Optimal use of ultra-thin plies in composite structures

Optimal use of ultra-thin plies in composite structures Carolina Furtado Pereira da Silva Supervisor: Prof. Dr. Pedro P. Camanho A Thesis submitted for the degree of Master of Science in Mechanical Engineering to the Faculty of Engineering, University of Porto Porto, June 2015 Acknowledgements I take this opportunity to express my gratitude to Prof. Dr. Pedro P. Camanho for the opportunity to participate in this project, for taking the time to share his expertise and for all the support and encouragement without which this dissertation would not have been possible. I would also like to thank him for the support throughout my MSc course, for all the advice, opportunities and for always expecting the best of me. To Albertino Arteiro, PhD candidate, for all his help and availability during this work, for taking the time to teach me the tricky aspects of experimental testing and for providing me the knowledge and tools needed to complete this work. To Ing. Miguel Figueiredo and Ing. Rui Silva, for the help and patience during the experimental work and to Dr. Jos´e Xavier, from the Center of Research and Technology of Agro-Environmental and Biological Sciences, for making it possible to use digital image correlation during the experimental program. I must also thank my work colleagues, Albertino Arteiro, Cl´audia Cardoso, Giuseppe Catalanotti, H´elder Mata and Ricardo Pinto for the valuable breaks and for being an example of hard work. I acknowledge Chomarat, Oxeon and Hexcel, for providing the material used in the experimental program carried out on this thesis. A special thanks to all my friends, in particular, Jo˜ao Sottomayor, Pedro Cavaleiro and Rodrigo Furtado, for taking this journey alongside me, for all the support and advice in the most joyful and tiresome moments. To Rodrigo Tavares for accompanying me during this work and for all the tip sharing breaks that helped me overcome inevitable punctual frustrations. Finally, I would also like to thank my family for the unconditional support and for acknowledging my own little successes, which has always given me the motivation to complete the sometimes overwhelming challenges I have in hand and yet the will to keep on looking for more. Abstract Thin-ply composites are a new generation of composite materials made of plies with fibre areal weight lower than 100 g/m2and as low as 25 g/m2. These materials offer a large set of advantages over conventional ones in terms of mechanical performance because they are able to suppress delamination and delay damage onset. However, this delay may lead to premature, brittle failure of notched structures loaded in tension, since it inhibits stress redistribution in the vicinity of the notches. This disadvantage, together with the higher manufacturing costs, have been the main obstacles to the market penetration and ways to overcome it have been sought out. The concept of ply hybridization, which is the combination of both thin and thick plies of the same material system in the same laminate, is introduced in this work. The consequences of ply hybridization in quasi-isotropic laminates loaded in tension were analysed by comparing the experimental results obtained for the hybrid lay-ups with those of thin and thick lay-ups with equivalent in-plane properties. Unnotched tension, open-hole tension tests and open-hole fatigue tests were performed to analyse the unnotched and notched behaviour of the laminates under static and dynamic loadings and double edge crack tests were performed to obtain the R-curve of the laminates. Combining thin plies with thicker plies of all fibre orientations resulted in a hybrid laminate with an intermediate notched and unnotched resistance. Combining thin an thicker 0oplies in the same laminate, resulted in equivalent unnotched strength to the thin lay-up, enhanced notched strength compared to the thick lay-up and in intermediate fatigue resistance when compared with thin and thick laminates. This means that ply-hybridization, when designed to trigger specific damage mechanics can result in the global enhanced behaviour, thus overcoming the main disadvantage of thin-ply composites. Analytical models, if physically-based, are able to deliver fast and accurate prediction and, therefore, gather all the conditions to be used as preliminary design and optimization tools. This is the case of the finite fracture mechanics model and, therefore, in this work, the predictions obtained with this model taking the R-curve into account were compared with the experimental test results. The predictions were in good agreement with the experimental results for the laminates and geometries tested and can, therefore, be used to predict failure for different geometries and to create design charts. An algorithm based on classical lamination theory and the finite fracture mev Contents i chanics model able to calculate a laminate’s unnotched and notched strength having only the ply elastic, strength and fracture properties as input variables is proposed. Its accuracy could not yet be accessed, but, given its potential to yield good results when applied to thin-ply laminates, it can be the base of an optimization algorithm able to select an appropriate lay-up for a specific application. Contents Contents i List of figures v List of tables ix 1 Introdution 1 1.1 Motivation and Objective . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Thesisoutline............................... 2 2 Thin-ply composites - Literature review 3 2.1 Unnotched tension and compression . . . . . . . . . . . . . . . . . . 6 2.2 Open-holetension ............................ 7 2.3 Summary ................................. 9 3 Experimental Work 11 3.1 Material and lay-up selection . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Manufacturing .............................. 14 3.3 Digital Image Correlation . . . . . . . . . . . . . . . . . . . . . . . . 18 3.4 Test plan and test procedures . . . . . . . . . . . . . . . . . . . . . . 19 3.4.1 Plain Strength tests . . . . . . . . . . . . . . . . . . . . . . . 19 3.4.2 Open-hole tension tests . . . . . . . . . . . . . . . . . . . . . 19 3.4.3 Open-hole fatigue tests . . . . . . . . . . . . . . . . . . . . . 20 3.4.4 Double edge crack tests . . . . . . . . . . . . . . . . . . . . . 21 4 Experimental Results 25 4.1 Experimental results - NCF T700GC/M21 . . . . . . . . . . . . . . 25 4.1.1 Unnotched tension test results . . . . . . . . . . . . . . . . . 26 4.1.2 Open-hole tension test results . . . . . . . . . . . . . . . . . . 30 4.1.3 Open-hole fatigue test results . . . . . . . . . . . . . . . . . . 39 4.1.4 Double edge crack test results . . . . . . . . . . . . . . . . . . 41 4.1.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 Experimental results - STF T700SC/M21 . . . . . . . . . . . . . . . 50 4.2.1 Unnotched tension test results . . . . . . . . . . . . . . . . . 50 4.2.2 Open-hole tension test results . . . . . . . . . . . . . . . . . . 54 4.2.3 Open-hole fatigue test results . . . . . . . . . . . . . . . . . . 62 4.2.4 Double edge crack test results . . . . . . . . . . . . . . . . . . 64 4.2.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . 72 iv Contents 5 Analysis Methods 73 5.1 Finite Fracture Mechanics Model . . . . . . . . . . . . . . . . . . . . 73 5.1.1 Finite Fracture Mechanics for the prediction of open-hole strength 74 5.1.2 Finite Fracture Mechanics for the prediction of open-hole strength (withR-curve) .......................... 76 5.1.3 Material properties . . . . . . . . . . . . . . . . . . . . . . . . 78 5.2 Open-hole tensile strength predictions . . . . . . . . . . . . . . . . . 78 5.3 DesignCharts............................... 85 6 Mechanical behaviour of composite laminates - Literature review 87 6.1 Classical Lamination Theory . . . . . . . . . . . . . . . . . . . . . . 87 6.2 Failure criteria for laminated composites . . . . . . . . . . . . . . . . 90 6.2.1 Tsai-Hill criterion . . . . . . . . . . . . . . . . . . . . . . . . 91 6.2.2 Three-dimensional invariant-based failure criteria for fibre-reinforced composites ............................ 91 6.2.2.1 Invariant-based failure criterion for transverse failure of unidirectional composites . . . . . . . . . . . . . 92 6.2.2.2 Failure criteria for longitudinal failure of unidirectional composites . . . . . . . . . . . . . . . . . . . 94 6.3 In-situ properties............................. 96 6.3.1 Transverse tensile and in-plane shear strengths . . . . . . . . 96 6.3.1.1 Thick plies . . . . . . . . . . . . . . . . . . . . . . . 96 6.3.1.2 Thin inner plies . . . . . . . . . . . . . . . . . . . . 98 6.3.1.3 Thin outer plies . . . . . . . . . . . . . . . . . . . . 98 6.3.1.4 General expression for the transverse tensile and inplane shear strengths . . . . . . . . . . . . . . . . . 99 6.3.2 Compressive transverse, biaxial transverse tensile and transverse shear strengths . . . . . . . . . . . . . . . . . . . . . . . 100 6.4 FractureToughness............................ 101 7 Modeling and performance prediction 103 7.1 Unnotched tensile and compressive strength . . . . . . . . . . . . . . 104 7.2 Notched tensile and compressive strength . . . . . . . . . . . . . . . 110 7.3 Concludingremarks ........................... 111 8 Conclusion and Future Work 113 8.1 Conclusion ................................ 113 8.2 FutureWork ............................... 115 List of Figures 2.1 Thin-ply 2.1a and thick-ply 2.1b morphology . . . . . . . . . . . . . 3 2.2 The in-situ effect: transverse strength of a 90oply constrained between two 0oplies as function of its thickness [5] . . . . . . . . . . . 4 2.3 Simulation 2.3a and onset 2.3b of free-edge delamination in a thickand thin-ply composite [45r/-45r/0r/90r]nS .............. 4 2.4 THIN (a) and THICK (b) laminates [35] . . . . . . . . . . . . . . . . 5 2.5 Ultimate strength and onset of damage with respect to ply thickness in unnotched quasi-isotropic tests, and failure modes observed for thick, intermediate and thin-ply laminates [4] . . . . . . . . . . . . . 6 2.6 Representative unnotched tension specimens after testing [6] . . . . 7 2.7 Notched laminate under tensile loading [17] . . . . . . . . . . . . . . 8 2.8 Damage in thin and thick specimens after OHT fatigue loading [35] 9 3.1 C-Ply from Chomarat 3.1a and Spread Tow Fabric from Oxeon 2.1b morphology................................ 12 3.2 Manufacturing: cutting the prepreg . . . . . . . . . . . . . . . . . . 14 3.3 Manufacturing: removing the protective layer of the prepreg . . . . 15 3.4 Manufacturing: lay-up . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.5 Manufacturing: removing trapped air between layers . . . . . . . . . 16 3.6 Manufacturing: plates before the curing cycle . . . . . . . . . . . . . 16 3.7 Manufacturing: cutting the plates into specimens . . . . . . . . . . 17 3.8 Manufacturing: cut specimens before machining . . . . . . . . . . . 17 3.9 Painted specimens for DIC analysis . . . . . . . . . . . . . . . . . . 18 3.10 Equipment used for digital image correlation . . . . . . . . . . . . . 18 3.11 Double edge crack specimens [18] . . . . . . . . . . . . . . . . . . . 23 3.12 Example of a R-curve [18] . . . . . . . . . . . . . . . . . . . . . . . . 24 4.1 Unnotched tension remote stress-displacement relations for NCF-THIN, NCF-THIN and NCF-HYBRID lay-ups. . . . . . . . . . . . . . . . 26 4.2 Representative NCF T700GC/M21 unnotched tension specimens aftertesting ................................ 27 4.3 Longitudinal strain field of NCF T700GC/M21 unnotched tension specimens just before failure . . . . . . . . . . . . . . . . . . . . . . . 29 4.4 Open-hole tension remote stress-displacement relations for d= 2mm for NCF-THIN, NCF-THIN and NCF-HYBRID lay-ups. . . . . . . 30 4.5 Open-hole tension remote stress-displacement relations for d= 5mm for NCF-THIN, NCF-THIN and NCF-HYBRID lay-ups. . . . . . . 31 2 Chapter 1. Introdution composites. The detailed study of the mechanical response of these kind of composite laminates, will enable the understanding of the consequences of ply hybridization. Firstly, a series of mechanical tests were performed to a thin-, a thickand a hybridstructure of the same material system. Since the major disadvantage of thin-ply composites is its comparatively lower notched tensile strength, priority was given to study the tensile behaviour of hybrid structures. The mechanical tests performed were unnotched tension, open-hole tension and open-hole fatigue and specimens with different sizes were tested so that the size effect could be accounted for. Since the effective use of composite materials in structural applications relies on the ability to predict their behaviour accurately, an analysis based on finite fracture mechanics was made and the experimental and computational results were compared. The second research line is based on the development of an algorithm that could possibly be the base of an optimization algorithm capable of selecting an optimal lay-up of thin-ply laminates having open-hole tension and plain strength as design drivers. Open-hole strength can be predicted using Finite Fracture Mechanics and, since, the onset of damage is delayed to the point just before failure, plain strength can be predicted using Classical Lamination Theory. Combining these models the notched strength for a given material and lay-up should be able to be predicted having only the ply elastic, strength and fracture properties as input variables. 1.2 Thesis outline In chapter 2, a literature review on the mechanical behaviour of thin-ply composites is given based on experimental work performed by Sihn et al [35], Amacher et al. [4] and Arteiro et al. [6]. In chapter 3, a detailed description of the of the material selection, manufacturing, the test plan and test procedures followed is given. In chapter 4 the experimental test results of unnotched tension tests, open-hole tension, open-hole fatigue and double edge crack tests for the NCF T700GC/M21 and STF T700SC/M21 are presented and discussed. In chapter 5, an analysis based on Finite Fracture Mechanics model is made the results are compared with the experimental open-hole tension test results available for NCF T700GC/M21 and STF T700SC/M21 lay-ups. In chapter 6, a review on the mechanical performance of composite laminates and analytical models used to predict the unnotched strength, in-situ strengths and fracture toughness of composite laminates is given. In chapter 7, an analytical methodology to calculate the notched strength for a given material and lay-up having only the ply elastic, strength and fracture properties as input variables is proposed. Chapter 8 presents the main conclusions of this study. Chapter 2 Thin-ply composites - Literature review Conventional composite laminates are made of plies with fibre areal weight (FAW) higher than 100 g/m2. However, a new generation of composite materials has been introduced in the market: thin-ply composites. This type of material is made out of plies with FAW of around 50 or even 25 g/m2, which corresponds to a ply thickness as low as 0.02 mm. The plies are produced by a method known as spread tow thin-ply technology in which large fibre tows are continuously spread to a flat thinner tape. Since the plies are thinner, the resin flows better between the fibres and, since the bundles are smaller, the fibres are better dispersed throughout the laminate, which results in a more homogeneous material than conventional laminates. A schematic representation of the thinand thick-ply composite morphology is presented in figure 2.1. (a) (b) Figure 2.1: Thin-ply 2.1a and thick-ply 2.1b morphology The use of thin-plies offers a large set of advantages over conventional composite materials. Firstly, thinner plies offer some advantages in terms of design. On one hand, design constrains such as quasi-isotropy or symmetry can be met with less total laminate thickness and, therefore, weight can be saved. On the other hand, since more plies can be stacked together for the same laminate thickness, the design freedom is improved, and, for example, smaller mismatch angles (angles between adjacent plies) can be used, which is shown to improve the interfacial fracture resistance [5]. This means that, for example, in a 0.9 mm thick laminate, instead of the standard three 0.3 mm thick plies stacking sequence [0/90/0], a more complex 4 Chapter 2. Thin-ply composites - Literature review stacking sequence of 0.03 mm thin plies as [0/45/90/-45/0]3ssequence could be used. [4] Secondly, in terms of manufacturing, thinner plies allow the production of both non-crimp fabrics and weaved fabrics with low crimp angles that offer mechanical performance equivalent to that of unidirectional reinforcement but which are much easier to handle and lay-up. Thirdly, the use of thinner plies has been proven to have a positive impact on the mechanical performance of the components due to improved design space, better homogenization and to positive size effects that the use of thinner plies represents. On one hand, by reducing of ply thickness in a multidirectional laminate, the in-situ effect, which is characterized by an increase of the strength of a ply that is constrained between other plies with different orientations, gains additional importance (fig. 2.2) [13]. This means that, for the same material system and for two different lay-ups with the same in-plane elastic properties, their ultimate strengths will be different because the strength of the plies within a laminate will be higher the thinner the plies used. On the other hand, the use of thin plies scattered throughout the laminate has been proven to reduce stress concentrations at the free-edges, thus avoiding subcritical damage such as transverse cracking and delaying the onset of free-edge delamination as shown in figure 2.3 [4] [35] [6]. (a) (b) Figure 2.2: The in-situ effect: transverse strength of a 90oply constrained between two 0oplies as function of its thickness [5] (a) (b) Figure 2.3: Simulation 2.3a and onset 2.3b of free-edge delamination in a thickand thin-ply composite [45r/-45r/0r/90r]nS 5 Various experimental studies were carried out as an attempt to: •Compare and quantify the performance of conventional (thick) and thin-ply composite laminates –Sihn et al. [35] performed unnotched tension and open-hole tension tests in both static and fatigue loadings as an attempt to characterize the performance of spread-tow, thin-ply laminates. Two quasi-isotropic CFRP laminates with the same in-plane properties were tested: THIN laminate with ply thickness of 0.04 mm and THICK laminate with ply thickness of 0.20 mm. Figure 2.4: THIN (a) and THICK (b) laminates [35] –Amacher et al. [4] performed unnotched tension tests, open-hole tensile tests, open-hole fatigue tests, open-hole compression tests and bearing tests to in quasi-isotropic thick-, intermediateand thin-ply laminates. The different types of laminate were produced with unidirectional prepreg tapes with different fibre areal weights: 30 g/m2(thin), 100 g/m2(intermediate) 300 g/m2(thick) •Evaluate the mechanical response of non-crimp fabrics e.g. Arteiro et al. [6] conducted a series of mechanical tests in two different thin-ply laminates of carbon NCFTM T700/AR-2527 epoxy system prepreg material from Aldida in order to understand the failure mechanisms of thin-ply composites. The lay-ups of both laminates are presented in table 2.1. Lay-up 1 is asymmetric and the mismatch angles between the plies are 45o. Lay-up 2 is symmetric by bi-angle layer but asymmetric by ply: in one half of the laminate, the mismatch angles between two different bi-angle layer is 90oand in the other half it is 0owhich means that, in this half, there is ply blocking. This investigation allowed a better insight of why the mechanical performance of thin-ply laminates revealed beneficial. Table 2.1: Lay-ups of the laminates tested in the experimental program performed in [6] Lay-up Ply thickness [mm] Nr. of plies Total thickness [mm] L 1 [(0/-45) / (90/45)]6T0.08 24 2.0 L 2 [(0/-45)/(45/0)/(90/45)/(-45/90)]S0.08 16 1.3 By careful analysis of the numerical and visual results of the tests performed in 6 Chapter 2. Thin-ply composites - Literature review these studies the benefits of using thin-plies can be better understood, and, therefore, the conclusions drawn in the studies will be presented hereafter. 2.1 Unnotched tension and compression In general, quasi-isotropic thin-ply laminates show enhanced ultimate plain strength. Unlike thick-ply composites, little severe damage such as delamination or transverse cracking before failure was detected in thin-ply composites. In fact, as reported in [6] and [4], the response of thin-ply laminates loaded in tension remains linear up to failure which indicates that the onset of damage is delayed until the point just before failure, as can be observed in Figure 2.5, which summarizes the results obtained by Amacher et at. [4]. Figure 2.5: Ultimate strength and onset of damage with respect to ply thickness in unnotched quasiisotropic tests, and failure modes observed for thick, intermediate and thin-ply laminates [4] In [6], Arteiro at al. compare the behaviour of two different thin-ply lay-ups (table 2.1). The failure stress of both tensile and compressive tests are presented in table 2.2 and figure 2.6 shows the typical fracture surface of lay-up 1 and 2 specimens loaded in tension. It can be concluded that lay-up 1 has a higher strength than lay-up 2 and while lay-up 1 the fracture was catastrophic with practically no visible delamination, lay-up 2 shows pull-out failure mode with splitting and delamination. The different behaviour is explained by the stacking order: lay-up 2 has mismatch angles of 90obetween bi-angle layers which means that the interlaminar stresses are higher that in lay-up 1 and, moreover, there is ply-blocking that results in higher stress concentration in adjacent plies and lower in-situ strength. Nonetheless, as in [4] both lay-ups exhibited linear response up to failure which means that severe damage before failure is delayed up to the point just before failure. Since there is less damage near the free-edges, delamination is delayed and 2.2 Open-hole tension 7 so thin-ply composites exhibit an improved fatigue behaviour (Sihn et al. [35] report that after 50000 fatigue cycles, while the strength of thick-ply composites was reduced by 30 %, thin-ply composites maintained their strength). Table 2.2: Unnotched tension and compression strengths for lay-ups 1 and 2 [6] Lay-up XL TMPa STVD XL CMPa STVD L 1 800.2 19.0 540.2 11.7 L 2 710.3 13.4 464.5 14.8 Figure 2.6: Representative unnotched tension specimens after testing [6] 2.2 Open-hole tension Open-hole tensile tests were also performed and, for this type of geometry and loading (figure 2.7), little damage before failure near the edge of the hole prior to failure is also reported in [35], which means that subcritical damage is suppressed. The experimental results obtained by Amacher et al. [4] show that, while for thickply composites the onset of damage in open-hole tensile tests occurred for stresses 50% lower than its failure stress, for thin-ply composites it occurs for stresses near the ultimate stress which confirms that the composite fails without significant damage growth. However, unlike for unnotched laminates, the absence of damage prior to failure in thin-ply composites inhibits the redistribution of local stresses near the hole and leads to premature brittle failure of the laminate. The results for open-hole tensile tests obtained by Amacher et al. [4] are presented in table 2.3. In general, under fatigue loading, thin-ply composites show enhanced mechanical behaviour since, as subcritical damage is suppressed, damage propagation is slower and less pronounced [4] [35]. Fatigue open-hole tensile tests performed in Amacher et al. [4] and summarized in table 2.3 showed that, while the thick-ply composites tested exhibited progressive propagation of transverse cracks in the 90o plies and shear cracks in the ±45 plies and of delamination, which lead to failure 8 Chapter 2. Thin-ply composites - Literature review Figure 2.7: Notched laminate under tensile loading [17] in a reduced number of cycles, the thin-ply composites tested could handle up to 1 million cycles without any degradation of its mechanical properties. This behaviour is clearly reported by Sihn et al. [35] and is shown in figure 2.8 where the severity of damage of quasi isotropic THIN and THICK lay-ups after 100k fatigue cycles at 70% of the laminate’s notched strength are shown. Even tough, in ”absolute values” thin-ply composites tested show a clear enhanced performance, it has to be taken into account that the maximum stresses for which its life can be considered nearly infinite (<320 MPa) were below the reported onset of damage stresses (352 MPa), while for the thick-ply composites tested, they were above this value (271 MPa vs 255 MPa). It is clear that the propagation of damage that already exists will be faster than of non-existent damage and this can explain the results. Nonetheless, the two types of materials tested have the same mechanical in-plane properties and were subjected to the same loading conditions, so the enhanced fatigue life of thin-ply composites is valid, even though it might only be a consequence of delayed onset of damage. Table 2.3: Open-hole onset of damage and failure stresses and open-hole fatigue number of cycles up to failure for different maximum applied stresses [4] Static Fatigue Onset of damage Final failure Max. Stress Number of cycles Thick 255 MPa 545 MPa 271 MPa 180 k 316 MPa 20 k 361 MPa 10 k Thin 352 MPa 380 MPa 268 MPa >1 million 315 MPa >1 million 342 MPa 8 k 2.3 Summary 9 Figure 2.8: Damage in thin and thick specimens after OHT fatigue loading [35] 2.3 Summary Thin-ply composites offer a large set of advantages over conventional ones both in terms of design space and mechanical performance and offer the possibility of producing lighter structures, which has always been one of the main concerns of the aeronautical industry. The use of thin-plies suppresses the appearance of damage in the free-edges and delays transverse cracking and delamination onset, thus improving the overall behaviour of the composite laminate. In general, thin-ply composites exhibit: •enhanced unnotched strength •lower notched tensile strength since there is almost no damage prior to failure and, therefore, redistribution of local stresses is inhibited which leads to premature brittle failure of the laminate •enhanced fatigue resistance since the onset of damage is delayed and, therefore, damage propagation is slower and less pronounced. 10 Chapter 2. Thin-ply composites - Literature review Chapter 3 Experimental Work The first objective of this work is to evaluate the consequences of ply hybridisation which is the combination of both thin and thick layers of the same material in a composite structure. To do so, experimental tests were performed using thin-, thickand hybridconfigurations for of the same material system. Some aspects of the material selection, manufacturing, the test plan and test procedures followed during this work will be explained hereafter. 3.1 Material and lay-up selection Two different carbon-epoxy system prepregs were used in this experimental study: •NCF T700GC/M21 : Chomarat’s C-Ply T700GC non-crimp-fabric (NCF) biangle layers with FAW of 75 g/m2per layer impregnated with M21 epoxy. CPly are made up of two unidirectional layers with different orientations that are sewn together which results in bi-angle layers that have equivalent mechanical performance and are easier to handle than unidirectional prepregs. In this work [0o/-45o] and [0o/+45o] C-ply were used. The ply nominal thickness is 0.075 mm per ply and, therefore, 0.150 mm per bi-angle layer. •STF T700SC/M21 : Oxeon’s T700SC spread tow fabric (STF) impregnated with M21 epoxy from Hexcel. This fabric is produced by interlacing Spread Tow tapes which results in a nearly crimp-less cross plied fabric with the mechanical properties of a cross plied UD and the handling of a fabric prepreg. Two fabrics were used: 160 g/m2with a ply nominal thickness of 0.160 mm and 240 g/m2with a ply nominal thickness of 0.240 mm per fabric layer. The mechanical properties of T700GC/M21 prepreg system are presented in tables 3.1 and 3.2 where, E1and E2are the longitudinal and transversal Young’s modulus, respectively, G12 is the shear modulus, ν12 is the major Poisson coefficient, XTand XCare longitudinal tensile and compressive strengths, respectively, YUD T and YUD Care transversal tensile and compressive strengths, respectively, SLis the in-plane shear strength and GIC and GIIC are the mode I and mode II interlaminar fracture toughnesses, respectively. Note that, even though the GC and SC fibre sizings are different, they should not influence the ply’s elastic properties. The same might not be true for the fracture as strength properties and, therefore, the properties presented in table 3.1 are only valid for NCF T700GC/M21. 18 Chapter 3. Experimental Work 3.3 Digital Image Correlation Digital image correlation is an optical-numerical full-field displacement measuring technique that can be used to evaluate the displacement and strain fields and to observe damage initiation and propagation [6]. In this work, digital image correlation was used to evaluate the surface displacement and strain field in the surface of some specimens. Before testing, the surface of the specimens was cleaned using sandpaper and acetone and the specimens were sprayed with white and black ink to generate the random distribution of granular dots required by the DIC system. An example of the painted specimens is shown in fig. 3.9. The ARAMIS DIC-2D v6.0.2 equipped with an 8-bit Baumer 138 Optronic FWX20 camera coupled with a 200 mm Nikkon lens was used. During the test, the optical system was positioned perpendicular to the surface of the specimen and the light system is used to assure an even lightening on the specimen’s surface (fig. 3.10). For all specimens, the displacement field was measured in the outer 90oply. Figure 3.9: Painted specimens for DIC analysis Figure 3.10: Equipment used for digital image correlation 3.4 Test plan and test procedures 19 3.4 Test plan and test procedures A series of mechanical tests were performed to the thin, thick and hybrid laminates of both material systems. Since the major disadvantage of thin-ply composites is its comparatively lower notched tensile strength, priority was given to study the tensile behaviour of hybrid structures. 3.4.1 Plain Strength tests The unnotched strength is necessary to characterize a composite laminate and, therefore, unnotched tensile tests were performed to the NCF-THIN, NCF-THICK, NCFHYBRID, STF-THIN, STF-THICK and STF-HYBRID lay-ups following the ASTM D3039 /D3039M standard [1]. The specimens length (L) is 300 mm and its nominal width (W) is 25 mm (table 3.4). The unnotched tensile strength on each specimen is calculated as: XT L=Pmax A(3.1) where Pmax is the maximum applied load during the test and Ais the cross-sectional area of the specimen. To calculate the Athe dimensions of each specimen were measured, instead of using their nominal dimensions. The tests were performed in displacement control in servo-hydraulic MTS 312.31 testing machine using a 250 kN load cell. Coarse-grain sandpaper was applied between the specimen and the grips to avoid sliding and grips were clamped with a 45 Nm bolt torque. The DIC technique was used to evaluate the surface displacement and strain field of one test specimen per laminate configuration using a 200mm Nikkon lens. The working distance was 660 mm, the acquisition frequency was 1 Hz and the shutter time was 5.0 ms. Table 3.4: Unnotched tension test matrix Test L (mm) W (mm) Nr. specimens/ lay-up Speed (mm/min) Acquisition (Hz) UNT 300 25 5 1 5 3.4.2 Open-hole tension tests Open-hole tensile tests are used to characterize the resistance of a composite laminate with stress concentrations and to evaluate the effect of size on the laminate strength that is characterized by a decrease in specimen strength as the size of the specimen increases for the same width-to-diameter (W/D) ratio. When a notched structure is loaded, subcritical damage that appears at the vicinity of the notch, and, while for larger specimens, the size of the damaged zone is negligible compared to the specimens in-plane dimensions, for smaller specimens it is not. This explains why, the notched strength tends to the unnotched strength as the specimens size 20 Chapter 3. Experimental Work decreases. [14] [30] The open-hole tensile tests were performed following the ASTM D5766/ D5766M standard [3] and three different sizes with the same width-to-diameter ratio W/D = 6 were tested. The dimensions of the specimens are presented in table 3.5. The central open-hole was obtained using a drilling machine. Open-hole tension tests performed to NCF-THIN, NCF-THICK and NCFHYBRID specimens were performed in displacement control in servo-hydraulic MTS 312.31 testing machine using a 250 kN load cell. Coarse-grain sandpaper was applied between the specimen and the grips to avoid sliding and grips were clamped with a 45 Nm bolt torque. Open-hole tension tests performed to STF-THIN, STF-THICK and STF-HYBRID specimens were performed in displacement control in an Instron testing machine. Digital image correlation was used in one specimen of each lay-up and hole diameter configuration to evaluate the surface displacement and strain field. A 200mm Nikkon lens and an acquisition frequency of 1 Hz were used. The specimens were loaded up to 90% of their notched strength and will be inspected using X-ray after testing. The width and thickness of all specimens were measured and used to calculate the cross-sectional area A. The notched strength σ∞ Tof each specimen reads: σ∞ T=Pmax A(3.2) where Pmax is the maximum applied load during the test. Table 3.5: Open-hole tension test matrix Test L (mm) W (mm) D (mm) Nr. specimens/ lay-up Speed (mm/min) Acquisition (Hz) OHT 300 48 8 4 1 5 OHT 300 30 5 4 1 5 OHT 300 12 2 4 1 5 3.4.3 Open-hole fatigue tests Open-hole fatigue tests were also performed. The dimensions of the specimens are presented in table 3.6 and followed the ASTM D5766/ D5766M standard [3] , however, as there is no standard to this type of test, the loading conditions were selected as proposed by Amacher et al. [4]: sinusoidal loading in load control with frequency of 2 Hz with peak stress of 70% of the laminate notched strength and a ratio of R=0.1. The specimen’s end life was considered reached when its stiffness was reduced by 10% of its initial value. 50k cycles were applied to all specimens. This allows, on one hand, to evaluate the stiffness and residual strength of the specimens after the same number of applied cycles. Also, by analysing the specimen’s stiffness during the test, it is possible to access the number of cycles they bear before the 3.4 Test plan and test procedures 21 failure criterion is reached. For each cycle, the maximum and minimum force and displacement is known and, therefore, the reduction of stiffness can be calculated. The applied stress reads: σ∞ T=Pmax A(3.3) where Pmax is the maximum applied load during the test and Ais the cross-sectional area of the specimen. Since they are both constants, the applied stress is also constant. The applied stress can also be calculated as follows: σ∞ T=E (3.4) where Eis the stiffness and is the applied strain. The applied stress is constant and therefore σ∞ Ti=σ∞ Td⇔Eii=Edd(3.5) where the index irefers to properties of the undamaged specimen and the index d refers to properties of the damaged specimen. The reduction of stiffness is given by the ratio Ed/Ei. For the failure criterion used, Ed/Ei= 90% and therefore, the number of cycles the specimen can withstand before its end life is the number of cycles it can withstand with i= 0.9d⇔∆ud=∆ui 0.9(3.6) The tests were performed in a servo-hydraulic MTS 312.31 testing machine using a 250 kN load cell, coarse-grain sandpaper was applied between the specimen and the grips to avoid sliding and grips were clamped with a 45 Nm bolt torque. Table 3.6: Open-hole fatigue test matrix Test L (mm) W (mm) D (mm) Nr. specimens/ lay-up Frequency (Hz) Max. Load R OHF 300 30 5 3 2 0.7 σ∞ T0.1 3.4.4 Double edge crack tests More advanced failure prediction models require not only the material’s fracture toughness, but also the material crack resistance curve (R-curve), which is the relation between the increment of crack length resistance and the fracture toughness. Catalanotti et al. [18] proposed a methodology to determine the R-curve of polymer composites reinforced by unidirectional fibres. It is based on the size effect law, which is the relation between the size of the specimens and their notched strength σ∞(w). According to this methodology, the driving force curves GIat the ultimate remote stress are tangent to the R-curve. This means that the ultimate remote stresses σ∞can be calculated solving the system of equations (GI(∆a) = R(∆a) GI(∆a ∂∆a=R(∆a) ∂∆a (3.7) 22 Chapter 3. Experimental Work According to [9] and [41] the energy release rate in mode I of a two-dimensional orthotropic body for a crack propagating in the x direction is given by: GI=1 ´ EK2 I(3.8) where KIis the mode I stress intensity factor and ´ Eis the the equivalent modulus which is given by ´ E=1 + ρ 2ExEy−1/2 µ1/4(3.9) with ρand µare given by ρ=(ExEy)1/2 2Gxy −(νxyνyx)1/2(3.10) and µ=Ey Ex (3.11) The stress intensity factor KIis a function of ρ, the notched remote stress σand of the specimen’s dimensions a,wand Land it is given by KI=σ√wκ(α, ρ, ζ) (3.12) where κis a correction factor that depends on ζ=µ−1/4w/L,α=a/w and ρ. For ζ < 1/2, κcan be expressed as a function of only κand ρ[10]. For not highly orthotropic laminates (0 <ρ<4) [10], κis given by κ=f(α)χ(ρ) (3.13) where χis the correction factor for the orthotropy of the material χ(ρ) = 1 + 0.1(ρ−1) −0.016(ρ−1)2+ 0.002(ρ−1)3(3.14) and ρis given by 3.10. fis a correction factor that accounts for the geometry of the specimens. For double edge crack specimens it reads [37] f(α) = √πα h1+0.122 cos4απ 2is2 απtan απ 2(3.15) Replacing 3.12 in 3.8, the energy release rate reads GI(∆a) = 1 ´ Ew(σ∞)2κ2(α0+∆a w, ρ, ζ) (3.16) where α0is the initial notch length-to-width ratio α0=a0/w. Replacing equation 3.8 in the first equation of 3.7, the R(∆a) yields R(∆a) = 1 ´ Ew(σ∞)2κ2(3.17) 3.4 Test plan and test procedures 23 Figure 3.11: Double edge crack specimens [18] For a constant w/L and a0/w and knowing that, by definition the R-curve is size independent (∂R ∂w = 0), differentiating equation 3.17 with respect to wyields: ∂ ∂w(wσ∞)2κ2= 0 (3.18) Given the size effect σ∞(w) is know, equation 3.18 can be solved in order of w(∆a) which can afterwards be replaced in equation 3.17. The size effect law can be determined experimentally testing geometrically similar double edge crack specimens, i.e. with the same width-to-crack length 2w/a ratio and different width 2was shown in figure 3.11 and applying one of three linear regressions proposed in [12] that best fits the experimental data: i) bilogarithmic regression ii) linear regression I or iii) linear regression II. The regressions and the R-curve parameters (length of the fracture process zone, lfpz, and the fracture toughness at propagation Rss) are shown in 3.7. Note that κ0=κ(α0) and ´κ0=∂κ/∂α(α0). It is useful and more convenient to express the R-curve analytically. Catalanotti et al. [18] suggest the following equation R(∆a) = Rss h1−(1 −γ∆a)βi(3.19) where γand βare the parameters that best fit the R-curve. In this study, to obtain the size effect law of the six different lay-ups, tension tests were performed to double edge notched specimens with width wfrom 5 to 25 mm and width-to-notch length a/w = 3/5 (see table 3.8). Three specimens of each 24 Chapter 3. Experimental Work Figure 3.12: Example of a R-curve [18] Table 3.7: Regressions and the R-curve parameters [18] Regression Formula Fitting parameters Rss lfpz Bilogarithmic ln(σ∞) = ln M √N+wM, N κ2 0 ´ EM2κ(α0) 2´κ0N Linear regression I 1 (σ∞)2=Aw +CA, C κ2 0 ´ E 1 A κ(α0) 2´κ0 C A Linear regression II 1 w(σ∞)2=A1 w+CA, C κ2 0 ´ E 1 C κ(α0) 2´κ0 A C specimen configuration were tested for each laminate configuration. The double edge cracks were machined in a CNC machine equipped with a 1 mm drill bit. Tests performed to NCF-THIN, NCF-THICK and NCF-HYBRID specimens were performed in displacement control in servo-hydraulic MTS 312.31 testing machine using a 250 kN load cell. Coarse-grain sandpaper was applied between the specimen and the grips to avoid sliding and grips were clamped with a 45 Nm bolt torque. Double edge cracks tests performed to STF-THIN, STF-THICK and STF-HYBRID specimens were performed in displacement control in an Instron testing machine. Table 3.8: Double edge crack test matrix Test L (mm) 2w (mm) a0 (mm) Nr. specimens / lay-up Speed (mm/min) Acquisition (Hz) G1+(∆a) A 300 10 3 3 1 5 G1+(∆a) B 300 20 6 3 1 5 G1+(∆a) C 300 30 9 3 1 5 G1+(∆a) D 300 40 12 3 1 5 G1+(∆a) E 300 50 15 3 1 5 Chapter 4 Experimental Results In this chapter, the experimental test results of unnotched tension tests, open-hole tension, open-hole fatigue and double edge crack tests for the NCF T700GC/M21 and STF T700SC/M21 are presented. Since the main goal of this experimental work is to compare the mechanical behaviour of the thin, thick and hybrid laminate configurations of the same material system, the results are presented in two separate sections: section 4.1 is dedicated to the experimental tests results of NCF T700GC/M21 lay-ups and section 4.2 is dedicated to the experimental test results of STF T700SC/M21 lay-ups. 4.1 Experimental results - NCF T700GC/M21 This section presents the experimental tests results of NCF T700GC/M21 lay-ups. To simplify the analysis, the lay-ups are, once again, presented below in table 4.1. Ply blocking is highlighted in red. Note that all plies are symmetric, quasi-isotropic and have the same in-plane properties. In NCF-THIN lay-up, there is no plyblocking, and, except for the central 45oply, all plies have nominal thickness of 0.075 mm. NCF-THICK lay-up, two plies with the same orientation are blocked together when possible and therefore, the nominal thickness of most plies is 0.150 mm. NCF-HYBRID lay-up has ply blocking of only two 0oplies near the center of the laminate. Table 4.1: NCF T700GC/M21 lay-ups Laminate ID Lay-up t (mm) NCF-THIN [(90/+45)/(0/-45)]3s1.8 NCF-THICK [(90/+45)/(+45/0)/(0/-45)/(-45/90)/(90/+45)/(0/-45)]s1.8 NCF-HYBRID [(90/+45)/(0/-45)(90/+45)/(90/-45)/(+45/0)/(0/-45)]s1.8 26 Chapter 4. Experimental Results 4.1.1 Unnotched tension test results The remote stress-displacement relations for plain strength tension of laminates NCF-THIN, NCF-THICK and NCF-HYBRID tests are presented in fig. 4.1. For the unnotched tension tests, all the laminates exhibit linear behaviour up to failure. This suggests that there is little severe transverse cracking before failure which is fibre-dominated. Representative unnotched tension specimens after testing are shown in figs. 4.2a and a close-up of the fracture planes of the specimens is shown in figures 4.2b and 4.2c. All lay-up NCF-THIN and NCF-THICK and some of the NCF-HYBRID specimens failed in two places, due to catastrophic failure. Lay-up NCF-THIN specimens exhibit brittle net-section failure. In NCF-THICK specimens some delamination can be observed. The different failure modes are related to the stacking sequence. Unlike lay-up NCF-THIN, lay-up NCF-THICK has ”ply blocking” i.e. two plies with the same orientation stacked together, which leads to lower in-situ strengths of those plies. This, as reported in [7], triggers delamination onset, pullout and splitting. NCF-HYBRID specimens revealed a similar fracture plane to NCF-THICK specimens, i.e. some delamination and pull-out failure mode is also observed. The mean values and standard deviation of the unnotched tension tests for lay-ups NCF-THIN, NCF-THICK and NCF-HYBRID are presented in table 4.2. As reported in [7] and [4], thin-ply structures have higher unnotched tensile strength than thick-ply structures since they are able to delay damage up to the point of final failure. The same is proven here and NCF-THIN specimens show 11.1% higher unnotched tensile strength than NCF-THICK specimens. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 100 200 300 400 500 600 700 800 Displacement [mm] Remote Stress [MPa] QI-NCF-THIN QI-NCF-THICK QI-NCF-HYBRID Figure 4.1: Unnotched tension remote stress-displacement relations for NCF-THIN, NCF-THIN and NCF-HYBRID lay-ups. 4.1 Experimental results - NCF T700GC/M21 27 (a) Representative NCF-THIN (above), NCF-THICK (middle) and NCF-HYBRID (below) specimens after testing (b) Fracture plane of representative NCF-THIN (left), NCF-THICK (middle) and NCFHYBRID (right) specimens after testing (c) Fracture plane of representative NCF-THIN (above), NCF-THICK (middle) and NCFHYBRID (below) specimens after testing (side view) Figure 4.2: Representative NCF T700GC/M21 unnotched tension specimens after testing 34 Chapter 4. Experimental Results 2345678 450 500 550 600 d [mm] Notched Strength [MPa] NCF-THIN NCF-THICK NCF-HYBRID Figure 4.8: Notched strength vs hole diameter for lay-ups NCF-THIN, NCF-THICK and NCFHYBRID the analytical models used to predict the notched strength of composite structures, as the Finite Fracture Mechanics Model, explained in section 5.1 [17]. Digital image correlation was used during testing of one specimen of each layup and hole diameter configuration to access the differences in damage evolution. The specimens were loaded up to 90% of their notched strength. Figures 4.9, 4.10 and 4.11 show the longitudinal strain at the surface of NCF-THIN, NCF-THICK and NCF-HYBRID specimens loaded at 90% of their notched strength. The bottom right images show the longitudinal strain along two lines positioned near the hole. Since no discontinuity of the strain field along those lines can be identified, it can be concluded that 90% of the specimen’s strength revealed to be insufficient to allow the formation of cracks at the vicinity of the hole. In general, the strain concentration near the hole is higher on smaller specimens. Although no free edge transverse cracks appeared in any monitored specimen, smaller specimens exhibit higher strain concentrations and are, therefore, more likely to develop transversal cracks. No relevant differences are visible between NCF-THIN, NCF-THICK and NCF-HYBRID lay-ups. In general, as reported in [17], for the same d/W ratio, the larger the hole diameter, the more notch sensitive the specimen is. The same conclusion can be taken from this study analysing fig. 4.12 where the normalized notched strength defined as σN=σ∞ T/XLfor the three lay-ups and hole diameters is shown. In this figure, two different types of behaviour are are pointed out in black: notch sensitivity which corresponds to a brittle behaviour where the normalized notched 4.1 Experimental results - NCF T700GC/M21 35 Stage: 167 0 50 100 150 200 0 200 400 600 time (s) stress (MPa) εx (−) stress = 473.8 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (a) NCF-THIN d=2mm Stage: 144 0 50 100 150 0 200 400 600 time (s) stress (MPa) εx (−) stress = 434.7 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (b) NCF-THIN d=5mm Stage: 170 0 50 100 150 200 0 5 10 15 time (s) stress (MPa) εx (−) stress = 14.6 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (c) NCF-THIN d=8mm Figure 4.9: Longitudinal strain field of NCF-THIN specimens at 90% of their failure stress 36 Chapter 4. Experimental Results Stage: 166 0 50 100 150 200 0 200 400 600 time (s) stress (MPa) εx (−) stress = 506.7 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (a) NCF-THICK d=2mm Stage: 148 0 50 100 150 0 200 400 600 time (s) stress (MPa) εx (−) stress = 441.5 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (b) NCF-THICK d=5mm Stage: 166 0 50 100 150 200 0 200 400 600 time (s) stress (MPa) εx (−) stress = 425.9 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (c) NCF-THICK d=8mm Figure 4.10: Longitudinal strain field of NCF-THICK specimens at 90% of their failure stress 4.1 Experimental results - NCF T700GC/M21 37 Stage: 177 0 50 100 150 200 0 200 400 600 time (s) stress (MPa) εx (−) stress = 501.9 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (a) NCF-HYBRID d=2mm Stage: 152 0 50 100 150 200 0 200 400 600 time (s) stress (MPa) εx (−) stress = 474.8 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (b) NCF-HYBRID d=5mm Stage: 174 0 50 100 150 200 0 200 400 600 time (s) stress (MPa) εx (−) stress = 446.7 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (c) NCF-HYBRID d=8mm Figure 4.11: Longitudinal strain field of NCF-HYBRID specimens at 90% of their failure stress 38 Chapter 4. Experimental Results strength is defined as σN= 1/KTand notch insensitivity which corresponds to a ductile behaviour and where the normalized notched strength of the laminate is defined as σN= 1 −2R/W. In this case, for d/W = 1/6, and for a quasi-isotropic lay-up ( K∞ T= 3), KTyields: KT=K∞ TRK= 3 3(1 −d/W) 2 + (1 −d/W)3−1 = 3.0944 The normalized notch strengths is therefore σN= 1/KT= 0.32316 for notch sensitivity and σN= 1−2R/W = 0.8333 for notch insensitivity. Analysing fig. 4.12 it can be accessed that NCF-THIN lay-up exhibits a more brittle response that both NCF-THIN and NCF-HYBRID lay-ups. These results will be addressed with more detail in chapter 5. 2345678 0.3 0.4 0.5 0.6 0.7 0.8 d [mm] Normalized Notched Strength [-] NCF-THIN NCF-THICK NCF-HYBRID Figure 4.12: Normalized notched strength vs hole diameter for lay-ups NCF-THIN, NCF-THICK and NCF-HYBRID 4.1 Experimental results - NCF T700GC/M21 39 4.1.3 Open-hole fatigue test results Open-hole fatigue tests were performed to three lay-ups of NCF T700GC/M21 to compare the evolution of damage in the three lay-ups. The specimen’s hole diameter is d= 5mm and d/w = 1/6 as shown in table 3.6. Although, three tests per laminate configuration were planned, only one was performed due to schedule problems. For this reason, the results presented hereafter, serve only as preliminary results, that should, in the future, be complemented with more experimental data. The reduction of stiffness during the tests is shown in figure 4.13. As presented in table 4.5 NCF-THIN, NCF-THICK and NCF-HYBRID specimens suffered a stiffness reduction of 2.486 %, 5.196 % and 3.231%, respectively. Table 4.5: Open-hole fatigue test results for lay-ups NCF-THIN, NCF-THICK and NCF-HYBRID Type σ∞ T[MPa] σmax = 0.7σ∞ T [MPa] Nr valid tests Modulus reduction after 50k cycles NCF-THIN 479.76 335.83 1 2.486% NCF-THICK 490.62 343.43 1 5.196% NCF-HYBRID 526.92 368.84 1 3.231 % 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ·104 0.95 0.96 0.97 0.98 0.99 1 Number of cycles Ed/Ei NCF-THIN NCF-THICK NCF-HYBRID Figure 4.13: Reduction of stiffness during the open-hole fatigue tests to NCF-THIN, NCF-THICK and NCF-HYBRID specimens While NCF-THIN specimen exhibit no visible damage on the surface, in NCFTHICK and NCF-HYBRID specimens a part of one of the outer 90oply delaminated 40 Chapter 4. Experimental Results near the hole. The surface of the NCF-THICK and NCF-HYBRID specimens after testing are shown in figures 4.14 and 4.15, respectively. The specimens will be inspected after testing using X-ray, so that, a better insight of the extent and type of damage present in each specimen can be accessed. As expected, NCF-THIN specimen show enhanced resistance to fatigue loadings compared to NCF-THICK specimen because they exhibit less subcritical damage prior to failure and therefore, damage propagation is slower and less pronounced. NCF-HYBRID, exhibited an intermediate response to fatigue loading. Figure 4.14: NCF-THICK specimen after fatigue loading Figure 4.15: NCF-HYBRID specimen after fatigue loading 4.1 Experimental results - NCF T700GC/M21 41 4.1.4 Double edge crack test results Double edge crack tests with widths of w= 5mm,w= 10mm,w= 15mm, w= 20mm and w= 25mm and notch length-to-width of a/w = 3/5 (see table 3.8) were performed to three lay-ups of NCF T700GC/M21 in order to characterize the size effect law required to obtain the crack resistance curve of the three lay-ups. Three specimens per geometry per laminate configuration were planned, however, some failed within the grips and, were therefore, considered invalid and were disregarded. The remote stress-displacement relations for double edge crack tests of laminates NCF-THIN, NCF-THICK and NCF-HYBRID are presented in fig. 4.16, 4.17, 4.18, 4.19 and 4.20. Specimens with width 2w= 10mm and 2w= 20mm exhibit linear behaviour up to failure. Specimens with 2w= 30mm, 2w= 40mm and 2w= 50mm exhibit linear behaviour with some load drops before final failure with negligible impact on the specimen’s stiffness. Representative double edge notch specimens are shown in figures 4.21a, 4.21b and 4.21c. 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 350 400 450 Displacement [mm] Remote Stress [MPa] QI-NCF-THIN QI-NCF-THICK QI-NCF-HYBRID Figure 4.16: Double edge crack remote stress-displacement relations for 2w= 10mm for NCFTHIN, NCF-THIN and NCF-HYBRID lay-ups. 42 Chapter 4. Experimental Results 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 350 Displacement [mm] Remote Stress [MPa] QI-NCF-THIN QI-NCF-THICK QI-NCF-HYBRID Figure 4.17: Double edge crack remote stress-displacement relations for 2w= 20mm for NCFTHIN, NCF-THIN and NCF-HYBRID lay-ups. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 50 100 150 200 250 300 Displacement [mm] Remote Stress [MPa] QI-NCF-THIN QI-NCF-THICK QI-NCF-HYBRID Figure 4.18: Double edge crack remote stress-displacement relations for 2w= 30mm for NCFTHIN, NCF-THIN and NCF-HYBRID lay-ups. 4.1 Experimental results - NCF T700GC/M21 43 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 Displacement [mm] Remote Stress [MPa] QI-NCF-THIN QI-NCF-THICK QI-NCF-HYBRID Figure 4.19: Double edge crack remote stress-displacement relations for 2w= 40mm for NCFTHIN, NCF-THIN and NCF-HYBRID lay-ups. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 50 100 150 200 250 Displacement [mm] Remote Stress [MPa] QI-NCF-THIN QI-NCF-THICK QI-NCF-HYBRID Figure 4.20: Double edge crack remote stress-displacement relations for 2w= 50mm for NCFTHIN, NCF-THIN and NCF-HYBRID lay-ups. 50 Chapter 4. Experimental Results 4.2 Experimental results - STF T700SC/M21 This section is dedicated to the experimental tests results of STF T700SC/M21 layups. To simplify the analysis, the lay-ups are, once again, presented below in table 4.9. Note that all plies are symmetric, quasi-isotropic and have the same in-plane properties. All plies of STF-THIN lay-up have nominal ply thickness of 0.08 mm (0.160 per bi-angle layer). All plies of NCF-THICK lay-up have nominal thickness of 0.120 mm (0.240 mm per bi-angle layer). NCF-HYBRID lay-up has thicker central layers than the outer layers: there are two (0o/90o) and two (45o/-45o) 0.240 mm thick layers and four (0o/90o) and four (45o/-45o) 0.160 mm thick layers. Table 4.9: STF T700SC/M21 lay-ups (160 g/m2STF;240 g/m2STF) Laminate ID Lay-up t (mm) STF-THIN [(0/90)/(+45/-45)]3s1.92 STF-THICK [(0/90)/(+45/-45)]2s1.92 STF-HYBRID [((0/90)/(+45/-45))2/(0/90)/(+45/-45)]s2.24 4.2.1 Unnotched tension test results The remote stress-displacement relations for plain strength tension of laminates STF-THIN, STF-THICK and STF-HYBRID tests are presented in fig. 4.26. All specimens exhibited linear response up to failure. This suggests that there is little severe transverse cracking before failure and that failure is fibre-dominated. 0 0.5 1 1.5 2 2.5 3 3.5 0 100 200 300 400 500 600 700 800 Displacement [mm] Remote Stress [MPa] QI-STF-THIN QI-STF-THICK QI-STF-HYBRID Figure 4.26: Unnotched tension remote stress-displacement relations for STF-THIN, STF-THIN and STF-HYBRID lay-ups. 4.2 Experimental results - STF T700SC/M21 51 Representative unnotched tension specimens after testing are shown in figs. 4.27 and 4.28. Some specimens failed in two places due to catastrophic failure characteristic of CFRP. STF-THIN specimens exhibit brittle net-section failure and the failure section is perpendicular to the loading direction. STF-THICK and STFHYBRID specimens exhibit a pull-out failure mode with some splitting and delamination. The different failure modes are related to the ply thickness of the fabric used each lay-up. While lay-up NCF-THIN is from 160 g/m2STF, NCF-THICK is made from 240 g/m2STF. The plies in-situ strengths are, therefore, lower in NCF-THICK lay-up which triggers delamination onset, splitting and pull-out. Figure 4.27: Representative STF-THIN (above), STF-THICK (middle) and STF-HYBRID (below) specimens after testing Figure 4.28: Close-up of the fracture plane of representative STF-THIN (left), STF-THICK (middle) and STF-HYBRID (right) specimens after testing The mean values and standard deviation of the unnotched tension tests for layups STF-THIN, STF-THICK and STF-HYBRID are presented in table 4.2. Even though five tests per laminate configuration were planned, some specimens tested 52 Chapter 4. Experimental Results failed within the grips, and were, therefore, not considered valid. STF-THIN specimens presented 1.57% higher unnotched strength than STF-THICK specimens. STF-HYBRID exhibit 1.70% and 0.14% lower unnotched strength than STF-THIN and STF-THICK specimens, respectively. Table 4.10: Unnotched tension results for lay-ups STF-THIN, STF-THICK and STF-HYBRID Property Type Nr valid tests Mean Value [MPa] STDV STF-THIN 2 887.36 10.79 XL TSTF-THICK 2 873.57 8.30 STF-HYBRID 2 872.31 20.18 Digital image correlation was during one test per laminate configuration to monitor the longitudinal strain field on the surface of the specimens. Figures 4.29a, 4.29b and 4.29c show the longitudinal strain just before failure on STF-THIN, STFTHICK and STF-HYBRID specimens, respectively. The specimens were loaded in the horizontal direction. Note that, even though the ultimate strength of the specimens presented in figures 4.29a, 4.29b and 4.29c was not considered valid because they failed within the grips (despite being in good agreement with the unnotched strength of the respective laminate), this does not invalidate the comparison between the three laminates. As explained before, the longitudinal strain along two lines near the specimen’s borders are shown in the right bottom images of each figure. Although no transverse cracks appeared in the outer ply of the specimens, the strain field near the free edges is less homogeneous and exhibits more strain concentrations in STFTHICK laminate than in STF-THIN and STF-HYBRID laminates. This suggests that STF-THICK should exhibit a lower unnotched strength than STF-THIN and STF-HYBRID lay-ups since the transverse cracks should be more likely to appear, eventually leading to premature failure of the specimens. However, the experimental results do not corroborate this tendency clearly since, STF-THIN specimens revealed an only slightly higher unnotched tensile strength that STF-THICK specimens. More experimental tests should, therefore, be performed to confirm the unnotched tensile strength of the three laminates. The elastic properties of each laminate were calculated using the Classical Lamination Theory and the results obtained are presented in table 4.3. Table 4.11: Elastic properties of STF-THIN, STF-THICK and STF-HYBRID calculated using the Classical Lamination Theory Laminate Ey[GPa] Ex[GPa] νxy Gxy [GPa] STF-THIN 49.78 49.78 0.311 18.98 STF-THICK 49.78 49.78 0.311 18.98 STF-HYBRID 49.78 49.78 0.311 18.98 4.2 Experimental results - STF T700SC/M21 53 Stage: 278 0 100 200 300 −500 0 500 1000 time (s) stress (MPa) εx (−) stress = 881.3 (MPa) 0 0.01 0.02 0.03 0 50 100 150 0 0.01 0.02 0.03 distance (subset) εx (−) (a) STF-THIN Stage: 263 0 100 200 300 0 500 1000 time (s) stress (MPa) εx (−) stress = 798.3 (MPa) 0 0.01 0.02 0.03 0 50 100 150 0 0.01 0.02 0.03 distance (subset) εx (−) (b) STF-THICK Stage: 295 0 100 200 300 0 500 1000 time (s) stress (MPa) εx (−) stress = 899.5 (MPa) 0 0.01 0.02 0.03 0 50 100 150 0 0.01 0.02 0.03 distance (subset) εx (−) (c) STF-HYBRID Figure 4.29: Longitudinal strain field for STF T700SC/M21 lay-ups 54 Chapter 4. Experimental Results 4.2.2 Open-hole tension test results In this study, and as mentioned in chapter 3, the notched strength of three layups of STF T700SC/M21 was accessed by testing specimens with hole diameters of d= 2mm,d= 5mm and d= 8mm and with hole diameter-to-width ratio of d/W = 1/6. The experimental results of the open-hole tension tests performed will be presented hereafter. Although three tests per laminate configuration and per geometry were planned, one STF-THICK specimen failed within the grips and were, for this reason, not considered valid. The results obtained for this specimen will not be addressed. The remote stress-displacement relations for open-hole tension tests of laminates STF-THIN, STF-THICK and STF-HYBRID are presented in fig. 4.30, 4.31 and 4.32. For open-hole tension tests, all the laminates exhibit almost linear behaviour up to failure. Representative open-hole tension specimens after testing are shown in figs. 4.33a, 4.33b and 4.33c. The failure surface of all specimens is perpendicular to the applied load. STF-THICK and STF-HYBRID specimens exhibit a more irregular fracture surface with some pull-out. No extensive delamination is observed. 0 0.5 1 1.5 2 2.5 3 3.5 4 0 100 200 300 400 500 600 Displacement [mm] Remote Stress [MPa] QI-STF-THIN QI-STF-THICK QI-STF-HYBRID Figure 4.30: Open-hole tension remote stress-displacement relations for d= 2mm for STF-THIN, STF-THIN and STF-HYBRID lay-ups. 4.2 Experimental results - STF T700SC/M21 55 0 0.5 1 1.5 2 2.5 3 3.5 4 0 100 200 300 400 500 Displacement [mm] Remote Stress [MPa] QI-STF-THIN QI-STF-THICK QI-STF-HYBRID Figure 4.31: Open-hole tension remote stress-displacement relations for d= 5mm for STF-THIN, STF-THIN and STF-HYBRID lay-ups. 0 0.5 1 1.5 2 2.5 3 3.5 4 0 50 100 150 200 250 300 350 400 450 500 Displacement [mm] Remote Stress [MPa] QI-STF-THIN QI-STF-THICK QI-STF-HYBRID Figure 4.32: Open-hole tension remote stress-displacement relations for d= 8mm for STF-THIN, STF-THIN and STF-HYBRID lay-ups. 56 Chapter 4. Experimental Results (a) STF-THIN (b) STF-THICK (c) STF-HYBRID Figure 4.33: Representative STF T700SC/M21 open-hole specimens after testing 4.2 Experimental results - STF T700SC/M21 57 The mean values and standard deviation of the open-hole tests are presented in table 4.12 and fig. 4.34. As expected[35] [4], thin-ply structures exhibit lower notched strength than thick-ply structures. In fact, STF-THICK lay-up exhibits 9.3 %, 14.04% and 7.62 % higher notched strength than STF-THIN lay-up for d=2mm, d=5mm and d=8 mm, respectively. In general, the selected hybrid lay-up revealed to have higher notched strength that STF-THIN lay-up and lower notched strength than STF-THICK lay-up: •For d=2mm, STF-HYBRID specimens exhibited 2.92% higher notched strength that STF-THIN and 5.84% lower that STF-THICK specimens. •For d=5mm, STF-HYBRID specimens exhibited 5.35% higher notched strength that STF-THIN and 7.62% lower that STF-THICK specimens. •For d=8mm, STF-HYBRID specimens exhibited 6.22% higher notched strength that STF-THIN and 1.30% lower that STF-THICK specimens. This intermediate behaviour can be explained by the type of ply hybridization of STF-HYBRID lay-up. In this lay-up, unlike NCF-HYBRID lay-up where only the 0oplies had double the thickness of the rest of the laminate, two (0o/90o) and (45o/-45o) plies are made from 240 g/m2STF while the rest of the laminate is made from 160 g/m2STF. While the ”thin” part of the laminate should be able to delay subcritical damage before failure, the ”thick” part of the laminate is responsible for redistributing the stresses at the vicinity of the notch, reducing the stress concentration. Its behaviour in the presence of stress concentrations is, therefore, better when compared to a STF-THIN specimens and, as stress redistribution is not as effective, worse than for STF-THICK specimens. Table 4.12: Open-hole test results for lay-ups STF-THIN, STF-THICK and STF-HYBRID Property Type d [mm] Nr valid tests Mean Value [MPa] STDV STF-THIN 2 3 557.73 4.36 σ∞ TSTF-THICK 2 2 609.6 30.23 STF-HYBRID 2 3 574.01 21.47 STF-THIN 5 3 497.68 12.77 σ∞ TSTF-THICK 5 3 567.92 15.5 STF-HYBRID 5 3 524.15 14.62 STF-THIN 8 3 462.68 7.47 σ∞ TSTF-THICK 8 3 497.92 21.39 STF-HYBRID 8 3 491.47 13.29 In table 4.12 and fig. 4.34 the same tendency reported in section 4.1.2 can be noted: the notched strength of the specimens increases as the hole diameter decreases. A reduction in hole diameter from 8 mm to 2 mm results in an increase of 20.54%, 22.43 % and 16.79% of the notched strength for STF-THIN, STF-THICK and STF-HYBRID lay-ups, respectively. As explained in section 4.1.2, in smaller specimens the length of the fracture process zone is not negligible when compared 58 Chapter 4. Experimental Results 2345678 450 500 550 600 d [mm] Notched Strength [MPa] STF-THIN STF-THICK STF-HYBRID Figure 4.34: Notched strength vs hole diameter for lay-ups STF-THIN, STF-THICK and STFHYBRID to the in-plane dimensions of the specimen and therefore, stresses near the hole are redistributed more effectively than in larger specimens. As a consequence, smaller specimens tend to be more notch insensitive than larger specimens. Digital image correlation was used during one test per geometry and per laminate configuration to monitor the evolution of the strain field and to access the formation of cracks at the vicinity of the holes. The specimens were loaded up to 90% of their notched strength will be inspected using X-ray. Figures 4.35, 4.36 and 4.37 show the strain field on the surface of the specimens when they are loaded at 90% of their notched strength. The bottom right images show the longitudinal strain along two lines positioned near the hole. It was not possible to obtain the strain field of STF-THICK specimens with d=2mm, but the a picture of the vicinity of the hole is shown in figures 4.36a and 4.36b. In STF-THIN specimens no discontinuity of the longitudinal strain along those lines can be identified and therefore, it can be concluded that no cracks appeared at the vicinity of the holes (fig.4.35a, 4.35b and 4.35c). Unlike in STF-THIN specimens, in STF-THICK and STF-HYBRID specimens with d=5mm (fig. 4.36d and 4.37b, respectively), a crack appeared in the vicinity of the hole. As shown in figure in figures 4.36a and 4.36b, a crack also appeared at the vicinity of the hole in STF-THICK specimen with d=2mm. Even though this is only reported for specimens with d=2mm and d=5mm, it suggests that cracks are more likely to appear in STF-THICK and STF-HYBRID specimens which justifies the enhanced notched strengths reported when compared to STFTHIN specimens. 4.2 Experimental results - STF T700SC/M21 59 Stage: 180 0 50 100 150 200 0 200 400 600 time (s) stress (MPa) εx (−) stress = 523.5 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (a) STF-THIN d=2mm Stage: 172 0 50 100 150 200 0 200 400 600 time (s) stress (MPa) εx (−) stress = 455.0 (MPa) 0 0.02 0.04 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (b) STF-THIN d=5mm Stage: 181 0 50 100 150 200 0 200 400 600 time (s) stress (MPa) εx (−) stress = 418.0 (MPa) 0 0.01 0.02 0.03 0.04 0.05 0 50 100 150 0 0.02 0.04 distance (subset) εx (−) (c) STF-THIN d=8mm Figure 4.35: Longitudinal strain field of STF-THIN specimens at 90% of their failure stress 66 Chapter 4. Experimental Results 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 350 Displacement [mm] Remote Stress [MPa] QI-STF-THIN QI-STF-THICK QI-STF-HYBRID Figure 4.44: Double edge crack remote stress-displacement relations for 2w= 30mm for STF-THIN, STF-THIN and STF-HYBRID lay-ups. 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 Displacement [mm] Remote Stress [MPa] QI-STF-THIN QI-STF-THICK QI-STF-HYBRID Figure 4.45: Double edge crack remote stress-displacement relations for 2w= 40mm for STF-THIN, STF-THIN and STF-HYBRID lay-ups. 4.2 Experimental results - STF T700SC/M21 67 0 0.5 1 1.5 2 2.5 3 0 50 100 150 200 250 300 Displacement [mm] Remote Stress [MPa] QI-STF-THIN QI-STF-THICK QI-STF-HYBRID Figure 4.46: Double edge crack remote stress-displacement relations for 2w= 50mm for STF-THIN, STF-THIN and STF-HYBRID lay-ups. The mean values and standard deviation of the double edge crack tests are presented in table 4.14 and fig. 4.48. Between the linear regression I and linear regression II [12] (see section 3.4.4), the regression which best fits the experimental data was determined for each laminate configuration. The three regressions are presented in figures 4.23 and 4.24. The size effect that best fits the experimental data is the linear regression I for STF-THIN and STF-HYBRID lay-ups and linear regression II for STF-THICK lay-up. The fitting parameters are shown in table 4.7. As explained in section 3.4.4, knowing the size effect law and the elastic properties of the laminate, the steady-state value of the R-curve (Rss) and the length of the fracture process zone (lfpz) can be calculated as shown in table 3.7. The elastic properties of the laminate were calculated using the Classical Lamination Theory and are presented in table 4.11. The R-curve parameters Rss,lfpz,γand βfor lay-ups STF-THIN, STF-THICK and STF-HYBRID are shown in table 4.8 and the R-curves are presented in 4.25. Note that the R-curve the analytical expression for the R-curve is: R(∆a) = Rss h1−(1 −γ∆a)βi(4.2) 68 Chapter 4. Experimental Results (a) STF-THIN (b) STF-THICK (c) STF-HYBRID Figure 4.47: Representative STF T700SC/M21 double edge crack specimens after testing 4.2 Experimental results - STF T700SC/M21 69 Table 4.14: Double edge crack test results for lay-ups STF-THIN, STF-THICK and STF-HYBRID Property Type 2w [mm] Nr valid tests Mean Value [MPa] STDV STF-THIN 10 3 361.72 24.99 σ∞ TSTF-THICK 10 3 429.22 29.88 STF-HYBRID 10 3 369.28 37.81 STF-THIN 20 3 317.05 19.99 σ∞ TSTF-THICK 20 3 382.53 17.88 STF-HYBRID 20 3 377.27 26.42 STF-THIN 30 3 281.66 11.96 σ∞ TSTF-THICK 30 3 354.72 7.44 STF-HYBRID 30 3 310.28 6.71 STF-THIN 40 3 270.69 4.89 σ∞ TSTF-THICK 40 3 332.98 3.93 STF-HYBRID 40 3 263.08 16.81 STF-THIN 50 3 250.70 4.47 σ∞ TSTF-THICK 50 3 335.21 1.933 STF-HYBRID 50 3 265.15 11.16 10 15 20 25 30 35 40 45 50 250 300 350 400 Width [mm] Notched Strength [MPa] STF-THIN STF-THICK STF-HYBRID Figure 4.48: Notched strength vs width for for lay-ups STF-THIN, STF-THICK and STF-HYBRID 70 Chapter 4. Experimental Results 4 6 8 10 12 14 16 18 20 22 24 26 60 80 100 120 140 160 w[mm] 1/σ2 T×107[MPa−2] STF-THIN STF-THICK STF-HYBRID Figure 4.49: Size effect law: Experimental results and linear regression I fitting for STF-THIN, STF-THICK and STF-HYBRID laminates 5·10−20.1 0.15 0.2 4 6 8 10 12 14 16 1/w [mm−1] 1/wσ2 T×107[mm−1MPa−2] STF-THIN STF-THICK STF-HYBRID Figure 4.50: Size effect law: Experimental results and linear regression II fitting for STF-THIN, STF-THICK and STF-HYBRID laminates 4.2 Experimental results - STF T700SC/M21 71 Table 4.15: Best fitting parameters of the size effect law for STF-THIN, STF-THICK and STFHYBRID lay-ups Laminate Best fitting A [MPa−2 mm−1]C [MPa−2]R2 STF-THIN LR I 4.0471 ×10−75.8803 ×10−60.9853 STF-HYBRID LR I 4.2406 ×10−74.3227 ×10−60.8747 Laminate Best fitting A [MPa−2]C [MPa−2 mm−1]R2 STF-THICK LR II 4.322 ×10−72.202 ×10−60.9916 Table 4.16: Parameters of the R-curves of STF-THIN, STF-THICK and STF-HYBRID lay-ups Laminate Rss [kJ/m2]lfpz γ[mm−1]β STF-THIN 140.64 4.756 0.1655 4.156 STF-THICK 258.48 6.425 0.1199 4.268 STF-HYBRID 134.222 3.3367 0.239 4.05 012345678 0 50 100 150 200 250 ∆a[mm] R[kJ /m2] STF-THIN STF-THICK STF-HYBRID Figure 4.51: R-curves of STF-THIN, STF-THICK and STF-HYBRID lay-ups 72 Chapter 4. Experimental Results 4.2.5 Concluding remarks Analysing the experimental data, it can be concluded that there are no relevant differences between the unnotched tensile strength of the three STF laminates. STFTHICK specimens exhibit a less homogeneous strain field and more strain concentrations near the specimen’s free edges which suggests that transverse cracks are more likely to appear in this laminate and, therefore, its unntoched tensile strength should be lower than those of STF-THIN and STF-HYBRID lay-ups. Since only 2 specimens per laminate configuration were considered valid, more unnotched tensile tests should be performed to confirm the values obtained. When loaded in tension, STF-THICK notched specimens show enhanced resistance when compared to STF-THIN and STF-HYBRID specimens since they are more likely to develop subcritical damage near the notches. While the appearance of damage near the hole will allow the redistribution of stresses and the reduction of stress concentrations in static loadings, it will hasten damage propagation in fatigue loadings. STF-HYBRID structure is more notch tolerant than STF-THIN but less than STF-THICK structures. This intermediate behaviour can be explained by the type of ply hybridization of STF-HYBRID lay-up: it has 66.6% of 0.160 mm thick plies and 33.3% of 0.240 mm plies. While the ”thin” part of the laminate should be able to delay subcritical damage before failure, the ”thick” part of the laminate is responsible for redistributing the stresses at the vicinity of the notch, reducing the stress concentrations. This is valid for both static and fatigue loadings. In fact, STFHYBRID showed 48.69% higher and 172.56% lower resistance to stiffness reduction than STF-THICK and STF-THIN specimens, respectively. Open-hole fatigue tests results serve as preliminary results for the same reasons presented in section 4.1.5. Chapter 5 Analysis Methods The process of selecting the material, geometry and lay-up of composite structures with stress concentrations requires the prediction of their notched strength. This prediction needs to be physically-based, accurate and, so that the process is effective, fast. Especially during preliminary design and optimization, the predictions should be obtained fast and rely as little as possible on experimental tests, since they are costly and time-consuming. Non-linear finite elements method can be used to predict notched strength of composite laminates, however, the process is time consuming and, therefore, avoided as a preliminary design and sizing tool. The Point Stress model and the Average Stress model [27] and the Inherent Flaw model [40] are predictions methods used to calculate notched strength of laminates composites and come as an alternative to FE models. The Point Stress model, the Average Stress model are stress-based criteria: the first one predicts failure when the stress in a point at a given distance from the notch reaches the material’s unnotched strength, and the second predicts failure when the average stress from the notch tip up to a characteristic distance reaches the material’s unnotched strength. These models flaw because they all rely on calibration from a baseline specimen to calculate the ”characteristic distance”, thus adding unnecessary costs to the predictions. Moreover, since this calibration is not physically based, the predictions tend to be inaccurate for geometries different from the one used for calibration. The Finite Fracture Mechanics model [17] enriches the Average Stress model, including a energy-based criteria to the stress criteria already defined, thus, not requiring model calibration. In this chapter, the Finite Fracture Mechanics Model is explained with more detail. Predictions using the IFM, PS, AS and FFM models are made and the values obtained are compared with the available experimental results of open-hole strength for NCF T700GC/M21 lay-ups (NCF-THIN, NCF-THICK and NCF-HYBRID) and STF T700SC/M21 lay-ups ( STF-THIN, STF-THICK and STF-HYBRID). 5.1 Finite Fracture Mechanics Model Using the finite fracture mechanics model proposed by Camanho et al. [17] the fracture strength of notched composites that exhibits brittle or pull-out failure can be predicted fast and accurately. If the main failure mechanism is delamination, the model cannot be applied. Fracture mechanics models assume that crack propagation is predicted when 74 Chapter 5. Analysis Methods both stress-based and energy-based criteria are satisfied and that failure occurs by the propagation of kinematically admissible cracks with finite length, i.e. failure is predicted if when two conditions are simultaneous met: 1. The average stress ahead of the crack tip until the crack length lreaches the material unnotched strength 2. The energy needed to propagate the crack the distance lis equal to the fracture toughness of the material. Other analytical models able to predict the notched strength of composite structures can be used, such as the Point Stress model [27], the Average Stress model [27] and the Inherent Flaw model [40]. Even tough these models appear to give good predictions of the remote failure stress of the laminate, they require calibration from a baseline specimen. In fact, a ”characteristic distance” l∗, incorrectly identified exclusively as a material property, has to be determined experimentally which adds unnecessary costs to the predictions and will lead to inaccurate predictions since it is ill-defined as a geometry independent property. The Finite Fracture Mechanics model has been used to predict the failure stress of composite structures with open-holes or cracks loaded in tension [17] and compression and to predict the large damage capability of notched composites [8]. The extensions of the Finite Fracture Mechanics Model to predict open-hole strength with ant without taking the R-curve into account will be presented hereafter. 5.1.1 Finite Fracture Mechanics for the prediction of open-hole strength The failure criterion for composite structures with open holes loaded in tension as shown in fig.5.1 reads          1 l R+l R R σyy(x, 0) dx =XL T 1 l R+l R R K2 I(a)da =K2 Ic (5.1) The first and second equations are the stress-based and energy-based criteria respectively. lis the crack length at failure, XL Tis the unnotched strength of the laminate and KIc is the mode I fracture toughness of the laminate. The system of equations 5.1 has two equations and two unknowns ( the crack length at failure land the remote stress at failure σ∞) and, therefore, unlike other models used to predict laminate failure ( [27] and [40] ), the model presented does not require the determination of a ”characteristic distance” l∗. Figure 5.1: Notched laminate under tensile loading [17] 1. Stress-based criterion 5.1 Finite Fracture Mechanics Model 75 The stress distribution in the center of the laminate along the x direction reads: σyy(x, 0) = Rk σ∞ 22 + ξ2+ 3ξ4−(K∞ T−3)(5ξ6−7ξ8)(5.2) where ξ=R x,σ∞is the remote stress applied, K∞ Tis the stress concentration factor of an infinity plane with hole in the center and RKis a finite width correlation factor. They read: K∞ T= 1 + s2 A22 pA11A22 −A12 +A11A22 −A2 12 2A66 (5.3) RK=KT K∞ T =(3(1 −2R/W) 2 + (1 −2R/W)3+1 22R WM6 (K∞ T−3) "1−2R WM2#)−1 (5.4) where Aij are the elements of the in-plane stiffness matrix that can be calculated using the Classical Lamination Theory (section 6.1) and Mis a parameter defined as: M2=r1−8h3(1−2R/W ) 2+(1−2R/W )3−1i−1 2(2R/W)2(5.5) 2. Energy-based criterion The stress intensity factor for two symmetrical cracks that appear in the edges of the hole in a rectangular isotropic plate loaded in tension (figure 5.1) is given by KI=σ∞FhFw√πa (5.6) where, Fw=ssec πR Wsec πa W(5.7) Fh=r1−R afn(5.8) fn= 1 + 0.358λ+ 1.425λ2−1.579λ3+ 2.156λ4(5.9) with λ=R/a In fact, laminates are not isotropic, but if the stacking sequence is such that the laminate exhibits a quasi-isotropic behaviour, equation 5.6 can be used. 82 Chapter 5. Analysis Methods (a) NCF-THIN (b) NCF-THICK (c) NCF-HYBRID Figure 5.2: Predictions for NCF T700GC/M21 lay-ups with d/W=1/6, obtained using IFM, PS, AS and FFM model with and without taking the material’s R-curve into account. 5.2 Open-hole tensile strength predictions 83 Table 5.4: Predictions for STF-THIN lay-up with d/W=1/6, obtained using IFM, PS, AS and FFM model with and without taking the material’s R-curve into account. IFM, PS and AS models were calibrated using the experimental result for d=5mm. d Exp. IFM PS AS FFM FFM (R-curve) 2 mm σ∞[MPa] 557.73 665.58 651.46 - 618.71 635.45 Error - 19.34% 16.81% - 10.93% 13.97% 5 mm σ∞[MPa] 497.53 497.53 476.77 - 497.53 536.80 Error - 0.00% -4.17% - 0.00% 7.89% 8 mm σ∞[MPa] 462.68 423.31 408.19 - 437.58 474.87 Error - -8.51% -11.78% - -5.42% 2.64% Table 5.5: Predictions for STF-THICK lay-up with d/W=1/6, obtained using IFM, PS, AS and FFM model with and without taking the material’s R-curve into account. IFM, PS and AS models were calibrated using the experimental result for d=5mm. d Exp. IFM PS AS FFM FFM (R-curve) 2 mm σ∞[MPa] 609.60 718.51 708.14 679.42 663.86 683.01 Error - 17.87% 16.16% 11.45% 8.90% 12.04% 5 mm σ∞[MPa] 567.40 567.40 543.73 567.40 567.41 628.82 Error - 0.00% -4.17% 0.00% 0.00% 10.83% 8 mm σ∞[MPa] 497.92 482.32 459.59 502.06 504.21 578.85 Error - -3.13% 8.34% 0.83% 1.26% 16.25% Table 5.6: Predictions for STF-HYBRID lay-up with d/W=1/6, obtained using IFM, PS, AS and FFM model with and without taking the material’s R-curve into account. IFM, PS and AS models were calibrated using the experimental result for d=5mm. d Exp. IFM PS AS FFM FFM (R-curve) 2 mm σ∞[MPa] 574.01 685.45 674.12 - 635.70 648.95 Error - 19.41% 17.44% - 10.75% 13.06% 5 mm σ∞[MPa] 524.15 524.15 502.28 - 524.15 555.09 Error - 0.00% -4.17% - 0.00% 5.90% 8 mm σ∞[MPa] 491.47 444.55 426.43 - 461.69 493.07 Error - -9.55% -13.23% - -6.06% 0.33% 84 Chapter 5. Analysis Methods (a) STF-THIN (b) STF-THICK (c) STF-HYBRID Figure 5.3: Predictions for STF T700SC/M21 lay-ups with d/W=1/6, obtained using IFM, PS, AS and FFM model with and without taking the material’s R-curve into account. 5.3 Design Charts 85 (a) (b) Figure 5.4: Normalized notched strength vs hole diameter for NCF T700GC/M21 (reffig:NCF-withRcurve) STF T700SC/M21 (5.4b) lay-ups and d/w=1/6: Experimental data and predictions using the FFM model taking the R-curve into account 5.3 Design Charts As the finite fracture mechanics model is able to predict the remote stress fast and accurately, it can be used to produce design charts for a certain material and layup relying only on information about the material’s elastic properties, unnotched strength and fracture toughness (or R-curve). In such design charts the normalized notch strength σNis given as a function of the hole diameter-to-width ratio d/W. Two limits are pointed out: notch sensitivity given by σN=1 KTand notch insensitivity σN= 1−2R W. The laminate behaviour and, therefore, the predictions obtained with the finite fracture mechanics model will be between the two limits. The design charts for NCF-THIN, NCF-THICK, NCF-HYBRID, STF-THIN, STF-THICK and STF-HYBRID lay-ups together with the available experimental data (see chapter 4) are presented in figure 5.5. The predictions were obtained using the finite fracture mechanics model accounting for the R-curve of each laminate since 86 Chapter 5. Analysis Methods it is the more physically accurate as it accounts for the increase of fracture toughness during the fracture process and, except for STF-THICK laminate, provided the more accurate predictions when compared to the available experimental data. It is not possible to make design charts made using IFM, PS and AS models because they require calibration from a baseline specimen for each diameter-to-width ratio, thus invalidating the purpose of the design tool. (a) NCF-THIN (b) STF-THIN (c) NCF-THICK (d) STF-THICK (e) NCF-HYBRID (f) STF-HYBRID Figure 5.5: Design Charts for open-hole tensile strength for NCF T700GC/M21 and STF T700SC/M21 lay-ups Chapter 6 Mechanical behaviour of composite laminates - Literature review In this chapter, some relevant aspects and some analytical models used to predict the mechanical properties of laminates composites will be explained in detail, since they were used and/or implemented in this thesis. This includes, the Classical Lamination Theory, failure criteria commonly used and analytical models able to predict the in-situ properties of composite laminae and the fracture toughness of laminated composites. 6.1 Classical Lamination Theory A laminated plate is composed by a N stacked orthotropic layers with the thickness given by h. There are two coordinate systems: the material and the problem coordinates systems. The coordinate system used in the problem formulation, in general, does not coincide with the principal material coordinate system, unless there is only 1 ply and the its angle is zero. Usually, the composite has several layers with different orientations of their material coordinates with respect to the laminate coordinates. (figure 6.1) Figure 6.1: Material and problem coordinates systems [34] The Classical Lamination theory follows the following assumptions [26]: •The layers of the laminate are perfectly bonded. 88 Chapter 6. Mechanical behaviour of composite laminates - Literature review •Each layer is a homogeneous material with known properties. •The plies can be isotropic, transversely isotropic or orthotropic. •Each layer is in a state of plane stress •It follows the Kirchoff assumptions for thin plates: –Normals to the midplane remain straight normal to the deformed midplane, which means that γzx =γzy = 0 –The length of the normals to the midplane do not change length, which means that zz = 0 Displacement field The displacement field in any point of the laminate u(x, y), v(x, y), w(x, y) reads u(x, y) = u0−z∂w ∂x v(x, y) = v0−z∂w ∂y w(x, y) = w0 (6.1) where u0,v0and w0are the displacements along the coordinate lines of a material point on the xy-plane. Figure 6.2: Coordinate syst.em and layer numbering used for a laminated plate [34] Strain Field The strain field reads {}x=   x y γxy   =   ∂u ∂x ∂y ∂v ∂u ∂y +∂v ∂x    =     ∂u0 ∂x ∂y0 ∂v ∂u0 ∂y +∂v0 ∂x      +z     −∂2w ∂x2 −∂2w ∂y2 −2∂2w ∂x∂y      ={0}+z{κ}(6.2) 6.1 Classical Lamination Theory 89 Stress Field The stiffness of each layer Qkis calculated as: [Q]k= [T]T[Q][T] (6.3) where [Q] is the stiffness matrix of a layer in the material coordinate system, [Q]k is the stiffness matrix of a layer in the global coordinate system and [T] is the transformation matrix. For a transversely isotropic material, [Q] reads [T] =   1 E1−ν12 E10 −ν12 E1 1 E20 0 0 1 G12   −1 (6.4) where E1,E2are the axial Young’s modulus respectively, ν12 is the axial Poisson coefficient and G12 is the axial shear modulus in the material coordinate system. The transformation matrix [T] reads [T] =   m2n2−2mn n2m22mn 2mn −2mn m2−n2 (6.5) where m= cos(θ) and n= sin(θ). Each layer khas the following stress-strain relation: {σ}k x= [Q]k{}x= [Q]k{0}+z[Q]k{κ}(6.6) In-plane forces per unit length The in-plane forces per unit length read {N}= h/2 Z −h/2 {σ}xdz = h/2 Z −h/2 [Q](k){}xdz = [A]{0}+ [B]{κ}(6.7) where [A] is the in-plane stiffness of the laminate and is defined as [A] = h/2 Z −h/2 [Q](k)dz = N X k=1 zk+1 Z zk [Q](k)dz = N X k=1 [Q](k)(zk+1 −zk) (6.8) and [B] is the in-plane/bending coupling stiffness of the laminate and is defined as [B] = h/2 Z −h/2 [Q](k)z dz = N X k=1 zk+1 Z zk [Q](k)z dz =1 2 N X k=1 [Q](k)(z2 k+1 −z2 k) (6.9) 90 Chapter 6. Mechanical behaviour of composite laminates - Literature review Figure 6.3: In-plane forces per unit length [26] Moments per unit length The moments per unit length read {M}= h/2 Z −h/2 {σ}xz, dz = h/2 Z −h/2 [Q](k){}xz dz = [B]{0}+ [D]{κ}(6.10) where [B] is the in-plane/bending coupling stiffness defined in 6.9 and [D] is the bending stiffness of the laminate and is defined as [D] = h/2 Z −h/2 [Q](k)z2dz = N X k=1 zk+1 Z zk [Q](k)z2dz =1 3 N X k=1 [Q](k)(z3 k+1 −z3 k) (6.11) Figure 6.4: Moments per unit length [26] 6.2 Failure criteria for laminated composites The effective use of laminated composites in structural applications relies on the ability to predict its strength. Stress- [20] [29] [25] [36] [28] and strain-based [25] failure criteria are simple and easy to implement, however, lack accuracy as they are purely empirical. For this reason, the definition of more physically-based and 6.2 Failure criteria for laminated composites 91 accurate failure criteria have been an important investigation subject over the last few years [33] [22] [21] [31] [19] [15]. An appropriate failure criteria should be applicable at the ply, laminate and structural level, yet simple enough so that it can be used in engineering applications. [15]. In this section, the stress-based Tsai-Hill and a three-dimensional invariant-based failure criteria for fibre-reinforced composites proposed by Camanho et al. [15] will be explained with detail. 6.2.1 Tsai-Hill criterion The Tsai-Hill failure criterion is a interactive stress-based criterion, but it does not distinguish different failure modes, i.e. does not identify if the composite is failing due to matrix cracking or fibre failure. It reads σ2 11 S2 11 −σ11σ22 S2 11 +σ2 22 S2 22 +σ2 12 S2 12 >0 (6.12) where S11 is the ultimate longitudinal tensile strength (XT) if σ11 >0 and the ultimate longitudinal compressive strength (XC) if σ11 <0, S22 is the ultimate transverse tensile strength (YT) if σ22 >0 and the ultimate transverse compressive strength (YC) if σ22 <0 and S12 is the in-plane shear stress S. 6.2.2 Three-dimensional invariant-based failure criteria for fibrereinforced composites This failure criteria is a combination of an invariant-based failure criterion for transverse failure and a failure criterion for longitudinal failure of unidirectional composites, i.e. a combination of criteria that predict matrix dominated failure and criteria that can predict fibre dominated failure. This results in failure criteria that are able to distinguish matrix and fibre failure, which is quite relevant for, e.g. damage models. The schematic representation of the failure criteria is presented in figure 6.5 and it will be explained hereafter. Stress state σ1>0? Longitudinal fibre failure Kinking failure Transverse failure Select minimum no yes Figure 6.5: Schematic representation of the three-dimensional invariant-based failure criteria for fiber-reinforced composites 98 Chapter 6. Mechanical behaviour of composite laminates - Literature review Combining equations 6.38 and 6.41, the transverse tensile in-situ strength for a thick ply yields: YT is = 1.12√2YT(6.43) Combining equations 6.40 and 6.42, the in-plane shear strength can be obtained solving the following equation for Sis L (SL)2 G12 +6 4β(SL)4=(Sis L)2 2G12 +3 4β(Sis L)4(6.44) 6.3.1.2 Thin inner plies In a thin plies embedded in a multidirectional laminate, a slit crack such as the one shown in figure 6.8 will propagate in the longitudinal direction since it is already extends through the ply thickness and, therefore the mode I and mode II energy release rate read [23]: GI(L) = πt 8Λo 22σ2 22 (6.45) GII (T) = πt 8χ(γ12) (6.46) Figure 6.8: Thin embedded ply [13] The transverse tensile in-situ strength can be obtained by solving equation 6.45 for YT is yielding YT is =s8GIc(L) πtΛ0 22 (6.47) Replacing equation 6.39 in equation 6.46 yields (SL is)2 8G12 +3 16β(SL is)4=GIIc(L) πt (6.48) which can be solved for the in-situ in-plane shear strength SL is. 6.3.1.3 Thin outer plies A thin outer ply is a special case of the thin ply for which the energy release rate is larger because the slit crack is closer to the laminate’s surface. The mode I fracture toughness reads 6.3 In-situ properties 99 GIIc =πt 2Zγ12 0 σ12dγ12 (6.49) Replacing equation 6.39 in 6.49, it yields: (SL o)2 4G12 +3 8β(SL o)4=GIIc πt (6.50) The in-situ in-plane shear strength is obtained solving equation 6.50 for SL o. Figure 6.9: Thin outer ply [13] 6.3.1.4 General expression for the transverse tensile and in-plane shear strengths For an inner ply: •the transverse tensile strength is the maximum between the transverse tensile strength of a thin embedded ply and a thick embedded ply, i.e., YT is =q8GIc πtΛo 22 and YT is = 1.12√2YT •the in-plane shear strength is the maximum between the in-plane shear strength of a thin embedded ply and a thick embedded ply, i.e., the maximum of SL is =s(1 + βφG2 12)1/2−1 3βG12 (6.51) obtained with φ=48GIIc πt and φ=12(SL)2 G12 +72 4β(SL)4 For an outer ply: •the transverse tensile strength is the maximum between YT is = 1.78qGIc πtΛo 22 and YT is =YT 100 Chapter 6. Mechanical behaviour of composite laminates - Literature review •The in-plane shear strength is the maximum between the in-plane shear strength of a UD ply and a thin outer ply, i.e., SL is =SLand SL is =r(1+βφG2 12)1/2−1 3βG12 with φ=24GIIc πt (6.52) 6.3.2 Compressive transverse, biaxial transverse tensile and transverse shear strengths The in situ transverse shear strength, Sis T, and the in-situ biaxial transverse tensile strength, Yis BT , are calculated imposing that the slope in the σ22-σ12 failure envelope when σ22 = 0, ηL, and that the slope in the σ22-σ23 failure envelope when σ22 = 0, ηT, are equal to the slope of the envelopes obtained with the in-situ properties (see figure 6.10): (η(+) L=η(+) L,is η(+) T=η(+) T,is (6.53) The slopes depend on the sign of σ22. In the tensile range, they read: η(+) L=∂σ12 ∂σ(+) 22 σ22=0+ =−1 2 αt 3 √α2 (6.54) η(+) L=∂σ23 ∂σ(+) 22 σ22=0+ =−1 2 αt 3 √α1 (6.55) where α1,α2and αt 3are defined in equations 6.18, 6.19 and 6.21, respectively. The in-situ transverse shear strength, Sis T, and the in-situ biaxial transverse tensile strength, Yis BT , can now be calculated solving the system of equations 6.53. Figure 6.10: Definition of ηLand ηT[32] It is assumed that the biaxial transverse compressive strength is constant which means that Yis BC =Yud BC. The transverse compressive stress Yis Ccan therefore, be calculated imposing that 6.4 Fracture Toughness 101 η(−) L=η(−) L,is (6.56) or η(−) T=η(−) T,is (6.57) with η(−) L=∂σ12 ∂σ(−) 22 σ22=0− =−1 2 αc 3 √α2 (6.58) η(−) L=∂σ23 ∂σ(−) 22 σ22=0− =−1 2 αc 3 √α1 (6.59) where αc 3are defined in equation 6.23. The in-situ transverse compressive strength, Yis BT , can now be calculated solving equations 6.56 or 6.57. 6.4 Fracture Toughness Camanho et al. [16] proposed an analytical model to calculate the mode I fracture toughness of multidirectional laminates, KL Ic, from the fracture toughness of the 0o plies, K0 Ic. The presence of a notch in a composite laminate will result in a complex three dimensional stress field that will trigger complex damage mechanisms such as delamination. In the model proposed, the effect of the three dimensional stress field is neglected and the damage mechanisms are assumed to result in a though-thethickness macro-crack. For this reason, as the Finite Fracture mechanics model [17] presented in section 5.1, if the main failure mechanism it delamination, the model cannot be applied. For a given laminate, the ratio between the mean remote failure stress of a group of plies that represent the balanced sub-laminate (i) and the remote failure stress of the a sub-laminate with all plies with the fibres aligned with the loading direction proposed by Vaidya and Sun [38] can be calculated using the Classical Lamination Theory since it only requires the ply elastic properties and the lay-up as input vaariables. The ratio reads: Ω(i) 0=¯σ(i) ¯σ0(6.60) ¯σ(i)and ¯σ(0) can be also be calculated from Linear-Elastic Fracture Mechanics: ¯σ(i)=K(i) Ic χ(i)Y√πa (6.61) ¯σ(0) =K(0) Ic χ(0)Y√πa (6.62) where χaccounts for the laminate’s orthotropy [11] and is given by: χ= 1 + 0.1(ρ−1) −0.016(ρ−1)2+ 0.002(ρ−1)3(6.63) 102 Chapter 6. Mechanical behaviour of composite laminates - Literature review and ρis given by ρ=(ExEy)1/2 2Gxy −(νxyνyx)1/2(6.64) where Exand Eyare the laminate’s Young Modulus in the orthotropy axes ( x being is the loading direction), Gxy is the laminate shear modulus in the orthotropy axes and νxy and νyx are the Poisson ratios. K(i) Ic and K(0) Ic are the fracture toughness of the sub-laminate (i) and of the 0oplies. Combining equations (6.60), (6.61) and (6.62), the fracture toughness of sub-laminate (i) yields: K(i) Ic =χ(i)Ω(i) 0 χ0K0 Ic (6.65) Assuming a self-similar crack propagation along all plies, the laminate’s fracture toughness KL Ic is calculated as KL Ic =PN (i)K(i) Ic t(i) tL,(i)6= 90o(6.66) where tLis the thickness of the laminate, t(i)it the thickness of the sublaminate (i) and N is the number of sub-laminates considered. Chapter 7 Modeling and performance prediction A algorithm capable of determining the notched strength of laminated composites using only the ply elastic, strength and fracture properties as input variables is presented in this chapter. Such an algorithm lays on two hypothesis: •delamination is suppressed and, therefore, unnotched tensile and compressive strength can be predicted using the Classical Lamination theory allied with an appropriate failure criteria. The failure criteria is a function of the in-situ properties, which can also be calculated analytically. •the effect of a three dimensional stress field at the vicinity of notches, which can trigger delamination, can be neglected and that the damage mechanisms can be lumped up into a through the thickness macrocrack. Since it has only ply properties as input variables, such a model would avoid the need of extensive and, therefore, costly and time-consuming experimental programs to determine properties for different lay-ups of the same material system and could possible be used as a preliminary design and optimization tool. For conventional and thick laminates, the effect of delamination cannot be neglected and, therefore, analytical models that discard its effect are not sophisticated enough to be able to predict their notched strength and cannot serve as an alternative to Finite Elements analysis. However, as shown in chapters 2 and 4 and reported in [4] [35] [6], thin-ply laminates are able to suppress delamination onset, and therefore, such a model could eventually be used. It could also be the base of an optimization algorithm capable of selecting an optimal lay-up of thin-ply laminates having open-hole tension and plain strength as design drivers. The model will be explained with more detail hereafter. It was only partially implemented and, therefore, no results will be presented in this stage of the work. 104 Chapter 7. Modeling and performance prediction 7.1 Unnotched tensile and compressive strength As explained in chapter 2, quasi-isotropic thin-ply composites loaded in tension and compression show little severe damage such as transverse cracking and delamination prior to failure and, therefore, Amacher et al. [4] suggests that the unnotched tensile and compressive strength of these kind of materials can be predicted combining the Classical Lamination Theory presented in 6.1 and a failure criteria as the ones presented in 6.2. The failure criteria is a function of each ply’s in-situ strengths, which can be determined as explained in 6.3. This means that, if there is in fact no severe delamination prior to failure, the unnotched strength can be predicted using analytical models having only the laminate lay-up and ply thickness, the ply elastic properties of the material and the ply strengths as input variables (see table 7.1). This avoids the expensive and time consuming process of experimental testing to obtain properties of different lay-ups of the same material system and will potentially allow the selection of a optimal lay-up for a specific application. For a plate loaded in tension or compression, some simplifications can be made to the Classical Lamination Theory. They will be presented hereafter. For a plate loaded in tension, the in-plane forces per unit length reads {N}=   Nx Ny Nxy   =   N 0 0   = [A]{0}+ [B]{κ}= [A]{0}(7.1) because {κ}={0}since w= 0 (see eq. 6.2). The stress distribution in a ply kreads {σ}k x=   σx σy σxy   k = [Q]k{0}= [Q]k[A]−1{N}(7.2) If the ply elastic properties E1, E2,G12 and ν12 and the stacking sequence and ply thickness are known, [Q]kand [A] can be computed, and therefore, the stresses in each ply for a given load Ncan be determined. Amacher et al. [4] applied the classical lamination theory allied with the TsaiHill criterion. In both cases, a virtual tensile test was performed, i.e. the applied remote stress was increased in 1 MPa per cycle, and the stress state for each ply was calculated. Two different hypothesis were followed: •In the first one, no damage is considered. In this case, the failure stress is the stress for which the Tsai-Hill failure criterion is met for 0oplies. This model revealed more accurate for thin-ply (30 g/m2) as shown in figure 7.1 since delamination and transverse cracking is suppressed until the point just before failure, which indicated that all the plies are able to carry load until the 0oplies fail. •In the second, damage is taken into account. In this case, when a ply’s stress state reaches the Tsai-Hill failure criteria, their elastic properties were reduced 7.1 Unnotched tensile and compressive strength 105 to 0.0001 of their initial value and the test continues until the 0oplies fails. This model proved more accurate for thick-ply composites (300 g/m2) as shown in figure 7.1 since delamination and transverse cracking are able to spread through the whole specimen, leaving the 0oplies to carry the load. Figure 7.1: Ultimate strength and onset of damage with respect to ply thickness in unnotched quasiisotropic tests, and failure modes observed for thick, intermediate and thin-ply laminates [4] In the present work, the Classical lamination theory model was implemented in a Matlab code but, since the final goal of this code is to be the basis of an optimization algorithm that is able to select lay-ups of a given material system for a specific application, a different approach that was believed to be less time consuming than that described above was used. Instead of increasing the applied remote stress until a given ply failed, the stresses in each ply were calculated as a function of the applied load N(eq. 7.2). The failure criterion is then applied to each ply which also yields a function of N. Solving this equation for N, the remote load required for each ply to fail can be calculated. The ply that actually fails is the one for which the remote load is minimum. The remote stress at failure is calculated dividing the load N by the total thickness of the laminate h. Two different models were implemented: •In the first, no damage is considered. In this case, the final failure is considered when the first ply fails. This model was implemented using the Tsai-Hill (hereafter referred to as TsHi. model) and the invariant-based criteria proposed by Camanho et al. [15] and explained in chapter 6.2.2 (hereafter referred to as Inv. model). The results obtained with both should be compared so that advantages of using a more complex criterion that is able to distinguish matrix 106 Chapter 7. Modeling and performance prediction and fibre failure could be accessed. A schematic representation of the TsHi and Inv. models are shown in figures 7.2 and 7.3 respectively. •In the second, damage is considered. In this case, if a ply fails due to matrix cracking (which can only be accessed if the invariant-based criteria proposed by Camanho et al.[15] and explained in chapter 6.2.2 is used) the transverse and shear elastic properties of that ply are reduced to 0.0001 of its original value, i.e. G0 12 = 0.0001G12 and E0 12 = 0.0001E12 and the process is repeated until the ply that fails fails due to fibre failure (kinking or maximum strain). A schematic representation of the model is shown in figure 7.4. Hereafter, this model will be referred to as as INV-D model. Any failure criteria is a function of the in-situ properties of the plies, that can be calculated using the analytical model presented in 6.3 [13] [32]. The in-situ properties are calculated using the required elastic, strength and fracture properties: the Young Moduli E1,E2, the Poisson coefficient ν12, the shear modulus G12, the mode I and II interlaminar fracture toughness, GIand GII, and the UD strengths XT,XC,YT,YC,YBT ,YBC,SLand ST. Table 7.1: Input variables required by the model Sym. Property Ply elastic E1Longitudinal Young’s modulus properties E2Transverse Young’s modulus ν12 Poisson coefficient G12 Shear Modulus Unidirectional XTLongitudinal tensile strength strengths XCLongitudinal compressive strength Yud TUniaxial transverse tensile strength Yud BT Biaxial transverse tensile strength Yud CUniaxial transverse compressive strength Yud BC Biaxial transverse compressive strength Sud LIn-plane shear strength Sud TTransverse shear strength Fracture GIc Mode I interlaminar fracture toughness toughness GIIc Mode II interlaminar fracture toughness K0 Ic Fracture toughness of the 0oplies Lay-up - Ply orientations and thicknesses Geometry d/W Hole diameter-to-width ratio d Hole diameter 7.1 Unnotched tensile and compressive strength 107 Ply Elastic Properties UD Strengths, Fracture Toughness Lay-up Calculate [T] and ¯ [Q] for each ply Calculate the laminate’s in-plane stiffness [A] Calculate {σ}=f(N) for each ply Apply Tsai-Hill failure criterion (section 6.2.1) Select minimum of all plies Unnotched Strength XL Tor XL C In-situ Properties: Yis T,Yis C,Yis BT ,Sis L and Sis T(section 6.3) Figure 7.2: Schematic representation of the TsHi model: CLT model using the Tsai-Hill failure criterion and not considering damage progression. 114 Chapter 8. Conclusion and Future Work to the thin lay-up which explains the similar unnotched tension strength between the two lay-ups. –higher notched strength when compared with the thick lay-up. The experimental study suggests that, by ply-blocking the 0oplies, fibre splitting is triggered while damage in the 45oand 90oplies is suppressed. This type of damage allows the redistribution of stresses near the hole, which reduces the stress concentration and, at the same time, as the damage is aligned with the loading direction, limits the damage to vicinity of the notch, which explains the enhanced notched strength in open-hole tension tests. –intermediate fatigue resistance. There is more extensive subcritical damage than in the thin laminated but, since the damage is aligned with the loading direction, its propagation will be slower and less pronounced than in thick laminates. •combining thick and thin plies of all fibre orientations (0o, -45o, 45o and 90o) in the same lay-up: this type of hybrid lay-up is more notch tolerant than thin but less tolerant than thick lay-ups. This intermediate behaviour can be explained by the type of ply hybridization: while the ”thin” part of the laminate should be able to delay subcritical damage before failure, the ”thick” part of the laminate is responsible for redistributing the stresses at the vicinity of the notch, reducing the stress concentrations. This is valid for both static and fatigue loadings. The fact that combining thin plies with thicker 0oplies increases the notched strength compared to thick laminates while maintaining the unnotched strength of thin laminates might be the solution to overcoming one of the main obstacle to market penetration thin-ply composites: their reduced tensile strength in the presence of stress concentrations. The process of selecting the material, geometry and lay-up of composite structures with stress concentrations requires the fast and accurate prediction of their notched strength which can be obtained using closed-form analytical models. In this work, the experimental open-hole tension test results were compared with predictions obtained using the Inherent flaw , the Point stress, the Average stress and the Finite Fracture Mechanics models with and without taking the material’s Rcurve into account. The IFM, PS and AS models require model calibration from a baseline specimen, which is a clear limitation as re-calibration is required for different geometries. The predictions obtained using the FFM model are in good agreement with the experimental results and are able to capture subtle differences is laminate configuration for the same material system. The material’s R-curve is useful to predict large damage capability of composite laminates without loss of accuracy in predictions for smaller specimens and should, therefore, be a included in the experimental characterization programs. However, as the R-curve varies with the laminate’s lay-up and because obtaining the size effect law needed to calculate the R-curve requires a very extensive and costly set of experimental tests, preliminary lay-up selection should not rely on the its determination, unless the prediction of the notched strength of large specimens is a relevant requirement. Having selected the lay-up, preliminary optimization and design should be made taking the 8.2 Future Work 115 material’s R-curve into account, because this method results in accurate predictions within a few seconds, avoiding the time consuming and the computational effort of Finite Element analysis. The second research line was based on the development of an algorithm that could serve as the base of an optimization algorithm capable of selecting an optimal lay-up of thin-ply laminates having open-hole tension and plain strength as design drivers. The model presented should be able to predict: •unnotched strength of laminated composites using a combination of the classical lamination theory, an anallytical model to calculate the ply’s in-situ properties and a failure criteria. Three models were proposed: – TsHi - Combination of the CLT with the Tsai-Hill failure criterion. In this model, no damage is considered, and, therefore, failure is predicted when the first ply fails. – INV - Combination of the CLT with a three-dimensional invariant-based failure criteria for fibre-reinforced composites. In this model, no damage is considered, and, therefore, failure is also predicted when the first ply fails. – INV-D - Combination of the CLT with a three-dimensional invariantbased failure criteria for fibre-reinforced composites. In this model, damage is considered and failure is predicted when a ply fails due to fibre failure (fibre kinking or maximum strain). •notched strength of laminated composites using the finite fracture mechanics model. The fracture toughness of the laminate is be predicted analytically from the fracture toughness of the 0oplies and the unnotched strength is predicted using the TsHi, INV or INV-D models. The model was only partially implemented and, up to date, its accuracy could not be accessed. Since it only requires the ply properties as input variables, proven it can predict notched strength of thin-ply laminates, such a model would avoid the need of extensive and, therefore, costly and time-consuming experimental programs to determine properties for different lay-ups of the same material system and could possible be used as a preliminary design and optimization tool. 8.2 Future Work Some aspects of the experimental work carried out should be addressed with more detail. Firstly, since only one specimen per laminate configuration was tested due to schedule problems, more open-hole fatigue tests should be performed to confirm the results obtained. These specimens should be subjected to fatigue loading until the defined failure criteria is reached (reduction of 10% in the specimen’s stiffness), so that a more valid comparison between lay-ups can be made. Moreover, the remaining open-hole fatigue specimens should be instrumented with strain gages rather than using the information provided by the testing machine’s LVDT, so that, the 116 Chapter 8. Conclusion and Future Work test results are more accurate. Secondly, the R-curve of the STF-THICK laminate appears to be overpredicted, which results in overprediction of open-hole tensile strengths using the finite fracture mechanics model. Even though, no anomalies were reported during double edge crack tests, and therefore, up to date, there is no reason to consider the R-curve invalid, it is important to understand if the results are in fact valid or not. Thirdly, since only 2 specimens per laminate configuration were considered valid, more unnotched tensile tests of STF T700SC/M21 lay-ups should be performed to confirm the values obtained. In the experimental work carried out, priority was given to studying the tensile response of hybrid laminates in comparison to thin and thick laminates. However, an experimental study to evaluate the consequences of ply hybridization when the laminates are loaded in compression should also be conducted. This experimental work should include unnotched compression, open-hole compression, open-hole fatigue tests and the determination of the laminate’s R-curve. The algorithm to calculate the notched strength having only the ply elastic, strength and fracture properties as input variables should be fully implemented and the predictions should be compared with available experimental results so that its accuracy can be accessed. Proven it can predict the notched strength accurately, it should be allied with an optimization algorithm so it becomes able to select an optimal lay-up of thin-ply laminates for a specific application having open-hole tension and plain strength as design drivers. 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