a) conical and (b) pyramidal geometries. ........... 129 xix Figure 4.20. Temperature evolution of each test with respect to the reference test (“PC 2 U TP0”) varying the (a) step down, (b) tool diameter, (c) spindle speed and (d) feed rate. ....................................... 130 Figure 4.21. Plot of the equation 16 for maximum temperature (𝑇𝑚𝑎𝑥) as a function of the step down and the spindle speed through for PC sheets (a) the 2D contour (b) the 3D logarithmic surface. .......... 133 Figure 4.22. Images of the failures on the specimens together with the SEM of the failure: (a) fracture surface on the thickness, (b) twisting surface and (c) crazing surface. ............................................. 134 Figure 4.23. Images of the failures on the specimens together with the SEM of the failure: (a) fracture on the specimen thickness and (b) SEM magnifications of the fracture on the thickness, (c) twisting in the specimen and (d) SEM magnifications of the twisting surface. ................................................... 135 Figure 4.24. (a) Image of the failure on the specimen together with the SEM of the failures: (b) SEM magnification of the fracture surface on the thickness and, (c) SEM magnification of the crazing surface. ............................................................................................................................................... 136 Figure 4.25. FLDs comparing the SPIF tests performed with oil vs. water for (a) “PC 2 U TC0”, (b) “PC 2 U TC1” and (c) “PC 2 U TC6”. .................................................................................................... 139 Figure 4.26. (a) Image of the failures on the specimen deformed by SPIF with oil and (b) SEM images of the post-crazing surface magnifications. ............................................................................................ 140 Figure 4.27. EDS extracted from the specimens for (a) “PC 2 U TC0” with oil and (b) “PC 2 U TC0” with water. ................................................................................................................................................. 140 Figure 4.28. Image of the UHMWPE specimens performed by SPIF with the conditions of spindle speed 500 rpm, unidirectional trajectory and step down of: (a) 0.1, (b) 0.3, and (c) 0.5 mm. ................... 142 Figure 4.29. Image of the UHMWPE specimens performed by SPIF with the conditions of spindle speed 20 rpm, unidirectional trajectory and step down of: (a) 0.1, (b) 0.3, and (c) 0.5 mm. .......................... 143 Figure 4.30. Image of the UHMWPE specimens performed by SPIF with the conditions of spindle speed 500 rpm, bidirectional trajectory and step down of: (a) 0.1, (b) 0.3, and (c) 0.5 mm. ..................... 143 Figure 4.31. Image of the fracture and non-fracture zones of the UHMWPE spifed in the truncated pyramidal geometry. .......................................................................................................................... 145 Figure 4.32. FLD obtained by measuring the fracture thickness for the truncated pyramidal geometry with 2 mm thickness UHMWPE. .............................................................................................................. 145 Figure 4.33. UHMWPE temperature evolution of each test for (a) unidirectional strategy with 500 rpm of spindle speed, (b) unidirectional strategy with 20 rpm of spindle speed and (c) bidirectional strategy with 500 rpm of spindle speed. .......................................................................................................... 147 Figure 4.34. Plot of the equation 16 with the parameters in Table 4.11 for depicting the maximum temperature (𝑇𝑚𝑎𝑥) as a function of the step down and the spindle speed through (a) the 2D contour (b) the 3D logarithmic surface for UHMWPE material. ................................................................... 149 Figure 4.35. (a) Truncated pyramidal geometry for performing the principal strain measurement using the ARGUS® system. FLDs depicting the experimental results obtained in SPIF for the 2 mm thickness xx PEEK sheet for free and 500 rpm spindle speed with (b) 0.1 mm, (c) 0.35, (d) 0.6 and (e) 1.2 mm of step downs. ........................................................................................................................................ 152 Figure 4.36. (a) Truncated conical geometry for performing the principal strain measurement the using ARGUS® system. FLDs depicting the experimental results obtained in SPIF for the 2 mm thickness PEEK sheet for free and 500 rpm spindle speed with (b) 0.35 mm, (c) 1.2 mm. ............................. 153 Figure 4.37. FLDs with the maximum major strains at fracture for the truncated (a) conical and (b) pyramidal geometries of 2 mm thickness PEEK sheets. .................................................................... 154 Figure 4.38. 3D evolution of temperature vs. time of each test for the PEEK truncated pyramidal geometry. (a) For the case of spindle (a) free and (b) 500 rpm. ........................................................................ 156 Figure 4.39. Plot of the equation 16 with the parameters in Table 4.13 for depicting the maximum temperature (𝑇𝑚𝑎𝑥) as a function of the step down and the spindle speed through (a) the 2D contour (b) the 3D logarithmic surface for PEEK material. .......................................................................... 157 Figure 4.40. Truncated pyramidal geometry spifed profiles with the ideal profile for spindle speed (a) free and (b) 500 rpm. ................................................................................................................................ 159 Figure 4.41. Strains achieved for the UHMWPE SPIF geometries by using the measurement of the final thickness in the FLD obtained independently from Nakajima tests. ................................................ 162 Figure 4.42. Differences between the 3D scanner plastic liner model and CAD model along with the image extracted from the 3D scanner software for (a) hemispherical geometry with 1 cycle, (b) hemispherical geometry with 3 cycles, and (c) hemispherical and cylindrical geometry with 3 cycles. ................... 163 Figure 4.43. Cheekbones prostheses manufactured by SPIF: (a) major strain distribution by ARGUS® and (b) the FLD obtained indicating the studied sections on the cheekbones. ........................................ 165 Figure 4.44. (a) PEEK cheekbones prostheses manufactured by SPIF and (b) thickness vs. position for the cheekbones. ........................................................................................................................................ 166 Figure 4.45. FLD obtained for the PEEK cranial implant manufactured by SPIF indicating the three studied sections by the ARGUS® system. ...................................................................................................... 168 Figure 4.46. (a) PEEK cranial implant manufactured by SPIF and (b) thickness vs. position for two sections on the cranial prosthesis. ................................................................................................................... 168 Figure 4.47. PEEK cranial prosthesis manufactured: (a) Isometric view of the assembly between the CAD model (grey) overlay with the scan (orange) with different transparency. (b) Assembly sliced by a vertical plane to show the contour of the CAD model and the scanned model. ............................... 169 Figure 4.48. Cranial prosthesis manufactured: (a) The ideal PEEK cranial profile versus the actual profile for (a) section 1 and (b) section 2. .................................................................................................... 170 Figure 4.49. (a) Cranial model and cranial implant and (b) adjustment of the customized implant to the half cranial bio-model. ....................................................................................................................... 171 xxi List of Tables Table 2.1. Mechanical properties of PC polymer (Legrand and Bendler, 1999). ........................................ 12 Table 2.2. Mechanical properties of UHMWPE polymer (Kurtz, 2004). .................................................... 13 Table 2.3. Mechanical properties of PEEK polymer (Kurtz, 2019). ........................................................... 14 Table 2.4. Cold forming for polymers adapted from Shaw (1980). ............................................................. 20 Table 2.5. SPIF schematic representation indicating the main components, benefits and limitations of the SPIF process. ...................................................................................................................................... 31 Table 2.6. TPIF schematic representation indicating the main components, benefits and limitations of the TPIF process. ..................................................................................................................................... 32 Table 2.7. State of stress and strain in the small localized plastic zone of the SPIF of thermoplastics (Marques et al., 2012). ........................................................................................................................ 43 Table 2.8. Categorization in ISF parameters classified by process, material, and design parameters. ....... 44 Table 2.9. Summary of the process parameters that affect the formability of polymers in ISF. ................ 47 Table 3.1. Dimensions of the Nakajima specimens (notation in concordance with Figure 3.1). ................. 68 Table 3.2. Summary of the SPIF tests conditions. ...................................................................................... 81 Table 3.3. Geometrical parameters for a PC truncated conical geometry. ................................................. 83 Table 3.4. SPIF experimental plan for the truncated conical geometry with 1 mm thickness PC sheet. ... 84 Table 3.5. SPIF experimental plan for the truncated conical geometry with 2 mm thickness PC sheets. . 84 Table 3.6. Geometrical parameters for a PC truncated pyramidal geometry. ............................................ 85 Table 3.7. Geometrical parameters for a UHMWPE truncated pyramidal geometry. ................................ 86 Table 3.8. SPIF experimental plan for the truncated pyramidal geometry with 2 mm thickness UHMWPE sheets. ................................................................................................................................................. 86 Table 3.9. Geometrical parameters for a PEEK truncated conical and pyramidal geometries. .................. 87 Table 3.10. SPIF experimental plan for the truncated pyramidal and conical geometry with 2 mm thickness PEEK sheets. ...................................................................................................................................... 88 Table 3.11. Geometrical parameters for the two geometries considered for manufacturing a plastic liner by UHMWPE. ......................................................................................................................................... 90 Table 3.12. Process parameters for the two geometries considered for manufacturing a plastic liner by UHMWPE. ......................................................................................................................................... 91 Table 3.13. Printing parameters used for the manufacturing of PLA backing plate. ................................. 92 xxii Table 3.14. SPIF experimental plan for the cheekbone and cranial prostheses manufactured using PEEK. ............................................................................................................................................................ 94 Table 4.1. Summary of strains pairs at the onset of necking for PC with 1 mm thickness. ...................... 101 Table 4.2. Summary of strains pairs at the onset of necking for PC with 2 mm thickness. ...................... 104 Table 4.3. Summary of strains pairs at the onset of necking for UHMWPE with 2 mm thickness. .......... 110 Table 4.4. Summary of strains pairs at the onset of necking for PEEK with 2 mm thickness. ................. 115 Table 4.5. SPIF experimental results for 1 mm thickness PC sheet for the truncated conical geometry. . 119 Table 4.6. SPIF experimental results for 2 mm thickness PC sheet using the truncated conical geometry. ........................................................................................................................................................... 119 Table 4.7. SPIF experimental results for 2 mm thickness PC sheet using the truncated pyramidal geometry. ........................................................................................................................................................... 123 Table 4.8. Calculated constants for the temperature empirical model for PC sheets. ............................... 132 Table 4.9. SPIF experiments considered to use water as lubricant in PC sheets. ..................................... 138 Table 4.10. SPIF results for the truncated pyramidal geometry for 2 mm thickness UHMWPE. ............ 141 Table 4.11 Calculated constants for the temperature empirical model for UHMWPE sheets. .................. 149 Table 4.12. SPIF experimental results for 2 mm thickness PEEK sheet. .................................................. 150 Table 4.13. Calculated constants for the temperature empirical model for PEEK sheets. ........................ 157 Table 4.14. Deviation results of the SPIF experimental work for three points located on the pyramids wall. ........................................................................................................................................................... 160 Table 4.15. Process conditions for manufacturing hemispherical and hemispherical +cylinder plastic liner. ........................................................................................................................................................... 161 Table 4.16. Results for major and minor strain using different values of beta for the hemispherical geometry with 1 SPIF cycle. ............................................................................................................................. 162 Table 4.17. Summary of the results obtained for the manufactured cheekbone prostheses by PEEK. ..... 164 Table 4.18. Results obtained for the cranial implant manufactured by PEEK. ........................................ 167 Table 4.19. Deviation results from the manufactured cranial implant by SPIF for different Z depths points. ........................................................................................................................................................... 170 Table 4.20. Deviation results of the manufactured cranial implant by SPIF for different X position points. ........................................................................................................................................................... 171 xxiii List of Symbols Latin Symbols 𝐷 – Diameter 𝐸 – Young modulus 𝐿𝑜 – Gauge length 𝐿 – Total length 𝑅 – Radius 𝑊𝑜 – Gauge width 𝑊 – Total width 𝑡0 – Initial thickness 𝑡𝑓 – Thickness at fracture 𝑅𝑓 – Reduction thickness at fracture Greek Symbols 𝛽 – Strain ratio 𝜀1 – In-plane major strain 𝜀2 – In-plane minor strain 𝜀1,𝑙𝑖𝑚 – Major strain at the onset of necking 𝜀2,𝑙𝑖𝑚 – Minor strain at the onset of necking 𝜀3 – Out-of-plane strain 𝜎𝜃 – Circumferential stress 𝜎𝑡 – Thickness stress 𝜎𝜑 – Meridional stress Introduction 5 Figure 1.1. Thesis road map. Introduction 6 State of the Art 7 Chapter 2 2. State of the Art This chapter presents the context related to the literature in which this thesis is developed. To this regard, the first part (section 2.1) introduces the environment of the polymeric materials, showing its theoretical fundamentals, types, and most typical manufacturing process. The second part (section 2.2) outlines the fundamentals of incremental sheet forming (ISF) by providing an overview of the process along with the main parameters. The third part (section 2.3) shows the basis of formability focusing on polymeric sheets. Finally, the last section (section 2.4) presents the state of the art of medical polymer applications. 2.1 Polymers This section introduces the principles of the polymeric material, addressing the different types of polymers and the general polymer's behavior. This section also contains a general outline of the thermoplastics to introduce the three polymers which have been used in this thesis: polycarbonate (PC), ultra-high-molecular-weight polyethylene (UHMWPE) and polyether ether ketone (PEEK). Engineering materials can be classified into four types: (1) metals, (2) ceramics, (3) polymers, and (4) composites. As engineering materials, polymers are relatively new compared to metals and ceramics (Patterson, 2014). A polymer material may be described as a compound consisting of long-chain molecules, each molecule made up of repeating units connected together. Polymers can be divided in three types: thermoplastic, thermosetting and elastomer. In this sense, thermoplastics polymers, are liquids when heated to temperatures of only a few hundred degrees. For this reason, thermoplastics are easily and economically shaped into products. In addition, thermoplastics can be submitted to heating and cooling cycles repeatedly without significant degradation. In contrast, thermosetting polymers cannot tolerate repeated heating cycles as thermoplastics, when initially heated, they soften and flow for molding, but high State of the Art 8 temperatures produce chemical reactions that harden the material into an infusible solid. The elastomers are polymers that exhibit extreme elastic extensibility when subjected to relatively low mechanical stress. Below the glass transition temperature, this kind of polymer is hard and brittle, and above the glass temperature, the material is in rubbery state (Frellmann and Seidler, 2001). Polymers stand out in the commercial and industrial fields for their various advantages (Frellmann and Seidler, 2001):  Plastics have attractive properties for many engineering applications as: low density relative to metals and ceramics, good strength-weight ratios, high corrosion resistance and low electrical and thermal conductivity.  On a volumetric basis, polymers generally require less energy to produce parts than metals, since the working temperatures are much lower than the ones for metals.  Plastics can be formed into intricate part geometries, usually not needing of postprocessing. On the other hand, polymers present the following limitations:  Relatively low strength when compared with metals and ceramics, as well as low elasticity modulus.  Limited service temperature because of the softening of thermoplastic polymer or the degradation of thermosetting and elastomers.  Polymers are viscoelastic materials, which can be limited in load-bearing applications. The above advantages and limitations are related to the internal structure of a polymer. To this respect, polymers are synthesized by joining together small molecules (monomers) to form very large molecules called macromolecules, that have a chain-like structure. The monomers are single unsaturated organic molecules such as ethylene C2H4 and the atoms in these molecules are held together by a strong primary covalent bonding. The bonding between macromolecules in the mass is due to the Van der Waals forces and other secondary bonding types. Therefore, the aggregate polymer material is held together by forces which are substantially weaker than the primary bonds holding the molecules together. This explains why plastics in general are not almost as stiff and strong as metals or ceramics (Rösler et al., 2007). Plastics can be shaped into a wide variety of products, such as molded parts, extruded sections, films and sheets, insulation coatings on electrical wires and fibers for textiles. Plastic-shaping processes may be classified according to the resulting product geometry as follows: continuous extruded products with constant cross sections other than sheets, films, and filaments, continuous sheets and films continuous fibers, molded parts which State of the Art 9 are mostly solid, hollow molded parts with relatively thin walls, discrete parts made from formed sheets and films, castings, and foam products (Groover, 2019). Figure 2.1 shows the plastic generation by the industrial sector extracted from Geyer et al. (2017). As it can be observed, in 2015, primary plastics production was 407 million tons. Packaging is the most prominent application for polymers, followed by building, construction, and textiles, which have a similar generation of tons. In this sense, the most important commercial processes are extrusion, blow molding and injection molding. These manufacturing processes, which will be discussed in detail later, are mass-producing plastic products, and it means higher efficiency, saves cost, and allows for making multiple parts simultaneously, among others advantages. Figure 2.1. Plastic generation by industrial sector in 2015 (Geyer et al., 2017). Globally, the industry is moving towards automation, flexibility and production customization (Popkova et al., 2006). As a consequence, since the last decades, many manufacturing companies are being challenged by the trend that their products need to be produced in lower volumes and in customized forms (Saniuk et al., 2020). From a global perspective, there are more variables that companies should take into account as shape, volume-cost ratio, production time and material. In this sense, Figure 2.2 shows the cost per part of different manufacturing processes vs. volume of parts. The typical polymer manufacturing processes such as injection molding (labeled in black as “Injection Molding” in Figure 2.2), extrusion (labeled in blue as “Extrusion” in Figure 2.2) and thermoforming, among others, are classified as conventional processes. They require expensive custom-designed tooling and are, State of the Art 10 therefore, economically feasible only for mass production. If only one or few components are to be manufactured, other processes are needed. In this sense, machining (labeled in yellow as “CNC Machining” in Figure 2.2) is an extended conventional process for manufacturing of certain parts, however, it has the drawback of wasting material and also the difficulty of manufacturing sheet parts. Furthermore, the cost per part is very high compared to all other processes. Figure 2.2. Cost per part versus volume of manufacturing processes for plastics adapted from FormLabs (2021). On the other hand, non-conventional manufacturing processes, such as additive manufacturing (labeled in orange as “Additive Manufacturing” in Figure 2.2), is used for manufacturing small-medium batches and has the advantage of allowing customized parts. Another unconventional method that allows the manufacture of small-medium batches in an inexpensive and flexible way is the incremental sheet forming (ISF) technology (labeled in red as “ISF” in Figure 2.2). ISF has the capacity to produce parts at a lower cost due to the flexibility and elimination of costly dies. Typical manufacturing processes for polymers will be explained in section 2.1.2. 2.1.1 Thermoplastics Commercially, thermoplastics are the most relevant of the three kinds of polymers (thermoplastics, thermosets and elastomers), constituting around 70% of the tonnage of all synthetic polymers produced. The remaining 30% is shared by thermosets and elastomers (Geyer et al., 2017). Thermoplastic polymers can suffer multiple heating and cooling cycles without degrading the polymer by contrast to thermosetting and elastomers. At room temperature, a thermoplastic is characterized by: (i) very low stiffness, elasticity State of the Art 11 is two or more orders of magnitude smaller than metals and ceramics, (ii) low tensile strength, (iii) very low hardness, and (iv) high ductility (Groover, 2019). Mechanical properties of thermoplastics depend on temperature. In this sense, two temperatures may be highlighted: the melting point (𝑇𝑚) and the glass-transition temperature (𝑇𝑔). The melting point is the temperature at which the polymer changes its state from solid to liquid, and the glass-transition temperature changes the polymer states from hard and brittle into a viscous or rubbery state. (a) (b) (c) (d) Figure 2.3. Structures (a) amorphous, (b) semi-crystalline and, (c) crystalline (Lampman, 2004). (d) Deformation resistance vs. temperature for different types of polymer structures (Groover, 2019). Thermoplastic polymers can have two structures and/or a combination of both: amorphous and crystalline. The terms amorphous and crystalline are commonly used to denote ordered and disordered regions of polymers. In this sense, Figure 2.3a shows the chains schematically in disorder (amorphous), Figure 2.3b when they are partially in order (semi-crystalline) and Figure 2.3c when they are in order (crystalline). Figure 2.3d represents schematically the deformation resistance versus temperature for different types of polymer structures. An amorphous thermoplastic is rigid and glass-like below its glasstransition temperature 𝑇𝑔 and flexible or rubber-like just above it. As temperature increases above 𝑇𝑔, the polymer becomes increasingly soft, finally becoming a viscous fluid. Below 𝑇𝑔, the material is elastic and resistant. At 𝑇𝑔, a rather sudden drop in deformation resistance is observed as the material transforms into its rubbery phase, its behavior is viscoelastic in this region. As temperature increases, it gradually becomes more fluid-like (Groover, 2019). State of the Art 12 The following is presenting a brief state of the art of the three polymers used in the experimental work of this thesis, polycarbonate (PC), ultra-high-molecular-weight polyethylene (UHMWPE) and polyether ether ketone (PEEK). Polycarbonate (PC) Polycarbonates (PCs) are amorphous thermoplastics characterized by a combination of toughness, transparency, heat and flame resistance, and dimensional stability. Table 2.1 indicates the PC mechanical properties (Legrand and Bendler, 1999). The insulating and other electrical characteristics of PCs are excellent and are almost unchanged by temperature and humidity conditions. One exception is the arc resistance, which is lower than that of many other plastics. PCs are soluble in chlorinated hydrocarbons and are attacked by most aromatic solvents, esters, and ketones, which cause crazing and cracking in stressed parts (Legrand and Bendler, 1999). PC is noted for high-notched izod impact strength, 600 to 850 J/m as well as high strength and stiffness. Table 2.1. Mechanical properties of PC polymer (Legrand and Bendler, 1999). Coefficient of friction 0.31 Elongation at break (%) 100-150 Hardness - Rockwell M70 Izod impact strength (J m⁻¹) 600-850 Poisson's ratio 0.37 Tensile modulus (GPa) 2.3 – 2.4 Tensile strength (MPa) 55-75 Glass-transition temperature (°C) 150 Melting point (°C) 220-230 Regarding the PCs polymer processes, injection molding (see section 2.1.2), profile extrusion (see section 2.1.2), blow molding, and foam molding are the most frequently used. Applications for PCs include: (i) components for business machines and telecommunication equipment, (ii) appliance parts, (iii) automotive components, (iv) sports equipment, (v) food, beverage containers, microwaves, cookware (vi) medical components and devices (Legrand and Bendler, 1999). State of the Art 13 Ultra-high-molecular-weight polyethylene (UHMWPE) Ultra-high-molecular-weight polyethylene (UHMWPE) belongs to the family of polyethylenes. UHMWPE is a semi-crystalline polymer characterized by good chemical resistance and excellent mechanical properties. Table 2.2 indicates the mechanical properties of UHMWPE. This thermoplastic material has a high impact strength and it is corrosion-resistant and exhibits practically no water absorption. It is also wear-resistant, non-sticky and self-lubricating (Kurtz, 2004). Table 2.2. Mechanical properties of UHMWPE polymer (Kurtz, 2004). Coefficient of friction 0.1-0.2 Elongation at break (%) 500 Hardness - Rockwell R50-70 Izod impact strength (J m⁻¹) < 199 Poisson's ratio 0.46 Tensile modulus (GPa) 0.2 – 1.2 Glass-transition temperature (°C) -150 Melting point (°C) 150 UHMWPE is produced as powder and must be consolidated under high temperatures and pressures because of its high melt viscosity. UHMWPE does not flow like lower molecular weight polyethylenes when raised above their melt temperature. This fact is that due to its high molecular weight, the material has very little fluidity. For this reason, many thermoplastic processing techniques, such as injection molding (see section 2.1.2), screw extrusion (see section 2.1.2), or blow molding, are not practical for UHMWPE. Instead, semi-finished UHMWPE is typically produced by compression molding (see section 2.1.2) and ram extrusion. UHMWPE is a biocompatible polymer strongly used in medicine, in applications such as knee or hip prostheses, due to its high resistance. It is also used in personal armor or vehicle armor (Kurtz, 2004). Further information on UHMWPE utilized in medical applications will be addressed in section 2.4. Polyether ether ketone (PEEK) PEEK is a semi-crystalline polymer which belongs to the polyketones family. PEEK is a high performance polymer with excellent chemical resistance, high strength, and excellent resistance to burning. Table 2.3 indicates the mechanical properties of PEEK (Kurtz, State of the Art 14 2019). Although they require high melt temperatures, polyketones can be extruded and injection molded with standard processing equipment (Kurtz, 2019). PEEK can be processed by conventional methods used to process other plastics such as injection molding, extrusion, blow molding, and thermoforming. In addition, during the last years the use of creating PEEK parts by additive manufacturing has increased fervently (Brandicourt et al., 2017; Dua et al., 2021; Yin et al., 2022), being this motivation addressed in the section 2.1.2. PEEK is used to produce items for demanding applications, including bearings, piston parts, pumps, high-performance liquid chromatography columns, etc. PEEK material is substantially used in medical implants because of the material's versatility, compatibility with modern imaging technologies, outstanding mechanical properties and biocompatibility. Table 2.3. Mechanical properties of PEEK polymer (Kurtz, 2019). Coefficient of friction 0.18 Elongation at break (%) 50 Hardness - Rockwell M99 Izod impact strength (J m⁻¹) 85 Poisson's ratio 0.4 Tensile modulus (GPa) 3.7 - 4.0 Glass-transition temperature (°C) 143 Melting point (°C) 343 In the medical field, the PEEK material is of particular interest to those manufacturers who develop applications that interact with bone, such as compression bone plates, spinal fusion cages, intramedullary nails, and hip prostheses, which are usually made from metal alloys with a significant stiffness greater than that of adjacent cortical bone by a factor from 10–20 times (Kurtz, 2019). The importance of PEEK as a biomedical material will be addressed more widely in section 2.4. 2.1.2 Manufacturing processes This section describes the key processing methods, design, manufacture, and application for polymers. Figure 2.4a presents the evolution that the industry has had from the first revolution to the fourth (called Industry 4.0), highlighting the particularities of each one. The Second Industrial Revolution is considered to have sparked the widespread use of the Bessemer process, ending with the implementation of mass production (Popkova et al., 2006). Since the born of the Industry 4.0, the paradigm of mass production has been State of the Art 21 formability allows exploring the accuracy and the limits of the processes, and one of the tools widely used in the analysis of formability is the forming limit diagrams (FLDs), which assess the workability of the sheets. The formability of polymeric materials plays an important role in the experimentation of this thesis, and it will be addressed in the following section (section 2.2). 2.2 Material formability This section presents a brief presentation of the material formability starting with the sheet metal formability to introduce the theoretical basis. Then, it will introduce more specifically the literature on sheet polymeric formability in section 2.2.1. As stated before, formability is the term used to determine the degree of deformation that a material can be subjected during a forming process. The extent of this deformation can be evaluated by using the major strain (𝜀1) and minor strain (𝜀2) in the so-called forming limit diagram (FLD). The FLD is an analysis tool in which the major strain is represented on the ordinate axis and the minor strain on the abscises axis in the Cartesian plane, and it presents the deformational state of the material, being the relation between the major strain 𝜀2 and the minor strain 𝜀1 the strain ratio (β), and is given by β=𝜀2 𝜀1. The FLD provides information about the sheet failure and deformation mode. In this sense, failure in sheet metal forming can occur by necking, fracture associated to crack opening by tension and by in-plane shear, and wrinkling. Figure 2.8a shows the schematic representation of these formability limits in principal strain space based on the original figure by Marciniak (1984), and revised by Martins et al. (2014). To this regard, the schematic Figure 2.8a shows the formability limits by necking (FLC, forming limit curve), by fracture in mode I (FFL, fracture forming limit line), by fracture in mode II (SFFL, shear fracture forming limit) and by wrinkling (WLC, wrinkling limit curve). This thesis is focused on determining the formability limits by necking and by fracture in Mode I of fracture mechanics. The forming limit curve (FLC) (or FLD at necking) was initially developed by Keeler (1968) in the first quadrant and then extended by Goodwin (1968) to the second quadrant of principal space. The forming limit curve represents the limit at necking occurs, in this sense, necking is a failure mode that occurs by tension, where relatively large amounts of strain are disproportionately located in a small region of the material. As can be seen in the schematic Figure 2.8b, the FLC is typically represented through a V-shaped for metals (red line in Figure 2.8b) and the strain values can be calculated from a series of State of the Art 22 experiments under different loading conditions, ranging from equibiaxial stretching (𝛽= 1) to uniaxial tension (𝛽=−1/2). On the other hand, the fracture forming limit (FFL) line (or FLD at fracture) was originally proposed by Embury and Duncan (1981), and it represents the initiation of fracture in a sheet, and is related to the maximum admissible thickness reduction (Atkins, 1996). Similarly, Figure 2.8b schematically shows the FFL as a red dotted line for different loading strain paths, from uniaxial tension (𝛽=−1/2) to equibiaxial stretching (𝛽=1). (a) (b) Figure 2.8. Schematic representation of (a) the formability limits on principal strain space for sheet forming (Magrinho, 2019) and (b) of the formability limits on principal strain space for sheet forming indicating the FLC and the FFL indicating different strain paths adapted from (Ajay and Mittal, 2020). Figure 2.9a and 2.9b shows a distinction presented by Vallellano et al. (2008) separating high ductility materials and low ductility materials. High ductility materials usually start the failure process with the onset of strain localization along a narrow stripe, leading to the formation of a neck (see Figure 2.9a). On the contrary, for low ductility materials the fracture may occurs in absence of the necking process, being the formability of the sheet controlled by ductile fracture mechanisms (see Figure 2.9b). State of the Art 23 (a) (b) Figure 2.9. FLD at necking (or FLC) and at fracture (FFL) for (a) high-ductility and (b) low-ductility material (Vallellano et al., 2008). The experimental determination methodologies of the in-plane strains at the onset of necking can be grouped into position-dependent (ASTM Standard E2218-02, 2008; ISO12004-2, 2008) or time-dependent (Iquilio et al., 2019; Merklein et al., 2010; Vacher et al., 1999). For instance, some of the position-dependent methodology is based on the circle grid analysis (CGA). This methodology requires an electro-chemical process, printing, lasers, among others, for impression circular marks on the surface of the test specimen. These circles after being deformed will become ellipses (see the deformed circles in Figure 2.8b for different strain loading paths) whose semi-axes allowed the measurement of the strain on the fractured specimens. This ellipses length variation can be later measured using optical devices (microscopes, magnifier lens, among others). Another methodology to obtain the FLC is by means of the standard ISO12004-2 (2008), which contains procedures and uniform laboratory application conditions to carry out the determination of the FLC. The time-dependent methodologies are based on digital image correlation (DIC), which allows information gathering during the test, and the exploration of temporary-based methods for the determination of FLCs. The biggest limitation of the FLC is the influence of the strain loading paths in the experimental FLC. Kikuma and Nakajima (1971) were the pioneers in this investigation, concluding that linear and nonlinear strain loading paths originate different FLCs. In what concerns the fracture forming limits in sheet forming, the fracture usually occurs as ductile fracture, rarely as brittle fracture, in two different opening modes: (i) tensile and (ii) in-plane shear (respectively, the same as modes I and II of fracture mechanics). Mode I is when sheet thinning is caused by localized necking along an inclined direction to the loading direction and mode II, in which the opening crack is in-plane shear. Focusing on mode I, the literature (Nielsen and Martins, 2021) and experimentation revealed that the crack opening by tension (mode I) occurs at an approximately constant thought-thickness true strain 𝜀3=ln( 𝑡𝑓𝑡0 ⁄)=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, where 𝑡𝑜 is the initial sheet thickness and 𝑡𝑓 sheet thickness at fracture. The reduction in thickness at fracture (𝑅𝑓) State of the Art 24 and 𝜀3𝑓 are related by 𝜀3𝑓 = 𝑙𝑛 (1−𝑅𝑓), and due to the volume incompressibility of plastic flow, the expression of the FFL line can be written as a line with a slope of ‘-1' in principal strain: 𝜀1𝑓 = −𝜀2𝑓 −𝜀3𝑓 =𝜀2𝑓 −ln(1−𝑅𝑓)=−𝜀2𝑓 −𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (1) As mentioned before, the experimental determination of the FLC and FFL can conducted by conventional formability tests using different strain loading paths. Due to its ease, the most used sheet formability tests are the tensile, bulge, and Nakajima tests (Silva et al., 2011). The tensile tests consist of subjecting a test specimen to uniaxial tensile stress until it fracture. The test specimens must be standardized (see the example of tensile specimen in Figure 2.10a), and this type of test allows knowing the resistance of a material to an applied force. Tensile tests allow characterizing the material and knowing different mechanical properties. Another test that allows characterized the material is the hydraulic bulge test (see elliptical and circular bulge specimens in Figure 2.10a). This test allowing characterizing the biaxial curves of stress and deformation, for this, the test piece is held between the matrix and the clamp. (a) (b) (c) Figure 2.10. (a) From left to right: tensile, elliptical bulge and circular bulge tests (Silva et al., 2011). (b) Universal sheet testing machine and Nakajima specimens (Borrego et al., 2015). (c) Formability limits by necking and fracture in mode I of fracture mechanics of AA1050-H111 aluminum sheet with 1 mm thickness (Isik et al., 2014). One of the most widely used assays due to its flexibility and simplicity is the Nakajima test. This test allows a variety of geometries to be used for the specimens and consists of pushing the specimen upwards with a hemispherical punch until failure, being the part State of the Art 25 held by means of a backing plate and blank holder. Figure 2.10b shows the universal sheet Erichsen testing machine in which the Nakajima tests can be performed together with different geometries for the specimens to obtain loading paths. The Nakajima tests to obtain the FLC are only effective for the following hypothesis: (1) proportional loading, (2) absence of bending, (3) negligible through-thickness shear and (4) plane stress (Emmens and van den Boogaard, 2009). Figure 2.10c presents the experimental FLC and FFL determined for AA1050-H111 aluminum sheets with 1 mm thickness. In this sense, the FLC was experimentally determined by the application of the ISO12004-2, 2008 with the previously mentioned formability tests (tensile, bulge and Nakajima), and the FFL was determined with the same tests, allowing the determination of the ‘gauge length’ strains by means of thickness and width measurement before and after a fracture. As said before, the knowledge of the formability limits in the principal strain space allows the establishment of a general framework for analyzing the fracture limit, which is relevant in sheet forming processes. There are widely used and validated methodologies to establish necking and fracture limits in sheet metal forming, however, there is a shortage of methodologies and procedures to apply to polymers, in this sense, the following section (section 2.2.1) deals with the literature found to determine the limits of forming in polymeric materials. 2.2.1 Sheet polymer formability This section describes the previous methods in the literature to obtain formability limits for necking (FLC) and fracture (FFL) in polymeric sheets. Martins et al. (2009) were the pioneers in the use of the FFL in the assessment of the formability of polymeric materials. Different tests such as tensile tests, circular bulges, and elliptical bulges were used during the experimental work, and, the thickness at fracture was measured to obtain the FFL (see the FFL for PVC material in 2.11a). The results of the experiments indicated that SPIF at room temperature has the potential to produce complex components with deep walls using commercial polymer sheets. State of the Art 26 (a) (b) Figure 2.11. (a) FFL for PVC material obtained by Martins et al. (2009) and (b) FFL for PC, PVC, PA and PET materials obtained by Marques et al. (2012). Later, Marques et al. (2012) proposed a methodology to determine the FLC and the FFL in polymers, more specifically in four different thermoplastics sheets: polyamide (PA), polycarbonate (PC), polyethylene terephthalate (PET), and polyvinyl chloride (PVC). This methodology is based on CGA analysis as shown previously in metals. However, the results were that the FFL and the FLC should be considered, unlike in metals, as a unique limit, due to the typical stable neck spread of polymers after the onset of necking as pointed out by Carothers and Hill (1932). The fracture thickness was measured to obtain the FFL gauge length strains. Figure 2.11b presents the FFLs for the different polymers considered in this research approximated by straight lines falling from left to right. As mentioned before, the literature has mainly focused on studying the formability limits of metal sheets, therefore, there are only a few works that address formability limits of polymeric sheet. Nevertheless, the knowledge of formability is of great importance, as well as characterizing the safe and failure zone for the processes that involve polymer sheets. In addition, the application of single point incremental forming process to polymeric sheets has raised in the interest for cold forming of polymers, its formability and failure. The reason for the interest is due to the experimental verification that the strains of the incremental formed sheet were far above the formability limit by necking. In this thesis, a methodology is developed to establish the forming limits of three different polymeric materials (PC, UHMWPE and PEEK), including the formability analysis of these polymers deformed by single point incremental forming. State of the Art 27 2.3 Incremental Sheet Forming As explained in section 2.1.2, one of the current flexible methods that allow the manufacturing of small-medium batches in an inexpensive and flexible way is the incremental sheet forming (ISF) process. ISF has the capacity to produce sheet material at a lower cost due to the flexibility and elimination of costly dies. The working principle of the ISF process is schematically in Figure 2.12 for a conical geometry as follows: (i) the sheet is fixed between the clamping and backing plates, (ii) the forming tool is fixed in the tool holder which is generally mounted on the tool head of the computer numerical control (CNC) milling machine, and (iii) the incremental deformation of the sheet in a downward direction is achieved by the forming tool at a specific step-depth, followed by a horizontal movement along a predetermined tool path. Figure 2.12. Schematic of the non-axisymmetric SPIF (Iseki et al., 1989). The first idea of the ISF process (in metals) with a single-point tool was patented by Leszak in 1967, and named dieless forming. The Leszak patent describes a process for the manufacturing of disc-like or cup-like products from metal sheet. The blank rotates and vertical displacement is created by local bending that is caused by pushing the sheet into an elastic medium by a roller. In 1967, the Berghahn patent described a process for manufacturing disc-like products, in which a blank is clamped and rotates, while a roller moves inward along a radial line, thus describing a contour that forms the final shape. Both proposals have a distinct difference: in the Leszak proposal the shape is created by bending of the sheet against an elastic medium, in the Berghahn proposal by the xyz movement of the roller (Emmens et al., 2010). State of the Art 28 Matsubara (1994) developed the incremental backward bulge forming process, in which the blank is clamped in a rig that allows downward movement, the blank center is supported by a support post and the forming tool with a rotation movement, controlled by CNC, describing trajectories necessary to obtain the desired part (see Figure 2.13). Jeswiet (2000) and Leach et al. (2001) applied that concept in a conventional CNC milling machine (see Figure 2.14a). Figure 2.13. Schematic representation of the Incremental Backward Bulge process (Hagan and Jeswiet, 2005). Jeswiet (2000) and Leach et al. (2001) utilized a conventional CNC milling machine to implement this concept, but without the use of a backing plate as seen in Figure 2.14a. Kitazawa et al. (Kitazawa, 1997; Kitazawa and Nakane, 1997) developed the Incremental Stretch Expanding process using a lathe-like device (see Figure 2.14b). The workpiece is held in place by a clamp and the chuck of the lathe and is shaped by a steel rod with a rounded tip that rotates. The process is only suitable for creating symmetrical shapes due to the rotating relationship between the workpiece and the tool. (a) (b) Figure 2.14. Schematic representation of (a) the Incremental Backward Bulge process in a conventional CNC milling machine (Jeswiet, 2000) and (b) Incremental Stretch Expanding process (Kitazawa and Nakane, 1997). State of the Art 29 Jeswiet (2001) and Filice et al. (2002) developed the incremental forming CNC, which consisted of the study of using a CNC milling machine instead of another purpose machine tool apparatus (see Figure 2.15). This was the beginning that began great advances and development in the process. Figure 2.15. Experimental equipment for ISF (Filice et al., 2002). 2.3.1 Process variants Once a brief description of the history of the ISF has been made, the following section covers a general overview of the ISF process, indicating the main classification of the processes and the main aspects to emphasize. In this sense, Figure 2.16a shows different classifications of the ISF, according to the typologies, the forming strategy, the forming tool and the machinery. This classification is the one that will be followed in sections from 2.3.1.1 to 2.3.1.4 explaining each of them. (a) Figure 2.16. State of the Art 30 (b) Figure 2.16. (a) Classifications of the ISF process and (b) process flow for manufacturing a part using ISF. Likewise, Figure 2.16b reflects the process stages followed from the design of a model until the final part is manufactured by ISF. The ISF process requires NC instructions (G-codes and M-codes using CAM packages) for the forming machinery. For that, a 2D/3D model has to be designed using suitable CAD software, the most common are Solidworks®, CATIA®, AutoCAD®, and CREO®, among others. The CAD model is exported to the CAM software in order to create the NC instructions. Finally, NC instruction files are loaded into the forming machinery in order to manufacture the part. 2.3.1.1 Typologies ISF can be classified depending on the typologies into: (i) single point incremental forming (SPIF), (ii) two point incremental forming (TPIF), (iii) double sided incremental forming (DSIF) and (iv) hybrid forming (see Figure 2.16a). In the single point incremental forming (SPIF) variant, only one point of the sheet is in contact with the forming tool (see Figure 2.17). This process is also known as “incremental negative formation” as the sheet is stretched into the support or fixture. In SPIF, the blank is simply clamped into a hollow fixture at its perimeter and a simple forming tool (usually spherical or hemispherical shape) is moved to a specified feed rate and predetermined tool path. Figure 2.17 shows the basic components for the SPIF process: the sheet metal blank, the blank holder, the backing plate and the forming tool. State of the Art 37 roller-ball in order to eliminate the possible scratches on the finished part. But the rollerball tool has the limitation to produce a high wall angle of the formed components due to the interference between the tool shank and workpiece (see Figure 2.23c). The tool diameter used also influences the surface quality and/or the manufacturing time and it will be discussed in section 2.3.3.1. 2.3.1.4 Machinery The forming machinery in ISF play an important role in the successful, efficient and accurate forming of parts. The categories are: (i) CNC milling machines, (ii) industrial robots and (iii) purpose-built machines (see Figure 2.16a). The CNC milling machines (see Figure 2.24a) are widely used because of their availability, high stiffness, high load capacity, large working area, and high flexibility, among others. The CNC milling machines have a high level of versatility, and can be used for other operations with a small change in the setup. As a disadvantage, they present a high cost and limited degrees of freedom but they are used extensively in the literature to perform variations of the ISF process. (a) (b) Figure 2.24. (a) CNC milling machine (Kurra et al., 2015). (b) Experimental set-up of roboforming (Meier et al., 2009). Tuominen (2003) patented the use of industrial robots for ISF (see Figure 2.24b). The use of an industrial robot as a forming machine allows the forming tool to be moved and positioned at different angles relative to the workpiece. Indeed, a robot has more degrees of freedom (DOFs) than the CNC milling machines, increasing the flexibility of the forming machinery. However, industrial robots offer the following limitations: lower range of stiffness, less load capacity (Meier et al., 2009) and lower accuracy (Kumar et al., 2019). State of the Art 38 Purpose built or dedicated machines have been developed for ISF, as for instance, the Amino ISF machine. This machine was developed in 1996 by AMINO corporation (Amino et al., 2014), as can be seen in Figure 2.25a, the machine is equipped with a pneumatic controlled work table that is able to move for pre-stretching the work material, as required in hybrid forming. Amino ISF machine is equipped with partial die set-up as required in TPIF. In Figure 2.25b is showed the incremental sheet forming machine developed for Allwood et al. (2005), in this sense, special designed machines for Incremental Forming are less flexible than robots and CNC milling machines (Jeswiet et al., 2005). (a) (b) Figure 2.25. Purpose built Incremental Forming machines: (a) AMINO (Amino et al., 2014) (b) Designed Incremental Forming machine (Allwood et al., 2005). 2.3.2 Formability in polymers This section deals with formability in polymeric sheets deformed by ISF. It begins presenting the literature on polymer forming in ISF, as well as the different failure modes that can occur and the works on forming limit diagrams. Next, essentials for the theoretical framework based on membrane analysis for the deformation mechanism in ISF of polymers are presented. The formability in ISF is much higher than that achieved with conventional forming processes due to the nature of the deformation mechanism (Silva et al., 2008). To this regard, the literature reveals that a necking stabilization occurs during the ISF process compared with the conventional process and as a result, the strains analyzed in ISF process are well above the forming limit curve (FLC). More specifically in polymers, authors such as Martins et al. (2009), Silva et al. (2010), Marques et al. (2012) and Bagudanch et al. (2017) among others, have experimentally shown that the formability achieved in ISF/SPIF is higher than in conventional forming. State of the Art 39 Polymeric formability in ISF can be characterized using the forming limit diagrams (FLDs), and due to that there is no obvious necking occurring before fracture, the FLD at necking is not applicable to characterize the formability in ISF. The FLD at fracture can be used to describe the formability of thermoplastic materials. In this sense, Martins et al. (2009) established the formability limits for various commercial polymers, including POM, HDPE, PA, PVC, and PC. The work determined the fracture points by calculating the thickness at fracture and CGA analysis to measure the strains on various sections of the final part. In addition, Martins et al. (2009) introduced the main principal modes of failure during the SPIF process of polymers, which are: a) Mode A, circumferential crack: crack opening along the circumferential direction (Figure 2.26a). b) Mode B, twisting or wrinkling: material twist in the cone and subsequent development of wrinkles at the inclined wall (Figure 2.26b). c) Mode C, oblique crack: crack opening along the bisector direction in the inclined wall of the part (Figure 2.26c). In general, the most common modes of failure in SPIF are mode A and mode B. In this sense, Le et al. (2008) observed both modes of failure in a cone-shaped part with a circular arc as generatrix for PP sheet of 3 mm of thickness, in addition, Davarpanah et al. (2015) tested two different geometries in SPIF, variable wall angle and fixed angle conical geometries for a PLA sheet of 0.7 mm of thickness, in both cases mode A and mode B were found. (a) (b) (c) Figure 2.26. Polymeric failure modes in SPIF: (a) circumferential crack, (b) twisting and (c) oblique crack observed in the work by Martins et al. (2009). In addition to the previously mentioned failure modes, the recent work by Rosa-Sainz et al. (2021) introduced the crazing failure mode for polycarbonate sheets in SPIF testing a truncated conical geometry. The work explored different values of spindle speed (20, 500, State of the Art 40 and 1000 rpm) for a truncated conical geometry using PC sheets of 2 mm thickness. The experimental work showed the crazing failure mode when the spindle speed was 1000 rpm, giving place to different micro-cracks on the deformed specimen. This result will be deeply addressed in chapter 4 of this thesis. Regarding the formability in SPIF, Marques et al. (2012) determined the formability limits for PC, PA, PBC and PET using the methods in the publication of Silva et al. (2008) and Martins et al. (2009). The FFL (black line in Figure 2.27a) was determined independently using tensile and bulge tests, and in addition, SPIF tests were carried out, providing fracture points above this FFL (see Figure 2.27a). Figure 2.27a also presents the strain loading paths obtained from CGA analysis in the principal space for the truncated conical and pyramidal SPIF parts for 3 mm thickness PC sheet. In addition, in Figure 2.27a the solid markers referred to strains at failure calculated by measuring the thickness at fracture are depicted. (a) (b) Figure 2.27. (a) Experimental strains in a truncated conical and pyramidal benchmark SPIF (Marques et al., 2012). (b) Principal strains on the outer surface within the principal strain space and fracture strains defining the FFL (Centeno et al., 2017). To this respect, Centeno et al. (2017) evaluated the formability limits of PC polymeric sheets processed through SPIF. The strain state of the tested sheets was analyzed offline on the final product using the 3D deformation digital measurement system ARGUS®. The fracture forming limit (FFL) resulting from the SPIF test, which involved measuring the sheet thickness at the point of fracture, is displayed in Figure 2.27b. The procedure required to assess the specimen using ARGUS® can be seen in the lower left corner of the same figure. This procedure enables the representation of the major strains at the outer surface of the specimen within the principal strains space (as shown in Figure 2.27b). Different strain paths along the fractured part, designated as S1, S2, and S3, were analyzed. Section S1, located in the center of the side, corresponds to plane strain, while State of the Art 41 S2 and S3, located near the corner, correspond to biaxial strain and close to an equibiaxial strain state, respectively. Regarding the deformation mechanism in ISF, the stretching leading to membrane strain is the dominant deformation mode, and there are three basic deformation modes including (i) plane strain stretching on flat surfaces, (b) plane strain stretching on rotational symmetrical surfaces and (iii) equibiaxial stretching at corners according to Silva et al. (2010) as illustrated in Figure 2.28. In this sense, the work of Silva et al. (2010), innovatively extended the membrane approach developed for metals to model the cold plastic deformation of thermoplastic materials with the typical pressure-sensitive yield surfaces, assuming: (i) bending moments were ignored and circumferential, meridional and thickness stresses are principal stresses, (ii) the material is rigid-perfectly plastic and strain hardening effects are ignored, (iii) the utilized yield criteria were the pressure-modified Tresca and von-Mises criteria, (iv) no anisotropic material effects are taken into account, (v) rate effects are neglected and (vi) the frictional stress at the contact surface between tool and sheet is just made of in-plane meridional and circumferential components. (a) (b) Figure 2.28. (a) Schematic representation of the local contact area (shell element) between the tool and sheet placed immediately ahead. (b) Instantaneous deformation zones and evidence of the extreme modes of deformation obtained from CGA technique (Silva et al., 2010). In this investigation cited above, the local shell element was used to analyze the membrane equilibrium conditions and the stress acting on the element (see Figure 2.29). The work presented three analytic equations to express force equilibrium along circumferential, meridional, and thickness directions: 𝑑𝜎𝜃=−𝜇𝜃𝜎𝑡𝑟𝑑𝜃 𝑡≅−𝜇𝜃𝜎𝑡 (4) 𝜎𝑡 𝑡+𝜎𝜑 𝑟1+𝜎𝜃 𝑟2=0 (5) State of the Art 42 𝑑𝜎𝜑 𝑑𝑟 +𝜎𝜑−𝜎𝜃 𝑟+𝜇𝜑𝜎𝑡 𝑡𝑠𝑖𝑛𝛼+𝜎𝜑 𝑡𝑑𝑡 𝑑𝑟=0 (6) Where 𝜎𝜃,𝜎𝑡 and 𝜎𝜑 are the circumferential, thickness and meridional stress, respectively, 𝜇 is the coefficient of friction, 𝑡 is the thickness of the sheet, 𝑟1 is the radius of curvature of meridian at the element. (a) (b) (c) Figure 2.29. Membrane analysis of SPIF : (a) Schematic representation of the local contact area between the tool and sheet placed immediately ahead. (b) Approximation of the local contact area by a shell element. (c) Cross-section view showing the acting stresses in meridional, circumferential and thickness directions (Silva et al., 2010). Deriving the stress state of the local shell element “CDEF” by taking into account the rigid plastic constitutive equations derived according to the modified version of Tresca and Von-Mises criteria, the principal stress distribution of the shell element is identified as follows: 𝜎𝜑=𝜎1=(𝜎𝑌√1−𝛽𝜎𝑘𝑘) (1+ 𝑡 𝑟𝑡𝑜𝑜𝑙)>0 (7) State of the Art 43 𝜎𝜃=𝜎2=1 2(𝜎𝜑+𝜎𝑡−𝛽𝜎𝑌) (8) 𝜎𝑡=𝜎3=−𝜎𝑌√1−𝛽𝜎𝑘𝑘 (𝑡 𝑟𝑡𝑜𝑜𝑙 +𝑡) <0 (9) Where 𝜎𝑌 is the geometric mean of the tensile and compressive yield strengths, and 𝛽 is the normalized form of the strength-differential effect of the cold deformation of thermoplastic materials. In addition, Marques et al. (2012) extended the analytical framework for the condition of rotational symmetric to the corner of the formed part by following the analytical procedures used by Silva et al. (2010) and obtained the stress distribution under the condition of equibiaxial stretching. Table 2.7 summarizes the stress and strain state in the small localized plastic zone of SPIF thermoplastic materials under both plane strain conditions and equibiaxial stretching conditions. Table 2.7. State of stress and strain in the small localized plastic zone of the SPIF of thermoplastics (Marques et al., 2012). State of strain State of stress Hydrostatic stress SPIF of thermoplastics Plane strain condition 𝑑𝜀𝜑=−𝑑𝜀𝑡 >0 𝜎𝜑=𝜎1 =(𝜎𝑌√1−𝛽𝜎𝑘𝑘) (1+ 𝑡 𝑟𝑡𝑜𝑜𝑙)>0 𝜎𝑚=(𝜎𝑌√1−𝛽𝜎𝑘𝑘 2) [(𝑟𝑡𝑜𝑜𝑙 −𝑡)/ (𝑟𝑡𝑜𝑜𝑙 +𝑡)] −(1/6)𝛽𝜎𝑌 𝑑𝜀𝜃=0 𝜎𝜃=𝜎2 =1 2(𝜎𝜑+𝜎𝑡−𝛽𝜎𝑌) 𝑑𝜀𝑡<0 𝜎𝑡=𝜎3 =−𝜎𝑌√1−𝛽𝜎𝑘𝑘 (𝑡 𝑟𝑡𝑜𝑜𝑙 +𝑡) <0 Equibiaxial condition 𝑑𝜀𝜑=𝑑𝜀𝜃 >0 𝜎𝜑=𝜎𝜃= 𝜎1 =(𝜎𝑌√1−𝛽𝜎𝑘𝑘 (1 +2𝑡 𝑡𝑡𝑜𝑜𝑙)>0 𝜎𝑚 =(2𝜎𝑌√1−𝛽𝜎𝑘𝑘 3)[(𝑟𝑡𝑜𝑜𝑙 −𝑡)/(𝑟𝑡𝑜𝑜𝑙 +2𝑡)] 𝑑𝜀𝑡<0 𝜎𝑡=𝜎3 =−2(𝜎𝑌√1−𝛽𝜎𝑘𝑘) /(𝑡/𝑟𝑡𝑜𝑜𝑙 +2𝑡)<0 State of the Art 44 2.3.3 Parameters Once a general overview of what the SPIF process consists of has been presented, this section presents the main process parameters that influenced the ISF process. These process parameters play a crucial role in running the ISF process safely and successfully. Table 2.8 shows the parameters categorized in ISF by process, material and design. These categories are then presented from section 2.3.3.1 to 2.3.3.3. Table 2.8. Categorization in ISF parameters classified by process, material, and design parameters. Parameters in ISF Process Material Design Tool Diameter Strain hardening Thickness of the sheet Step Down Normal anisotropy Shape of the part Spindle Speed Young modulus Tool path Feed Rate Maximum drawing angle Lubricant In the following subsections, the most important parameters in ISF are described along with notable references in the literature for metals and polymers and their relation to formability. 2.3.3.1 Process The process parameters in ISF are: tool diameter, step down, spindle speed, feed rate and lubricant (see Table 2.8). The tool diameter is related to the smallest concave radius of the part's geometry. As mentioned before in section 2.3.1.3, the diameter also influences the surface quality and/or the manufacturing time. In the literature one of the most used values is the diameter 12 mm (Filice et al., 2002; Matsubara, 1994), also the typical range varies between values of 5 and 20 mm (Kridli et al., 2021). Smaller tools are claimed to be able to concentrate the strain at the area of deformation in the sheet below the forming tool, whereas larger tools tend to distribute the strains over a more extended area. As a result, enhanced formability is observed with the use of small tools. Hirt et al. (2002) showed an improvement in formability by decreasing the tool diameter for DC04 material with 1.5 mm of thickness, it explored tool diameters from 6 to 30 mm. In polymers, the tool diameter has an influence in formability and geometry accuracy. In general terms, the increase in the tool diameter State of the Art 45 produces an increment in the local heat due to the increase in the sheet-tool contact zone. In this sense, Silva et al. (2010) demonstrated that the increase in tool radius from 5 mm to 6 mm gave place to an increase in formability for PVC sheets. The same result was found by Bagudanch et al. (2015), testing values of 6 and 10 mm of tool diameters for PVC material, and Le et al. (2008), evaluated values of 6 and 12 mm of tool diameter for PP material. In addition, Marques et al. (2012) investigated the impact of varying tool radius (4 mm, 5 mm, and 6 mm) on the formability of SPIF parts produced from PC and PVC sheets. The findings revealed that increasing the tool radius resulted in reduced formability of the produced parts from both PC and PVC materials The step down is the amount of material deformed per revolution. The step down is a crucial variable in the ISF process, as far as it affects the forming force, formability, dimensional accuracy, and surface roughness. The relation between the step down and the aforementioned variables depends on the material. In the literature, the typical values of step down are within the range of 0.2 and 0.6 mm. Obikawa et al. (2009) also studied values as 100 μm in micro-incremental forming for two types of aluminum. This work showed that low step down values cause normal and frictional stresses to be repeatedly applied to the same parts of the material and it was suggested that this exacerbates defects in the materials and resulted in early failure. Authors such as Kim and Park (2002) showed that the decrease in the step down gave place to an increase in the formability for AA1050-0 material. The same conclusion was observed by Centeno et al. (2014) for AISI304 material. Liu et al. (2013) showed the opposite conclusion, i.e. the increase in the step down resulted in an increase in the formability of AA7075-0. From the point of view of energy consumption in polymers, the step down is a remarkable variable. According to the work by Bagudanch et al. (2016) in PC and PVC polymers, the increase in step down leads to a decrease in energy consumption. In this sense, some authors have been exploring higher values of the step down in polymers, as in the case of the recent work by Yang et al. (2020) with values of 0.8 mm and 1.2 mm of the step down in incremental hot forming of PEEK material. The work by Yang et al. (2020) showed that with the increasing of step down, the processing cycle of the entire forming process is shortened, and the corresponding forming force is significantly increased. In terms of formability, the work by Davarpanah et al. (2015) analyzes the effect of step down on polymer parts using two biodegradable polymers, PLA and PVA. The experimental work considered values of 0.2, 0.4, 0.6, 0.8, 1.0 mm for PLA, and 0.2, 0.6, 1.0, 1.4, 1.8 mm for PVC, and it obtained an increase in the formability with an increase of the step down for both materials. In the work by Bagudanch et al. (2015) was observed an increase in the formability of PVC material as a result of an increase in the step down from 0.2 mm to 0.5 mm. The opposite result was found by Le et al. (2008), i.e. an increase in the step down from 0.2 to 1 mm gave place to a decrease in the formability of PP sheets. State of the Art 46 The feed rate process parameter is the velocity at which the forming tool moves on the stationary sheet during the ISF process. Feed rate parameter determines the forming time of the formed shape. ISF is usually performed with very low values of feed rate and high values of feed rate. In this sense, higher values of feed rate allow for less forming time to complete the desired component. Depending on the material, the feed rate parameter could have more influence or less. For instance, Azevedo et al. (2015) found small effects on formability with different feed rates from 1500 to 12000 mm/min. Hussain et al. (2009) showed that the feed rate did not have a significant effect on formability for AA2024-0 testing values in a range from 373 to 4500 mm/min. Hussain et al. (2007) showed an increase in the formability due to a decrease in the feed rate, testing values of 1200, 2600 and 4000 mm/min for Titanium. In the case of polymers, in the work by Bagudanch et al. (2015) an increase in the formability was observed as a consequence of an increase in the feed rate for PVC material, testing values of 1500 and 3000 mm/min. Le et al. (2008) proved the contrary conclusion, i.e. a decrease in the feed rate gave place to an increase in the formability for PP material, testing values of 1000 and 3000 mm/min of feed rate. The other process parameter related to the velocity during the ISF process is the spindle speed. The spindle speed is the speed at which the tool rotates at its axis during forming. The ISF tool can rotate at different speeds: (i) blocked zero spindle speed, (ii) keep the spindle free for rotation and (iii) the spindle rotates with a specific value of spindle speed. An increase in the spindle speed increases the friction at the tool sheet zone and as a consequence, an increase in the temperature of the sheet. In the literature values from 0 rpm to 25000 rpm can be found, although it can also be set as free rotation (Khalil et al., 2018). In general, higher values of spindle speed can damage the surface quality, as it was reported on the investigation by Durante et al. (2011), in which it compared the results obtained for 0 rpm and 600 rpm on the surface finish for AA7075 sheet material. The increase in spindle speed leads to a rise in temperature levels, and consequently, the levels of formability are higher. This conclusion was observed by Xu et al. (2013) for a AA5052- H32 material, testing values of spindle speed from 0 to 7000 rpm. Buffa et al. (2012) showed the same effect for three different materials: AA1050-O, AA1050-H24, AA6082- T6, for a values of spindle speed from 100 to 10000 rpm. In polymers, higher values of spindle speed give place to improve the formability as studied by Le et al. (2008) for PP materials using 200 and 700 rpm of spindle speed. Another work which showed the same result was by Bagudanch et al. (2015) for PVC material, testing values of free, 1000, and 2000 rpm of spindle speed. State of the Art 53 Furthermore, using the so called (ii) constant scallop height, in which the parameter that determines the Z movement is an established maximum scallop (see Figure 2.35d). This strategy produce better surface finishing than the constant step down (Callegari et al., 2006). And, (iii) constant angular increment (see Figure 2.35e), in which the angle increment between two successive layers has to be constant. This strategy does not permit acceptable surface finishing for very steep walls (Fiorentino et al., 2009). The constant straight step down can be performed following two trajectories: unidirectional (see Figure 2.36a) and bidirectional (see Figure 2.36b). (a) (b) Figure 2.36. Representation of (a) unidirectional tool path and (b) bidirectional tool path (Ajay and Mittal, 2020). In the unidirectional tool path, the tool moves one way in the plane and reaches the initial point, then, descent follows the step down and produces the next contour in the same direction. On the other hand, in the case of the bidirectional tool path, the tool follows the previous profile path except that in each subsequent cycle the tool changes the direction of movement. The choice of the appropriate tool path will be of great importance in the experimental work developed in this thesis. 2.3.4 Outputs Different outputs can be studied ISF such as: (i) forming forces, (ii) formability, (iii) accuracy and (iv) roughness. In this sense, formability was already explained above (section 2.3.2), and the other outputs are discussed below and their relation to formability in polymers. State of the Art 54 2.3.4.1 Forming force The forming-force is the force required to deform the sheet locally at the tool–sheet interface. The force components 𝐹𝑥, 𝐹𝑦 and 𝐹𝑧 along the x, y and z directions are usually measured using a dynamometer or load cell placer under the ISF set up, these data are recorded help of a data acquisition system, charge amplifier and computer environment. Next, the effects that the process parameters (focusing on tool diameter, step down, spindle speed and feed rate) have on the forces in ISF of polymers are presented. The process parameters of the ISF process significantly affect the forming-force required to produce local deformation in the sheet during the forming operation. Starting from the tool diameter, the forming force increases with the increase in the tool diameter (Centeno et al., 2014; Kumar et al., 2018). The same result has been proved for polymers, such as in work by Bagudanch et al. (2015) testing values of 6 and 100 mm of tool diameter for PVC material and in work by Sabater et al. (2018) testing values of 6, 10 and 14 mm for PCL and UHMWPE polymers. In the case of the step down, smaller step downs implies less deformation and less formingforce required (Kumar et al., 2019). In polymers, this effect has been studied on the work by Bagudanch et al. (2015), testing values of 0.2 and 0.5 mm of step down for PVC material. The same result was found in the work by Davarpanah et al. (2015), in which different values of step down were tested, 0.2, 0.4, 0.6, 0.8, 1.0 mm for PLA and 0.2, 0.6, 1.0, 1.4, 1.8 mm for PVC. Regarding the spindle speed, the forming force decreases with the increase in spindle speed. This fact is due to a higher spindle speed increases the friction at the tool–sheet interface resulting in more friction and heat generation, and an increase in ductility of the material (Kumar et al., 2019). In polymers, the effect of spindle speed has been studied by Bagudanch et al. (2015), testing values of free and 2000 rpm for PVC material, and showing that for higher values of spindle speed, the forming forces decrease. The same result was found by Davarpanah et al. (2015) for PLA and PVC material with values of 0, 1250, 5000, 7000 rpm of spindle speed. Sabater et al. (2018) shown a decrease in the forming forces as a result of an increase in the spindle speed from free to 2000 rpm for PCL and UHMWPE polymers. The feed rate has not a noticeable influence in the forming forces in polymers, as point out by authors such as Bagudanch et al. (2016) for values of 1500 and 3000 mm/min for PC and PVC materials, and Medina-Sanchez et al. (2018) for values of 1500 and 3000 mm/min for PC and PVC materials. State of the Art 55 2.3.4.2 Geometrical accuracy In SPIF, the forming of components in the desired shape is governed by the tool path information based on component geometry. The forming-tool tries to produce the target shape on the blank following the tool-path instructions. The geometric accuracy will be affected by two effects: (i) the elastic property of the sheet material which will produce a local springback effect and (ii) the residual stress. Furthermore, in SPIF the sheet is not supported from the bottom side and is only clamped along the periphery, as a result, different causes of the deviations from the desire shape can be: (i) sheet bending near the fixed zone, (ii) wall deviation, and (iii) pillow effect (see Figure 2.37). Figure 2.37. Potential geometric errors in the SPIF process (Nasulea and Oancea, 2021). Sheet bending occurs because of the distance between the clamping edge and the forming area, minimizing this gap and using a backing plate can minimize this effect. As a result of the springback of the material, the pillow effect and the sheet springback on the wall can occur, being the pillow effect the concave shape formed at the minor diameter of the base. In general, geometry accuracy can be improved using partial dies or specified forming punch, optimizing process parameters and tool paths and using heat assisted ISF process among others (Nasulea and Oancea, 2021). In polymers, Durante et al., (2018) showed that the springback is significantly influenced by the tool type, indicating that the springback of the part shaped by the forming tool with a fixed end is lower than that in the condition of the rotary one. Bagudanch et al. (2015) studied the geometry accuracy using a 3D scanner and comparing the real and ideal model, the result was the sheet part would be recovered once it was taken off from the clamping system because of the springback, but the accuracy was still in an acceptable degree. Regarding the parameters in relation to the geometry accuracy, Edwards et al. (2017) showed an improvement in the accuracy due to an increase in the step down for PC State of the Art 56 material. Moreover, Martins et al. (2009) studied the effect of the initial wall angle (Ψ0), showing that a decrease in Ψ0 the can lead to reducing in springback, leading to the increased accuracy of the shaped PVC parts. With regard to the spindle speed, authors such as Centeno et al. (2017) and Bagudanch et al. (2018) pointed out better geometry accuracy as a result of increasing the spindle speed. 2.3.4.3 Surface roughness Roughness (𝑅𝑎) is defined as the arithmetic mean of the surface profile departure from ideal form. The use of lubricant can improve the surface finish because the friction between the tool and the workpiece can be reduced (see lubricants in section 2.3.3.1). Apart from using the appropriate lubricant, the work by Sabater et al. (2018) showed that due to an increase in temperature due to friction and the increased surface contact area as a consequence of the increase in spindle speed and tool diameter, the surface roughness achieved was worse. In the same line, Bagudanch et al. (2015) identified as the most influential parameters on the surface roughness, the spindle speed and the step down. In this sense, the larger the step down the more generated tool path differs slightly from the geometry profile due to the interpolation. 2.4 Biomedical applications This section presents an overview of the current state of the art in the medical applications of polymers. The first subsection outlines the relevant manufacturing processes for UHMWPE and PEEK polymeric materials, which are commonly employed in the medical field. The subsequent subsection (section 2.4.2) highlights various studies over the past decade that have focused on the fabrication of medical prostheses through ISF using metals (section 2.4.2.1) and polymers (section 2.4.2.2). 2.4.1 Industrial This section outlines the current methodologies employed for achieving target polymer prostheses geometries. In this context, biomaterials refer to materials specifically State of the Art 57 engineered to interact with biological systems, with the aim of treating, enhancing, or substituting biological functions (Vigmond, 2019). Biomaterials must have biocompatibility, i.e., they must be able to be in long-term contact with human body tissues and not damage those tissues, which is achieved through chemical and biological inertness (Tathe et al., 2010). The common metals for biomedical applications are titanium, 316L stainless steel, cobalt chromium alloys (CoCrMo), titanium based alloys (Ti-6Al-4V) and miscellaneous others (including tantalum, gold, dental amalgams (Santos, 2017). These materials suffer from drawbacks in case of sustained and long-term use as cytotoxicity, the release of metal ions, corrosion, and wear (Chilukoti and Periyasam, 2012). During the last decades, great advances have been made in medical applications with biocompatible polymeric materials, they allowed less toxicity in vivo, are easy to process and sterilized, have a better shelf life, are lightweight, and have remarkable properties suitable for the applications (Galaev and Mattiasson, 2002). In this thesis, different medical applications are made with two biocompatible polymers (UHMWPE and PEEK), a brief description of both polymers and their uses in the medical field is developed below. UHMWPE has become the material of choice as a surface-bearing material in full joint replacement since its introduction in the early 1960s. The material is applied, for example, in artificial hips, knees, as well as in shoulders, elbows, wrists, ankles and spinal disks (Chilukoti and Periyasam, 2012). Since its introduction as a bearing component for total joint replacements (TJR) by Dr. John Charnley in 1962 (Musib, 2011), UHMWPE has become the gold standard to manufacture one of the articulating surfaces of total hip, total knee, and total shoulder prostheses. A standard total hip replacement consists of four individual components represented in Figure 2.38a: (i) acetabular cup (shell), which fits into the pelvis and is made of metal (the majority of titanium or tantalum metal), (ii) the acetabular liner, which fits into the acetabular cup, the most commonly used materials are ceramic, cobalt-chrome alloys, and polyethylenes (called plastic liners). To this respect, polyethylene has been the most used since it provides a great resistance to wear. (iii) The femoral head (ball) fits on top of the stem, and the end of the stem is taper shaped to allow the ball to wedge into position and be held tightly in place with friction (made from ceramic or metal) and, (iv) the femoral stem is the part of the replacement that fits into the thigh bone (made from titanium and cobalt-chromium) (Hallab and Jacobs, 2013). Total hip replacement became popular during the 1980s and then grew steadily until these days, where the most widespread prosthesis configuration includes a long metallic stem and a metallic head (usually Co-Cr) articulating against a polymeric component, as shown in the hip replacement in Figure 2.38b. State of the Art 58 (a) (b) Figure 2.38. (a) The individual components of a total hip replacement and (b) the components merged into an implant (Hospital Padmaja, 2022). The current acetabular implant is a 2-component cup: a metal shell for bony ingrowth and a liner to articulate with femoral head. The acetabular shell provides the base for bony ingrowth, while the liner clips into the shell and articulates directly with the femoral head. As explained before, polyethylene liner is the most common material type for the acetabular liner, polyethylene is a long-chain biocompatible polymer, which demonstrated high wear rates (about 0.2 mm/year) (Ardestani et al., 2017). The development and research in polymeric materials allowed the use of high-density polyethylene (HDPE) in the 1970s (wear 0.10 mm/year), and then to ultrahigh molecular weight polyethylene (UHMWPE) in the early 2000s, which has progressively demonstrated significantly less wear (<0.02 mm/year) (Kurtz et al., 2011). In this sense, UHMWPE stands out because of it high wear-resistance, toughness, durability, and biocompatibility. Thus, it is commonly used as a bearing material with ceramic or metallic counter surfaces in joint arthroplasty (Hussain et al., 2020). More than 90% of all hip implants in the last decade used UHMWPE (Kurtz, 2004; Wang et al., 2019). As explained in section 2.1.1, UHMWPE has a high melt viscosity and is not able to flow due to its molecular weight, thus, the ram extrusion and compression molding are the two most typical methods to produce finished or semi-finished components. Next, the machining operation is capable of changing the surface and subsurface of the polymer. To this regard, the machining temperature needs to be carefully monitored as the UHMWPE can be damaged by excessive heat (Zaribaf, 2018). Figure 2.39 resumes the steps followed to process a UHMWPE implant: (i) starting with the resin powder (ii) the semi-finished rods obtained by ram extrusion or compression molding, (iii) the machining of the UHMWPE into the desired shape, and (iv) the UHMWPE plastic liner component. State of the Art 59 Figure 2.39. Processing steps in the manufacture of UHMWPE implants (Kurtz, 2016). The second polymer material used for a medical application in this thesis is the PEEK material. PEEK is an organic semi-crystalline thermoplastic polymer that throughout its recent fifties, since its creation in 1972 and its introduction in the industry at the end of the 1980s, has achieved a recognized and outstanding position among engineering materials and polymers (Kurtz, 2019). As commented in section 2.1.1, PEEK material presents properties like physical-chemical stability in the human body, besides it presents radiolucency, biocompatibility, low density, and mechanical properties resembling human bone, i.e. the elastic modulus of PEEK is relatively low, with a close to cortical bone value (Dua et al., 2021; Yin et al., 2022). Thus, PEEK polymers offer the possibility of adjusting their elastic modulus to closely match either cortical bone (18 GPa) or titanium alloy (110 GPa) by carbon fiber reinforced composites with varying length and orientation (Skinner, 1988). These properties have provoked that PEEK is an important polymer in the medical field, more specifically, in the prostheses field, used for the replacement of a defect issue. In this sense, the use of PEEK implants has increased and displayed promising results (Brandicourt et al., 2017; Gerbino et al., 2015; Goodson et al., 2012; Rosenthal et al., 2014). However, the main disadvantage is that there is a risk of postoperative infection. This infection might be solved with treatment, sterilization and repositioning of the implant, or in the event that there is an active infection, the best option is to remove it (Kurtz, 2019). Despite the limitations, the use of PEEK in maxillofacial applications have also shown optimistic results. For instance, the work by Kim et al. (2009) presented a series of four cases of trauma and oncological defects that were reconstructed using customized PEEK implants. After 16–20 months, no patients had any implant-related complications, including infection, extrusion, or malposition. State of the Art 60 (a) (b) Figure 2.40. (a) Temperature-high laser build of cranial implants manufactured at several orientations with respect to the building direction and (b) location of the cranial implant (Berretta et al., 2018). There are various manufacturing processes for PEEK: injection molding, extrusion, and compression molding. The extrusion of PEEK stock shapes followed by machining remains the prevailing method of manufacturing medical device components. Before machining, it is recommended that components formed from PEEK are annealed to relieve stresses (Kurtz, 2019). AM has become an attractive industry over the last few years (Berretta et al., 2018, 2015; Massocchi et al., 2021). New manufacturing processes have been incorporated to achieve PEEK medical implants using technologies such as selective laser sintering (SLS) and fused deposition modeling (FDM). Recently, high-temperature laser sintering studies have been focusing on the effect of build orientation of PEEK to cranial implants and the health sector in general. In this sense, the recent work of Berretta et al. (2018), studied 13 PEEK cranial implants which were laser sintered with different build orientations (see Figure 2.40a and 2.40b), showing that this variable affects the mechanical performance of the implants. 2.4.2 ISF This section details various notable research studies conducted over the past decade pertaining to the manufacture of prostheses through ISF. This section is divided into two sections, one covering the ISF medical applications utilizing metals, and the other covering those utilizing polymers. State of the Art 61 2.4.2.1 Metals Overall, the use of metals with ISF for medical applications has the potential to improve patient outcomes by enabling the production of customized, high-quality implants that are optimized for each individual patient. To this respect, the work by Ambrogio et al. (2005) investigated the use of incremental forming processes in the production of a custom-made ankle support using DDQ (Deep Drawing Quality) steel with a thickness of 1 mm, as illustrated in Figure 2.41a. The study outlines the steps involved in the production of a custom-made ankle support: (i) determining the ankle's geometry through a non-contact, three-dimensional laser scanning technique, (ii) acquiring the ankle data in digital format as a "cloud of points" and generating a continuous surface to represent the ankle's CAD model, (iii) generating an ISO part program using a CAD/CAM system with a technique similar to milling and using a hemispherical cutter, and (iv) deforming the sheet during the manufacturing process according to the designed tool trajectory and parameters. The authors successfully applied the ISF to the production of a custom-made ankle support and measured its dimensional accuracy, which was found to be satisfactory for the desired application. They also highlight the potential of incremental forming technology in the production of complex, individual products and the possibility of using aluminum alloy as an alternative material. (a) (b) Figure 2.41. (a) CAD model and final part of the ankle support (Ambrogio et al., 2005). (b) Uncompensated Titanium cranial implant (Duflou et al., 2013). The work by Duflou et al. (2013) focuses on the development of a systematic methodology for the accurate manufacture of cranio-facial implants using SPIF, as shown in Figure 2.41b. The process involves creating a CAD model of the implant from a CT scan of the patient's skull, followed by the manufacture of the implant using SPIF. The authors tested the methodology using three different materials: AA 1050, AISI 304 and medical Titanium grade 1. The accuracy requirements for cranial implants are divided into two categories: State of the Art 62 the edges and the central region. The authors found that single pass uncompensated tool paths for forming freeform shapes showed inaccuracies and therefore optimized the tool paths to meet accuracy specifications. To further enhance the process limits and improve the accuracy of the final formed part, the authors used intermediate part design and feature analysis. The results showed improved accuracy with optimized tool paths, but further process strategies may be necessary to achieve higher accuracy in future work. The work by Vanhove et al. (2017) evaluated the potential of using SPIF for producing thin-shelled patient-specific titanium grade 2 implants that could replace bulk generic clavicle implants. The authors showed that by compensating the forming toolpath, the part could be brought into an acceptable accuracy range. The accuracy of the final implant was validated after forming, thermal treatment and cutting, and was fit to a reference validation bone with limited spread in accuracy, as illustrated in Figure 2.42a. In this work it was concluded that SPIF has the potential to produce clavicle implants with high accuracy and that further research is needed to further improve the process. (a) (b) Figure 2.42. (a) Designed produced and mounted clavicle implant on a generic synthetic bone (Vanhove et al., 2017). (b) Cheekbone area for obtaining the CAD model and cheekbones produced by SPIF (Guglielmi et al., 2021). Recently, a study was conducted by Guglielmi et al. (2021) to evaluate the feasibility of producing a resorbable cheekbone prosthesis (see Figure 2.42b) using two innovative sheet forming processes, Super Plastic Forming (SPF) and SPIF. The material characterization and simulation steps were performed to determine the plastic and superplastic behavior of the material, AZ31B-H24 magnesium alloy, and to design the manufacturing processes. The SPF process was performed at high temperatures and uses a gas to push the blank against a die for pure stretching. The results showed that both processes produced adequate results in terms of shape and thickness distribution. However, the final choice between the two processes should be based on the medical and economic requirements. Materials and methods 69 Figure 3.2 presents the schematic setup used for the Nakajima tests. In this sense, three parts can be differentiated: (i) the universal sheet testing machine Erichsen model 142- 20, (ii) the digital image correlation (DIC) system and, (iii) the force and displacement acquisition system. The Erichsen model 142-20 is schematically indicated in Figure 3.2. The capability of the universal testing machine machine is 400 kN of drawing force, 200 kN of blank holder, and a drawing velocity range from 0 to 600 mm/min. A punch with 100 mm diameter was used to perform the Nakajima tests. The test area magnificated on the left presents the essential elements for the Nakajima test (blank holder, backing plate and punch). In this sense, the specimen is positioned and fixed by the force of the blank holder. According to the ISO 12004 standard, the speed of the punch was set to 1 mm/s (60 mm/min) and in order to provide statistical meaning, the tests were performed in arbitrary order and at least 3 repetitions were performed for each specimen geometry. To diminish friction, a layer of Polytetrafluoroethylene (PTFE) was placed along with two layers of Vaseline between the tool and the specimens. All the tests were performed at room temperature. Figure 3.2. Schematic representation of the universal sheet testing machine indicating the main components. The measurements of principal strains within the deforming area at the vicinity of the zones where cracks appeared were carried out by means of the digital image correlation (DIC) ARAMIS®-v6.2.0-6 system. The ARAMIS® system includes two CCD cameras with 1.3 megapixels, lighting system, and the processor system. The frame rate was set to 12 frames per second until fracture. In Figure 3.2, the schematic representation of the Materials and methods 70 Nakajima test for an equibiaxial geometry shows a black and white stochastic pattern on the specimen's surface obtained by a fine spray of matte black specks on a white background required by the DIC system. One of the main objectives of this investigation is aimed at provide a methodology for the determination of the formability limits by necking and fracture in principal strain space for polymeric sheets. This methodology is the first attempt to adapt to polymeric sheet the methodologies commonly applied for metals by Martínez-Donaire et al. (2014). Sections 3.1.2 and 3.1.3 show the methodology followed to determine formability limits by necking and fracture, respectively. 3.1.2 Necking assessment Necking is a failure mode that occurs by tension where relatively large amounts of strain are located disproportionately in a small region of the material (see section 2.2 in chapter 2). As mentioned before, in this investigation two different approaches are considered and adapted for the determination of the onset of necking for the polymeric sheets: a timedependent and a time‐position dependent (“flat-valley”) originally proposed for metals by Martínez-Donaire et al. (2014). 3.1.2.1 Time-dependent methodology The time-dependent methodology for metals is based on the experimental evidence of the necking initiation and its development. This methodology uses the major strain (𝜀1) temporal analysis and its first time derivative of major strain rate (𝜀1), for a series of points along a section perpendicular to the crack. The time-dependent approach to polymers arises from the difference between necking behavior in polymers. In a polymeric sheet, the necking may start on a different crosssection than the fracture cross-section of the specimen due to the high capacity of the necking spread and/or propagation. To this respect, Figure 3.3 schematically presents the procedure to apply the time-dependent methodology. Figure 3.3a shows a tensile test Nakajima specimen in which the necking is visible and Figure 3.3b, the representation of major strain with time for several points along a section perpendicular to the site of necking initiation (points A, P1, …, PN, B). This representation allows to identify the two reference points at the necking zone: point A and point B. Point A corresponds to the point where necking initiates, the points between these reference points have a Materials and methods 71 monotonically increase of strains (see Figure 3.3b) and, point B is the first point where the strain starts to cease. To this respect, the necking zone is determined by the two points of reference (point A and point B) temporarily identifying the boundary of the instability region. (a) (b) (c) Figure 3.3. Schematic representation of (a) major strain distribution of a TS specimen in the Nakajima specimen indicating the points considered, (b) evolution of major strains with time for the necking region, (c) time‐dependent approach application. Figure 3.3c schematically presents the following step of the time-dependent approach methodology. In this sense, it is represented the major strain evolution of points A and B with time and the strain rate evolution of point B with time. The onset of necking is established when the strain rate for point B reaches a local maximum, 𝜀1,𝑚𝑎𝑥 𝐵, that time instant is denoted as tnecking (time instant at the onset of necking), consequently, the limit strains at the onset of necking will correspond to the strains for point A (𝜀1,𝑙𝑖𝑚, 𝜀2,𝑙𝑖𝑚) at the time instant tnecking (see Figure 3.3c). 3.1.2.2 Flat-valley methodology The second approach applied is a time-position dependent approach, also known as “flatvalley”, which are based on the direct observation and analysis of the displacement of the outer surface of the sheet during necking. In this sense, Figure 3.4 shows the schematic procedure to obtain the onset of necking by applying the flat-valley methodology on a polymeric sheet. Figure 3.4a shows the section localized perpendicular to the necking area of a tensile strain Nakajima test. Figure 3.4b represents the evolution of the Z- displacement (normal direction to the initial surface) over the position X along the aforementioned section, and each profile corresponds to an instant of time (t1,t2, and t3 in Figure 3.4b). The profile evolution before the onset of necking follows the punch Materials and methods 72 geometry (t1 in Figure 3.4b), then, when necking occurs, the profile evolution reveals the inability to follow the punch and it is visible as a flat profile or flat-valley (t2 in Figure 3.4b). Then, the propagation of necking gives place and the profile evolution reveals the visible valley (t3 in Figure 3.4b). (a) (b) (c) Figure 3.4. Schematic representation of (a) a section perpendicular to the failure area of a Nakajima test for a TS specimen, (b) Temporary evolution of the Z displacement over the X position for instants before, after, and at the onset of necking, and (c) its spatial derivative on a section normal to the failure area. Figure 3.4c presents the Z-displacement spatial derivative for three distinct stages of the same section perpendicular to the necking region. The utilization of the spatial derivative allows detecting the initiation of necking, as a locally constant slope corresponds to a flat profile at the onset of necking (t2 in Figure 3.4c). 3.1.2 Fracture assessment This section addresses the fracture analysis to determine the formability limits by fracture. According to Centeno et al. (2015), the methodology applied for metals is based on the measurement of the fracture thickness from the fractographies of the fractured specimens. Due to the propagation of necking in polymers along the whole length of the specimen, the initial methodology for the determination of the fracture forming limit in sheet metal needed to be adjusted to the behavior of polymeric sheets. To this regard, Figure 3.5a presents a schematic representation of a TS geometry Nakajima specimen, showing two different zones when necking has started, (i) the transition between the necking zone and the elongated area and, (ii) the propagation of the necking zone. Figure 3.5b presents the same specimen when fracture occurs, identifying the thickness at fracture. Materials and methods 73 (a) (b) Figure 3.5. Schematic representation of the TS Nakajima specimen (a) during the test, depicting the necking propagation and the transition zone and (b) after fracture, depicting the thickness at fracture. The procedure employed for obtaining the strains at fracture entails the calculation of several parameters, which are detailed below. The logarithmic strain in the thickness direction is calculated as follows: 𝜀3,𝑓 =ln𝑡𝑓 𝑡0 (10) where 𝑡𝑓 is the current sheet thickness at fracture and 𝑡0 is the initial sheet thickness. The general application of this methodology to metals considers that the fracture minor strain variation/gradient in the sheet surface is practically null after necking (Embury and Duncan, 1981), and it can be estimated as approximately the same as the necking one, which is: 𝜀2,𝑓 ≅ 𝜀2,𝑛 (11) Finally, the fracture major strain is obtained assuming volume constancy: 𝜀1,𝑓 = −𝜀2,𝑓 −𝜀3,𝑓 (12) In polymers, due to neck propagation along the length of the specimen, the original methodology developed for determining the fracture forming limit for sheet metal forming (Centeno et al., 2015) needs to be adjusted for the polymers’ behaviour. In this sense, it Materials and methods 74 is more accurate to consider that the minor strain at fracture 𝜀2,𝑓 ∗ is obtained considering that the local strain loading path slope 𝛽∗ remains constant. The slope is obtained at the last measured strains by the DIC system (𝜀1 𝐷𝐼𝐶,𝜀2 𝐷𝐼𝐶), 𝛽∗=𝑑𝜀2 𝐷𝐼𝐶 𝑑𝜀1 𝐷𝐼𝐶 (13) The local major strain at fracture 𝜀1,𝑓 ∗ is calculated from the thickness reduction at fracture (equation 10) and using the previous equation (equation 13): 𝜀1,𝑓 ∗=−𝜀3,𝑓 1+ 𝛽∗ (14) And the minor strain at fracture: 𝜀2,𝑓 ∗= 𝛽∗∗ 𝜀1,𝑓 ∗ (15) This procedure allowed determining the strain pair at fracture to determine the formability limits by fracture. Thermoplastic polymeric materials present a modulus of elasticity very low, which produces a significant elastic recovery of the material after a fracture. In addition to the springback due to the low modulus of elasticity, thermoplastic materials are viscoelastic, in this sense, this nature causes a thickening of the material to occur after the fracture, which varied with time. Because of these facts, the last strain pairs obtained by the DIC system will be compared with the fracture strains obtained by the adapted methodology previously presented usually applied to sheet metals. 3.2 SPIF tests This section shows the materials and methods used in the experimental plan. For this, sections 3.2.1 and 3.2.2 present the methodology to determine the formability of SPIF and the SPIF experimental setup, respectively. From section 3.2.3 to section 3.2.5 is presented the experimental plan for the three polymeric materials: PC, UHMWPE, and PEEK. Materials and methods 75 3.2.1 Procedure to determine formability in SPIF As it was explained in detail in the state of the art in chapter 2, Single Point Incremental Forming (SPIF) is a process that consists of the deformation of a sheet clamped in a rig in which a die is not necessary. Figure 3.6 shows the schematic representation of the SPIF process performed on a CNC milling machine for carrying out the experiments. In this sense, the sheet is clamped between the blank holder and the backing plate, and the forming tool performed a previously established trajectory using a CAD software, as can be seen in the magnification on the left, the final formed part is a truncated conical geometry. Figure 3.6. Schematic representation of the SPIF process performed on a CNC milling machine for a truncated conical geometry indicating the main components. The results of the SPIF tests were evaluated in terms of principal strains and modes of failure. The display of the CNC milling machine allowed determining the maximum depth for each replicate at the instant that the sheet failure occurs. After the SPIF deformation, the principal strain state was evaluated on the specimens deformed by utilizing the offline 3D deformation digital measurement system ARGUS®, which is based in circle grid analysis (CGA). The working principle of the ARGUS® system is based on photogrammetry, also called remote sensing. This method allows to compute a threedimensional geometry on the basis of a set of two-dimensional pictures. The schematic Figures 3.7a and 3.7b present the ARGUS® system. In these Figures is showed the “circular barcode markers”, these markers should be placed in the region of the interest and are required for calculating the camera position with respect to the object for each Materials and methods 76 picture. In addition, to measure strains at the surface of the object, it is necessary that a grid of dots is clearly visible on the object. For that, prior to the tests, a circle pattern was produced on the polymeric sheet blank surface by an ink printing process. (a) (b) Figure 3.7. Schematic view of the utilization of the ARGUS® system for a (a) truncated conical and (b) pyramidal geometries. Figure 3.7a shows the schematic representation for a truncated conical geometry, the strain states which occur on the wall are similar and close to plane strain conditions, and the undeformed part is formed by the initial dot pattern. In Figure 3.7b, the truncated pyramidal geometry provide strain states close to plane strain (on the wall), and produce biaxial strain conditions on the flat lateral surfaces (on the corners), besides, the undeformed parts are formed by the initial dot pattern. Figure 3.8 represents the procedure to obtain the contour of the principal strains on the outer surface of the polymeric sheet testing geometry. For the case of truncated conical geometry, the strain state of the section situated on the wall are close to plane strain conditions. Two longitudinal sections can be analyzed on the truncated pyramid, positioned on the corner and on the wall. The strain states that occur in sections on the wall are similar and close to plane strain conditions, and the section on the corner is close to equi-biaxial and biaxial strain conditions (see section 2.3.2 in chapter 2). Materials and methods 77 Figure 3.8. The final conical and pyramidal spifed specimens depicting the sections of analysis and the resulting strains within the FLD material. Regarding the evaluation of strains within the principal strains space, Figure 3.8 depicts a schematic representation of the FLD obtained by performing Nakajima tests with different strain loading paths, thus providing the conventional forming limits at necking (FLC) and fracture (FFL). In the same Figure 3.8, is represented a schematic illustration of the expected evolution of the principal strains along a number of sections attained in SPIF on the surface of the final testing specimen. For the case of the truncated conical geometry, the strain states will be close to plane strain (yellow section on the conical geometry). Pyramidal geometries provide strain states close to plane strain (orange section on the pyramidal geometry), and produce biaxial strain conditions on the flat lateral surfaces (green section on the pyramidal geometry). These strain and stress conditions are explained in chapter 2, section 2.3.2. 3.2.2 Experimental setup The SPIF experimental plan is divided in function of the polymeric material, i.e. polycarbonate (PC), Ultra-high-molecular-weight polyethylene (UHMWPE) and Polyether ether ketone (PEEK). All the SPIF experiments were performed using a spherical-end forming tool, driven by a CNC milling machine, which follows incrementally a pre-established tool path deforming the clamped polymeric sheet blank into a final component at room temperature (see the SPIF schematic illustration in Figure 3.6). The experiments with PC and UHMWPE were carried out at the Department of Mechanical and Manufacturing Engineering, University of Seville (US), and in the case of PEEK material, at the Department of Mechanical Engineering and Industrial Construction, University of Girona (UdG). In this sense, two different CNC milling Materials and methods 78 machines were used to perform the SPIF tests as follows: (i) for PC and UHMWPE, the CNC milling EMCO® model VMC 200 with Emcotronic TM02 controller and, (ii) for PEEK, the CNC milling Kondia® HS1000 3-axis milling machine equipped with Fidia® numerical control. In both CNC milling machines, the geometries performed were truncated conical and pyramidal geometries, and the dimensions of which were different for each material. The setup and the dimensions in mm of the backing plate used for the conical and pyramidal geometries performed at the University of Seville (with the EMCO® CNC milling) are indicated in Figures 3.9a and 3.9b, and the setup used at the University of Girona (with the CNC milling Kondia®) is in Figure 3.9c. (a) (b) (c) Figure 3.9. View of the setup used along with the backing plate dimensions in mm for (a) truncated conical and (b) pyramidal geometries with fixed wall angles in CNC EMCO® and, (c) truncated pyramidal geometry with a variable wall angle in CNC Kondia®. A number of replicates of the different sets of process parameters were performed in order to provide statistical meaning to the SPIF results. Indeed, 2 replicates were carried out in the case that the results were consistent in terms of final depth at fracture and mode of failure. In case of discrepancy, 3 or more replicates had to be performed. The maximum depth for each replicate of these SPIF tests were controlled directly from the display of the CNC milling machine at the instant that the sheet failure occurs. For all the SPIF experimental tests, the process parameters considered were: Φ𝑡𝑜𝑜𝑙 (mm) is the tool diameter , ∆𝑍 (mm) is the step down for each contour, 𝑆 (rpm) is the spindle speed of the tool, and 𝐹 (mm/min) is the feed rate of the trajectory. As previously explained, the experimental work for PC and UHMWPE was carried out at the University Materials and methods 85 changing one of the parameters and leaving the others selected. Thus, it can be observed the influence of the modified parameter. For instance, the influence of the step down with respect to the reference test (0.1 mm of the step down) was observed for 0.2 mm (labeled as “PC 2 U TC1”) and 0.5 mm (labeled as “PC 2 U TC2”). 3.3.2.2 Truncated pyramidal geometry Table 3.6 presents the dimensions for the truncated pyramidal geometry for the 2 mm PC sheet. Table 3.6. Geometrical parameters for a PC truncated pyramidal geometry. Geometry Dimensions Wall angle LA (mm) LB (mm) R1 (mm) H (mm) ψ t0 (mm) Fixed 29.5 30 20 50 89.5 2 For the PC polymeric material, the dimensions of the conical and truncated pyramidal geometries were kept equal, this decision was made with the objective of comparing the differences between these geometries in terms of their formability and mode of failure. For the same reason, the SPIF work plan that was carried out was the same as for the conical geometry indicated in Table 3.5, calling each test as TPx (Test Pyramidal geometry number). Once again, the main objective of the experimental plan was to observe and isolate the effect of each of the process parameters. 3.2.4 UHMWPE experimental plan The SPIF experimental work with 2 mm thickness UHMWPE was carried out a truncated pyramidal geometry with wall fixed angle depicted in Table 3.7. As mentioned before, the CNC was the CNC milling EMCO® model VMC 200 and, as lubricant, water was poured onto the sheet surface to avoid an excessive heating of the material and tool. The selection of water as lubricant instead of oil for this material was motivated by the results obtained for PC sheets, which will be discussed in chapter 4. Materials and methods 86 Table 3.7. Geometrical parameters for a UHMWPE truncated pyramidal geometry. Geometry Dimensions Wall angle LA (mm) LB (mm) R1 (mm) H (mm) ψ t0 (mm) Fixed 25 40 5 50 20 2 The respective operating parameters for UHMWPE associated with each experiment are synthesized in Table 3.8. Due to the results obtained for PC, the main motivation to study the UHMWPE was how temperature affects the failure modes, especially twisting, in this sense, the variables to analyze were: how the spindle speed and step down affected the temperature, and how the imposed trajectory affected the failure mode in SPIF. For that, the tool diameter was fixed in 10 mm and the feed rate in 1000 mm/min. According to the experience gained in polymeric sheet, the spindle speed and the step down have a great influence on the modes of failure. To study this effect, two different values of spindle speed were tested, 20 and 500 rpm, and three different values of step down, 0.1, 0.2 and 0.5 mm. Two trajectories were studied: the unidirectional trajectory (named U in Table 3.8) and the bidirectional trajectory (named B in Table 3.8). Table 3.8. SPIF experimental plan for the truncated pyramidal geometry with 2 mm thickness UHMWPE sheets. Test condition* 𝚽𝒕𝒐𝒐𝒍 (mm) 𝑺 (rpm) 𝑭 (mm/min)  𝒛 (mm) UHMWPE 2 U TP1 10 500 1000 0.5 UHMWPE 2 U TP2 10 500 1000 0.3 UHMWPE 2 U TP3 10 500 1000 0.1 UHMWPE 2 U TP4 10 20 1000 0.5 UHMWPE 2 U TP5 10 20 1000 0.3 UHMWPE 2 U TP6 10 20 1000 0.1 UHMWPE 2 B TP1 10 500 1000 0.5 UHMWPE 2 B TP2 10 500 1000 0.3 UHMWPE 2 B TP3 10 500 1000 0.1 *Material – Thickness - Trajectory Test (Unidirectional or Bidirectional) - Geometry (Conical or Pyramidal) - Number test In this sense, for a value of spindle speed of 500 rpm, the influence of step down was studied with 0.5 mm (“UHMWPE 2 U TP1”), 0.3 mm (“UHMWPE 2 U TP2”) and 0.1 mm (“UHMWPE 2 U TP3”) considering the unidirectional trajectory. With the same type of trajectory and with a value of 20 rpm of spindle speed, again the influence of the step down was studied with 0.5 mm (“UHMWPE 2 U TP4”), 0.3 mm (“UHMWPE 2 U Materials and methods 87 TP5”) and 0.1 mm (“UHMWPE 2 U TP6”). And finally, for analyzing the effect of the trajectory on the failure modes with a value of 500 rpm of spindle speed, the influence of the step down was studied for 0.5 mm (“UHMWPE 2 B TP1”), 0.3 mm (“UHMWPE 2 B TP2”) and 0.1 mm (“UHMWPE 2 B TP3”) with the bidirectional trajectory. 3.2.5 PEEK experimental plan The SPIF tests were carried out on a Kondia® HS1000 3-axis milling machine equipped with Fidia® numerical control at the UdG. All experiments were performed with water as lubricant, following a procedure to extract and empty continuously to maintain uniform temperature. The experimental plan for PEEK consists of testing two geometries with the same dimensional parameter: truncated pyramidal and conical geometries depicted in Table 3.9, both with wall variable angle. Table 3.9. Geometrical parameters for a PEEK truncated conical and pyramidal geometries. Geometry Dimensions Wall angle R (mm) Gr (mm) H (mm) ψ t0 (mm) Variable C 52.5 80 43 45 2 L (mm) P 52.5 The main objectives with PEEK were based on: (i) minimization of the time process, and for that, the increase in the values of step down versus the possible loss of geometrical accuracy and final finish of the specimen and, (ii) the improvement in terms of formability due to temperature increase versus the occurrence of typical failure modes in polymers (twisting and/or crazing). Materials and methods 88 Table 3.10. SPIF experimental plan for the truncated pyramidal and conical geometry with 2 mm thickness PEEK sheets. Test condition* 𝚽𝒕𝒐𝒐𝒍 (mm) 𝑺 (rpm) 𝑭 (mm/min)  𝒛 (mm) PEEK 2 B TP1 6 500 600 0.1 PEEK 2 B TP2 6 Free 600 0.1 PEEK 2 B TP3 6 500 600 0.35 PEEK 2 B TP4 6 Free 600 0.35 PEEK 2 B TP5 6 500 600 0.6 PEEK 2 B TP6 6 Free 600 0.6 PEEK 2 B TP7 6 500 600 1.2 PEEK 2 B TC1 6 500 600 0.35 PEEK 2 B TC2 6 Free 600 0.35 PEEK 2 B TC3 6 500 600 1.2 PEEK 2 B TC4 6 Free 600 1.2 *Material – Thickness - Trajectory Test (Unidirectional or Bidirectional) - Geometry (Conical or Pyramidal) - Number test To this regard, Table 3.10 presents the process parameters for the experimental work. For all the tests, the tool diameter used was 6 mm and the feed rate was 600 mm/min. The experimental work allowed to investigate the influence of the step down and the spindle speed on PEEK processing. The testing parameters for step down were 0.1, 0.35, 0.6, and 1.2 mm, and for the spindle speed were free rotation and 500 rpm. All of the tests were performed using the bidirectional trajectory (“B” in each test) according to the results obtained for the previous polymeric materials. From “PEEK 2 B TP1” to “PEEK 2 B TP7” are indicated the process parameters considered for the truncated pyramidal geometry with variable wall angle considered (see dimensions in Table 3.9). And for the case of truncated conical geometry with variable wall angle, from “PEEK 2 B TC1” to “PEEK 2 B TC4”. In this sense, the tests were performed using a 6 mm tool diameter and 600 mm/min of feed rate, and testing values of free and 500 rpm of spindle speed for a value of step down considered, for instance, in order to analyse the influence of the spindle speed with 0.1 mm of step down, 500 rpm (“PEEK 2 B TP2”) and free rpm (“PEEK 2 B TP1”) tests were performed. Materials and methods 89 3.3 Medical applications This section presents the methodology followed for the manufacturing of medical prostheses using SPIF for: (i) the plastic liner that comprises the articulating surface of a total artificial hip using UHMWPE material and, (ii) the cheekbone defect on the zygomatic bone and cranial defect that covered the temporary and parietal bones using PEEK material. 3.3.1 Plastic Liner device Hip replacement surgery is a procedure where degenerated bone and cartilage in the hip joint are exchanged for new implants. As explained in chapter 2, section 2.4, a standard total hip replacement consists of four individual components schematically represented in Figure 3.14: (i) acetabular cup (shell), which fits into the pelvis and is made of metal, (ii) the acetabular liner, which fits into the acetabular cup, (iii) the femoral head (ball) fits on top of the stem, and the end of the stem is taper shaped to allow the ball to wedge into position and be held tightly in place with friction and, (iv) the femoral stem is the part of the replacement that fits into the thigh bone (Hallab and Jacobs, 2013). As is schematically indicated in Figure, 4.14b, the damaged femoral head is removed and replaced with a metal stem that is positioned in the hollow center of the femur. The femoral stem may be cemented or "snap-fit" into the bone. As explained in chapter 2 in section 2.4, polyethylene liner is the most common material type for the acetabular liner, more specifically, ultrahigh molecular weight polyethylene (UHMWPE) which has shown significantly less wear (<0.02 mm/year) (Kurtz et al., 2011). In this sense, the experimental work approaches on the manufacture of the plastic liner using SPIF with UHMWPE. The design of the plastic liner depends on the shell (acetabular cup), to this regard, the catalogs from various manufacturers show the appropriate dimension depending on the shell depending on the patient. The Zimmer Biomet Institute, a manufacturer specializing in medical applications will serve as a reference for this study (Zimmer Biomet Institute, 2021). The manufacturer offers a catalog for the acetabular system, and according to the catalog, a 44 mm plastic liner is recommended for use with a 62 mm shell. The selection of this diameter is driven by both the thickness of the plastic sheet and the diameter of the shell. Plastic liners for 62 mm shells typically range in thickness from 2-5 mm, while thicker sheets are required for larger shell diameters. Materials and methods 90 (a) (b) Figure 3.14. (a) Schematic diagram of a total hip replacement, depicting the different components. (b) Assembly of the artificial hip prosthesis into a pelvis. It was considered two approaches for the plastic liner design: one of the geometries is a simple hemispherical geometry with a diameter of 44 mm, while the other combines a hemispherical geometry with the same diameter and an additional cylindrical component of 10 mm in height. Table 3.11 shows the dimensions for the two geometries. The first approach is more straight-forward, and the second arises from the idea of merging a hemispherical geometry with a cylinder stem for a better fitting between the articulating surface and the stem and head part of the prosthesis. Table 3.11. Geometrical parameters for the two geometries considered for manufacturing a plastic liner by UHMWPE. Geometry Parameters (mm) Hemispherical geometry Dimensions Ø t0 44 2 Cylindrical and a hemispherical zone H Ø t0 10 44 2 Materials and methods 91 The proposed medical application with UHMWPE considered two variables: (i) minimize the forming time and study the feasibility of manufacturing a plastic liner under this premise and, (ii) with this aim of reducing the forming time, improve the springback produced in SPIF. Therefore, all tests for the case of the hemispherical geometry and the case of cylinder + hemispherical geometry were carried out with a step down of 0.5 mm to reduce the forming time. All tests were performed at a spindle speed of 20 rpm in order not to overheat the material (according to the results obtained for the truncated pyramidal geometries by SPIF with UHMWPE). As a means to reduce the springback, two approaches were considered for the hemisphere: 1 cycle and 3 cycles. A cycle was defined as a full tool trajectory to deform the part complete up to the final depth. If the test comprises 3 cycles, it means the forming process is repeated 3 times continuously. Table 3.12 indicates the process parameters used for manufacturing the plastic liner component. Table 3.12. Process parameters for the two geometries considered for manufacturing a plastic liner by UHMWPE. Test condition* 𝚽𝒕𝒐𝒐𝒍 (mm) 𝑺 (rpm) 𝑭 (mm/min)  𝒛 (mm) Cycles UHMWPE 2 B H1 10 20 1000 0.5 1 UHMWPE 2 B H2 10 20 1000 0.5 3 UHMWPE 2 B CH1 10 20 1000 0.5 3 *Material – Thickness - Trajectory Test (Unidirectional or Bidirectional) - Geometry (Hemispherical or Cylinder + Hemispherical geometries) - Number test All the tests were formed using the bidirectional trajectory according to the results obtained for the pyramidal truncated geometry with UHMWPE, and Table 3.12 indicates the hemispherical geometry (designated as “H” in Table 3.12) and for cylinder+hemispherical geometry (designated as “CH” in Table 3.12). To ensure repeatability, two repetitions were performed for each test. The experimental work was performed in the CNC milling EMCO® model VMC 200 at the US. The available backing plate had dimensions considerably larger than the geometries that were intended to be deformed from the hemispherical geometry and cylinder+hemispherical geometry for which it was necessary to manufacture a backing plate for a better fit. The design of the backing plate was made using the SolidWorks® CAD software and the fabrication using a 3D printing by Fusion Deposition Modeling (FDM) with PLA filament. Materials and methods 92 (a) (b) (c) Figure 3.15. (a) 3D printed backing plate in the SPIF setup along with dimensions in mm (b) 3D model printed using CURA software and, (c) PLA 3D printed backing plate mount in SPIF setup. Table 3.13. Printing parameters used for the manufacturing of PLA backing plate. Material Temperature (°C) Speed (mm/s) Pattern Infill PLA filament Printing Bed Printing Raster angle 100% 200 60 70 45°/-45° As it can be seen in Figure 3.15b, a backing plate of 46 mm diameter was implemented and by means of the CURA software the 3D printing process was carried out in an Ultimaker™ S5, meeting the parameters listed in Table 3.13, which guarantee an appropriate stiffness. 3.2.2 Cranio-maxillofacial implants The medical applications of PEEK were two cranio-maxillofacial implants performed by SPIF: (i) a cheekbone defect on the zygomatic bone (see the schematic representation in Figure 3.16a) and (ii) a cranial defect that covered the temporary and parietal bones (see the schematic representation in Figure 3.16b). Figure 3.16 indicates the cheekbone (Figure 3.16a) and cranial defect (Figure 3.16b) from different patients indicating the cranial bones and the defect area for the implant. The procedure for obtaining the cranial reconstruction was explained in section 2.4, in this sense, starting from the computed tomography (CT) scans of the axial, sagittal, and coronal planes the 3D cranial model is obtained. With the 3D model of the cranial, the implant design can be carried out using the Rhinoceros® software, with which the tool Materials and methods 93 path is developed using CAM software (Bagudanch et al., 2018). Finally, it could proceed with the manufacturing of the implant. (a) (b) Figure 3.16. 3D cranial model indicating the cranial bones and the planned reconstruction for (a) a zygomatic bone defect (cheekbone implant) and, (b) a temporary and parietal defect (cranial implant). Concerning the process parameters for the SPIF tests, Table 3.14 indicates the experimental work for the PEEK medical applications. In one PEEK sheet, four experiments for cheekbone implants were performed named as “PEEK 2 B CBTx” (test from x=1 to x=4). According to the results obtained by SPIF for the other polymeric materials, all the tests were performed using the bidirectional trajectory. As observed in Table 3.14, a fixed feed rate of 600 mm/min and a tool diameter of 4 mm was used instead 6 mm, due to the small size of the part. The small dimensions of the cheekbone geometry allowed to test various experiments in one sheet using a backing plate with 4 holes to perform 4 different conditions. Table 3.14 also indicates the process parameters for the cranial implant, designated as “CR”. The dimensions of the cranial implant were larger and due to the number of sheets being limited by their price, only one experiment was carried out considering the most optimized testing process parameters. Materials and methods 94 Table 3.14. SPIF experimental plan for the cheekbone and cranial prostheses manufactured using PEEK. Test condition* 𝚽𝒕𝒐𝒐𝒍 (mm) 𝑺 (rpm) 𝑭 (mm/min)  𝒛 (mm) PEEK 2 B CBT1 4 Free 600 0.1 PEEK 2 B CBT2 4 500 600 0.1 PEEK 2 B CBT3 4 Free 600 0.35 PEEK 2 B CBT4 4 500 600 0.35 PEEK 2 B CRT1 6 500 600 0.35 *Material – Thickness - Trajectory Test (Unidirectional or Bidirectional) - Geometry (Cheekbone or Cranial) – Number test According to the results obtained for the truncated pyramidal manufactured with PEEK, two different values of step down were considered (0.1 and 0.35 mm) and two different conditions of spindle speed (free and 500 rpm) were tested. As mentioned above, due to the small dimensions of the cheekbone it was possible to manufacture 4 in a single PEEK sheet, however, due to limited cost and material stock, no further tests were carried out for the cranial implant. Results 101 Table 4.1 presents the strain pairs at the onset of necking by the two approaches for the three replications for each Nakajima specimen considered in the experimental work and the standard deviation (SD) results. The obtained necking strain pairs for the TS and PS specimens obtained for the two approaches are almost coincident, for all the three specimens considered for each of the geometries. With respect to the BS specimen, the time-dependent approach allowed to identify the onset of necking while the flat-valley allowed to identify a stage interval at which the onset of necking can occur. Table 4.1 indicated that necking was not a failure mode for the case of EBS Nakajima specimen with 1 mm of thickness PC sheets. In this case, either time-dependent or flatvalley approaches did not detect the onset of necking. Table 4.1. Summary of strains pairs at the onset of necking for PC with 1 mm thickness. Test Geometry (PC material) Specimen Necking Determination Approaches Time-dependent Flat-Valley 𝜺𝟏𝒍𝒊𝒎 𝜺𝟐𝒍𝒊𝒎 𝜺𝟏𝒍𝒊𝒎 𝜺𝟐𝒍𝒊𝒎 TS 1 mm I 0.100 -0.019 0.106 -0.020 II 0.093 -0.019 0.104 -0.024 III 0.093 -0.022 0.105 -0.026 Mean 0.095 -0.020 0.105 -0.023 SD 0.004 0.002 0.001 0.003 PS 1 mm I 0.099 0.003 0.109 0.002 II 0.090 0.003 0.081 0.002 III 0.100 0.001 0.105 0.000 Mean 0.096 0.002 0.097 0.001 SD 0.005 0.001 0.015 0.001 BS 1 mm I 0.095 0.057 - - II 0.084 0.055 - - III 0.081 0.047 - - Mean 0.086 0.053 - - SD 0.007 0.005 - - EBS 1 mm I,II,III No necking No necking No necking No necking Results 102 Regarding the determination of the onset of necking for the PC sheets with 2 mm thickness the previous methodologies were applied. Figure 4.4 depicts the results of both approaches for a 2 mm thickness TS Nakajima specimen. Figure 4.4a indicates the major strain distribution and the surface of the TS specimen. The time-dependent method allowed identifying point A and point B defining the necking region (Figure 4.4b), where point B is the first location where the strain starts stopping. The local maximum, 𝜀1,𝑚𝑎𝑥 𝐵, clearly allowed obtaining the strains at the occurrence of necking corresponding to point A 𝜀1,𝑙𝑖𝑚, 𝜀2,𝑙𝑖𝑚 at the instant tnecking (Figure 4.4c). Regarding the flat-valley application, the Z displacement along the target section (perpendicular to the necking region) is represented in Figure 4.4d, being highlighted in green the instant at which necking initiates because this is the stage where the slope remains constant, i.e. the curve becomes flat. Using the derivative of Z displacement the necking identification is possible as follows: the instants in which the slope remains locally constant confirms the corresponding stage (Figure 4.4e highlighted in green), and a significant change for the stages before (Figure 4.4e highlighted in blue) and after necking (Figure 4.4e). The application of the two approaches to the PS Nakajima with a 2 mm thickness specimen was similar to the TS specimen. Time-dependent and flat-valley allowed to detect the onset of necking and the results are included in appendix A. Regarding the BS Nakajima specimen with 2 mm thickness, the time-dependent approach allowed to detect of the onset of necking by identifying the local maximum using the derivative of the major strain. On the one hand, as it happened for 1 mm thickness, the flat-valley approach did not enable the strain pairs at the onset of necking due to it not being possible to observe the flat-valley profile. The two approaches were applied to the EBS Nakajima specimen with 2 mm thickness. In this sense, similar to the EBS specimen with 1 mm thickness for PC sheet, both approaches indicated that the necking was not a failure mode for the EBS Nakajima specimen, not being possible to identify a local maximum (using the time-dependent methodology) or any flat profile (using the flatvalley methodology). These results can be consulted in appendix A. Results 103 (a) (b) (c) (d) (e) Figure 4.4. Application of the methodologies to obtain the onset of necking strains for a TS Nakajima specimen of PC with 2 mm of thickness. (a) Major strain (left) and surface shape (right) of the specimen’s failure area obtained by the DIC system. (b) Experimental time evolution of the major strain along the points of the selected section. (c) Time‐dependent approach application. (d) Z‐displacement along the selected section. (e) The spatial derivative of Z‐displacement along the selected section. Results 104 Table 4.2 summarizes the results of the principal strains at the onset of necking evaluated with the two methodologies and the standard deviation for the 2 mm thickness PC sheets. The results obtained regarding the application of the methodologies were quite similar to those of 1 mm thickness, showing that TS, PS and BS did have necking as a failure mode but EBS did not. Likewise, the flat-valley methodology could not be used to detect the onset of necking for the BS Nakajima specimen with 2 mm thickness. Both approaches shown that the necking mode of failure did not occur for the EBS Nakajima specimens with 2 mm thickness. Table 4.2. Summary of strains pairs at the onset of necking for PC with 2 mm thickness. Test Geometry (PC material) Specimen Necking Determination Approaches Time-dependent Flat-Valley TS 2 mm 𝜺𝟏𝒍𝒊𝒎 𝜺𝟐𝒍𝒊𝒎 𝜺𝟏𝒍𝒊𝒎 𝜺𝟐𝒍𝒊𝒎 I 0.131 -0.023 0.147 -0.021 II 0.134 -0.025 0.134 -0.031 III 0.110 -0.020 0.134 -0.030 Mean 0.124 0.023 0.138 0.026 SD 0.013 0.002 0.007 0.005 PS 2 mm I 0.135 0.011 0.123 0.013 II 0.112 0.010 0.128 0.014 III 0.131 0.012 0.140 0.018 Mean 0.125 0.011 0.130 0.014 SD 0.012 0.001 0.008 0.002 BS 2 mm I 0.057 0.035 - - II 0.053 0.031 - - III 0.055 0.032 - - Mean 0.056 0.032 - - SD 0.002 0.002 - - EBS 2 mm I,II,III No necking No necking No necking No necking This investigation was published for 1 mm thickness PC sheets in Rosa-Sainz et al. (2020), and, as far as it is known, this is the first time in which time-dependent and flat-valley methodologies for metal sheet forming are applied to the polymeric sheets to detect the onset of necking, which in addition, allows observing if there exists the instability for certain Nakajima geometries. To this regard, the doctoral thesis of Magrinho (2019) followed the time-dependent and flat-valley approaches to characterize the formability limits by necking for PVC material with 3 mm thickness. In the thesis by Magrinho, TS and PS Nakajima specimens presented the necking instability, however, it was shown that Results 105 the necking was not a failure mode in the case of BS and EBS Nakajima specimens for the PVC material. This part of the section shows the results to determine the fracture strain pairs following the methodology described in section 3.1.2 in chapter 3. The measurement of the fracture thickness was performed using a NIKON® SMZ800N optical microscope. Figure 4.5 presents the fractography for a TS Nakajima specimen for 1 mm thickness (Figure 4.5a) and 2 mm thickness (Figure 4.5b). In both pictures, three areas can be clearly observed: (i) the fracture zone, which corresponds to where the fracture of the specimen occurs (see Figures 4.5a and 4.5b where the fracture is identified as “I”), (ii) the transition zone, which corresponds to the transition between the necked area and the elongated zone (see Figures 4.5a and 4.5b in which transition zone is identified with “II”), and (iii) the necking propagation, which occurs between these two zones and is typical of polymers when loaded in tension. (a) (b) Figure 4.5. Fractography of a TS Nakajima specimen showing the magnification of the fracture zone, the transition zone and the necking propagation for (a) 1 mm and (b) 2 mm thickness of PC sheets. The fracture strain pairs for 1 and 2 mm thickness PC sheets were obtained by measuring the fracture thickness from the fractography of the fractured specimens in agreement with the methodology presented in the previous chapter 3. Because of the very low modulus of elasticity (in PC around 2.4GPa) and the visco-elastic plastic behavior inherent in the polymer, the last strain pairs obtained by the DIC system (referred to as FFL-DIC) will be considered and compared with the fracture strains obtained by the adapted methodology described in chapter 3 usually applied to sheet metals (referred to as FFL- thickness). According to the obtained results, the proposed methodology is to characterize the FFL by means of the last strain measurement by the DIC system. Results 106 This part of the section presents the formability limits results in principal strain space for 1 and 2 mm thickness PC sheets. The formability limits by necking (FLC) and by fracture (FFL) were determined by means of Nakajima tests using the methodology described in section 3.1 in chapter 3. Figure 4.6a and 4.6b present the forming limit diagram (FLD) for PC sheets for 1 and 2 mm thickness in principal strain space, respectively. (a) (b) Figure 4.6. Formability limits by necking (FLC) and by Fracture (FFL) obtained for TS, PS, BS and EBS Nakajima specimens for (a) 1 mm and (b) 2 mm thickness PC sheets. The use of the DIC system was suitable to apply the two different methodologies to detect the onset of necking. For both thicknesses, only TS, PS, and BS exhibited necking as a mode of failure, which is depicted by an empty marker in the Nakajima specimen function: for TS, a square marker is used, for PS, a rhombus marker is used, and for BS, a triangular marker is used as shown in Figure 4.6. These strain pairs at the onset of necking allowed to characterize the FLC (represented as straight grey line in Figure 4.6a and 4.6b). The methodology to determine the FFL for metal sheets was followed and the strain pairs at fracture are indicated as a fill gray marker in Figure 4.6. As can be observed in both Figures 4.6a and 4.6b, the fracture limit strains, represented by the dotted grey line in Figure 4.6a and 4.6b, based on the FFL-thickness are lower than those obtained from the FFL-DIC method, represented by the black line in Figure 4.6a and 4.6b, due to the significant elastic recovery after fracture. In light of this, the novel methodology presented in this work proposes that it is more precise to characterize the forming limit by fracture Results 107 through strains measured by DIC considering that the local strain loading path slope 𝛽∗ remains constant (see section 3.1.2 in chapter 3). 4.1.2 UHMWPE The first part of this section presents the experimental results for the Nakajima tests to enable the determination of the major strain pairs at the onset of necking and fracture of the 2 mm thickness UHMWPE specimens tested. As was described in chapter 3, four geometries were considered for the Nakajima tests for UHMWPE: TS, PS, BS and EBS (see Figure 3.1 in chapter 3). The strain pairs at the onset of necking were determined using the time-dependent approach for the Nakajima specimens. Figure 4.7 presents the results for applying the time-dependent methodology to a UHMWPE with 2 mm thickness TS Nakajima specimen. Figure 4.7a shows the distribution of the major strain in the specimen and the surface extracted from the DIC system. As it can be observed, the necking instability is not as located as in the case of the PC sheets, showing a uniform major strain on broadband in the specimen. This result is in agreement with the natural behavior of polyethylene’s, such as HDPE (Kida et al., 2015) or UHMWPE (Fager and Bassani, 1990). To this respect, the necking phenomenon in UHMWPE is characterized by a stabilizing effect of the chain entanglements, resulting in the complete propagation of necking across the specimen (Bartczak, 2010). As a consequence, necking propagation occurs throughout the entire specimen and fracture typically occurs when a defect in the polymeric material is encountered or when the chains are unable to align further. This phenomenon is attributed to the partially crystalline nature of UHMWPE (Kurtz, 2004), in contrast to the amorphous nature of PC, for example. As a result of this non-strong localized necking, the points gradually deform in the necking region, leading to the maximum strain at point B (at which the strain stops) not being fully zero (refer to Figure 4.7b). After defining the necking region, the next step is to calculate the first derivative of the maximum strain for point B (refer to Figure 4.7c) in order to obtain its local maximum 𝜀1,𝑚𝑎𝑥 𝐵, which can be recognized in the Figure 4.7c on the right. The limit strains at the onset of necking, 𝜀1,𝑙𝑖𝑚, 𝜀2,𝑙𝑖𝑚, are the strains of point A at the instant tnecking . Results 108 (a) (b) (c) Figure 4.7. Application of the methodologies to obtain the onset of necking strains for a TS Nakajima specimen of UHMWPE with 2 mm of thickness. (a) Major strain (left) and surface shape (right) of the specimen’s failure area obtained by the DIC system. (b) Experimental time evolution of the major strain along the points of the selected section. (c) Time‐dependent approach application. The application of the time-dependent methodology to a PS Nakajima specimen for 2 mm thickness UHMWPE sheets was similar to the TS Nakajima specimen. The approach was applied to determine the strain pairs at the onset of necking and the results are included in appendix A. Figure 4.8 presents the results for the application of the time-dependent for BS and EBS Nakajima specimens with 2 mm thickness UHMWPE sheets. The application of a timedependent approach for the BS specimen (as shown in Figure 4.8a) revealed a steady increase in the maximum strain for various points studied (ranging from point A to point N, a total of 9 points). The DIC system indicated a uniform distribution of the maximum strain across the specimen (as depicted in Figure 4.8c). With regards to the EBS Nakajima specimen, an attempt to apply the time-dependent approach is shown in Figure 4.8b. Similar to the BS specimen, no point appeared to cease deformation in order to define the instability region. Additionally, a uniform distribution of the maximum strain was observed (as depicted in Figure 4.8c). Results 109 The results obtained from the time-dependent approach indicated that necking was not a mode of failure for the BS and EBS specimens of the UHMWPE sheet. This conclusion is further supported by the evolution of the force with displacement (as depicted in Figure 4.8d). This illustration displays a slight decrease in force at the moment of necking for the Nakajima TS and PS specimens and a uniform distribution of the maximum strain for the Nakajima BS and EBS specimens until failure due to fracture. The same outcome was reported by Magrinho (2019), where only the TS and PS specimens exhibited necking for the 3mm thickness PVC material, while the BS and EBS specimens did not. (a) (b) (c) (d) Figure 4.8. Application of the time-dependent to the (a) BS and (b) EBS specimens of UHMWPE with 2 mm thickness. (c) Major strain distribution and fracture specimen of BS (above) and EBS (below) and (d) force-displacement for the Nakajima UHMWPE specimens. Results 110 Table 4.3 presents the strain pairs at the initiation of necking determined through the time-dependent approach for the Nakajima specimens under study and the corresponding standard deviation. The results demonstrate the suitability of this approach in determining the time instant at the onset of necking, as well as the corresponding strain pairs. It was also observed that only the TS and PS specimens exhibited necking as a mode of failure. In contrast, the results obtained from the time-dependent approach for the BS and EBS specimens indicated that necking was not a mode of failure for these Nakajima specimens. This result was further supported by the evolution of the forcedisplacement relationship (as shown in Figure 4.8d), which displayed a slight decrease in force at the onset of necking for the TS and PS Nakajima geometries, and by the uniform distribution of the maximum strain for the BS and EBS Nakajima geometries until failure due to fracture (as depicted in Figure 4.8c). Table 4.3. Summary of strains pairs at the onset of necking for UHMWPE with 2 mm thickness. Test geometry (UHMWPE material) Specimen Time-dependent 𝜺𝟏𝒍𝒊𝒎 𝜺𝟐𝒍𝒊𝒎 TS 2 mm I 0.064 0.003 II 0.042 0.003 III 0.041 -0.003 Mean 0.049 0.001 SD 0.013 0.003 PS 2 mm I 0.079 0.011 II 0.080 0.015 III 0.081 0.009 Mean 0.080 0.012 SD 0.001 0.003 The second part of the section shows the results for determining the fracture limits for UHMWPE with 2 mm thickness. To this respect, Figure 4.9 shows the x10 magnification fractography using the NIKON® microscope SMZ800N of the TS specimen of UHMWPE. Two distinct zones can be differentiated: (i) fracture, identified as “I”, and (ii) uniform necking propagation, identified as “II”. As observed, it was not feasible to demonstrate the transition zone of the necking due to the extensive propagation area of the necking in the UHMWPE specimen. Results 117 4.2 SPIF Tests This section contains the results corresponding to the SPIF tests of the polymeric materials. To this regard, three polymeric materials were considered: PC with 1 and 2 mm thicknesses, UHMWPE with 2 mm thickness and, PEEK with 2 mm thickness. 4.2.1 PC This section presents the results of the experimental plan performed for PC sheets with 1 and 2 mm thickness by SPIF. The result analysis is focused on: (i) the formability in SPIF or spifability, (ii) the temperature data, (iii) the scanning electron microscopy (SEM) analysis of the different modes of failure obtained and, (iv) the effect of lubricant during the SPIF tests. Two different geometries were considered, the truncated conical geometry was used to perform SPIF tests with 1 and 2 mm thickness, and the truncated pyramidal geometry for 2 mm thickness PC sheets. 4.2.1.1 Formability and failure in SPIF This section has the objective of analyzing the spifability (formability in SPIF) of the PC sheets, as well as the modes of failure in SPIF through an experimental analysis assessing the influence of the main process parameters considered for the SPIF tests. For this purpose, the first geometry analyzed is the truncated conical geometry for the two different thicknesses, 1 and 2 mm PC sheets. All the tests for PC sheets were performed using Houghton Iloform™ TDN 81 oil as lubricant. Table 4.5 presents the SPIF results obtained for 1 mm thickness using the conical geometry for the five different conditions considered. As explained in section 3.2 in chapter 3, the tests are labeled depending on the: material, thickness, trajectory and geometry considered, i.e. for the case of “PC 1 U TC1”, PC is the material, 1 mm is the thickness, U means unidirectional trajectory, TC is “test conical” geometry and 1 is the test condition number 1. “PC 1 U TC1” was performed using the following process parameters 10 mm of tool diameter, 20 rpm of spindle speed, 1000 mm/min of feed rate and 0.1 mm of step down, and the failure mode attained was twisting. The effect of the tool diameter keeping the other fixed parameters was tested in “PC 1 U TC2”, increasing the tool diameter from 10 Results 118 mm to 20 mm, it was observed that the test presented twisting again. For an intermediate value of the tool diameter, 12 mm in “PC 1 U TC3”, the same mode of failure occurred for a PC sheet with 1 mm thickness. The increase in the material temperature (increasing the spindle speed) may be favored the appearance of twisting, for that, “PC 1 U TC4” was performed using 0 rpm of spindle speed and 400 mm/min for feed rate, although, in the same manner, the result was twisting mode of failure. Finally, in test “PC 1 U TC5” the step down was increased to 0.5 mm, increasing the spindle speed from 0 to 20 and keeping the feed rate at 400 mm/min. In this case, the mode of failure was identified as twisting once again. As mentioned before, previous works on polymers such as Bagudanch et al. (2015), it proved that when the spindle speed increases, the friction between the sheet and the tool increases, and an increase in temperature is produced. An increase in temperature is associated with an improvement in formability as shown in the literature for PVC sheets in the work by Bagudanch et al. (2015), and for PP in the work by Le et al. (2008), but it can lead to an undesirable failure mode, twisting (wrinkling). In the experimental plan performed in the present study, the most favorable conditions to obtain a different mode of failure, such as ductile fracture instead of twisting were defined by a step down of 0.1 mm, a spindle speed of 0 rpm, a feed rate of 400 mm/min, and a 12 mm of tool diameter (“PC 1 U TC5”). As exposed above, even in this case it was not possible to get any another mode of failure. These results indicate that twisting was the predominant mode of failure for the 1 mm thickness PC sheet, as evidenced by the truncated conical geometry depicted in the image contained in Table 4.5, as far as it was not possible to achieve another mode of failure by varying the conditions within a certain range of the main process parameters. The twisting is the first failure mode to occur due to the reduced thickness that have influence on the low rigidity of the sheet. In conclusion, the materials tends to twist rather than continue to deform until the fracture. This result is in concordance with the work by Silva et al. (2010), in which it is demonstrated that the thickness of the material is crucial for defining the predominant mode of failure. Results 119 Table 4.5. SPIF experimental results for 1 mm thickness PC sheet for the truncated conical geometry. Test condition* 𝚽𝒕𝒐𝒐𝒍 (mm) 𝑺 (rpm) 𝑭 (mm/ min) ∆𝒁 (mm) Z twisting appearance (mm) Failure PC 1 U TC1 10 20 1000 0.1 24.6 T PC 1 U TC2 20 20 1000 0.1 21.9 T PC 1 U TC3 12 20 1000 0.1 21.0 T PC 1 U TC4 12 0 400 0.1 23.8 T PC 1 U TC5 12 20 400 0.5 22.5 T *Material – Thickness - Trajectory Test (Unidirectional or Bidirectional) - Geometry (Conical or Pyramidal) - Number test Table 4.6 presents the results obtained for the truncated conical geometry with a 2 mm thickness PC sheet. Table 4.6 collects the results in terms of maximum depth reached and mode of failure of the different SPIF tests. The experimental work was conducted and resulted in the identification of three distinct modes of failure: fracture (F), twisting (T), and crazing (C). As outlined in section 3.2.3, a reference test designated as "PC 2 U TC0" (highlighted in bold in Table 4.6) was carried out with four process parameters, followed by eight additional tests in which one of the reference test process parameters was altered while the others remained unchanged. The results in terms of formability and failure will be analyzed below. Table 4.6. SPIF experimental results for 2 mm thickness PC sheet using the truncated conical geometry. Test condition* 𝚽𝒕𝒐𝒐𝒍 (mm) 𝑺 (rpm) 𝑭 (mm/min)  𝒛 (mm) Fracture depth (mm) Failure PC 2 U TC0 20 20 1000 0.1 26.5 F PC 2 U TC1 20 20 1000 0.2 34.6 T PC 2 U TC2 20 20 1000 0.5 31.5 T PC 2 U TC3 12 20 1000 0.1 25.0 F PC 2 U TC4 10 20 1000 0.1 25.9 F PC 2 U TC5 20 500 1000 0.1 27.7 F PC 2 U TC6 20 1000 1000 0.1 12.7 C+F PC 2 U TC7 20 20 500 0.1 31.6 F PC 2 U TC8 20 20 250 0.1 31.8 F *Material – Thickness - Trajectory Test (Unidirectional or Bidirectional) - Geometry (Conical or Pyramidal) - Number test Results 120 As a summary of the various modes of failure observed for the 2 mm thickness PC sheet deformed through SPIF, Figure 4.15 presents visual representations of the distinct modes of failure: fracture (F), twisting (T), and a combination of fracture and crazing (C). With respect to this, the fracture observed manifested as a crack opening along the circumferential direction, as depicted in Figure 4.15a. In the case of twisting, the material twisted in the cone and developed wrinkles on the inclined wall, as shown in Figure 4.15b. In Figure 4.15c, the crazing was characterized by fine cracks on the surface, resulting in a whitening of the crazed region, accompanied by a fracture through a small crack opening along the circumferential direction. PC 2 U TC0 (Reference test) PC 2 U TC1 (∆𝑍 0.2 mm) PC 2 U TC6 (𝑆 1000 rpm) (a) (b) (c) Figure 4.15. Modes of failure of 2 mm thickness PC sheets deformed by SPIF in the conical geometry: (a) fracture, (b) twisting and (c) fracture and crazing. Regarding the formability in SPIF, Figure 4.16 presents the forming limit diagrams (FLDs) for the selected conical SPIF tests, establishing a general framework for assessing the formability and the mode of failure attained for each set of process parameters. As depicted in Figure 4.16a (left), the final conical SPIF test part was analyzed to evaluate the strain distribution in accordance with the methodology outlined in section 3.2.1, utilizing the ARGUS® system. The results for “PC 2 U TC0”, which is considered the "reference test" and resulted in failure by fracture, are presented in Figure 4.16a (right). The FFLs, determined through the Nakajima tests for the PC material with a thickness of 2mm, are displayed in each FLD, represented as a black line (refer to the formability limits in section 4.1.1). Figure 4.16b presents the results related to a variation in the step down with respect to the 0.1 mm of the reference test (“PC 2 U TC0”). “PC 2 U TC1” and “PC 2 U TC2” correspond to 0.2 mm and 0.5 mm of step down, respectively, and in both cases, the mode of failure was twisting. An increase in formability was observed when a larger step down Results 121 was tested (“PC 2 U TC2”). This can be attributed to the fact that an increase in the step down results in an increase in the maximum attainable wall angle and, therefore, formability. The work by Davarpanah et al. (2015) showed that an increase in the step down may improve formability in SPIF of polymers (PLA and PVC), but is restricted by the occurrence of twisting/wrinkling for excessive values of the step down. Figure 4.16c displays the results related to a variation in the tool diameter with respect to the 20 mm of the reference test (“PC 2 U TC0”). The tests with a tool diameter of 12 mm (“PC 2 U TC3”) and 10 mm (“PC 2 U TC4”) resulted in fracture. As illustrated in Figure 4.16c, a decrease in the tool diameter appears to enhance the spifability. This may be due to the fact that smaller tool diameters concentrate the deformation in a smaller area and induce a bending effect in the sheet zone in contact with the tool. This result is consistent with the work of Marques et al. (2012), which decreasing the tool diameter value produced increased formability for PC and PVC polymers. In the recent work by Rosca et al. (2022), it was shown that a decrease in the tool diameter (testing values of 6, 8 and 10 mm) produced an increase in the formability for HDPE than and PA. Figure 4.16d shows the results to note the influence of the spindle speed, the reference test was performed with a 20 rpm of spindle speed, and two tests were performed, “PC 2 U TC5” with 500 rpm, in which fracture occurred, and, “PC 2 U TC6”, with 1000 rpm, in which the mode of failure was combined fracture with crazing during the test. “PC 2 U TC5” (500 rpm) achieved higher level of formability than “PC 2 U TC0” (20 rpm). This result is in agreement with the previous work by Bagudanch et al. (2013), in which it was demonstrated that higher values of spindle speed increased formability due to the increase in the forming temperature. Nevertheless, this experimental result (for 1000 rpm) showed that the increase in formability could be restricted due to the crazing mode of failure using excessive higher values of spindle speed. Finally, Figure 4.16e presents the results for varying the feed rate, from the reference test (1000 mm/min in “PC 2 U TC0” to “PC 2 U TC7” (500 mm/min) and “PC 2 U TC8” (250 mm/min) tests. Both tests presented fracture (“PC 2 U TC7” and “PC 2 U TC8”), and a decrease in the feed rate resulted in an increase in the spifability allowing to reach strains above the FFL. In this context, reducing the feed rate at specific spindle speeds may also enhance the time for local heat dissipation prior to the next tool pass, leading to an improvement in formability due to this localized heat. This effect is related to the response of polymer to different strain rates. In this sense, as discussed in Bagudanch et al. (2017), the decrease of the feed rate is related to a decrease in the strain rate, resulting in the achievement of larger strains. Results 122 PC 2 U TC0 (Reference) (F) ∆𝒁 0.1 mm ; 𝚽𝒕𝒐𝒐𝒍 20 mm ; 𝑺 20 rpm ; 𝑭 1000 mm/min (a) PC 2 U TC1: ∆𝑍 0.2 mm (T) PC 2 U TC2: ∆𝑍 0.5 mm (T) PC 2 U TC3 : Φ𝑡𝑜𝑜𝑙 12 mm (F) PC 2 U TC4: Φ𝑡𝑜𝑜𝑙 10 mm (F) (b) (c) PC 2 U TC5: 𝑆 500 rpm (F) PC 2 U TC6 𝑆 1000 rpm (F+C) PC 2 U TC7: 𝐹 500 mm/min (F) PC 2 TC8: 𝐹 250 mm/min (F) (d) (e) Figure 4.16. FLDs depicting the experimental results obtained in SPIF for the truncated conical geometry with 2 mm thickness PC sheet. (a) Truncated conical geometry for performing the principal strain measurement using ARGUS® for the reference test and, analysis of the influence of the: (b) step down, (c) tool diameter (d) spindle speed, and (e) feed rate. Results 123 In addition to the truncated conical geometry, the influence of the selected geometry on the 2 mm thickness PC sheets with truncated pyramidal geometry was studied. To achieve this, the same tests were conducted using the truncated pyramidal geometry, as shown in Table 4.7. As can be observed, the PC sheet displayed three distinct modes of failure, namely fracture (F), twisting (T), and crazing (C), as a result of changing the process parameters. In fact, these results showed that, for all parameter sets considered, twisting occurred first and then fracture, i.e. at a certain level of tool depth depending on the test, twisting was visually assessed in the pyramid defining the so-called “twisting visible depth”, whereas the “final depth” corresponds to the onset of fracture. Table 4.7. SPIF experimental results for 2 mm thickness PC sheet using the truncated pyramidal geometry. Test condition* 𝚽𝒕𝒐𝒐𝒍 (mm) 𝑺 (rpm) 𝑭 (mm/min)  𝒛 (mm) Twisting visible depth (mm) Fracture depth (mm) Failure PC 2 U TP0 20 20 1000 0.1 20.2 25.2 T+F PC 2 U TP1 20 20 1000 0.2 20.1 28.3 T+F PC 2 U TP2 20 20 1000 0.5 21.0 30.7 T+F PC 2 U TP3 12 20 1000 0.1 23.8 24.9 T+F PC 2 U TP4 10 20 1000 0.1 23.7 24.8 T+F PC 2 U TP5 20 500 1000 0.1 20.1 25.5 T+F PC 2 U TP6 20 1000 1000 0.1 20.1 24.8 T+F+C PC 2 U TP7 20 20 500 0.1 21.7 25.0 T+F PC 2 U TP8 20 20 250 0.1 21.2 26.5 T+F *Material – Thickness - Trajectory Test (Unidirectional or Bidirectional) - Geometry (Conical or Pyramidal) - Number test Figure 4.17 shows visually the modes of failure observed for the truncated pyramidal geometry with 2 mm thickness PC sheet: fracture (F) combined with twisting (T), and fracture combined with twisting and crazing (C). Regarding the modes of failure, the fracture appears on the corner due to the larger thinning area due to the tool passes. For the case of the truncated pyramidal geometry, all the tests presented combined twisting and fracture, the increase in the step down gave place to the same failure combination but with more severe twisting (see Figure 4.17b), and the increase in spindle speed caused combined twisting, fracture and crazing (see Figure 4.17c). Results 124 PC 2 U TP0 (Reference test) PC 2 U TP1 (∆𝑍 0.2 mm) PC 2 U TP6 (𝑆 1000 rpm) (a) (b) (c) Figure 4.17. Modes of failure of 2 mm thickness PC sheets deformed by SPIF in the pyramidal geometry: (a) fracture, (b) twisting and (c) fracture and crazing. In order to establish a general framework for assessing formability and the mode of failure attained for each set of the process parameters considered, Figure 4.18 depicts the forming limit diagram (FLDs) for the pyramidal tests performed. The ARGUS® system (Figure 4.18a left indicates the final pyramidal spifed specimen) was used to obtain the contour of the major principal strain provided onto the final test specimen. As was explained in chapter 3 section 3.2.1, two sections are differentiated in the pyramidal geometry corresponding both to the principal strains states until fracture in (i) plane strain conditions (labelled as “S0” in the major strain distribution) on the flat lateral surfaces and (ii) biaxial strain states (labelled as “S1” in the major strain distribution) on the region close to the pyramid edges. The FFLs determined by means of the Nakajima tests are presented in each FLDs, represented as a black line (see section 4.1.1.). Figure 4.18a right present the FLD for the reference test (“PC 2 U TP0”), in which the process parameters considered were: step down of 0.1 mm, tool diameter of 20 mm, spindle speed of 20 rpm and feed rate of 1000 mm/min. This test presented twisting and finally, fracture. The section analyzed in the corner zone on the pyramid showed tension and compression states due to the twisting effect. On the other hand, the analyzed section on the wall zone remained close to the plane strain condition. As a brief conclusion, the use of a large diameter tool produces a large friction effect with the wall of the sheet, generating a twisting effect in the corners that extends to the rest of the wall. Results 125 Figure. 4.18. PC 2 U TP0 (Reference) ∆𝑍 0.1 mm ; Φ𝑡𝑜𝑜𝑙 20 mm ; 𝑆 20 rpm ; 𝐹 1000 mm/min (a) PC 2 U TP1: ∆𝑍 0.2 mm PC 2 U TP2: ∆𝑍 0.5 mm (b) (c) PC 2 U TP3: Φ𝑡𝑜𝑜𝑙 12 mm PC 2 U TP4: Φ𝑡𝑜𝑜𝑙 10 mm (d) (e) Results 126 Figure 4.18. FLDs along with the contour of major principal strain on the final specimen tested for each of the SPIF testing conditions considered. (a) Truncated pyramidal geometry for performing the principal strain measurement using ARGUS® with the reference test and, for changing in (b) and (c) step down, (d) and (e) in tool diameter, (f) and (g) in spindle speed, (h) and, (i) in feed rate. Figure 4.18b and 4.18c presents the results corresponding to the variation of the step down concerning to test conditions “PC 2 U TP1” (0.2 mm) and “PC 2 U TP2” (0.5 mm), respectively, presenting both tests twisting combined with later fracture. In the case of “PC 2 U TP1” and “PC 2 U TP2”, the principal strains corresponding to S0 and S1 are in conditions of nearly plane strain and biaxial strain, respectively, showing the effect of twisting in this principal strain distribution. Analysing the sections in “PC 2 U TP1” (0.2 mm), S0 has tension and compression states on the pyramid wall zone, deviating the principal strains along S0 to negative values of the principal strain ratio, β, due to the twisting. S1, located on the pyramidal corner, presented a change in the strain distribution along the section from plane strain to biaxial strain states, i.e., S1 shows a deviation towards higher positive values of β prior to reaching fracture. In Figure 4.18c is presented the results for “PC 2 U TP2” (step down of 0.5 mm), in which is more notable the effect PC 2 U TP5: S 500 rpm PC 2 U TP6: S 1000 rpm (f) (g) PC 2 U TP7: F 500 mm/min PC 2 U TP8: F 250 mm/min (h) (i)