Back stress and strength contributions evolution of a heterogeneous austenitic stainless steel obtained after one pass by equal channel angular sheet extrusion (ECASE)

The International Journal of Advanced Manufacturing Technology Back-stress and strength contributions evolution of a heterogeneous austenitic stainless steel obtained after one pass by Equal Channel Angular Sheet Extrusion (ECASE). --Manuscript Draft-- Manuscript Number: JAMT-D-20-01656R1 Full Title: Back-stress and strength contributions evolution of a heterogeneous austenitic stainless steel obtained after one pass by Equal Channel Angular Sheet Extrusion (ECASE). Article Type: Original Research Keywords: Phase transformation; Dislocations; Grain size; Hardness; Strength; Back stress Corresponding Author: Jairo Alberto Muñoz Universidad Nacional de Rosario Rosario, Santa Fe ARGENTINA Corresponding Author Secondary Information: Corresponding Author's Institution: Universidad Nacional de Rosario Corresponding Author's Secondary Institution: First Author: Jairo Alberto Muñoz First Author Secondary Information: Order of Authors: Jairo Alberto Muñoz Alexander Komissarov Order of Authors Secondary Information: Funding Information: Consejo Nacional de Investigaciones Científicas y Técnicas (Grant number CONICET D 4263) Dr Jairo Alberto Muñoz Ministry of Science and Higher Education of the Russian Federation (Grant number:К4-2019-045) Dr Jairo Alberto Muñoz Abstract: This research work studies the different strength contributions of a sheet-shaped heterogeneous austenitic stainless steel, after having been processed at room temperature by one ECASE pass. A significant hardness increase was found throughout its thickness, showing higher values near the edges while the middle area presents the smallest gains. The material heterogeneity gives rise to a plastic gradient deformation between the soft and hard areas of the microstructure. As a consequence, a more significant amount of geometrically necessary dislocations concentrates on the interfaces of these areas, which helps the material to maintain a reliable strengthductility ratio. After the dislocations contribution to the material strength, the second contribution comes from the back stress mechanism, followed by grain size contributions. All types of contributions were higher in the edge neighborhoods than in the middle zone. Unlike the contributions from dislocations and grain size that decrease as they approach the interfaces between the hard and soft areas, the backstress contribution does the opposite, showing high increments in these zones. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation Dr. Jairo Alberto Muñoz Bolaños Instituto Física de Rosario, Universidad Nacional de Rosario, Bv. 27 de Febrero, S2000EKF Rosario, Santa Fe, Argentina. National University of Science and Technology “MISIS”, Moscow 119049, Russia E-mail: [email protected] Tel.: +79161624057 Prof. Dr. David W Russell Editor of the International Journal of Advanced Manufacturing Technology June 2, 2020 Subject: Revision manuscript: JAMT-D-20-01656 Dear Professor, Please find in attached files of our manuscript entitled " Back stress and strength contributions evolution of a heterogeneous austenitic stainless steel obtained after one pass by Equal Channel Angular Sheet Extrusion (ECASE). " to be submitted electronically for publication in the International Journal of Advanced Manufacturing Technology. The manuscript has not been published before and is not currently submitted for publication to any other journal and will not be submitted elsewhere before a decision is made by this journal. This research work has been revised and approved by all the co-authors and institutions. We appreciate the detailed comments by the reviewers. They raised new topics that enriched the content of the paper. Our responses are marked in Italics below and the changes in the manuscript are marked using yellow highlighting. First reviewer comments: 1. In Fig. 3, the range of the Edge 1 is 0 to 0.6 mm, but there is no detailed upper bound for the Edge 2. Answer: Thank you for the comment. Detailed information regarding the lower and upper bounds has been included in the manuscript. Response to Reviewer Comments (1) Is the upper bound for the Edge 2 at 5 mm? The total thickness is 5 mm, right? Answer: Thank you for the comment. The initial thickness was 5 mm. However, after ECASE processing, the sheet got a little bit thinner to 4.4mm final thickness. (2) What is the detailed range for Edge 2? Is seems around 3.8 to 4.4 mm in this manuscript. Why is it not from 4.4 to 5 mm? Answer: Thank you for the comment. Yes, you are right; it is from 3.8 to 4.4 mm. The reason is the thickness reduction after ECASE processing. (3) From Edge 1 to Middle region, the range from 0.6 to 1.8 mm has been skipped. However, if the upper bound is 5 mm, why the skipped range is not from 3.8 to 4.4 mm in the upper bound for Edge 2? Answer: Thank you for the comment. The reason is that the final thickness after ECASE processing is 4.4 mm. (4) From Fig 3(b), the central line of the Middle layer is at 2.2 mm, why? Even the heterogeneous behavior is not symmetric for Edge 1 and Edge 2, the central line should be at 2.5 mm, right? Answer: Thank you for the comment. The reason is that the final thickness after ECASE processing is 4.4 mm, so the central line corresponds with 2.2 mm. 2. Similar questions are happened in Fig. 2, Fig. 5, Fig. 7, Fig. 9(b), as mentioned in Question 1. Answer: Thank you for the comment. Images have been edited to specify each zone better. Figure 2 Figure 3 Figure 5 Figure 7 Figure 9(b) 3. There are some sentence is too long to realize what the meaning as Authors would like to deliver. It is suggested to make shorter. For example, in Page 5, Line 22-28, "It is worth mentioning that the final strength-deformation combination (650 MPa yield stress and 31% uniform deformation) stand out and are similar to those of other heterogeneous ASSs obtained by various and more exhaustive processing methods such as the ASS obtained by Zheng et al. [31] combining ECAP + annealing treatments (725 MPa and 35% uniform deformation) or the investigation of Karavaeva et al. [32] by ECAP + rolling (830 MPa and 33% uniform deformation), and the harmonic structure of Park et al. [33] (450 MPa and 38% uniform deformation)." Answer: Thank you for the comment. The sentence has been re-written. 4. Several scientific notations should be modified. For example: (1) Page 7, Line 8: "8‧ 10^14 " should be " 8 x 10^14 " (2) Page 7, Line 10: "1‧ 10^14 " should be " 1 x 10^14 " (3) Page 7, Line 10: "3‧ 10^14 " should be " 3 x 10^14 " (4) Page 7, Line 13: "1‧ 10^13 " should be " 1 x 10^13 " (5) Page 7, Line 13: "4‧ 10^13 " should be " 4 x 10^13 " (6) Page 7, Line 16: "3‧ 10^13 " should be " 3 x 10^13 " (7) Page 7, Line 16: "4.5‧ 10^12 " should be " 4.5 x 10^12 " Answer: Thank you for the comment. Scientific notations have been modified. 5. Some typo should be modified. (1) Page 6, Line 7: "0 = 0⁄ y = ⁄," should be "0 = 0⁄, = ⁄," (2) Page 7, Line 13: "1‧ 10^13 y 4‧ 10^13 " should be should be " 1 x 10^13 to 4 x 10^13 " Answer: Thank you for the comment. Typos have been corrected. Yours sincerely Dr. Jairo Alberto Muñoz Bolaños Corresponding author On behalf of all authors. 1 Back-stress and strength contributions evolution of a heterogeneous austenitic stainless steel obtained after one pass by Equal Channel Angular Sheet Extrusion (ECASE). Jairo Alberto Muñoz1,2, a, Alexander Komissarov2, b. 1Instituto de Física Rosario, Consejo Nacional de Investigaciones Científicas y TécnicasCONICET, Universidad Nacional de Rosario, Ocampo y Esmeralda, 2000 Rosario, Argentina. 2National University of Science and Technology “MISIS”, Moscow 119049, Russia. a[email protected], b[email protected]. Abstract This research work studies the different strength contributions of a sheet-shaped heterogeneous austenitic stainless steel, after having been processed at room temperature by one ECASE pass. A significant hardness increase was found throughout its thickness, showing higher values near the edges while the middle area presents the smallest gains. The material heterogeneity gives rise to a plastic gradient deformation between the soft and hard areas of the microstructure. As a consequence, a more significant amount of geometrically necessary dislocations concentrates on the interfaces of these areas, which helps the material to maintain a reliable strength-ductility ratio. After the dislocations contribution to the material strength, the second contribution comes from the back stress mechanism, followed by grain size contributions. All types of contributions were higher in the edge neighborhoods than in the middle zone. Unlike the contributions from dislocations and grain size that decrease as they approach the interfaces between the hard and soft areas, the back-stress contribution does the opposite, showing high increments in these zones. Keywords: Phase transformation, Dislocations, Grain size, Hardness, Strength, Back stress. 1 Introduction The constant worldwide demand for materials with better mechanical characteristics that allow building parts and structural elements more efficiently and with a favorable cost-benefit ratio have led the scientific community to seek and develop new materials and processes. Within the new type of materials, materials with heterogeneous structures have begun to attract attention during the last five years [1,2]. This type of materials has demonstrated an acceptable Click here to download Manuscript Manuscript marked-up.docx Click here to view linked References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 8 𝜎0𝑖=[ 𝜒𝑖∙𝜎0−𝑏𝑐𝑐+(1−𝜒𝑖) ∙𝜎0−𝑓𝑐𝑐] (6) 𝜎𝐷𝑖=[𝜒𝑖∙𝐾𝑏𝑐𝑐∙𝐷𝑖−1/2+(1−𝜒𝑖) ∙𝐾𝑓𝑐𝑐∙𝐷𝑖−1/2] (7) 𝜎𝜌𝑖=𝛼𝐺𝑀𝑏∙√1 13.5∙(𝐻𝑉𝑖−𝐻𝑉0 𝛼𝐺𝑀𝑏 ) (8) Where the sub-index 𝑖 refers to the strength value at any point of the sheet thickness. Thus, using equations (6) to (8) and the values in Table 1, an evolution of each of the strength components is obtained. From Fig 7b is verified that the most significant strength contributions come from the areas near the edges, forming a decreasing gradient as it moves away from the edge. Besides, dislocations appear as the most significant contribution in the three zones. Table 1. Material constants values used to calculate the strength contributions. Parameter bcc fcc Reference σ0 [MPa] 122.2 180 [35][36] K [Mpa∙m1/2] 0.36 0.24 [35][37] α 0.3 [37] M 3.05 [38] b [m] √3𝑎 2 ⁄ √2𝑎 2 ⁄ with a as the lattice parameter G [GPa] 77 Fig 8 shows the GNDs maps near the edge and in the middle zone. Fig 8a, corroborates the larger presence of the martensite phase around the edge with higher dislocation densities than in the middle area of the sheet. On the other hand, Fig 8b demonstrates that the middle zone is dominated by the more significant presence of austenite, demonstrating a GNDs arrangement different from that of the edge zone. GNDs pile-ups around the martensite islands can be seen in Fig 8b, as indicated by the black arrows. This behavior also clarifies the existence of heterogeneity in the middle zone due to the interaction between the austenite and martensite phases. These two phases have different microstructural characteristics, e.g., marked 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 9 differences in their grain sizes, which results in tougher (martensite) and more ductile areas (austenite). Several authors [2,9] have explained that in the heterogeneous materials the GNDs piled up in the soft zone generates a stress on the hard zone depending on the number of aligned dislocations giving rise to a new hardening mechanism. Therefore, Fig 7a and Fig 8b allows seeing that the material has a double heterogeneity. First, the heterogeneity induced by the ECASE process that modifies the areas near the edges, and secondly, is the heterogeneity due to the manufacturing process that resulted in a distribution of martensite islands along with austenite grains as demonstrated by the initial material microstructure. In addition to the different contributions mentioned above, the interactions which take place at the interfaces between hard and soft areas as a consequence of the strain partition give rise to a new hardening component known as back-stress. Several researchers suggest that a good approximation of this contribution is obtained through a loading-unloading loop, as shown in Fig 9a, and then using the following equation to calculate its magnitude [3,4,39]: 𝜎𝑏=(𝜎𝑢+𝜎𝑟)/2 (9) Where 𝜎𝑢 and 𝜎𝑟 correspond to the unload and load yield stresses in each cycle, respectively. Fig 9a shows the back-stress evolution, where it is appreciated that this contribution represents about 35% of the material yield stress. Taking into account this contribution to the overall material strength, the new equation describing the yield stress is [9]: 𝜎𝑦𝑖=𝜎0𝑖+𝐾∙𝐷𝑖−1/2+𝛼𝐺𝑀𝑏√𝜌𝑠𝑖+𝜌𝐺𝑁𝐷𝑖+𝜎𝑏𝑖 (10) Through equation (10), Fig 9b displays the back-stress contribution and its evolution across the sheet thickness. This figure shows that the areas around the edges register the biggest contributions with higher values at the interfaces between the hard and soft areas than in the edges or middle regions, and it keeps good correlation with values obtained by the loading and unloading loop. The high back-stress values in the edge vicinities correspond well with the high GNDs density in these areas, especially at the interfaces located around 600 microns from each edge. This observation is in good agreement with the research work of Park et al. [39] who also registered higher GNDs concentrations in the interfaces defining the material heterogeneity for an heterogeneous 304L austenitic steel with harmonic structure. As a consequence of the material heterogeneity, Fig 9c demonstrates the strain partition, where initially, the maximum deformations in the εxx component situate around the edge 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 10 vicinities for tensile deformations lower than 20%. Beyond this point, higher deformations move towards the middle area until its final fracture at 45% of deformation. This situation demonstrates that the areas near the edge (hard-soft interface) withstand the highest deformations as a result of the interaction of geometrically necessary dislocations until they reach a balance between the two zones. Once the GNDs differences between the two zones are reduced, the deformation process continues like an homogeneous material. To confirm the ease with which a material can flow, Fig 10 shows the Schmid factor evolution in the area that encompasses the zone near the edge and the interface between the hard and soft regions. Therefore, the higher the Schmid factor, the easier the deformation will be. Through Fig 10a-Fig 10b, it is easy to identify that there are more grains of martensite with Schmid factors of 0.5 than the austenite phase, which is confirmed by Fig 10b showing a peak with an approximate frequency of 35 % for Schmid factors around 0.5, while austenite only reaches a fraction of ~ 14%. Also, in the inset of Fig 10b it is shown that for the area near the edge (mostly bcc martensite) the most active system corresponds to {123}⟨111⟩ followed by the systems {110}⟨111⟩ and {112}⟨111⟩, respectively. The high values of the Schmid factor in the tensile direction for the edge zone corroborate the observations of the deformation measurements. Where, material flows more easily in the edge vicinity than in the middle zone. Finally, Fig 11 summarizes the different strength contributions of the heterogeneous material in each of the areas that comprise it. The main strength contribution around the edges is the back stress, with more than 35% and the dislocations with around 30% of the overall edge contribution. Conversely, the main contribution for the middle region is coming from the Peierls mechanism representing ~33% of the strength followed closely by the back stress and dislocations contributions. This behavior demonstrates that although the most significant back stress contribution occurs in the border areas, there is also a significant contribution in the middle zone. The fact of the high back stress contribution in the middle zone is due to the presence of two phases (martensite and austenite) with different grain sizes and GND densities, generating a second heterogeneity in the material. 4 Conclusions After having subjected a sheet-shaped heterogeneous austenitic stainless steel to plastic deformation at room temperature, the following conclusions summarize the main findings of this work: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 11 The ECASE process produced a material with a gradient microstructure formed mainly by the heterogeneous distribution of phases, i.e., high amount of austenite in the nucleus, and a more considerable amount of martensite induced by deformation at the edge, different grain size distributions, and quite different dislocations densities between edges and the sheet core. The high GNDs densities in the edge vicinities generated a plastic gradient that allowed to obtain a material with a good strength-ductility ratio, where the regions near the edge initially assumed larger strains than the sheet core as evidenced by the Schmid factor and the strain maps. The different strength contributions across the plate thickness demonstrated higher values around the edges region than in the middle zone. All of them, except the back-stress, decreases as they moved away from the edges. While, in the central area, all the contributions behave homogeneously. The most significant strength contributions of the material correspond with the regions near the edge, being the back stress and dislocations contributions the most important. The back-stress mechanism also plays an essential role in the middle zone, being the second strength contribution after the Peierls mechanism due to the second heterogeneity generated between austenite and martensite before ECASE. Credit authorship statement Jairo Alberto Muñoz: Investigation, methodology, formal analysis, writing original draft, writing review and editing, data curation Alexander Komissarov: Supervision, funding acquisition, resources, investigation, project administration. Acknowledges JAMB thanks the Latin-American Postdoctoral scholarship (Grant number CONICET D 4263) received from the Argentine Ministry of Science, Technology and Productive Innovation and the National Council of Scientific and Technical Research (CONICET). The authors gratefully acknowledge the financial support of the Ministry of Science and Higher Education of the Russian Federation in the framework of Increase Competitiveness Program of NUST «MISiS» (№ К4-2019-045), implemented by a governmental decree dated 16th of March 2013, N 211. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 12 Authors also thank professors Raúl Bolmaro and Martina Avalos for their help with EBSD characterization. Conflict of interest: The authors declare that they have no conflict of interest. References [1] E. Ma, T. Zhu, Towards strength–ductility synergy through the design of heterogeneous nanostructures in metals, Mater. Today. 20 (2017) 323–331. doi:10.1016/j.mattod.2017.02.003. [2] X. Wu, Y. Zhu, Heterogeneous materials: a new class of materials with unprecedented mechanical properties, Mater. Res. 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Cabrera, Microstructural and mechanical study in the plastic zone of ARMCO iron processed by ECAP, Mater. Sci. Eng. A. 697 (2017) 24–36. doi:10.1016/j.msea.2017.04.108. [38] M. Karavaeva, M. Abramova, N. Enikeev, G. Raab, R. Valiev, Superior Strength of Austenitic Steel Produced by Combined Processing, including Equal-Channel Angular Pressing and Rolling, Metals (Basel). 6 (2016) 310. doi:10.3390/met6120310. [39] H.K. Park, K. Ameyama, J. Yoo, H. Hwang, H.S. Kim, Additional hardening in harmonic structured materials by strain partitioning and back stress, Mater. Res. Lett. 6 (2018) 261–267. doi:10.1080/21663831.2018.1439115. Figure captions Fig 1. ECASE process sketch. Fig 2. Microstructure characterization, EBSD phases maps a) after 1 ECASE pass, b) initial material and c) bcc phase variation along the sheet thickness. Fig 3. EBSD calculations for the heterogeneous material, a) grain size maps, b) average grain size along the sheet thickness, c) KAM maps and b) KAM values along the sheet thickness. Fig 4. Microstructure zones along the sheet thickness. Fig 5. Mechanical properties a) hardness values on the TD plane, b) stress-strain curves for the heterogeneous material, and c) dislocation density evolution. Fig 6. Microstructure measurements (phase percentages-𝝌, grain size-𝑫 and dislocation densities-𝝆) sketch. Fig 7. Microstructure and hardening contributions a) dislocation densities along the sheet thickness and b) strength contributions across the material thickness. Fig 8. GNDs maps around the (a) edge, and (b) in the middle zone. Fig 9. Back stress and strain calculation, a) loading reloading loop and b) back stress evolution along the sheet thickness and c) maximum strain εxx component localization. Fig 10. Schmid factor evolution around the sheet edge after 1 ECASE pass, a) EBSD Schmid factor maps, b) Schmid factor values for bcc and fcc phases after 1 ECASE pass. Fig 11. Strength contributions for each zone of the heterogeneous material. Table captions Table 1. Material constants values used to calculate the strength contributions. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 15 Fig 1. ECASE process sketch. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 16 Fig 2. Microstructure characterization, EBSD phases maps a) after 1 ECASE pass, b) initial material and c) bcc phase variation along the sheet thickness. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 17 Fig 3. EBSD calculations for the heterogeneous material, a) grain size maps, b) average grain size along the sheet thickness, c) KAM maps and b) KAM values along the sheet thickness. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Figure1 Click here to download Figure Fig 1.jpg Figure2 Click here to download Figure Fig 2.jpg Figure3 Click here to download Figure Fig 3.jpg Figure4 Click here to download Figure Fig 4.jpg Figure5 Click here to download Figure Fig 5.jpg Figure6 Click here to download Figure Fig 6.jpg Figure7 Click here to download Figure Fig 7.jpg Figure8 Click here to download Figure Fig 8.jpg Figure9 Click here to download Figure Fig 9.jpg Figure10 Click here to download Figure Fig 10.jpg