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Towards mitigation of wrinkles during forming of woven fabric composites : an experimental characterization Rashidi Mehrabadi, Armin 2016

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TOWARDS MITIGATION OF WRINKLES DURING FORMING OF WOVEN FABRIC COMPOSITES: AN EXPERIMENTAL CHARACTERIZATION  by  Armin Rashidi Mehrabadi    A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  THE COLLEGE OF GRADUATE STUDIES  (Mechanical Engineering)     THE UNIVERSITY OF BRITISH COLUMBIA  (Okanagan)  September 2016   © Armin Rashidi Mehrabadi, 2016  ii Abstract  Woven fiber-reinforced polymer composites have become superior materials of choice in industries such as aerospace, energy and automotive, partly due to increased conformability to complex 3D shapes. Formability of woven composite reinforcements, however, is restricted by failure mechanisms such as wrinkling, and remains as a challenging issue for thermo-stamping operations. Wrinkling is today one of the most frequent defects arising during forming processes of composite materials, adversely affecting the quality of the final product, and coping with this defect requires fundamental knowledge and understanding of the fabric’s deformation mechanisms.  This MASc thesis presents an analytical and experimental study on the shear deformation behavior of woven reinforcements from a multi-level standpoint as to more closely investigate the mechanisms behind formation of wrinkles. Namely, in the first stage of the research, sources of observed conflicts in the literature regarding the trend of tension-shear coupling in woven fabrics are discussed and resolved using a new characterization framework and a custom-design combined loading fixture. It is shown that in order to correctly characterize the tension-shear coupling behaviour in woven fabrics, instead of using global measured data, local normalized forces and displacements should be driven via a non-orthogonal transformation procedure, while considering kinematic force coupling in the test setup. In the second stage, a new characterization technique, namely a multi-step biaxial bias extension (MBBE) test, is proposed to determine the amount of required transverse de-wrinkling force, to flatten the wrinkles of different sizes. The underlying deformation mechanisms and the wrinkling/de-winkling force responses of the fabric are investigated, resulting into some potential practical design considerations for future 3D forming applications. Furthermore, the influence of yarn contact forces, bending rigidity, and tow slippage is highlighted for devising the de-wrinkling strategies.  Finally, hemisphere forming experiments are carried out, attempting to find correlations between the results of 2D characterization experiments and those of 3D forming. Subsequently, a practical idea on modifying the blank holder geometry is proposed and validated for effectively suppressing the wrinkles and possibly other forming-induced defects during the fabric forming processes.   iii Preface Portions of this thesis have been published as part of a poster presentation as follows.   Rashidi, S. Sultana, B. Crawford, M. DeWachter, A. S. Milani (2015) “Towards wrinkling-free forming of woven composite materials”, 2nd Annual Engineering Graduate Symposium, June 8th , School of Engineering, UBC Okanagan  A version of Chapter 2 has been published (cited below) based on a joint work conducted in the Composites Research Network Laboratory at UBC Okanagan by the author and Mr. Masoud Haghi Kashani (PhD student). We conducted the testing and wrote the manuscript collectively. Dr. Abbas Milani closely guided us through data analysis and developing the analytical framework and reviewed the article. Mr. Bryn Crawford provided valuable assistance in identifying and resolving problems associated with the test fixture. The published article is as follows.   M. Haghi Kashani, A. Rashidi, B. Crawford, Bryn, A. S. Milani (2016) “Analysis of a two-way tension-shear coupling in woven fabrics under combined loading tests: Global to local transformation of non-orthogonal normalized forces and displacements”, Composites Part A, 88: 272–285  Some parts of Chapters 4 have been published in the following conference proceedings. I was responsible for conducting the experiments, data analysis and writing the article. Dr. Milani reviewed the article and supervised the project.   A. Rashidi, A. S. Milani (2016) ”Characterization of wrinkling and de-wrinkling behaviour of woven fabrics using a multi-step biaxial bias extension test”, 17th European Conference on Composite Materials (ECCM17), June 26-30, Munich, Germany  A version of chapters 4 and 5 has been submitted for journal publication.   iv Table of Contents  Abstract .................................................................................................................................... ii Preface ..................................................................................................................................... iii Table of Contents ................................................................................................................... iv List of Tables ......................................................................................................................... vii List of Figures ....................................................................................................................... viii List of Abbreviations ........................................................................................................... xiv List of Symbols ...................................................................................................................... xv Acknowledgements ............................................................................................................. xvii Dedication ........................................................................................................................... xviii Chapter 1: Background and Thesis Organization ............................................................... 1 1.1 Introduction ........................................................................................................................... 1 1.2 Motivation and objectives ..................................................................................................... 2 1.3 Thesis framework .................................................................................................................. 3 Chapter 2: Literature Review ................................................................................................ 5 2.1 Fiber-reinforced composites ................................................................................................. 5 2.2 Woven textile reinforcements ............................................................................................... 6 2.3 Thermoforming of woven fabric composites ........................................................................ 7 2.4 Wrinkling in composite manufacturing ................................................................................ 8 2.5 Characterization of textile reinforcements .......................................................................... 10 2.5.1 Shear Characterization .................................................................................................... 10 2.5.2 Tension-shear coupling in woven fabrics ....................................................................... 15 2.5.2.1 Experimental approaches: A conflict in the literature results ................................ 15 2.5.2.2 Numerical approaches ............................................................................................ 17 2.5.3 Influence of bending stiffness on wrinkling ................................................................... 17 2.5.4 Characterization of wrinkling ......................................................................................... 18 2.6 Experimental investigations of single and multi-layer forming of fabric reinforcements .. 19 2.6.1 Mitigation of wrinkling in thermo-stamping processes .................................................. 20  v Chapter 3: Analysis of a Two-way Tension-shear Coupling in Woven Fabrics Under Combined Loading................................................................................................................ 22 3.1 Overview ............................................................................................................................. 22 3.2 Experimental setup .............................................................................................................. 22 3.2.1 Material ........................................................................................................................... 22 3.2.2 Custom biaxial-picture frame test fixture ....................................................................... 23 3.2.3 Sample shape and clamping ............................................................................................ 24 3.2.4 Loading modes and friction consideration...................................................................... 25 3.2.5 Characterization plan ...................................................................................................... 26 3.3 Analytical transformation of coupled global test measurements to net shear and longitudinal local values .................................................................................................................. 27 3.4 Results and discussion ........................................................................................................ 35 3.4.1 Influence of fabric tension on shear response ................................................................. 35 3.4.2 Assessment of the coupling trend using the local net force and displacement values .... 38 3.4.3 Simultaneous loading mode and the influence of shear on yarns tensile behavior ......... 39 3.4.4 A comparison of the two coupling effects ...................................................................... 45 3.5 Summary of findings ........................................................................................................... 46 Chapter 4: Characterization of Wrinkling and De-wrinkling Behavior of Woven Fabrics Using a Multi-step Biaxial Bias Extension Test ................................................... 48 4.1 Overview ............................................................................................................................. 48 4.2 Methodology ....................................................................................................................... 48 4.2.1 Test setup ........................................................................................................................ 48 4.2.2 Multi-step biaxial bias extension (MBBE) test method .................................................. 49 4.2.3 Sequential biaxial bias extension (SBBE) test method ................................................... 50 4.2.4 Measurement setup for shear angle and geometrical properties of wrinkles .................. 50 4.3 Results and discussion ........................................................................................................ 51 4.3.1 Observed deformation mechanisms ................................................................................ 51 4.3.2 Wrinkling results: forces and geometries ....................................................................... 52 4.3.3 De-wrinkling results ....................................................................................................... 58 4.3.3.1 De-wrinkling forces ............................................................................................... 58 4.3.3.1.1 Remark 1:  More discussion on the full-path yarn tensioning effect ................ 62 4.3.3.2 Comparison of normalized longitudinal and transverse bias extension tests ......... 64 4.3.3.3 Investigating the effect of fabric bending stiffness on the shape of wrinkles ........ 65  vi 4.3.4 Comparison to a sequential biaxial bias extension test ................................................... 67 4.3.4.1 Remark 2: Local tensile and shear forces along the yarns in the MBBE test ........ 69 4.3.5 Some practical considerations ........................................................................................ 69 4.4 Summary of findings ........................................................................................................... 70 Chapter 5: Experimental Investigation of Tension-Assisted 3D Forming ...................... 72 5.1 Overview ............................................................................................................................. 72 5.2 Experimental forming test setup ......................................................................................... 72 5.3 Results and discussion ........................................................................................................ 73 5.3.1 Correlation of 2D characterization to 3D forming .......................................................... 73 5.3.1.1 3D hemisphere forming without the blank holder geometry modification ............ 73 5.3.1.2 3D hemisphere forming with a blank holder geometry modification .................... 76 5.3.1.2.1 Further geometrical modification: Considering implementation issues............ 78 5.4 Summary of findings ........................................................................................................... 82 Chapter 6: Conclusions and Future Work Recommendations ........................................ 83 6.1 Summary ............................................................................................................................. 83 6.2 Contributions to knowledge ................................................................................................ 87 6.3 Future work ......................................................................................................................... 88 Bibliography or References .................................................................................................. 91    vii List of Tables   Table 3.1    Specifications and geometrical properties of the tested PP/glass plain weave… 23 Table 4.1    Geometrical properties of generated wrinkles obtained using 3D scanning ....... 56    viii List of Figures Figure 1.1    Organization of the thesis…………………………………….……………………………. 4 Figure 2.1    Load transfer to fibers in a fiber-reinforced composite. F1 carries the major part of the load through fiber bundles while the matrix is responsible for bearing the minor portion of the load, F2. ................................................................................ 6 Figure 2.2   Representation of the warp and weft directions in a typical woven fabric roll (here TWINTEX) along with a zoomed view of its plain weave unit cell (generated using TEXGEN software). .................................................................. 7 Figure 2.3   Process cycle in liquid compression moulding (LCM).. ....................................... 8 Figure 2.4   Initiation of wrinkling at large shear deformations due to locking. .................... 10 Figure 2.5   Geometrical configuration of PF test: (a) Geometry of the frame; (b) Specimen mounted in the fixture (adapted from [39]). ....................................................... 12 Figure 2.6   Geometrical configuration of the BE test: (a) Geometry of the frame and distinguished deformation zones before and after deformation; (b) Specimen mounted in the tensile machine and tested. Three distinguished deformation zones can be observed. ........................................................................................ 13 Figure 2.7   Fiber slippage in BE test: (a) A unit cell in a woven reinforcement; the cell undergoes cross-over slip. Dotted lines designate initial yarn positions, and solid lines indicate yarn positions after slippage. The circles indicate the centres of the crossovers before (grey) and after (black) crossover slip; (b) Schematic of one set of yarns in the deforming zones of a specimen (left) with no inter-tow slippage and (right) with inter-tow slip. The total ‘slip’ displacement shown in the sketch is calculated as the sum of s1 to s4 (adapted from [36]). ................... 14 Figure 2.8   The surprising trend of shear force at higher shear angles (adapted from [26]). 16 Figure 3.1   Woven architecture of the tested material. .......................................................... 23 Figure 3.2   Customized biaxial-picture frame test fixture employed for applying simultaneous and sequential combined loading modes. ..................................... 24 Figure 3.3   (a) Using needles instead of the conventional plate-bolts clamping to allow yarns rotate freely without local bending, (b) the resulting uniform shear deformation within the sample (the upper plates in these images have been removed after the  ix test to better visualize the effect of the needles in building homogenous deformation in the jaw’s neighborhood.) ............................................................ 25 Figure 3.4   Different deformation mode configurations: (a) the original state, (b) picture frame mode, (c) biaxial tensile loading, (d) simultaneous biaxial-shear loading. Note that in (a), (b) and (c), the local fabric (material covariant) coordinate system (f1-f2) is aligned with the fixture covariant coordinate system (1-2); however, f1 and f2 directions are not parallel to 1 and 2 under the simultaneous mode in (d). ......................................................................................................... 26 Figure 3.5   Shear deformation of the picture frame fixture. .................................................. 28 Figure 3.6   The angle α1 between the yarn in direction f1 and the fixture arm in direction 1, due to the tensile loading of motors in direction 1. Note that 1 and 2 are the bases of fixture covariant coordinate system, and f1 and f2 the bases of the material covariant (local) coordinate system. ................................................................... 30 Figure 3.7   Decomposition of the global external forces of the biaxial and shear motors into their normalized shear and longitudinal components imposed on the fixture frame (i.e., in 1-2 directions), in order to measure the net shear force (Nbs+N3s), denoting a kinematic coupling between the global forces due the mechanism of the combined loading fixture. The normalized force vectors are shown as dashed lines and are related to the external motor forces via Eqs. 3.11-13). .................. 32 Figure 3.8   Schematic of the normalized net global forces and the resolved normalized local forces along yarns (Ns and Nl) within the inner region of interest. Note that Fs and Nbl are parallel to the fixture arms (directions 1 and 2), whereas Ns and N l are aligned with the yarn directions (f1 and f2). ................................................... 33 Figure 3.9   Free body diagram of the normalized net global and local forces on a triangular material element within the fabric based on Figure 3.8. ..................................... 34 Figure 3.10 (a) Comparison between normalized global shear forces resulting from the shear motor for two picture frame tests with different pre-tension levels, and (b) the same comparison using the normalized net local shear force applied to the fabric. Notice the significance of considering the global shear force component resulting from the biaxial motors (coupling effect) in the resulting trends between the two curves with 0.8 and 3.1 N/mm pre-tensions, especially at higher  x shear angles. More specifically, by performing the force analysis in the local coordinate, the effect of pre-tension is consistent (the distance between the curves remain consistent across the fabric shear angles). For comparison purposes, the pure shear (without pre-tension) data has been added from [71] which used an independent shear frame device with a vertical test lay-up with minimum friction effect. ..................................................................................... 35 Figure 3.11 Variation of the global force of biaxial motors during picture frame test with 3.1 N/mm (total of 280 N) pre-tension; from the origin to point A (stage 1): applying pre-tension up to 380 N; from point A to point B (stage 2): the relaxation of the sample and causing reduction in the force from 380 N to 280 N; after point B (stage 3): applying the shear deformation. .......................................................... 37 Figure 3.12 Normalized global force components of the biaxial motors during shear frame testing with 3.1 N/mm pre-tension; (a) the longitudinal (tensile) component, and (b) the shear component. Note that as outlined in section 3.3, during the analysis Nl is assumed to be almost equal to Nbl in the shear tests with a small yarn pre-tension level. ....................................................................................................... 38 Figure 3.13 (a) Change in the required load of the shear motor over time in the simultaneous loading test (showing the kinematic coupling effect between the biaxial and shear motors), and (b) the global force of the biaxial motors under this mode, which reaches to a considerably high load magnitude. ....................................... 40 Figure 3.14 Deviation of the shear angle within the sample under simultaneous loading from the shear angle of the picture frame fixture based on the analytical procedure. The deviation between the curve and the dashed line represents the difference between the shear angle of the frame and fabric (2α). ........................................ 41 Figure 3.15  (a) The global net normalized shear force in the fixture, and (b) the local normalized net shear force in the fabric under simultaneous loading mode; the difference between the magnitudes of the two curves roots in the fact that the difference between the magnitudes of the two curves roots in the fact that the difference between the angle of yarns and the angle of arms is significant under simultaneous loading. .......................................................................................... 42  xi Figure 3.16 Comparison of the constitutive behavior of the fabric’s tensile behavior under biaxial and simultaneous loading modes, implying the effect of fabric shear on its tensile behavior. Arrows show the estimated straightening and stretching regimes of yarns under each mode. Results show that the fabric shearing lessens its tensile stiffness (as opposed to the reverse effect where the fabric tension, significantly increases its shear rigidity; also compare with Figure 3.10b). ....... 43 Figure 3.17 Idealized change in the contact area at crossover points during (a) biaxial and (b) shear deformation; Notice that the right side rhomboid area is smaller, assuming identical yarn width in both cases. ...................................................................... 44 Figure 3.18 Comparison between the elongation of fiber yarns during biaxial and simultaneous loading modes. .............................................................................. 45 Figure 3.19  Comparison of two coupling effects: (a) the normalized local net shear force in the simultaneous loading divided by that of pure shear, and (b) the normalized local tensile force in the simultaneous mode divided by that of the biaxial load. From the magnitudes of the two curves, notice that the tension-on-shear coupling effect in the fabric is much more dominant than the shear-on-tension coupling effect. However, a reduction of yarn tensile behaviour in the range of 50% (according to Figure 3.19b) under simultaneous loading may not be ignored, especially for structural analysis/design of the final formed part. ...................... 46 Figure 4.1    (a) The custom biaxial fixture used for the multi-step biaxial bias extension tests; (b) Four servomotors mounted on the arms shear the biaxial fabric specimen in the bias (originally mounted at ±45°) direction. ............................. 49 Figure 4.2    Test sequence in the MBBE experiment. ........................................................... 50 Figure 4.3    (a) The test fixture equipped with optical measurement system; sample positioning was monitored via DIC cameras; (b) Scanning the sample surface profile using a portable 3D scanner after formation of each wrinkle; (c) Scanned profile of a wrinkled sample. .............................................................................. 51 Figure 4.4   A de-wrinkled state of the fabric; distinguishing different deformed regions; the red line shows a full fiber path connecting longitudinal (X-direction) and transverse (Y-direction) clamps. Blue paths indicate different regions developed after de-wrinkling; in fact two transverse BE-like tests on either side of the  xii region A are formed during the de-wrinkling stage; Note that in particular region A would be the main region of interest for the final product. A zoomed area of region D is also shown in the figure. .................................................................. 52 Figure 4.5   Generated wrinkles in the x-direction along with their corresponding shear angles; some regions of wrinkles are zoomed in to show the shear angle uniformity. ........................................................................................................... 53 Figure 4.6   (a) Applied force in the longitudinal direction versus shear angles for the three wrinkle levels; After smoothing out each wrinkle using transverse forces and retrieving the transverse strip back to the initial wrinkle, a slight drop was observed in the force and shear angle (e.g., to relaxation) as notices in figures (a) and (b); (b) Evolution of shear angle during formation of each wrinkle level. Intra-ply slippage occurred after around 50° of shear......................................... 55 Figure 4.7   Surface profile of (a) low-level wrinkle; (b) medium-level wrinkle; (c) high-level wrinkle generated using 3D scanner. .................................................................. 56 Figure 4.8   Geometrical properties of the wrinkles obtained using 3D scanning; (a) area; (b) length; (c) width; (d) height. ............................................................................... 57 Figure 4.9   Investigation of the yarn tensioning effect in the de-wrinkling process of medium-level wrinkle. (a) comparison of de-wrinkling force and longitudinal force for cases with and without full fiber path; (b) Evolution of the shear angle in the triangular region ‘a’ (see Figure 4.4) versus time. Cross marks correspond to the point when the wrinkles were effectively flattened. ................................. 64 Figure 5.1   (a) Experimental setup employed for stamping operation; (b) Ply orientation during the double layer forming experiments. In single forming experiments, the 0° ply was used. .................................................................................................. 73 Figure 5.2   Correlation between the 2D bias extension test and the actual 3D forming trial 74 Figure 5.3   The deformed hemisphere via unbalanced clamping pressure. (a) Single ply forming; (b) Double ply forming with a 45° relative orientation. Shear angles at some regions are shown in the images. ............................................................... 75 Figure 5.4   Implementation of blank holder geometry modification in the 3D forming trials (a) Forming test configuration; (b) front and bottom views of the actual setup. 77  xiii Figure 5.5   (a) Outer view of weave pattern heterogeneity near the part edges using the modified forming set-up with no customization of conical part in the blank holder system; (b) the tow sliding was prevented by further customizing the conical part and hence removing excessive tension imposed to the fabric during forming. ............................................................................................................... 78 Figure 5.6   Detailed view of defects in single ply forming using the final modification shown in Figure 5.5. ....................................................................................................... 79 Figure 5.7   Detailed view of defects in double ply forming using the final modification shown in Figure 5.5. ............................................................................................ 80 Figure 5.8   Comparison between the inner views of the formed fabric with and without the final blank holder geometry modification. The general deformation zones in both images are quite similar, thanks to repeatability of the tests. Note that the local defects have been closely alleviated with the modified blank holder. ................ 81 Figure 5.9   Force-displacement curve response for (a) single ply forming and; (b) double ply forming; the preforms are made using the final geometry modification process described in section 5.3.1.2.1. ............................................................................. 82 Figure 6.1   The proposed geometry modification (shown in green). Shear slip will result in the formation of an S-shaped wrinkle in a 90 or ± 45 ply (adapted from [80]). . 90   xiv List of Abbreviations  CAD   Computer Aided Design CRN   Composites Research Network BE   Bias Extension    BBE   Biaxial Bias Extension BH   Blank holder DIC   Digital Image Correlation LVDT   Linear Variable Differential Transducers MBBE   Multi-step Biaxial Bias Extension  PF   Picture Frame  PP   Polypropylene  TWINTEX®   Commercial name for comingled E-glass/Polypropylene fabric tested       xv List of Symbols  2∅ angle of the picture frame arms 𝑢𝑠 displacement in the direction of the shear motor 𝜃𝑃𝐹 shear angle of the sample directly resulting from the picture frame deformation 𝜃𝐵𝐸  shear angle of the sample directly resulting from the bias extension deformation 𝐿 length of the fixture arms 𝐿1′  instantaneous length of yarns under simultaneous loading mode in direction 1 𝐿2′  instantaneous length of yarns under simultaneous loading mode in direction 2 𝑢1 displacement of biaxial motor 1 𝑢2 displacement of biaxial motor 2 𝛼1,𝛼2 angle between the fixture arm and the corresponding family of yarns while undergoing simultaneous loading (for a balanced case: 𝛼1=𝛼2=𝛼)  𝜀1, 𝜀2 longitudinal strains in yarn directions  𝜃 net shear angle 1-2 fixture covariant coordinate system a yarn width (warp direction) b yarn width (weft direction) 𝐹𝑠 normalized net global shear force  𝑁1, 𝑁2 global forces of biaxial motors (for a balanced case: 𝑁1 = 𝑁2 = 𝑁𝑏) 𝑁3 global force of shear motor 𝑁3𝑠 normalized global shear force of shear motor 𝑁𝑏𝑙 normalized longitudinal force component of biaxial motors along the arms direction 𝑁𝑏𝑠 normalized shear force component of biaxial motors 𝑁𝑙 normalized local longitudinal force applied to yarns within the region of interest 𝑁𝑠 normalized local net shear force applied to yarns within the region of interest 𝑤 width of fixture jaws d cross-head extension Lframe the distance between the pins in the frame  xvi W Width of bias extension sample H Height of bias extension sample 𝑓1 − 𝑓2 material covariant (local) coordinate system Fsh Normalized shear load in bias extension test W1,W2 Width of the irregular bias extension samples in de-wrinkling experiments                            xvii Acknowledgements  First, I would like to extend my sincere gratitude to my supervisor Dr. Abbas Milani for all of his guidance, motivation, and support throughout this project. Dr. Milani played an influential role in broadening my vision of composites science and engineering, and delivered coherent answers to my endless questions, always encouraging me to keep ‘The Big Picture’ in mind and learn from failures.   I would also like to thank Mr. Kurtis Willden from Boeing Research and Technology Center for his insightful comments and suggestions throughout the project. Also, I deeply appreciate constructive comments from my committee members, Drs. Mina Hoorfar and Rudulf Seethaler.  I want to pass on many thanks to Mr. Masoud Haghi Kashani, Mr. Bryn Crawford, Mr. Edward Smith Griffiths, Ms. Meesh Bono, Ms. Ronak Vahed, and Mr. Safat Rashif, my friends at CRN Okanagan laboratory who made it an enjoyable place to work in.  Many thanks also go to Dr. Mohammad Nouroz Islam for the long and fruitful discussions regarding our custom-made fixture. I would like to extend my gratitude to the amazing machinist, Mr. Durwin Bossy, for assisting me in the School of Engineering machine shop and making sure that all machined components required for our test fixture were completed with exceptional quality.  I would like to thank my friends in Kelowna for all the countless laughs and memorable times in these past two years.  Finally and most importantly, thanks are due to my beloved family for supporting me tirelessly throughout my years of education. Their unlimited love, encouragement, and care make it all worthwhile.     xviii Dedication To my ever-caring grandmother Parvin, You are truly missed.   1 Chapter 1: Background and Thesis Organization Chapter Title use Heading 2, will auto-generate the chapter number 1.1 Introduction Since the 1970s, applications of composite materials have extensively increased due to development of new fibers and reinforcements, such that today nearly 50 percent (by weight) of the Boeing 787’s airframe including the wings and fuselage are fabricated from advanced composites [1]. Composite materials are made of high-strength and high-stiffness reinforcements impregnated by a polymer matrix resin. They are lightweight, stiff, and strong materials that provide weight savings and improved fuel efficiency for transportation vehicles [2, 3]. Their properties can be tailored as required for optimal load paths. From production point of view, they are unique in a sense that complex 3D shapes that would be infeasible, or very costly, to manufacture with metals can be produced today with this genre of materials at low costs [4].   A variety of continuous fibre-reinforced composites have been adopted in different sectors of industry where the weight and performance benefits overshadow the application of monolithic materials such as steel. Examples of such sectors include aerospace, energy, and marine industries. In particular, ‘textile’ composites (woven knitted, braided, etc) have been recognized as an attractive reinforcement category due to their integral fibrous architectures, formability, and multi-directional material properties. The moderately low tooling costs in textile composite manufacturing processes have made them today be employed in numerous low-volume productions or prototyping [5]. Yet there is a growing interest to employ such fibre-reinforced composites in higher volume applications such as the mainstream automotive industry. In order to remain viable in such industries, fiber-reinforced textile composites and their forming must be predictable, reliable, and significantly inexpensive at high-volume productions. In turn, this requires sound and comprehensive understanding of their mechanical behaviour so that the upstream design methodologies can take into account both optimal processing parameters and final product design features of selected textile preforms.     2 1.2 Motivation and objectives One of the principal goals in optimizing textile composite structures is to improve the forming of the material into the structure’s shape, by mitigating forming-induced defects during manufacturing. In particular, wrinkling is currently one of the commonplace defects occurring during textile composites forming. In order to eliminate this defect for manufacturers, fundamental deformation mechanisms of fabrics (particularly shear deformation) must be characterized and advanced numerical models are required so that forming simulations can become accurate and efficient for optimization purposes. The motive for this thesis is to arrive at an enhanced understanding regarding the mechanisms behind wrinkling in woven fabrics and to primarily seek for new methods to cope with this forming-induced defect by means of experimental trials. To this end, the following specific objectives are defined:  1. Conduct full characterization of the tension-shear interaction in woven fabrics by means of a new characterization framework and a custom-design combined loading fixture.  Deliverable: It has been suggested that the coupling between in-plane tension and shear response can delay the onset of wrinkling and hence here this coupling is fully characterized to devise proper de-wrinkling strategies.  2. Characterize the wrinkling and de-wrinkling behavior of woven fabric composites by proposing a new characterization method, namely here a ‘multi-step biaxial bias extension’ (MBBE) test.  Deliverable: Results will provide new insights regarding the underlying mechanism behind formation and mitigation of wrinkles, assisting to develop efficient de-wrinkling strategies.  3. Correlate the findings obtained in objectives 1 and 2 to an actual/3D forming process. Deliverable: Some new potential practical guidelines will be provided for fabric thermo-forming optimization applications.     3 1.3 Thesis framework The thesis is composed of six chapters. Chapter 2 reviews the background research conducted on the characterization and modeling of woven fabrics, as well as the studies concerning wrinkling and experimental forming. Chapter 3, 4 & 5 form the main body of this research, each having its methodology, results and discussion sections. Namely, Chapter 3 presents the analytical and experimental study on the tension-shear coupling (i.e., fulfilling Objective 1). It includes the analytical transformation of global test measurements to local values, as well as the analysis of the results obtained by experiments under combined loading. Chapter 4 is devoted to characterization of the wrinkling and de-wrinkling behavior of woven fabrics (i.e., Objective 2). The multi-step biaxial bias extension method is explained followed by analysis of results and discussions on some practical design aspects. Chapter 5 focuses on a hemi-sphere experimental forming setup along with results and discussions on the tension-assisted forming trials (i.e., Objective 3). Finally, Chapter 6 summarizes the main findings of the thesis and outlines recommendations for future work. Figure 1.1 illustrates the summary of the topics presented in each chapter and the organizational framework of the thesis.                  4                                 Figure 1.1    Organization of the thesis.   Chapter 1: Background and Thesis Organization Chapter 2: Literature Review Chapter 6: Conclusions and Future Work Chapter 3:Analysis of a Two-way Tension-shear Coupling in Woven Fabrics Under Combined Loading Chapter 4:2D Characterization of Wrinkling and De-wrinkling  Behavior of Woven FabricsChapter 5:Experimental Investigation of Tension-assisted 3D Forming  5 Chapter 2: Literature Review  2.1 Fiber-reinforced composites  Today, studies of stiff, strong, and lightweight materials for applications to various engineering structures, from submarines and aircrafts to automobiles, robot components and civil structures, highly concentrate on using fiber-reinforced composite materials. Fiber-reinforced composites can offer numerous advantages over metallic materials. For conventional monolithic materials, the tailorability of properties in one direction often come at the expense of the properties in other directions; e.g., the material is weaker in directions perpendicular to the stronger directions in rolled formed steel. As the smallest unit cell of a composite, fibers are processed in such a way that the strong and stiff direction of the unit can be aligned in arbitrary directions (fiber directions). A group/bundle of fibers aligned together is called a yarn (or tow), composed of thousands of filaments. When surrounded by a more flexible and lighter material, namely the matrix material, the ensuing fiber/matrix composite system can provide both high strength and stiffness and at the same time lightweight characteristics. During loading of such composite systems, external loads can be transmitted by the matrix to the strong fibers [2] (see Figure 2.1); in general, 70 to 80 percent of the loads imposed to a composite is carried out by fibers [3]. The matrix material is often composed of polymer, metal or ceramic, which links the fibers together, dispenses the load among them, protects fibers against the environmental conditions, as well as keeping them aligned with the tows [3]. Arrangement and architecture of fibers inside the matrix material can be in various forms such as continuous fibers (UD or textile), felt/matting, and short (chopped) fibers. Generally speaking, continuous long-fiber composites have the highest load bearing capacity and the short fibers have the lowest [4]. Fiber-reinforced composites provide designers with an opportunity to alter the components’ stiffens or strength in different directions according to the loading conditions imposed to the part (e.g., tensile and shear loads), making these type of composites a viable choice for advanced and high-risk applications.  6  Figure 2.1    Load transfer to fibers in a fiber-reinforced composite. F1 carries the major part of the load through fiber bundles while the matrix is responsible for bearing the minor portion of the load, F2.   2.2 Woven textile reinforcements The demand for heavy duty and high performance applications in the composites industry has gradually led to emergence of ‘textile’ fiber reinforcements as a strong choice over conventionally used unidirectional (UD) fibers [5]. In addition, in recent years, the textile reinforcements have been considered as a major competitor in the market race to decrease manufacturing costs of large structures [2]. Among various types of textile composites, woven fiber-reinforced polymers have become a superior material of choice particularly in industries such as automotive, defense, and aerospace, mainly due to their high out-of-plane impact resistance capacity along with conformability to complex 3D contours and sharp edges [6].  As a result, fundamental knowledge and understanding of woven fabrics’ forming processes and deformation mechanisms have become essential for taking full advantage of their performance in high-volume productions [7]. As shown in Figure 2.2, woven fabrics are essentially interlaced by two sets of yarns. These lengthwise and crosswise yarns are called ‘warp’, and ‘weft’, respectively.    7  Figure 2.2    Representation of the warp and weft directions in a typical woven fabric roll (here TWINTEX) along with a zoomed view of its plain weave unit cell (generated using TEXGEN software).  2.3 Thermoforming of woven fabric composites Fiber-reinforced composites can be classified into broad categories according to the matrix used in them; e.g., polymer, metal, ceramic, and carbon-matrix composites. The most widely used matrices in composites today remain to be polymers, which can be thermosets or thermoplastics. Once a thermosetting matrix/resin is completely cured, the cross-linked material remains non-recyclable. Conversely, thermoplastics are melt-processable and can be heated and melted several times, as they do not comprise permanent chemical reactions during solidification [4]. As thermoplastics can be processed (heated, melted, and cooled down) within the order of minutes (as opposed to some thermosets that can take up to hours), the processing of thermoplastic composites has become popular in e.g., automotive industry where fast production rate is of concern [2-4].   Because of the high consolidation pressures and temperatures required for processing thermoplastic composites, the parts normally need to be formed in a hot press setup, by means of thermoforming or liquid compression moulding (LCM) [8, 9]. LCM has gained advantages over many other processing techniques due to its traits such as reduced solvent emissions, improved quality of near-net-shape processing, processing repeatability and its speed [8]. In general, LCM is used for producing complex part geometries with ‘long-fiber’ reinforced composites (such as woven). In this process (Figure 2.3), first, the resin is applied (e.g., by means of heating) to the fabric layup ‘before’ moulding. Then the material system is pressed inside the mould, and subsequently the resin can flow to fill the cavity. The layup is pressed until the complete cure of the part, upon which the de-moulding takes place. One of the key  8 benefits of this (as well as other LCM techniques normally used for thermosets such as resin transfer molding (RTM) and structural reaction injection molding (SRIM)) is the use of fiber preforms which makes it possible to achieve near-net shape of the part apart from the moulding cycle [10]. This preforming/draping stage has a significant influence on the subsequent resin flow impregnation and effective permeability characteristics 11-14], and hence properties of the final part [15-18]. Given the good conformability of woven fabrics via LCM processes, manufacturers often aim at applying these reinforcements to complex 3D shapes containing corners and double curvatures.   Figure 2.3   Process cycle in liquid compression moulding (LCM).   2.4 Wrinkling in composite manufacturing Composite thermoforming designers may occasionally confront challenges as to how properly form woven fabric reinforcements without causing manufacturing faults and defects, especially when it comes to draping over double-curved geometries which necessitates large in-plane shear deformation of the fabric [19]. Depending on the geometry of a final part, as well as the  9 given fabric characteristics and manufacturing parameters (e.g., blank-holder load, tool load, friction, weave type, etc.), the double-curved shape forming can be problematic to control and leads to defects such as wrinkling (out of plane deformation), in-plane waviness, tow buckling, fiber fracture, and inter-tow slippage, all of which tend to significantly degrade the performance characteristics of the final composite structure [20, 21]. Among these defects, wrinkling is perhaps the most severe one arising during both automated and manual forming processes of composite materials [10]. Wrinkles can lead to unexpected failures during the manufacturing, or cause a significant reduction in strength and damage tolerance of the final product [22, 23].  A number of processing parameters affect the wrinkling phenomenon, e.g., forming temperature, forming rate, the number of composite plies, blank holder pressure and fabric orientation, etc. Numerous attempts have been made in order to understand the mechanisms behind formation of fabric wrinkles, both in the context of 2D characterization and 3D draping process. Prodromou and Chen [21] investigated the relationship between the shear angle and wrinkling of textile preforms.  They demonstrated that as the shear deformation proceeds and the fabric continues to be deformed, local shear and in-plane compressive forces start to build up at cross-over points, which in turn is compensated in the form of wrinkling [24] (see Figure 2.4). Hence, they suggested that shear angle between the warp and weft yarns may be deemed to be the significant parameter to measure during shear deformation. Once the shear angle reaches a certain critical angle, namely the locking angle, fabric buckling may start in the weft/warp overlapping regions. To assess the potential of the fabric to be draped over a particular surface, the locking angle can be obtained using picture frame (PF) [21, 24] or bias-extension (BE) [19, 20] tests, as well as commercial software packages for mapping yarn placement onto 3D surfaces. The locking angle has been also modelled analytically in some investigations [25, 26], nevertheless manufacturers are often obliged to use trial and error to optimize the design and forming process parameters. In addition, other fabric parameters (such as tow spacing, width, etc.) can contribute to the onset of wrinkling [21]. For many years, the aforementioned locking angle was considered to be the key characteristic (limiting value) to characterize wrinkling; however, recent evidences have revealed that wrinkling can arise from a multi-scale mechanical problem depending on the yarn rigidities and strains applied to them  10 via the fabric architecture and global boundary conditions [19]. Accordingly, more comprehensive studies began in order to better characterize this phenomenon and ultimately develop feasible and cost effective strategies to mitigate wrinkling during the forming process of different types of fabric reinforced composites.   Figure 2.4    Initiation of wrinkling at large shear deformations due to locking.  2.5 Characterization of textile reinforcements Coping with defects such as wrinkling requires advanced and detailed characterization of the material’s behavior under various deformation modes. Even though the characterization measurements are commonly conducted under individual material deformation modes, in reality these deformation modes are possibly coupled/occur together. In fact, during a forming process, deformation modes of the fabric yarns can include large in-plane and out-of-plane modes; namely, in-plane shear, in-plane tension, and out of plane bending [27].  2.5.1 Shear Characterization Past studies have been carried out to characterize the shear response of fabric reinforcements as it is the primary forming mechanism for draping over doubly curved geometries [28, 29]. Two principal methods of characterizing the intra-ply (a ply here is referred to as a layer of woven fabric) shearing behavior of textile reinforcements (also called trellising) include: the picture frame (PF) test [30-36] and the bias extension (BE) test [37,38], both of which demonstrating their drawbacks and advantages according to an intensive bench-mark study conducted by research laboratories from around the world [36,39].  Picture frame test is, in general, more favorable for pure shear characterization of woven fabrics, and recently for cross-ply uni-directional laminates [40]. The PF test configuration of  11 a regular shear frame fixture and its schematic are shown in Figure 2.5. The PF is a hinged frame equipped with four rigid arms with equal lengths.  A tensile load is applied across diagonally opposing corners of the fixture, causing the frame to move from an initially square shape into a rhomboid. Ideally, the kinematics of deformation imposes the required deformation onto the specimen in the region of interest (the rectangular piece in the middle). The angle of the frame during deformation can be found as [41]:   𝑐𝑜𝑠𝜃 =√2𝐿𝑓𝑟𝑎𝑚𝑒+𝑑2×𝐿𝑓𝑟𝑎𝑚𝑒                                                        (2.1)  Where 𝐿𝑓𝑟𝑎𝑚𝑒 is the distance between the pins in the frame (side length of the frame) and d is the cross-head extension. The shear angle, 𝜃𝑃𝐹 is calculated from the geometry of the picture frame:  𝜃𝑃𝐹 = 90° − 2𝜃                                                            (2.2)  The picture frame test theoretically offers homogenous shear deformation across the sample as well as a simple deformation analysis framework; however extreme clamping conditions in the frame rig can cause local bending and tensioning of yarns, resulting into a major change in the shear response of the material due to the induced additional forces [39]. Generally speaking, this test setup is highly sensitive to the pre-conditioning or misplacement (handling) of the specimen in the frame. Moreover, tight or non-uniform clamping conditions can lead to high tensile loads within the fabric, which is deemed to be one of the main causes of data scatter using this test mode [36]. Alteration of boundary conditions in the picture frame has been the subject of past studies. For instance, Milani et al. [42] pinned the specimens only in the sample corners to implement a boundary condition more similar to that of the bias extension test. Removal of the adjacent fibers also allows compressive forces to relax in the region of interest [43, 44]. As another recent solution [45, 46], the use of needles at clamps was shown to permit yarns to rotate more freely during PF trellising tests, hence avoiding fiber bending nearby the clamp boundaries.   12   (a) (b) Figure 2.5    Geometrical configuration of a PF test: (a) Geometry of the frame; (b) Specimen mounted in the fixture (adapted from [39]).  The bias extension (BE) test is an alternative to the PF test, consisting of a rectangular sample such that the weft and warp yarns are originally oriented at 45° to the orientation of the applied tension. The initial length of the specimen must be more than twice the width of the specimen in a BE test [39]. Under this condition, yarns in the central zone are free at their both ends. If there is no slip between warp and weft yarn, and assuming yarns being inextensible, the deformation in central zone is pure trellising shear similar to the PF test [39]. As shown in Figure 2.6, in the BE test, the shear angle in white zones is half of that in the central zone. One end of both warp and weft yarns of black zones is fixed in the clamp; consequently, assuming yarns being inextensible and no slippage occurs, triangles in the black zones remain un-deformed. It is assumed that the in-plane shear is fairly constant in each zone—an assumption that should be first verified experimentally accordingly to recommendation in [47].  A simple kinematic analysis of a bias-extension sample, shown in Figure 2.6, provides the shear angle in the grey zone, 𝜃𝐵𝐸  , as a function of fabric size and the displacement, d:  𝜃𝐵𝐸  = 90° – 2 cos-1 (𝐿0+𝑑√2𝐿0)                                                          (2.3)   13 Where L0 = H-W and W and H are width and height of the sample, respectively. The normalized BE shear force can be obtained using an iterative process following the assumption of uniform shear distribution in the grey zone in Figure 2.6 [39]:  𝐹𝑠ℎ(𝜃𝐵𝐸 ) =12𝐻−3𝑊((𝐻𝑊− 1) . 𝐹. (𝑐𝑜𝑠𝜃𝐵𝐸2− 𝑠𝑖𝑛𝜃𝐵𝐸2) − 𝑊.𝐹𝑠ℎ (𝜃𝐵𝐸2) 𝑐𝑜𝑠𝜃𝐵𝐸2)                    (2.4)  Where F is the clamping force and 𝜃𝐵𝐸  is the shear angle.      (a) (b) Figure 2.6    Geometrical configuration of a BE test: (a) Geometry of the frame and distinguished deformation zones before and after deformation; (b) Specimen mounted in the tensile machine and tested. Three distinguished deformation zones can be observed.  The bias extension test differs from the picture frame test in that the test is easier to setup and it is not as significantly influenced by the boundary/clamping conditions. The main advantage of the BE test is that induced tensions in the yarns are small and hence the in-plane shear measurement is not disrupted [47]. However, as disadvantage, specimen is submitted to a more complex shear deformation field and requires demanding optical measurements so as to trace the test kinematics [36]. In addition, intra-ply slippage can occur during the test and is known as another limiting factor/disadvantage [36]. Nevertheless, it can serve as a practical means to qualitatively investigate the fiber slippage effect during shearing, which actually occurs along with wrinkling in the presence of complex boundary conditions in thermo-stamping processes [48]. At the initial stage, similar to the PF test, the dominant deformation mechanism in the  14 bias extension specimens is the in-plane shear, as it provides the most energy efficient mechanism to extend the sample in the off-axis. However, as the shear proceeds and the shear angle increases, the material’s shear rigidity increases [36]. In the bias extension test, because intra-ply slippage provides an alternative energy absorption mechanism by which the material can accommodate the imposed material extension, its probability increases with respect to the enhanced resistance offered by the shear deformation mechanism. Hence, at some point during the course of the bias extension test, slippage becomes a significant deformation mechanism. Equation (2.3) predicts the deformation of the picture frame sample and has been based on the assumption that the sample undergoes pure shear deformation. However, the alternative intra-ply slip deformation mechanism possible in the bias extension samples means this equation is not necessarily true for BE tests. For this reason, the shear angle in BE tests must be measured by alternative means such as digital image correlation (DIC) or optical methods. Two possible forms of intra-ply slip taking place in the bias extension test, namely; cross-over slip and inter-tow slip (Figure 2.7). Both modes are likely to occur in the actual forming process of fabric reinforcements as the fabric is semi-constrained by the blank holder. Harrison et al. suggested a method to determine the onset of slippage in the bias extension test [32], however, more extensive research is needed to be carried out to fully characterize this phenomenon under each corresponding mode and further correlate it to the 3D forming procedures.   (a) (b) Figure 2.7    Fiber slippage in BE test: (a) A unit cell in a woven reinforcement; the cell undergoes cross-over slip. Dotted lines designate initial yarn positions, and solid lines indicate yarn positions after slippage. The circles indicate the centres of the crossovers before (grey) and after (black) slip; (b) Schematic of one set of yarns in the deforming zones of a specimen (left) with no tow slippage and (right) with tow slippage. The total ‘slip’ displacement shown in the sketch is calculated as the sum of tow slips (adapted from [36]).  15 2.5.2 Tension-shear coupling in woven fabrics 2.5.2.1 Experimental approaches: A conflict in the literature results Due to interwoven architecture, the shear rigidity of woven fabric plies would be hypothetically dependent of their membrane tension levels along fiber tows. Experimental approaches have been adapted to examine this tension-shear coupling in woven fabrics. One of the earliest investigations of this kind [33] reported minor evidence of coupling using a biaxial bias extension setup, in which the fabric is pulled simultaneously in two perpendicular directions while the fibers are initially oriented at ±45o. The study suggested that it may not be essential to take into account the effect of biaxial in-plane forces in the forming simulation of fabric; however, results were not fully conclusive due to the existence of large scatter in the measured data and varying transverse forces. Harrison et al. [34], on the other hand, used a similar experimental approach by applying constant transverse tensile forces to the uniaxial bias extension samples. Reporting low variability, they observed a clear tension-shear coupling effect, yielding up to 30-40 times increase in the shearing force. Nevertheless, the non-uniformity of induced deformation mode across the sample may be a disadvantage of this type of test, although later a novel normalization technique was proposed to obtain more reliable coupling characterization results [49]. In another study, by applying different pre-tension levels to a woven fabric using a biaxial tension device, Willems et al. [34, 35] suggested that the shear response in the tested modes exhibits comparable trends, concluding that the fabric shear stiffness may not be significantly affected by the yarns tensile state. However, it was difficult to fully assess the importance of this tension-shear interaction against large data scatter from the tests.  Launay et al. [27] implemented a more sophisticated characterization device including load cells on the side arms, making the setup capable of monitoring the state of fabric tensile loads while shearing the fabric. Monitoring the load cells during their picture frame tests clearly showed that the fibers underwent tension due to the tight plate clamping condition, reconfirming that the picture frame test may not always induce a pure shear deformation. Furthermore, their results showed that a higher yarn pre-tension level results in a higher fabric shear resistance at low shear angles, whereas surprisingly an inverse trend was noticed at high  16 shear angles. That is, in the high shear angle regime the required global forming force for the fabric material was higher at lower pre-tension levels. Although a compelling explanation was provided for this effect of tension on the shear rigidity of the fabric, especially at low shear angle regime, further research was needed to better understand the above surprising behavior at higher angles.   Recently, Nezami et al. [45] designed an advanced picture frame fixture incorporating separate tensioning devices to both principal axes of the sample. Specifically, using pneumatic cylinders, tensile loading was imposed on fabric samples during picture frame shearing; hence the boundary condition in their study was force-control. The results pointed out that a higher force pre-tension level not only causes a higher shear force at high shear angles, but also its increase was much more significant in comparison with low shear angles. This observation was in conflict with the results obtained earlier in [27].   Remark 1: It is also worth mentioning that despite the above reviewed researches focused on the effect of yarn tension on fabrics shear behavior, the influence of fabric shear on its tensile behavior has not received adequate attention to date. Buet-Gautier and Boisse [50] reported a slight decrease in tensile stiffness of a woven fabric when the angle between yarns was initially set to a value different than 90o. However, this did not fully represent an actual simultaneous shear forming deformation in the presence of tension.   Figure 2.8    The surprising trend of shear force at higher shear angles (adapted from [26]).    17 2.5.2.2 Numerical approaches Regardless of the employed test modes, an ultimate goal of most experimental characterization studies on woven fabrics is to simulate their forming processes accurately. Numerous numerical modelling investigations have been already performed on woven fabrics (e.g., [19, 51-53]). Some of these models employed simplified assumptions such as intertwisted yarns’ linear elastic behavior and independence of fabric shear rigidity on the yarns tensile behavior. As an example, the numerical model in [51] examined the effect of material properties, such as fabric tensile and shear moduli, on the number and shape of induced wrinkles during a stamping process. Although the model could correctly predict the general shape of the deformed sample under stamping, no experimental-numerical comparisons between shear angles in different part regions, the punch load, and the height of wrinkles were drawn. In another numerical simulation [52], a comparison between the numerical prediction and experimental results of shear angle in a certain specimen zone revealed that the predicted shear angles are higher than the measured values. As a result, further attempts were made toward enhancing modelling of fabric reinforcements. Firstly, fiber rotation was taken into account by introducing a non-orthogonal constitutive model [53]. Then, as the effect of tension on the shear rigidity of dry fabrics was evidenced, Boisse et al. [19] devoted efforts to incorporate this coupling factor into the aforementioned non-orthogonal model. Results of their macro-level simulation showed a relatively higher punch load in the coupled model as compared to the uncoupled model. However, because low computational time was sacrificed by adding the tension-shear coupling term, the effectiveness of the coupling to obtain more accurate results was regarded as a challenging question to be investigated by further numerical and experimental studies. Overall, the implementation of the tension-shear coupling into fabric forming simulations would be expected to result into more accurate punch force and stress distribution predictions, albeit it may not change the general shape of the deformed part [71].  2.5.3 Influence of bending stiffness on wrinkling From a meso-level deformation point of view, the primary shear deformation mechanism during textile forming can be coupled to bending of yarns [29]. Compared to their tensile behavior, the bending rigidity of woven fabrics is very low. This is due to their fibrous microstructural nature and relative motion of fibers within the tows [54]. Boisse et al. [19]  18 included the bending behavior of yarns in a fabric forming model, implying that it is of significant importance to correctly predict the size and shape of ensuing wrinkles. It was observed that increasing the bending stiffness results into larger wrinkle sizes. This would suggest membrane finite element approaches are not an appropriate means to model the forming process of woven fabric reinforcements. A more recent study has implemented the yarn flexural rigidity into a beam/shell model to predict the shape of wrinkles and captured the compressive response of the fabric [55].  2.5.4 Characterization of wrinkling  Wrinkling has been investigated as part of many studies undertaken for shear characterization of fabric reinforcements. The studies have employed the PF or BE test in order to understand woven materials formability and to eventually develop accurate constitutive models for forming simulations. Among such studies, Harrison et al. [36] devised a new characterization approach, biaxial bias extension (BBE) test, in which constant transverse forces were applied to the sample while performing the conventional uniaxial bias extension test. It was observed that increasing membrane tensions would effectively delay the onset of wrinkling. The onset of intra-ply slippage was also determined using optical measurements. Employing a modified PF fixture in which the two middle joints deviated from the plane where the fabric is clamped, Zhu et al. [56] showed that in large shear deformations, yarn width is reduced and the onset of wrinkling is significantly delayed due to the delayed lateral compressibility of the tows. The surface profile of the sample during the PF test was also scanned, closely detecting the locking angle of the fabric around 50° and 58° using standard and modified PF fixtures, respectively [43]. Same authors carried out another investigation, this time using the BE test, characterizing both types of failures, wrinkling and slippage [47, 57]. Test samples with various aspect ratios, and the material behavior under different loading conditions were analyzed and the onset of possible failure modes was determined. It was shown that depending on the loading ratio and boundary conditions, the onset of wrinkling can be far before the locking angle; this may also happen in practice, where the in-plane tensile forces resulting from the blank holder are not sufficient to suppress the wrinkles, leading to formation of wrinkles with at low shear angles [58]. Moreover, compression, compaction, and friction between the composite lay-up layers have potential to expedite the onset of wrinkles in thermo-forming processes [56]. Conversely,  19 some forming simulations based on both kinematic and kinetic models have captured wrinkles with higher shear angles than the locking angle [59-61]. These results suggest that the locking angle is not the key parameter to characterize wrinkles and this issue can be addressed further by employing the inherent nature of bias-extension test which allows characterizing wrinkles at low shear angles while taking into account the intra-ply slippage modes.  2.6 Experimental investigations of single and multi-layer forming of fabric reinforcements A great portion of composite fabric literature has been devoted to experimental tests on the determination of basic manufacturing properties such as drapability. The forming of a fabric into a three-dimensional shape is often investigated using hemispherical forming devices or various extended hemispherical geometries [62–65]. The hemispherical shape is simple, double-curved and leads to large shear angles (up to ~50°). It is often desirable to extend single-ply forming experiments to multi-layer forming investigations as to more closely investigate the actual forming processes where multiple fabric layers are stacked. In addition to defects such as wrinkling, in-plane waviness, tow-slippage and yarn jamming that take place in the single ply forming trials, there are additional challenges and defects associated with multi-layer forming of fabric composites. When reinforcing fabrics are stacked and formed simultaneously, new interacting mechanisms between the layers can bring about flaws such as further yarn jamming, fiber pull-out, and fiber nesting, as well as friction-caused wrinkling; all of which adding more complexity into the deformation analysis of reinforcement plies during forming. Studies have been carried out to understand the ply-ply interaction of woven fabrics. Experimental results have confirmed that a substantial decrease in formability is to be expected when the relative orientation between two neighboring plies increases [62]. This phenomenon is in fact initiated by the friction coefficient between plies. Ten Thije [63] suggested that a quasi-isotropic lay-up of woven fabrics causes severe wrinkling during forming. He attributed this phenomenon to the ‘restriction’ of the inter-ply slip by the stiff fibers in the neighboring layers, in that, loads are transferred between the single plies by interface frictional tractions, and hence wrinkling takes place. Friedrich et al. [64] exhibited that slippage of the individual plies across one another is critical to accommodate complex part geometries. When inter-ply slip is prevented, local fiber micro-buckling (or jamming) may also occur more severalty,  20 resulting in unacceptable aesthetical and mechanical characteristics. Recently Nazemi et al. [65] investigated the interaction mechanisms of textile layers during a forming process. They observed that fabric shearing and the acting normal forces have a great contribution in triggering defects arising from elevated frictional forces between the plies.  2.6.1 Mitigation of wrinkling in thermo-stamping processes The addition of forming constrains e.g., segmented blank holders with variable pressure, clamps, and rollers, to induce membrane tensions along the yarns is a common practice to prevent defects during composite forming processes [66, 67]. Applying tensions at the tow extremities would delay the appearance of wrinkles as well as controlling the fiber orientation [68], thus resulting into manufacture of high quality preforms. A wide range of experimental and numerical studies have concentrated on preforming specific double-curved surfaces and the process parameters such as blank holder force have been investigated. Examples of punch geometries included double dome, prism, square box, and tetrahedral shapes [20, 67-69]. It is essential to optimize the blank holder pressure so that the excessive tensile strains along the yarns do not cause fiber tearing [70]. As mentioned in section 2.5, the shear response of material is related to the in plane membrane tensions applied to the tows, in other words, the shear compliance of the fabric reinforcements is dependent on the membrane tension levels acting along the yarns; nevertheless, it has been shown that implementation of strong coupling between tension and shear in fabric numerical simulations is not necessary to predict the wrinkling phenomena [19, 71]. In fact, considering the coupled behavior of tension and shear has been demonstrated in some cases to be less effective in predicting the distribution of shear angles and deformation regions when applying low blank holder pressures; yet it is shown to strongly affect the fabric force response which can yield residual stresses in the final composite part [71] (i.e., critical for final part design aspects).   Overall, based on the above reviewed works, the author believes that more accurate characterization and implementation of tension-shear coupling into fabric constitutive models is worthwhile as it can lead to (a) new tension-assisted de-wrinkling strategies and (b) assist designers to correctly estimate the mechanical properties of the composite ‘upon’ forming. In  21 fact it has been on the basis of the latter two motivations that three succeeding objectives in section 1.2 were defined and pursued in the subsequent three chapters.   22 Chapter 3: Analysis of a Two-way Tension-shear Coupling in Woven Fabrics Under Combined Loading   3.1 Overview This chapter provides methodology, results, and discussions regarding the analysis of a new two-way tension-shear coupling in woven fabrics. Namely, the existing conflict in the literature as reviewed in section 2.5.2.1, regarding the effect of yarn tension on the fabrics shear response, is addressed herein and resolved through developing a new local force-displacement transformation framework. It will be shown that the analysis of global force and deformation without this transformation has rooted in the above conflict, and hence may not be a good representative of the real tension-shear coupling in woven fabrics. Instead, the local transformed forces and displacements as experienced by the yarns in the region of interest should be employed to characterize the tension-shear interaction. Section 3.2 presents the employed sample woven fabric, the test setup and characterization plan; section 3.4 develops the proposed transformation framework; section 3.4 discusses the obtained experimental and analytical results; and section 3.5 outlines the chapter’s main conclusions.  3.2 Experimental setup 3.2.1 Material Example woven fabric material used in experiments (Figure 3.1) was a comingled polypropylene/glass plain weave, which is composed of 60% (by weight) E-glass reinforcement fibers and 40% Polypropylene (PP) thermoplastic fibers. Specifications and geometrical properties of the material are provided in Table 3.1. It should be noted that the same material was used for conducting also all other experiments in the following chapters throughout the thesis.   23  Figure 3.1   Woven architecture of the tested material.  Table 3.1    Specifications and geometrical properties of the tested PP/glass plain weave Commercial code TWINTEX® TPP60N22P-060 Weight fraction (glass) 60% Area density, g/ m2 745 Yarn linear density, tex 1870 Nominal fiber diameter, μm 18.5 Nominal thickness, mm 1.0~1.5 Nominal yarn spacing, warp,  mm 4.9 Nominal yarn spacing, weft,  mm 5.2 Nominal yarn width, warp, mm 4.2 Nominal yarn width, weft,  mm 4.5  3.2.2 Custom biaxial-picture frame test fixture Shown in Figure 3.2, the employed test fixture embraced eight aluminum arms with equal lengths of 300mm, hinged to each other using tubular bearings. Four servomotors were mounted perpendicular to each arm to apply axial tension along the warp and weft yarns. Another synchronous motor was oriented in the bias direction, by which a tensile force was applied across the diagonally opposing corners of the picture frame and causing the arms to move from a primarily square shape into a rhomboid. The device orientation was horizontal to facilitate the sample mounting and to avoid local misalignments due to mishandling of the material. Besides picture frame testing, the sliding shear mode was also accessible using the device, though it was out of the scope of the present work. Each biaxial and shear motor had a load cell and linear variable differential transformer (LVDT) to monitor the global forces and displacements over time. The load cells were connected to a data acquisition unit, to program  24 the device for a variety of simultaneous loading modes. Moreover, it can be set to run a sequence of loading modes on the sample to investigate, e.g., the effect of loading history on the material response.    As reviewed in Chapter 2, the clamping mechanism of picture frame test is known to be important in obtaining reliable results. Tight plate clamping condition can be responsible for generating local bending of yarns as well as their spurious tensions during the test [36]; in fact it is deemed that different clamping conditions have been one of the main sources of large discrepancy seen in the benchmark investigation [39] in comparing results of different shear fixtures on the same material.  To induce a deformation close to pure shear, following [45], in this work needles were employed in the clamp jaws as described in section 3.2.3.   Figure 3.2    Customized biaxial-picture frame test fixture employed for applying simultaneous and sequential combined loading modes.  3.2.3 Sample shape and clamping A cross shaped sample (Figure 3.2) was mounted on the device for all the experiments. On one hand, because tensile forces were to be applied to the sample, a higher ratio of width-to-length may bring about more homogenous deformation. On the other hand, to avoid misalignments and unintentional errors—among obstacles of having uniform shear deformation in the gauge section— the specimen size should be small enough to provide an easy mounting process. As the fixture’s effective arm length was 300 mm, using 18 yarns per jaw width were found to give most repeatable tests. Each strip of the cross-shape sample was cut to 450 mm in length so that the sample ends could be folded two times, when mounting on the spaces between 30 needles placed in a distance of 4mm from each other in 3 rows (see Figure 3.3a). The latter  25 condition provided a very good gripping as the fiber slippage during the biaxial loading was fully hindered. No extra pressure (e.g., bolts) was applied to the aluminum upper plate. The upper plate’s small weight (50g) was just sufficient to keep the yarns at the same level within the jaw, causing fiber yarns to rotate uniformly together. Two layers of separate fabric cut-offs (rectangular 95 mm by 40 mm) were stacked below and above the needled sample to engage the most effective load distribution of the upper plate weight while preventing it from crushing the yarns. It should be mentioned that in spite of the same number of filaments in both warp and weft directions, due to the slight inherent unbalance in the material (see yarn widths and spacing in Table 3.1), the width of the sample strips in these directions was cut to 87.6mm and 92.3mm, respectively. Although the studied plain weave is nominally manufactured to be balanced along warp and weft, the source of the above difference in the yarn widths is related to the weaving process. That is, warp and weft yarns undergo various trends of tension and bending while being interweaved [5]. The statistical significance of such inherent irregularities in the response of fabrics has been reported, e.g., in [71, 72]     (a) (b) Figure 3.3    (a) Using needles instead of the conventional plate-bolts clamping to allow yarns rotate freely without local bending, (b) the resulting uniform shear deformation within the sample (the upper plates in these images have been removed after the test to better visualize the effect of the needles in building homogenous deformation in the jaw’s neighborhood.)  3.2.4 Loading modes and friction consideration Figure 3.4 schematically shows three fundamental deformation modes induced by the biaxial-shear test fixture; namely the picture frame, biaxial tension, and combined loading modes. The displacement rate for the biaxial and shear motors was 4.5 and 2.6 mm/min (i.e., quasi-static), respectively. Three replications were performed for each experiment and force-displacement  26 data were recorded. To account for mechanical friction in the fixture, prior to actual testing, the friction force was recorded without the material mounted. The repeatability of this effect was observed through three replications and an average value was regarded as the effective friction force in the device. This force was then subtracted from the output curves for each subsequent experiment with the material mounted. The friction effect between the fabric and needles was neglected.     (a) (b)   (c) (d)  Figure 3.4    Different deformation mode configurations: (a) the original state, (b) picture frame mode, (c) biaxial tensile loading, (d) simultaneous biaxial-shear loading. Note that in (a), (b) and (c), the local fabric (material covariant) coordinate system (f1-f2) is aligned with the fixture covariant coordinate system (1-2); however, f1 and f2 directions are not parallel to 1 and 2 under the simultaneous mode in (d).  3.2.5 Characterization plan The experimental characterization was divided into two categories, the first of which was the picture frame testing with different yarn pre-tension levels. The second category was  27 comprised of equi-biaxial tensile loading and a simultaneous biaxial-shear loading. Assessment of the effect of tension on the shear response of the plain weave was achieved by comparing the results of the test pairs under the first category. On the other hand, comparing the test results within the second category could disclose the influence of shear on the tensile behavior of the fabric. For both categories, the global force and displacement measurements needed to be correctly transformed into the fabric (local) coordinate. Such a transformation, however, must accompany the required amendments pertinent to each given test setup (in the present case, Figure 3.2). More specifically, one may notice from Figure 3.2 that in the given test setup, the global tensile and shear motor forces are coupled through the kinematics of the device mechanism (a notion that has not been addressed in the previous reports on local characterization of woven fabrics using similar setups). Hence, in transforming the measured forces to local values, this global force coupling was taken into account as detailed in section 3.3.  3.3 Analytical transformation of coupled global test measurements to net shear and longitudinal local values Characterization of woven fabrics can be conducted by transforming the global measured data to normalized local force-displacement (or stress-strain) response within the region of interest of sample. An analytical approach is presented here to derive explicit expressions for local stresses and strains based on the global forces and displacements. First, a geometrical analysis is performed to find the relationship between the deformation output parameters (yarn longitudinal strain and shear angle) and pertinent inputs such as global biaxial and shear displacement (𝑢1, 𝑢2, and 𝑢𝑠). Figure 3.4 illustrates these three independent global deformation parameters. As depicted in Figure 3.4, the deformation of specimens under combined loading is most complicated in which the angle between yarns in the central gauge section is not the same as the angle between the arms of picture frame. It should be noted that tension-shear combined loading can be conducted under a simultaneous or a sequential regime (e.g., first pre-tension and then shear). The subsequent deformation analysis of the cross-shape sample is followed under simultaneous regime, through which general expressions can be obtained and then applied to other simpler modes including the sequential loading.   28 In the first step of the solution, the angle of the rhombus-shape fixture at a given time, which is dependent on the shear displacement (𝑢𝑠), should be obtained. According to Figure 3.5, this angle (2∅) can be defined in terms of 𝑢𝑠 as [53]:    2∅ = 2 arccos (𝑢𝑠𝐿+1√2)                                                             (3.1)  Where, L is the length of fixture arms. If the biaxial motors are off while the shear motor is on, a pure picture frame test is conducted; thus the warp and weft yarns remain theoretically parallel to the arms. The shear angle of the sample over time can be determined under the picture frame mode by: 𝜃𝑃𝐹 = 90 − 2∅        (3.2)   Figure 3.5    Shear deformation of the picture frame fixture.  On the other hand, if both the biaxial and shear motors are turned on simultaneously, the angle between the warp and weft yarns will be different from that of the fixture arms, as shown in Figures 3.4d and 3.6. Accordingly, in the picture frame and pure biaxial tensile tests, the 𝑓1 − 29 𝑓2 local coordinate system remains parallel to the fixture coordinate system 1-2, while in the simultaneous loading, the local fabric coordinate bases do not remain parallel to the bases of fixture coordinate (Figure 3.4d). Figure 3.6 demonstrates the position of a yarn in direction 𝑓1 under simultaneous loading, which leads to the angle 𝛼1 between the yarn and the arm in the corresponding direction due to loading motor 1. To calculate this angle with respect to the dimensions of fixture and the input displacement parameter (𝑢1), the following trigonometric equations are employed:  (𝐿1′2)2 = 𝑢12 + (𝐿2)2 − 2𝑢1𝐿cos (90 + 2∅) (3.3) sin 𝛼1𝑢1=sin (90 + 2∅)𝐿1′  (3.4) where 𝐿1′  corresponds to the instantaneous length of yarn under simultaneous loading. By substituting Equation 3.3 into Equation 3.4 and rearranging, we obtain:  𝛼1 = arcsin [   cos (2∅)𝑢12√𝑢12 + (𝐿2)2 + 2 ∗ 𝑢1 ∗ 𝐿 ∗ sin (2∅)]                (3.5) Similarly, 𝐿2′  and 𝛼2 arising from the axial tension in direction-2, can be obtained as:  (𝐿2′2)2 = 𝑢22 + (𝐿2)2 − 2 ∗ 𝑢1 ∗ 𝐿 ∗ cos (90 + 2∅) (3.6) 𝛼2 = arcsin [   cos (2∅)𝑢22√𝑢22 + (𝐿2)2 + 2 ∗ 𝑢2 ∗ 𝐿 ∗ sin (2∅)]    (3.7) Consequently, the net shear angle is calculated as:  𝜃 = 90 − 2∅ − 𝛼1 − 𝛼2 (3.8)  30 The difference between 𝐿1′  or 𝐿2′  and L represents the increase in the yarn length in direction 1 or 2. Thus, assuming infinitesimal deformation in the fibers directions, given their high normal moduli, the strain along the fabric principal directions is obtained by:  𝜀1 =𝐿1′ − 𝐿𝐿 (3.9) 𝜀2 =𝐿2′ − 𝐿𝐿 (3.10)   Figure 3.6    The angle α1 between the yarn in direction f1 and the fixture arm in direction 1, due to the tensile loading of motors in direction 1. Note that 1 and 2 are the bases of fixture covariant coordinate system, and f1 and f2 the bases of the material covariant (local) coordinate system.  A noteworthy point regarding the deformation of sample under simultaneous loading is that the same displacement rate of biaxial motors (𝑢1 = 𝑢2) causes 𝛼1 and 𝛼2 to be the same according to Equations 3.5 and 3.7, as was also observed in the test replications. Accordingly, 𝛼1 and 𝛼2 are hereafter referred to as 𝛼.  The next step of solution is to develop expressions for local stresses in terms of the applied global forces and displacements. Normalized forces (force per length) are typically studied instead of stresses for dry fabrics [33], as also employed in this study. As mentioned in section 3.2.3, a slight imbalance was noticed in the tested fabric material (Table 3.1), hypothetically  31 causing differences in the required forces in warp and weft directions for the same amount of extension. However, monitoring the load history of both biaxial motors showed less than 10% for such difference. Consequently, the average value of 𝑁1 and 𝑁2 was reassigned as 𝑁𝑏 for both directions in subsequent calculations. Also, to obtain the normalized force values, the average width of warp and weft strips were used.  The global force from the shear motor can cause the specimen to experience shear loading, whereas the global pulling forces from the biaxial motors, as a result of being always perpendicular to the arms in the fixture mechanism, produce two components. One component induces extra force in addition to the shear motor to apply picture frame shear deformation and the other one results in pure tension in the direction of arms. In other words, in the given setup the global force of the biaxial motors (𝑁1 and 𝑁2) and that of the shear motor (𝑁3) are not independent of each other. Figure 3.7 represents the coupling between these forces. The normalized resultant shear force of the shear motor (𝑁3𝑠) can be found based on its global value, as shown in Eq. 11, where 𝑤 refers to the clamping width (here 90 mm). Furthermore, Equations 3.12 and 3.13 express the normalized longitudinal and shear force components of the biaxial motors. It is noted that there are two terms of sin 2∅ in Equation 3.13, one of which is incorporated to transfer 𝑁𝑏 to the direction of yarn. The second one comes from considering the intra-yarn shear which has been experimentally and numerically proven as one of the contributing shear deformation mechanisms in fabrics [34, 73], next to the inter-yarn rotation. Employing needle-type clamps freely allows the filaments relative movement (i.e., intra-yarn shear), causing a uniform deformation close to the jaws (i.e., with the yarns edge remaining parallel to the arm as shown in Figure 3.7; this point will also be experimentally elaborated on in section 3.4.1). Therefore, owing to the rotation of yarns’ cross sections via intra-yarn shear, 𝑁𝑏𝑙 is not perpendicular to the jaw. Subsequently, instead of jaw width, its projection should be used to calculate the normalized longitudinal force component of the biaxial motors.  𝑁3𝑠 =𝑁32𝑤𝑐𝑜𝑠 ∅ (3.11) 𝑁𝑏𝑠 = 𝑁𝑏𝑤𝑡𝑎𝑛 2∅ (3.12)  32 𝑁𝑏𝑙 =𝑁𝑏𝑤𝑠𝑖𝑛22∅ (3.13)  Experimental evidence of the above coupling between global forces of biaxial and shear motors will be provided in section 3.4.2. The main outcome drawn from Figure 3.7 is that the net shear force applied to the fabric sample should be obtained by:  𝐹𝑠 = 𝑁3𝑠 + 𝑁𝑏𝑠     (3.14)   Figure 3.7    Decomposition of the global external forces of the biaxial and shear motors into their normalized shear and longitudinal components imposed on the fixture frame (i.e., in 1-2 directions), in order to measure the net shear force (Nbs+N3s), denoting a kinematic coupling between the global forces due the mechanism of the combined loading fixture. The normalized force vectors are shown as dashed lines and are related to the external motor forces via Eqs. 3.11-13).  Next, given the inherent coupling between global biaxial and picture frame deformations, it is essential to reemphasize that the angle between yarns during combined loading does not follow the frame shear angle (Figure 3.8). As a result, the obtained net normalized forces 𝑁𝑏𝑙 & 𝐹𝑠 in Figure 3.7 cannot be deemed as in the actual local fabric direction (i.e., parallel to yarns) in the middle region of interest. For the picture frame testing with small pre-tension, however, the yarns nearly remain parallel to the arms during shearing. Hence, for the latter tests, the normalized local tensile force applied to yarns (𝑁𝑙) may be regarded the same as the  33 normalized global force component of the biaxial motors (𝑁𝑏𝑙 = 𝑁𝑙); and similarly, the normalized local tensile shear force imposed on the yarns (𝑁𝑠) may be equated to the normalized global net shear force on the sample (𝐹𝑠 = 𝑁3𝑠).   Figure 3.8    Schematic of the normalized net global forces and the resolved normalized local forces along yarns (Ns and Nl) within the inner region of interest. Note that Fs and Nbl are parallel to the fixture arms (directions 1 and 2), whereas Ns and N l are aligned with the yarn directions (f1 and f2).  For the simultaneous loading, to complete the transformation analysis from the frame of non-orthogonal fixture coordinate to the frame of non-orthogonal fabric coordinate, an approach analogous to [27] was implemented. Namely, Figure 3.8 displays a rhombic element within the sample region of interest, in which the normalized global forces are applied, and another inside rhomboid whose sides are parallel to the warp and weft directions. To acquire the relationships for the normalized local forces, a triangular material element was extracted from Figure 3.8 and shown in Figure 3.9. Considering force equilibrium conditions on this element, Equations. 3.15 and 3.16 were arbitrarily formulated in the directions 1’ and 2’—perpendicular to the original directions 1 and 2, respectively, which were merely chosen to attain more straightforward formulation. The terms sin (2∅) and sin (2∅ + 2𝛼) stem from the fact that 𝑁𝑏𝑙 and 𝑁𝑙, respectively, are not perpendicular to the sides of the triangle. Also, sin𝛼sin(2∅+𝛼) and sin2∅sin(2∅+𝛼) are utilized to consider different length of material element edges in Figure 3.9, on which the normalized forces are applied.   34 Equilibrium in Direction 1’: [𝑁𝑏𝑙 × sin 2∅] ×sin𝛼sin(2∅+𝛼)× sin 2∅ + 𝐹𝑠 × sin 2∅ =  𝑁𝑠 ×sin2∅sin (2∅+𝛼)× sin(2∅ + 𝛼) − [𝑁𝑙 × sin (2∅ + 2𝛼)] ×sin2∅sin(2∅+𝛼)× sin 𝛼                              (3.15)                                                                        Equilibrium in Direction 2’: [𝑁𝑏𝑙 × sin 2∅] × sin  2∅ + 𝐹𝑠 ×sin𝛼sin(2∅+𝛼)× sin 2∅ =  −𝑁𝑠 ×sin2∅sin(2∅+𝛼)× sin α + [𝑁𝑙 × sin(2∅ + 2𝛼)] ×sin2∅sin(2∅+𝛼)× sin (2∅ + 𝛼)                              (3.16)                                                                             Finally, rearranging and solving Eqs. 3.15 and 3.16, the normalized local longitudinal and shear forces were calculated as in Eqs. 3.17 and 3.18. These equations, in combination with Eqs. 3.11-14, give the on-axis net normalized forces in the most general form as a function of global forces applied to the balanced woven fabric. As a check point, by setting the value of 2∅ = 90° as well as 𝛼=0° in Equation 3.17 and 𝛼=0 in Eq. 3.18, relationships for a conventional biaxial and pure picture frame mode can be obtained, respectively.  𝑁𝑙 =sin(2∅+𝛼)sin(2∅+2𝛼)(sin2(2∅+𝛼)−sin2 𝛼)[𝑁𝑏𝑙(sin 2∅  sin2 𝛼sin(2∅+𝛼)+ 𝑠𝑖𝑛 2∅ sin (2∅ + 𝛼)) + 2𝐹𝑠sin𝛼]                         (3.17) 𝑁𝑠 =sin(2∅+𝛼)sin2(2∅+𝛼)−sin2 𝛼[𝑁𝑏𝑙 sin α (1 + sin 2∅)+ 𝐹𝑠 (sin(2∅ + 𝛼) +sin2 𝛼sin(2∅+𝛼))]       (3.18)                                        Figure 3.9    Free body diagram of the normalized net global and local forces on a triangular material element within the fabric based on Figure 3.8.   35 3.4 Results and discussion 3.4.1 Influence of fabric tension on shear response Figure 3.10a demonstrates the normalized global force of the shear motor versus shear angle of the test fabric at two different pre-tension levels (0.8 and 3.1 N/mm). The global results in this figure are in full agreement with the results of Launay et al. (Figure 15 of [27]). Namely, the observed significant increase in the magnitude of global force of picture frame shear motor at initial stages of the loading is an evidence of the yarn tension effect on the shear response of the fabric. Despite the substantial deviation between the two curves with different levels of pre-tension (0.8 and 3.1 N/mm) in the small shear angles, they become closer to one another in the larger shear angle region. This convergence may mistakenly imply that the effect of tension on the fabric shear behaviour fades at the higher forming angles. Even in the study [27], the shear force at some low pre-tension levels exceeded that of higher pre-tension. On the other hand, the study conducted by Nezami et al. [45] showed a more significant deviation between the shear responses of tensioned samples at higher shear angles, suggesting a higher coupling factor at high forming angles.     (a) (b) Figure 3.10    (a) Comparison between normalized global shear forces resulting from the shear motor for two picture frame tests with different pre-tension levels, and (b) the same comparison using the normalized net local shear force applied to the fabric. Notice the significance of considering the global shear force component resulting from the biaxial motors (coupling effect) in the resulting trends between the two curves with 0.8 and 3.1 N/mm pre-tensions, especially at higher shear angles. More specifically, by performing the force analysis in the local coordinate, the effect of pre-tension is consistent (the distance between the curves remain consistent across the fabric shear angles). For comparison purposes, the pure shear (without pre-tension) data has been added from [71] which used an independent shear frame device with a vertical test lay-up with minimum friction effect.  This conflict may be rooted in two points. The first and main point is that neither of the past studies performed the coupling characterization in the local fabric coordinate (the effect to be  36 further elucidated in the next section). The second point is that Launay et al. [27] applied pre-tension by fixing the yarns at a given displacement; hence the tensile force level varied over shear loading, whereas the device in [45] employed pneumatic cylinders to keep the pre-tension force constant. The boundary condition of fabric samples in the current study was also displacement-control in which the displacement could be controlled while the force varies. Figure 3.11 depicts the measured force of the biaxial motors against time in the picture frame test when a 3.1 N/mm pre-tension level (i.e., initial force per sample width) was applied, corresponding to an initial yarn displacement of ~3 mm from each side (total of 6 mm). In fact, this sequential experiment was comprised of three stages, the first of which corresponded to turning on the biaxial motors to reach a certain level of pre-tension. The second stage referred to the interval between turning off the biaxial motors and turning on the shear motor (relaxation/settling time), and at the third stage the picture frame/shear loading was applied. The allocated time span between applying the pre-tension and starting the shear test was to perform the experiment in a fashion comparable to practice. That is, during the stamping process of fabrics, normally there is a delay between the clamping of the fabric via blank holders and the initiation of draping. By performing the test in a sequential manner, the effect of viscoelasticity—the reason of reduction in force value in the second stage in Figure 3. 11 could be accurately identified and removed from the third stage so that the perceived quasi-static behavior under the shear mode regime became intact.   Recalling the third stage of response in Figure 3.11, it is noted that that the global biaxial force illustrates a reduction in its magnitude. This can be justified in that, by applying shear deformation, a non-zero angle is created between the yarn direction and the corresponding pulling direction of the biaxial motor, resulting in a decline in the stiffness against fiber pulling in that direction. For the same reason, during the shear test, the pre-tension effect abates, and the global force response curves get closer at higher shear deformation ranges (Figure 3.10a).   37  Figure 3.11    Variation of the global force of biaxial motors during picture frame test with 3.1 N/mm (total of 280 N) pre-tension; from the origin to point A (stage 1): applying pre-tension up to 380 N; from point A to point B (stage 2): the relaxation of the sample and causing reduction in the force from 380 N to 280 N; after point B (stage 3): applying the shear deformation.  Remark 2: Another notable observation was that by performing additional picture frame tests with a strictly clamped boundary, the effect of clamping condition was confirmed. Namely, with full-plate clamping the third stage of the load history did not mimic the same behavior as in Figure 3.11. In some cases, a decreasing trend was followed by an increasing trend, or vice versa; and in some other repeats, the load in both directions continuously rose. Similar random (uncontrollable) behavior using strict clamping condition was reported in [27]. In a following study, some techniques such as accurately positioning the sample and using aluminum plates with silicon glue were suggested to reduce the level of the resultant tension within yarns during picture frame tests with clamped boundary conditions [28]. However, there was still non-homogenous deformations close the clamp regions, causing error in the characterization data. On the contrary, using needles in the fixture jaws highly assisted in inducing a homogenous deformation and consistent test results (Figure 3.3b). Moreover, it was noticed that using needle clamps, acceptable test repeatability can be attained even without pre-conditioning of the fabric (as seen from the small range of error bars in Figure 3.10, and also previously reported in [45]). Pre-conditioning of fabrics is normally employed to get repeatable results between tests within a laboratory and among laboratories [39]. The aforementioned observation in the present study, though on one type of fabric, suggests that modifying boundary conditions of tooling to needle clamping may rectify the need for pre-conditioning. While the precise ‘statistical’ effect of boundary condition on forming repeatability of different types of fabrics remains the subject of a future study via ‘hypothesis testing’ tools, it is believed that the main reason for this effect is as follows. Using needle clamps, the angle of intra-yarn  38 shear as well as the fabric trellising angle is virtually the same as that of shear frame; while using full clamps, the shear angle within yarns can be as high as 30% less than the shear angel of the fabric [31].   3.4.2 Assessment of the coupling trend using the local net force and displacement values In the previous section, the trend of tensile biaxial forces confirmed that the global tension level declines during the shear frame test, which was a convincing explanation of the convergence between the response curves in Figure 3.10a at higher shear angles. However, it is more accurate to assess the normalized local tensile force in the fabric coordinate (𝑁𝑙), rather than the global force. It cannot be readily presumed that the axial force level also diminishes in the fabric level as the shear angle increases. To assess this effect and reveal the yarn’s axial force variation, the normalized local tensile force was plotted using Eq. 13, and shown in Figure 3.12a. According to this figure, the yarns pertinently experience lower tensile forces as the shear angle proceeds.    (a) (b) Figure 3.12    Normalized global force components of the biaxial motors during shear frame testing with 3.1 N/mm pre-tension; (a) the longitudinal (tensile) component, and (b) the shear component. Note that as outlined in section 3.3, during the analysis Nl is assumed to be almost equal to Nbl in the shear tests with a small yarn pre-tension level.  The main underlying point helping to eliminate the conflict outlined in Chapter 2 and section 3.4.1 is that the comparison between the global shear loads measured by the shear motor load cell in two tests with distinct pre-tension levels is not a good representation of the coupling effect of yarn tension on fabric shear. As substantiated in the analytical part (Section 3.3), the biaxial motors due to their alignment relative to the frame arms not only exert fiber elongation,  39 but also an extra shear force. Consequently, an accurate collation on the coupling effect was accomplished by comparing the normalized local shear force applied to the yarns (𝑁𝑠). To obtain the variation of this force, first the contributed shear component of the biaxial load was obtained via Eq. 3.12 and results were shown in Figure 3.12b. Comparison of Figures 3.12a and b illustrates that in spite of the reduction in the longitudinal force component, the shear force component increases at the frame coordinate, owing to their dependence on the angle between the arms. Finally, the normalized local (fabric) net shear force can be obtained using Eq. 18 (results shown in Figure 3.10b). In fact, this figure discloses that the deviation between the two curves corresponding to pre-tensioned samples is maintained by the material and applying yarn tension increases the shear rigidity of the fabric at both low and high shear angles. This macro-level behavior may be explained at meso-level by the fact that the shear resistance of woven fabrics partly results from the friction between yarns at cross-over points [27], which can be a function of contact force at cross-over points, which in turn can be a function of applied tension and yarn de-crimping.   3.4.3 Simultaneous loading mode and the influence of shear on yarns tensile behavior Under a simultaneous biaxial extension-picture frame loading mode, the presence of kinematic coupling between the global axial and shear forces was first needed to be confirmed, as it was a cornerstone of the analytical framework in section 3.3. Figure 3.13a reveals that the required global force of the shear motor under this test is negative (opposite to direction 3 in Figure 3.4a), meaning that to induce shear deformation in the frame diagonal direction, the only external force responsible to supply the necessary positive net load is not the shear component from the biaxial motors. In other words, it confirms that biaxial motors contribute to shear deformation for the current combined loading setup. To further scrutinize this observation, an extra experiment was undertaken in which the shear motor was turned off after imposing 10 degrees of shear and then detached from the device, resulting in a complete degree of freedom in the shear direction 3 in Figure 3.4a. It should be mentioned that during this trial the fixture and the sample did not come back to their original state, owing to the existing friction. Thereafter, the biaxial motors were turned on to start supplying tension. It was observed that the angle between the arms of the picture frame declined from the initial 80° (10° of shear) to 70° (20° of shear); hence, reconfirming that the biaxial motors via the kinematic coupling  40 within the setups can help to apply a fraction of the shear on the material under simultaneous loading modes.     (a) (b) Figure 3.13    (a) Change in the required load of the shear motor over time in the simultaneous loading test (showing the kinematic coupling effect between the biaxial and shear motors), and (b) the global force of the biaxial motors under this mode, which reaches to a considerably high load magnitude.  Under this loading mode, however, based on the geometrical analysis in section 3.3 (Figure 3.8) the local angle between the warp and weft yarns does not follow the frame angle. According to Eq. 8, this deviation for a symmetric loading condition and balanced fabric can be calculated over deformation through Eqs. 3.3-7 and measured data of the global displacements. The result has been plotted in Figure 3.14. Next to the analytical solution, the local angle between adjacent yarns was measured by employing image analysis (taking photos at the end of each test), confirming the validity of the analytical solution for estimating α (error less than 2%). Figure 3.14 illustrates that this deviation between the rhomboid sample shape and the rhomboid fixture is nonlinear and it becomes larger at higher deformation ranges. At the end of the simultaneous test, the angle in the fabric was 25° while the angle of the main fixture was 30.8°.   41  Figure 3.14    Deviation of the shear angle within the sample under simultaneous loading from the shear angle of the picture frame fixture based on the analytical procedure. The deviation between the curve and the dashed line represents the difference between the shear angle of the frame and fabric (2α).  Another difference between the simultaneous loading and the earlier shear loading tests (e.g., Figure 3.11) was that the force magnitude of biaxial motors reached as high as 4500 N (50 N/mm), as shown in Figure 3.13b. Therefore, both 𝑁𝑏𝑠 and 𝑁𝑏𝑙, the resulting components of this force, also increased considerably. Such high magnitude of biaxial load, and in turn its shear component, has overweighed the negative shear force arising from the shear motor, causing a positive net shear force imposed on the sample (𝐹𝑠) under simultaneous loading as seen in Figure 3.15a. After 𝑁𝑏𝑙 and 𝐹𝑠 were obtained over the loading time, Equation 3.18 was employed to determine the normalized local shear force (Figure 3.15b). Substantial rise in the magnitude of the fabric shear force is noted, e.g., when compared to the low force magnitude in the picture frame test in Figure 3.10b. Such difference is mainly due to a considerably higher global tension level (up to 50 N/mm) induced in the simultaneous mode. The theoretical conclusion from this test is in agreement with the result of section 3.4.1 regarding the positive effect of yarns tension on the shear rigidity of fabric reinforcement.     42   (a) (b) Figure 3.15    (a) The global net normalized shear force in the fixture, and (b) the local normalized net shear force in the fabric under simultaneous loading mode; the difference between the magnitudes of the two curves roots in the fact that the difference between the magnitudes of the two curves roots in the fact that the difference between the angle of yarns and the angle of arms is significant under simultaneous loading.  Another practical finding in this section was achieved by drawing a comparison between the normalized local longitudinal force of a pure biaxial experiment and that of the simultaneous mode. Figure 3.16 illustrates the normalized local tensile force in the direction of yarns against longitudinal strain of the fabric under the two modes. Although both curves show two distinct deformation regimes, including straightening and stretching of yarns, the significant difference between their load magnitudes suggest the effect of fabric shear on its tensile behaviour. In fact, from Figure 3.16 a longer straightening region and a lower slope in the stretching region are seen when the fabric undergoes simultaneous tension-shear loading. This may suggest that designers in defining the final mechanical properties of the part should take into account the two-way tension-shearing coupling imbedded during the stamping, especially at tight curvatures.       43  Figure 3.16    Comparison of the constitutive behavior of the fabric’s tensile behavior under biaxial and simultaneous loading modes, implying the effect of fabric shear on its tensile behavior. Arrows show the estimated straightening and stretching regimes of yarns under each mode. Results show that the fabric shearing lessens its tensile stiffness (as opposed to the reverse effect where the fabric tension, significantly increases its shear rigidity; also compare with Figure 3.10b).  More specifically, based on the obtained results, shear loading causes a more compliant tensile behavior of the woven fabric reinforcement in the yarn directions. To further explore the meso-level mechanisms leading to this macro-level observation, future numerical studies are worthwhile. Based on the fact that the shear has affected both the straightening and stretching response of the yarns (Figure 3.16), one hypothesis would be that yarns experience more pronounced de-crimping at cross-over points under pure biaxial loading. The level of crimping is one of the effective factors affecting both the straightening and stretching responses of fabrics. Generally, the higher the crimping magnitude, the more compliant the tensile behavior of the fabric. Warp and weft yarns inherently have interaction with each other due to the interlaced fiber architecture in woven fabrics. The interaction between fibers implies that applying deformation on either yarn direction could cause a crimping change in the other direction, similar to the network of curved beams supporting one another [74]. The higher interaction between yarns would bring about a stiffer material medium. Several other factors, including the contact area at the intersection points, weaving type, and yarn spacing, can also have an influence on the extent of coupling between yarns. In pure biaxial loading, the contact area is a square whose length is the width of yarns. When shear loading is applied to the fabric, a non-orthogonal angle between yarns is formed and the contact area becomes rhombus and smaller than that of the biaxial model (Figure 3.17). This larger contact area in the fabric under biaxial loading would be a possible responsible source to yield more interactive fiber network during deformation, a greater decrease in yarn crimping, and, hence, a stiffer macro-level  44 tensile material behavior. Another potential explanation regarding the more compliant response of woven fabrics against tensile loading while sheared can be sought according to the numerical study [73]. That numerical simulation demonstrated that the crimping of yarns increases during pure shear loading. Such increase in the crimping of yarns can result in a more compliant tensile behavior of the fabric. In brief, less interaction between yarns due to decrease in contact area as well as the increased amplitude of out-of-plane waviness of yarns may be regarded as two potential sources for the effect of fabric shear on yarns tensile response in woven fabrics.   Figure 3.17    Idealized change in the contact area at crossover points during (a) biaxial and (b) shear deformation; Notice that the right side rhomboid area is smaller, assuming identical yarn width in both cases.  Remark 3:  To accurately compare the tensile behavior of fabrics under different deformation configurations, the elongation rate must also be checked, as it has been well-established that polymer composites are rate/time-dependent materials [75], even in the dry form as was seen in Figure 3.11 and earlier noted even for a pure fiberglass dry reinforcement [76]. These composites in general behave stiffer under higher deformation rates. On the other hand, based on the obtained geometrical equations (Equations 3.3 and 3.6), the elongation of tows under the simultaneous loading is not exactly the same as that of the biaxial motors (𝑢𝑏) at a given time. Hence, the deformation rates may not be exactly identical in the conducted tests, though they are all in quasi-static regime as specified in Section 3.2. The fiber-direction elongation over time for both biaxial and simultaneous loading experiments is shown in Figure 3.18. According to this figure, the elongation in the first stages of loading is almost identical for both modes, whereas there is a deviation between them in the later stages of loading. The slopes at each point of these curves were furthermore calculated and results confirmed that the rate of  45 elongation in the conducted biaxial test remain constant (about 4.5 mm/min). On the other hand, the initial strain rate for the simultaneous loading mode was about 4.5 mm/min and diminished to about 2.9 mm/min as the fabric shearing proceeded. However, there is little probability that the dissimilarity seen between the two force responses in Figure 3.16 is due to this minor strain rate difference in Figure 3.18. Nevertheless, to decouple the effect of deformation rate and the loading mode on the tension-shear coupling characterization of fabrics, series of new tests with more sophisticated experimental designs are worthwhile in future studies.    Figure 3.18    Comparison between the elongation of fiber yarns during biaxial and simultaneous loading modes.  3.4.4 A comparison of the two coupling effects Here it was of interest to compare the effect of the yarn tensions on the shear behaviour of the fabric versus the reverse (i.e., the effect of the fabric shear on yarns tensile behaviour). To this end, following a similar idea to [45], two types of coupling factors were defined, using the normalized local forces. In the first type, using Figures 3.10a and 3.15b, the normalized local shear force in the simultaneous loading was divided by that of pure shear. For the second factor, utilizing Figure 3.16 data, the normalized local tensile force in the simultaneous mode was divided to that of the biaxial loading. The variation of these two coupling factors against the corresponding deformation parameter is shown in Figure 3.19. Comparing Figures 3.19a and b, it is evident that the effect of tension on shear on the fabric behavior is more dominant than that of the reverse; albeit neither effect may be neglected for precise constitutive modeling of woven fabrics for numerical simulations. Another noteworthy point is that by magnifying the  46 first region of Figure 3.19a, it is observed that at around 7 degrees of shear, the coupling factor starts to rise significantly. By making a correlation between the shear angle and longitudinal strain of yarns under simultaneous loading, it was found that this degree of shear corresponds to the initiation of yarn stretching (~2.7% elongation), inferring that different pre-tension levels induce different significance levels of coupling through different mechanisms. To elaborate on, applying pre-tension to certain extent within the yarn de-crimping region would only increase the contact force at crossovers, which in turn raises the fabric shear resistance moderately. If the applied pre-tension level goes beyond the de-crimping region, the filaments become more twisted and the yarn flattens (crushing effect [27, 50]), hence increasing the fabric shear stiffness much more notably.     (a) (b) Figure 3.19    Comparison of two coupling effects: (a) the normalized local net shear force in the simultaneous loading divided by that of pure shear, and (b) the normalized local tensile force in the simultaneous mode divided by that of the biaxial load. From the magnitudes of the two curves, notice that the tension-on-shear coupling effect in the fabric is much more dominant than the shear-on-tension coupling effect. However, a reduction of yarn tensile behaviour in the range of 50% (according to Figure 3.19b) under simultaneous loading may not be ignored, especially for structural analysis/design of the final formed part.  3.5 Summary of findings This chapter undertook an investigation into the interaction between tension and shear responses of woven fabrics. A new experimental device was used to conduct biaxial, picture frame with pre-tensions and simultaneous tension-shear tests. Advantages of using needles over fully clamped boundary condition were verified through real-time monitoring of the yarns tensile load. In addition, it was shown that the analysis of global force results cannot provide a reliable characterization of the tension-shear coupling, given that the global measured parameters are inter-dependent due to a kinematic coupling in the device mechanism, and  47 hence not a true representative of local forces as experienced by the woven yarns. An analytical approach was presented to transform the global force-displacement measurements to the fabric local coordinates while considering the aforementioned kinematic coupling and its effect on the net shear force and deformation. Comparison between the picture-frame experiments with two different pre-tension levels pointed to a consistent impact of in-plane tension on the shear resistance of the fabric at both low and high shear angles. This observation stands on the hypothesis that imposing yarn tension increases the compression contact forces at cross-over points as well as between filaments, and hence the friction forces, which in turn increases the fabric shear rigidity. Moreover, analyzing local force responses between the biaxial and simultaneous loading tests suggested that the less underlying interaction between non-orthogonal yarns due to the fabric shearing is perhaps the cause of a more compliant tensile behavior under simultaneous loading mode. However, under simultaneous loading, the shear resistance of the fabric amplified notably. Finally, it was perceived that the fabric even in the dry form at room temperature can show a sizable visco-elastic behavior which, in addition to the studied two-way tension-shear coupling effect, may be taken into account in future implementation of fabric constitutive models.     48 Chapter 4: Characterization of Wrinkling and De-wrinkling Behavior of Woven Fabrics Using a Multi-step Biaxial Bias Extension Test   4.1 Overview Chapter 3 investigated the relationship between the shear response and membrane stresses in woven fabrics by taking into account the changes in yarns configuration while shearing under the effect of biaxial forces. Such interaction needs to be carefully considered in fabric material models so that the onset of wrinkling and optimum blank holding conditions can be predicted; hence the tension-shear coupling would be a basis for the following wrinkling/de-wrinkling characterization work presented in chapters 4 and 5.  The current chapter focuses on an enhanced understanding of wrinkling and de-wrinkling behavior of woven fabrics using a new 2D characterization technique, namely a multi-step biaxial bias extension (MBBE) test. Employing a 3D scanning technique, the underlying deformation and the wrinkling/de-wrinkling force responses of the fabric is investigated. Furthermore, the influence of fabric rigidity, yarn contact forces, and tow slippage will be highlighted in devising de-wrinkling strategies, all of which resulting into some potential practical design considerations for future 3D forming applications. Section 4.2 presents the experimental setup and methodology. The observed deformation mechanisms will be elaborated in section 4.3 followed by results and discussion in section 4.4. Finally, the summary of findings from the chapter will be presented in section 4.5.  4.2 Methodology 4.2.1 Test setup Shown in Figure 4.1a, experiments were conducted using the same custom designed biaxial fixture presented in Chapter 3. The device consists of four aluminum bars connected using tubular bearings while positioned orthogonally. Four servomotors are installed perpendicular to the arms along with their corresponding jaws in order to apply global axial displacement to the test material (Figure 4.1b). The biaxial motors are equipped with load-cells and linear variable differential transformers (LVDT) to monitor forces and displacements over time. Fixture arms can be moved apart by a test speed of 4mm/min in all four directions. The grips  49 holding the material include vertical needles, between which the test sample is held with no slippage. The loading width was chosen as 70 mm for both transverse and longitudinal clamps. As shown in Figure 4.1b, the specimens were cut with an aspect ratio of 3.85 where L=270 mm and W=70 mm are the length and width of the sample, respectively. A white base plate was placed underneath the sample to facilitate the 3D scanning process and prevent scanning undesirable objects around the sample. A minimum of three replications were performed for all tests with the maximum error range being 5-7 %.   (a) (b) Figure 4.1    (a) The custom biaxial fixture used for the multi-step biaxial bias extension tests; (b) Four servomotors mounted on the arms shear the biaxial fabric specimen in the bias (originally mounted at ±45°) direction.  4.2.2 Multi-step biaxial bias extension (MBBE) test method Figure 4.2 illustrates the proposed multi-step biaxial bias extension test procedure. Namely, a wrinkle via the longitudinal (x-direction) loading is generated while the transverse edges of the cross-shape fabric are free (as if performing a conventional uniaxial bias extension test where the wrinkling may initiate in early stages of shearing far before the locking, especially for reinforcements with higher yarn bending stiffness [19] which can be experimentally mimicked e.g. by partial pre-consolidation of the fabric). After generating the first (low-level) wrinkle, the motors in the longitudinal direction (x-direction) are stopped and the transverse edges of the fabric are clamped to the jaws on the y-direction. Subsequently, the transverse motors are turned on and the previously formed wrinkle is smoothed-out (de-wrinkles) by extending the fabric in the transverse direction (Stage A in the diagram of Figure 4.2). Once the wrinkle is flattened and de-wrinkling force is recorded, the transverse edges can be retrieved to the initial  50 stage by moving the transverse motors to the initial zero-displacement position, leading into formation of the original wrinkle (Stage B in the diagram). Afterwards, the transverse edges are unclamped and the next-level wrinkle can be generated along the longitudinal direction. The same procedure is repeated for the third wrinkle and the force-displacement curves for forming the three wrinkles and their corresponding de-wrinkling process are obtained. It is to note that in this method, each subsequent wrinkle automatically results in a higher state of defected region at a higher shear angle.  Figure 4.2    Test sequence in the MBBE experiment.  4.2.3 Sequential biaxial bias extension (SBBE) test method For comparison purposes, another series of experiments were carried out using a similar test configurations described in section 4.2.2 but this time the specimen was fully clamped on both longitudinal and transverse directions from the beginning, with the latter imposing a displacement-control boundary condition. Two different transverse pre-loading magnitudes were applied to the either side of the specimen; namely, clamped fabric with no transverse pre-force applied (material was merely restrained in the transverse (y) direction), and 15 N of transverse per-load. Then, the bias-extension test in the longitudinal (x) direction was pursued. It is worth mentioning that as opposed to the MBBE test, in the SBBE test force-displacement curves were recorded in a single-step.  4.2.4 Measurement setup for shear angle and geometrical properties of wrinkles Tests were recorded using two digital cameras (Dantec Dynamics Hisense Zyla SCMOS) mounted at the top of the setup (Figure 4.3a), and sample kinematics were measured manually using the image processing software Image J [77]. Straight lines were drawn along individual  51 yarns on the fabric so as to simplify measuring the shear angles at various regions of the sample.  For each test repeat, photos were taken every five seconds to track the sample kinematics. In order to measure the geometrical properties of each wrinkle, as depicted in Figure 4.3b, a Creaform Viuscan portable 3D scanner was used to scan the surface profile of the defected sample with precision of 0.5 mm. The mesh was generated subsequently via DesignX software.  Since the uncertainties due to the sample positioning and measuring the shear angles could affect the characterization process of the textile reinforcement, the sample positioning was monitored from two different angles using the above-mentioned cameras mounted on top of the test setup, to ensure the fabric is well aligned with the jaws.     (a) (b) (c) Figure 4.3    (a) The test fixture equipped with an optical measurement system; sample positioning was monitored via DIC cameras; (b) Scanning the sample surface profile using a portable 3D scanner after formation of each wrinkle; (c) Scanned profile of a wrinkled sample.  4.3 Results and discussion 4.3.1 Observed deformation mechanisms For the uniaxial and biaxial bias extension tests, the shear distribution is not uniform throughout the sample (Figure 4.4): regions A, B and C indicate the areas that, under an ideal trellising shear kinematics, possess shear angles of θ, θ /2 and 0, respectively during a standard BE test step. Such angle distribution is theoretically valid if the fabric is assumed to be a pin-jointed net (PJN) without inter-ply slippage [36]. A rectangular region of interest with uniform shear strain was defined in the middle section of the MBBE samples, whose length and width were variable for each wrinkle level. In particular, the aforementioned theoretical angle distribution is approximately met, as long as the aspect ratio of the specimen is greater than  52 two [39]. During the transverse loading stage (i.e., de-wrinkling) two smaller BE-like regions were formed on either side of region A, as shown in Figure 4.4 (each with unequal W1 and W2 widths). Note that during the latter loading step, the sample in the x-direction is clamped while the x-motors are off, and hence the x-movement of region A is restricted.    Figure 4.4    A de-wrinkled state of the fabric; distinguishing different deformed regions; the red line shows a full fiber path connecting longitudinal (X-direction) and transverse (Y-direction) clamps. Blue paths indicate different regions developed after de-wrinkling; in fact two transverse BE-like tests on either side of the region A are formed during the de-wrinkling stage; Note that in particular region A would be the main region of interest for the final product. A zoomed area of region D is also shown in the figure.  4.3.2 Wrinkling results: forces and geometries Figure 4.5 shows the generated wrinkles according to the test procedure of Figure 4.2, along with their force-shear angle response during each step of the test. The final shear angles at each step were measured from the photos taken upon the formation of each wrinkle and stopping the test. The reported angles in Figure 4.5a were at the corner of the middle region where the fabric was flat, and averaged over three test replicates. With an aspect ratio of greater than two, the existence of yarns with free ends in the middle region of the specimen allows having wrinkles with shear angles less than that of seen using the typical picture frame tests (typically occurring around 55° [39]), hence mimicking a boundary condition somewhat closer to the practical deformation during the actual thermo-forming process. Two potential hypotheses for early wrinkling (the  onset at 32° shear as seen in Figure 4.5a) may be offered, both relying on the fact that during the BE test the inward y-axis resultant forces in the middle of the specimen  53 (Zone A in Figure 4.4) help the sample to buckle with a minimum resistance. First, the formation of a smaller loading width (during the x-direction BE loading) compared to the width of sample at the grips may intensify stresses in the mid region. Second, handling errors during mounting of the specimen, or even a slight inherent misalignment inside the fabric, can be spurring the fabric during the deformation to wrinkle via premature mismatch between the local shear of the fabric and that of the global fixture. The latter may be further explained by the minimum potential energy principal [48] and the contribution of different mechanisms to deformation energy; namely, the required energy for slippage occurrence (e.g., for yarns with one free end in the mid-region) is relatively larger than that for wrinkling, hence causing the latter to occur earlier with no slippage involved (see Figure 4.5). In summary, depending on the geometry of the mould, some wrinkles at small shear angles can form, especially when sufficient in-plane tensile forces are not available within the fabric [58]. The study [19] has shown that these premature wrinkles are even more severe for samples with yarns of higher bending stiffness.                                                                         (a)                    (b)               (c) Figure 4.5    Generated wrinkles in the x-direction along with their corresponding shear angles; some regions of wrinkles are zoomed in to show the shear angle uniformity.                                                                         54 Figure 4.6a represents the clamping force in the longitudinal direction for the three successive winkles versus the shear angle. After smoothing out each wrinkle using transverse forces and retrieving the transverse strip back to the initial wrinkle, a slight drop was observed in the force and shear angle; however, it was decided to conduct the test using the same specimen rather than generating each wrinkle level with a new specimen so as to have a consistent boundary condition and produce more reliable and repeatable results. In general, the uniaxial bias extension test shows an initial low stiffness trend at low shear angles (strains) followed by a higher stiffness region at higher shear angles once the locking begins to take place. This behavior is caused by the successive dominance of friction at tow cross overs, and the lateral tow compression. During the MBBE test, the same trend was observed when plotting the force curves combined (Figure 4.6a), confirming the choice of carrying out each multi-step experiment with the same specimen.   The evolution of shear angle over time is plotted in Figure 4.6b for each wrinkling state. The actual lock-up behavior was observed at around 55° degrees of shear, confirming the results of [48]. Once the adjacent yarns become closer to each other during trellising, high compressive forces start to build up, resulting in a sudden increase in the force response. Furthermore, the yarns’ width tends to slightly decrease (and the thickness increase) as the shear angle increases [43], offering slightly extra space for yarns to be sheared. No further change in the angle of wrinkled area was observed after the lock-up and a faster wrinkle growth took place. Subsequently, the ongoing increase in bias-extension without further increase in the shear angle revealed another deformation mechanism, namely the inter-tow and cross-over slips, similar to [36]. The rate of shear angle decreased around 50° which marked the onset of excessive inter-tow slippage throughout the sample in region A in which the yarns are free-ended. As the static friction under yarns’ bias-extension reaches a certain maximum value, cross-over slip also started from the rectangular edges of un-deformed zones C (Figure 4.4). This point of deformation was also associated with the extension of the third wrinkle to a larger area where the shear deformation significantly slowed down and the yarns began to slip locally in region B (see Figure 4.4).     55   (a) (b) Figure 4.6  (a) Applied force in the longitudinal direction versus shear angles for three wrinkle levels; After smoothing out each wrinkle using transverse forces and retrieving the transverse strip back to the initial wrinkle, a slight drop was observed in the force and shear angle (e.g., due to relaxation) as noticed in the plots; (b) Evolution of shear angle during formation of each wrinkle level. Intra-ply slippage occurred in zone D after around 50° shear; also notice that during winkle 3 step, the change of local shear angle over time is slower (due to locking).    In order to obtain the geometrical properties of each wrinkle, the surface profile of the sample was scanned after formation of wrinkles before the de-wrinkling began. Point clouds (meshes) were created and imported to the post-processing software Design X, and a CAD file based on the scanning data was created subsequently. Combining multiple sketches across the mesh, it was ensured that the obtained geometry lies perfectly on the mesh. Figure 4.7 depicts the scanning results for the three wrinkles. The geometrical properties of the wrinkles are presented in Table 4.1, and also plotted in Figure 4.8.  Based on these results, the projected area of wrinkles is decreased as the shear proceeds. During the course of bias extension test, the length of the specimen increases along the x-direction; during the shear deformation, weft/warp yarns become closer at sides, resulting into decrease in the overall width of the specimen in the y-direction. A similar trend was observed for wrinkles as their length and width vary conversely. It is worth mentioning that no conclusive trend could be found for the wrinkles height measurement, as it can be dependent on the bending rigidity of the fabric and its interaction with shear angle. This notion will be further elaborated in 4.1.5. In the current composites industry practice, the wrinkle height is normally taken as the most important criterion when it comes to visually inspecting the parts quality. Hence, according to results in Figure 4.8d, care should be taken as the height appears to be not a fully consistent measure to  56 assess the wrinkle severity level, since other associated factors such as shear angle and area should be taken into account.     (a) (b) (c) Figure 4.7    Surface profile of (a) low-level wrinkle; (b) medium-level wrinkle; (c) high-level wrinkle generated using 3D scanner.   Table 4.1 Geometrical properties of generated wrinkles using Design X   Area  (mm2) Length (Projected) (mm)  Width (Projected) (mm)  Height  (Left)  (mm)  Height  (Right)  (mm)  Height  (Average)  (mm)  Wrinkle 1 11297 177.4015 78.158 11.52 8.63 10.075 Wrinkle 2 8015 203.573 52.969 17.68 15.63 16.655 Wrinkle 3 3994 249.521 29.2419 10.92 18.39 14.655            57   (a) (b)   (c) (d) Figure 4.8    Geometrical properties of the wrinkles obtained using 3D scanning; (a) area; (b) length; (c) width; (d) height.  Figure 4.9 reveals the geometrical properties, namely the width, length, and height of the wrinkles, against the shear angle. Observing the rate (slope) of length and width, it can be seen that the change in length from step 2 to 3 of the test varies non-linearly and is faster than that of the width. This would support the hypothesis that the width change in the middle of sample gradually slows down and actually would stop at some point around the locking (since there is no gap left for the fabric yarns to rotate in the locked region). In fact, after locking, the wrinkle length expands to the area outside zone A (see Figure 4.5) and that is when some small tension may be imposed on the fibers in the middle region, which in turn lowers the height of the high-level wrinkle to some extent. Needless to add, these speculations need to be further investigated in future using numerical models at meso-level.   58  Figure 4.9    Width, length, and height of wrinkles versus shear angle. The graph shows length is changing non-linearly compared to width of the wrinkles. As the gaps between the yarns vanish around 55°, width increases slower compared to length.  4.3.3 De-wrinkling results 4.3.3.1 De-wrinkling forces The results of the de-wrinkling of the medium level wrinkle (i.e., wrinkle 2 as an example) is shown in Figure 4.10 where the net y-axis force is plotted against the net displacement of the transverse clamps. For all the three defect levels, the de-wrinkling force exhibited a non-linear behavior. As the wrinkles were smoothed out, two bias extension tests with irregular geometries were formed on either side of the wrinkle in the rectangular region of interest (Figure 4.4). The latter irregularity is due to the difference between the given clamping width in the left side (W2) and the ‘varying’ width of the right side (W1) which increases along the x-axis during each test step. As the de-wrinkling process began, the transverse sample strips started to shear, assisting to flatten the associated wrinkle in region A. Similar to the conventional bias extension test, there existed regions containing approximately θ, θ /2 and 0 shear angles in each smaller BE test in the transverse direction. These regions are marked as a, b, and c, respectively, in Figure 4.4. Video analysis of the de-wrinkling course indicated that the de-wrinkling rate throughout the sample is not uniform; especially once the shear angle in the middle region of the transverse strips reached the locking angle due the transverse loading, the entire transverse strips acted similar to a rigid body and extended out the wrinkle with a high rate until it is totally vanished. Hypothetically, if the upper un-deformed triangle (zone D in Figure 4.4) nearby wrinkle was fixed (clamped), the fabric would start buckling again in the middle zone ‘a’ due to the lock-up. Furthermore, the small sample sizes of the two transverse  59 BE tests resulted in a higher shearing rate (compared to the x-axis BE test stage) and consequently, the fabric underwent higher shear deformation in the middle zone (e.g., 53° shear in zone ‘a’ during the transverse BE test compared to 48° shear in zone A for the mid-level wrinkle in the longitudinal BE test). It is worth mentioning that after the complete de-wrinkling, the shear angle of original zone A was moderately reduced (for example, it reduced from 48° (Figure 4.5b) to 40° (Figure 4.10b) in the case of mid-level wrinkle test; suggesting that some level of de-shearing is taking place during the course of de-wrinkling in the current test procedure.    (a)   (b)  60   (c)  Figure 4.10    The de-wrinkling force versus displacement in the transverse direction (y-direction) along with the image of the specimen after de-wrinkling, for (a) Wrinkle 1; (b) Wrinkle 2, and (c) Wrinkle 3. The shear angles are shown in selected regions. The ‘reaction’ motor force in the longitudinal (x-direction) during the transverse loading has also been added in the left plots for comparison purposes (note the two curves almost run in parallel).  In addition to the de-wrinkling force in the transverse direction, the reaction force in the longitudinal direction was measured as shown in Figure 4.10. Although during the de-wrinkling the fabric was locked along the longitudinal direction (ux=0), an increase in the force was observed in that direction as the de-wrinkling proceeded in y-direction (with the two force curves rising almost parallel to each other). The increase in the x-axis ‘reaction’ force is due to the shear residual effect in the x-direction as well as the presence of some full yarn paths directly connecting the longitudinal and transverse clamps (shown in red in Figure 4.4). More specifically, during the course of the de-wrinkling, as the transverse bias extension test progresses, it attempts to de-shear the x-axis BE test region; however, this is not readily feasible since the x-axis clamps are fixed. Thus there becomes a reaction force in the x-motors; i.e., shear coupling between bias extension tests in x and y-directions. Video analysis revealed that point M (shown in Figure 4.4) in the ‘theoretically’ un-deformed triangle (region D) remains literally fixed  in the early stages of the test while de-wrinkling takes place; this would suggest that the tip of the wrinkle (around point P) does not move towards the center of region A during the de-wrinkling. As a result, it can be concluded that tensile forces would develop in the longitudinal direction. Another source of initiation of tensile forces would be the two triangles nearby the wrinkle (zones D). As the transverse bias extension proceeds, these triangles tend to move in y-direction, hence pulling the yarns paths connected to the un-deformed triangle in the longitudinal region (zone C). In the y-axis triangular zones D,  61 however, some cross-over slippage also took place, meaning that the above mentioned triangles do not go under tension as much as they would in a non-slippage scenario like pin-joint network. This suggests that in practice some yarns neighboring e.g. blank holder under tension, while fabric is shearing, can contribute to the onset of local yarn slippage in the part, as also reported in past 3D forming case studies [58].   Next, in order to characterize the fabric de-wrinkling behavior more distinctively, the de-wrinkling force values from Figure 4.10 were normalized by the area of the wrinkle at the end of the test, quantified using 3D scanning as explained in section 4.2.4. After removing the effect of area, the theoretically known influence of crossover contact forces [36] at different stages of the shear deformation manifested themselves clearly as follows. The area of wrinkles and normalized de-wrinkling force are plotted against the shear angle of generated wrinkles in Figure 4.11a. The nonlinear trend of the de-wrinkling force would implicitly account for the higher normal forces at cross-over points at higher shear angles. That is, in order to smooth out severe wrinkles, the de-wrinkling force should overcome higher level of established contacts between adjacent years when compared to low-level wrinkles. Also, the area of wrinkles decreased during the course of MBBE test (namely, the length of affected area increased while the width decreased; see also Figure 4.7c). This can be explained by the fact that as the shear deformation (forming) proceeds, gaps between yarns vanishes and, thus, more severe wrinkles may appear in smaller sizes. It is important to add that in each measured wrinkle state, within the affected area the fiber angles were fairly uniform and the same as that of the corner of the middle region where the fabric was flat (Figure 4.5). After ~55o shear in the middle region, the fiber angle within the wrinkled area stopped increasing (i.e., reaching the lock-up state as shown in Figure 4.6a), and hence the wrinkle 3 began expanding faster to a region with a much larger length and smaller width when compared to wrinkles 1 and 2.  It would be also interesting to compare the de-wrinkling and wrinkling normalized forces of each wrinkle, as depicted in Figure 4.11b. While the magnitude of transverse de-wrinkling normalized force is always lower than the wrinkling one, their variation is non-linear with respect to each other. This can be explained by the fact that during the de-wrinkling test, under the present setup, some regions as explained earlier are submitted to tensile loads, and the  62 effect of these forces increases sharply in the case of wrinkle 3 at high shear angle (see Figure 4.10). Therefore, higher de-wrinkling force would be needed to overcome the induced tensile forces for wrinkle 3 and eventually to flatten it from the transverse direction. In addition, due to the inherent tension-shear coupling discussed in Chapter 3, frictional forces established at cross-over points at higher shear angles would demand higher de-wrinkling forces to enable the compacted fibers slide over each other.    (a) (b) Figure 4.11    (a) Normalized de-wrinkling force versus shear angles of generated wrinkles; (b) Normalized de-wrinkling force vs. normalized wrinkling force for low, medium, and high level wrinkles; in all cases the normalization is done by dividing the force by the area of wrinkle. Note that wrinkle 3 may be considered most severe here, yet it has the least area. This suggests that in practice the geometrical features of formed wrinkles in a part should be assessed next to the formed shear angle.  4.3.3.1.1 Remark 1:  More discussion on the full-path yarn tensioning effect  For the sake of better understanding of the effect of yarn tension in the MBBE test, two experiments were carried out using two different specimens of slightly different widths (~5mm difference). In the former, as in the original case, the yarn path in Figure 4.4 (highlighted in red) connecting the transverse clamps all the way to the longitudinal clamps was kept. In the second (new) specimen, the so-called yarn path was cut/removed. It was of interest to investigate in what manner the existence of the full fiber path would affect the de-wrinkling forces, in spite of the fact that upon de-wrinkling stage it would instantly undergo tension. From a practical point of view, during the actual draping process, depending on the geometry of the final part and the boundary conditions, some of the yarns adjacent to wrinkles may go under similar tensioning; hence investigating their contribution to the amount of de-wrinkling force would be beneficial to better devise de-wrinkling strategies. Figure 4.12a shows the  63 comparison of the de-wrinkling force of the medium level wrinkle with and without the above continuous yarn path. As it can be seen, removing the full yarn path effect has led to a smaller force required to flatten the wrinkle (namely 38 N vs 57 N according to the end points of the de-wrinkling (transverse) curves in Figure 4.12a); and similarly less tensile reaction force in the longitudinal direction. Figure 4.12b displays the rate of shear angle for both tensioned and un-tensioned cases. By comparing video recordings of the two cases, it was noticed that the full fiber paths were causing pivot points (uy= 0 in the D triangle in Figure 4.4 with pivot point M) during the transverse BE test, and hence the de-wrinkling in zone A began very slowly in the beginning of transverse loading. This trend was apparent until the locking angle was approached in zone ‘a’, after which zone D started moving faster and caused clear de-wrinkling in zone A. When analyzing the sample with no full fiber path, however, there was no such pivot point effect and the coupling between the x and y-direction BE tests was merely through shear mechanism, leading to a more consistent de-wrinkling rate from the beginning of the test; yet again it become slightly faster after the locking point. Also, in the latter case, the slippage in transverse triangle of zone D became less apparent; i.e., a better part quality in the final product. As a result, the difference in shear rates seems to be a direct result of the existence of full yarn paths and hence a slower change in shear angle in the θ/2 regions. After 220s, the curves in Figure 4.12b cross each other as the sample without the full yarn path has been already de-wrinkled for the most part and the locking in the transverse side is approached. The above difference between the two shear rates is also partly due to the fact that the sample without full fiber path has had slightly lower width, and based on the BE theoretical formula in [39] it should yield a higher shear rate.      64  (a) (b) Figure 4.12    Investigation of the yarn tensioning effect in the de-wrinkling process of medium-level wrinkle. (a) Comparison of de-wrinkling force and longitudinal force for cases with and without full fiber path; (b) Evolution of the shear angle in the triangular region ‘a’ (see Figure 4.4) versus time. Cross marks correspond to the point when the wrinkles were effectively flattened.  4.3.3.2 Comparison of normalized longitudinal and transverse bias extension tests Since there exist two BE tests in the transverse sides of the MBBE (Figure 4.4), it was of interest to derive their normalized (local or yarn level) shear forces based on [39] and compare to that of the longitudinal BE loading stage. It must be mentioned that currently there is no standard method available to normalize the results of such irregular transverse bias extension tests as the width of the sample is different at the top and bottom (𝑊1 ≠ 𝑊2), leading to formation of un-symmetric deformation zones in the fabric; also one side of each transverse BE test (close to the A zone) is not fully fixed, as opposed to the standard BE test. Hence, for simplicity, an average width of upper and bottom side of the small BE transverse tests was opted to normalize the force results using Eq. 2.4. However, a more elaborated technique can be developed in future to take into account the above mentioned un-symmetric deformation regions. Figure 4.13 shows the resulting normalized shear force for the main bias extension test (the low-level wrinkle with 32° shear angle) compared to that of the transverse bias extension tests with and without full yarn path effect. Note that the force of one transverse BE test was normalized separately and then multiplied by two, as there are two transverse BE tests on the sides of the zone A in Figure 4.4. Comparing the results in Figure 4.13, it can be hypothesized that regardless of existence of fiber full paths, the shear responses in both directions are almost identical up to ~35 degrees of deformation. The induced fiber tensioning, however, manifests itself at higher shear deformation regime where stiffer shear response is     65 present while flattening wrinkles (note that the full fiber paths has necessitated large shear to accommodate the full de-wrinkling).    Figure 4.13    Comparison between the normalized shear forces of longitudinal BE and the transverse BE tests with, and without the full yarn path; for the low-level wrinkle. The curves are based on zones “A” and “a” for x-direction and y-direction BE tests, respectively. Cross marks represent the point where wrinkle is flattened. Notice that the full fiber paths (i.e., tensioning) has necessitated large shear to accommodate the full de-wrinkling.  4.3.3.3 Investigating the effect of fabric bending stiffness on the shape of wrinkles Due to the possible relative motions of fibers with yarns, woven fabrics possess a very low bending rigidity compared to continuous materials such as metals. It has been shown that the bending stiffness is of great importance when performing wrinkling simulations [19]. In fact, it needs to be implemented in the fabric material models so as to compute the actual shape and geometry of wrinkles. Herein, in order to investigate the effect of bending stiffness on the shape and size of wrinkles, the test fabric was slightly pre-consolidated using a hot press with a pressure of 0.5 bar and temperature of 165°C. Slightly pre-consolidating the fabric resulted in a higher bending stiffness as the gaps between the filaments become smaller and the matrix slightly solidifies. Then, the level-1 wrinkle possessing shear angle of 32° was formed and subsequently smoothed out using the same procedure described in section 4.2.2. Figure 4.14 shows the wrinkles formed using low and high bending rigidity samples. It can be observed  66 that the height of the wrinkle after pre-consolidation dramatically increases, confirming the results of Boisse et al. [19]. The increase in height can be explained by stiffer behavior of yarns’ cross-section: while shearing the fabric with partially solidified cross-sections, early buckling is to be anticipated since yarns cannot follow the shearing flow from the test fixture boundaries and therefore the compressive forces in the transverse bias-direction are formed sooner. For the case of stiff fabric, the first wrinkle started around 25°, whereas for the dry sample it was apparent around 32°.  Figure 4.15 compares the wrinkling and de-wrinkling forces for both cases up to 32° of shear (low-level wrinkle). For the stiffer fabric sample, a larger shear resistance can be observed, due to the wider contacting areas at cross-overs and also the partial consolidation of fibers within the yarns. These effects would increase the inter-yarn and intra-yarn frictional forces, which should be overcome for fabric shearing [39]. The de-wrinkling force is also seen to be much higher in the stiff fabric than the dry fabric, per Figure 4.15b. This may be explained by the increase in the tensile force within the yarns owing to partial consolidation. Namely, during the de-wrinkling, rigid triangles nearby the wrinkle (zone D in Figure 4.4.) are submitted to tensile forces and hence, more de-wrinkling force would be needed to flatten the wrinkle, while the bending stiffness is likely to be coupled to tensile behavior of the material [45].    (a)                                                        (b) Figure 4.14    Effect of bending stiffness on the size of wrinkle 1: (a) dry sample; (b) slightly pre-consolidated (stiffer) sample; notice larger wrinkle with the stiffer fabric at the same shear level (32°).   67   (a) (b) Figure 4.15    (a) Applied longitudinal force versus shear angle for low rigidity (dry) fabric and high rigidity (stiff) fabric; (b) Comparison of the de-wrinkling force for the two fabrics. Stiffer bending behavior resulted into higher de-wrinkling force required to flatten the wrinkle in transverse direction.  4.3.4 Comparison to a sequential biaxial bias extension test Figure 4.16a compares the longitudinal forces in the course of a bias extension tests conducted in x-direction, while being pre-tensioned and kept constrained in the y-direction. A greater longitudinal force was needed in this sequential biaxial test with a non-zero transverse pre-load, compared with the case without transverse pre-load (i.e., when sample is merely constrained in the y-direction without any displacement exerted). Given the tests were conducted under a displacement-control condition, after reaching a certain shear angle (20° and 16°, for 0 N and 15 N transverse force cases, respectively), the full fiber paths within the sample started to break, leading to easier shear deformation of the specimen in the longitudinal direction. Figure 4.16b shows all components of the measured forces versus global x-direction displacement. Although the fabric was constrained in the y-direction and the transverse motors were turned off, longitudinal and transverse force curves seem to arise almost with the same slope for either pre-load condition. This ties back to the fact that the fibers in the biaxially-loaded region undergo tension and thus mechanically transfers the x-direction load to the y-direction. Furthermore, from Figure 4.16a, the shear force is highly affected by the presence of induced tensile forces, which is another proof of presence of tension-shear coupling (similar to Figure 3.10 in Chapter 3 where PF test was used). In either of the tests in the presence of transverse load, no wrinkling was observed.  For the case of 15N transverse pre-load, after 30 mm of deformation the full fiber path began to fail, hence the x-direction force increased rapidly per Figure 4.16b. An image of the 15N pre-loaded sample before and after deformation  68 is shown in Figure 4.17. As represented in the Figure 4.17b, the shear angle in the θ/2 regions are quite higher than that of the central biaxially-loaded region. (57° vs. 25°). The presence of excessive yarn forces in the transverse direction would restrain the central region to undergo shear deformation and offers an explanation for the smaller shear angle in this region of interest.    (a) (b) Figure 4.16 (a) The applied force along the longitudinal axis against the shear angle; (b) Longitudinal and transverse force against x-direction displacement for both cases with 0N and 15N pre-applied transverse force. Cross marks show the onset of yarn breakage.     (a) (b) Figure 4.17 (a) Transversely pre-tensioned bias extension sample before loading in x-direction (b) Formed shear angles at different sample regions upon loading; slippage areas are indicated by yellow triangles. F1-F2 coordinate system shows the initial fiber directions at ±45° with respect to the global coordinate. It was noticed that under this deformation mode the fabric began to show slippage from where its movement is constrained (i.e., in the y-direction clamps). If the shearing continues via the x-direction bias-extension test, the slippage region would expand along the y-direction to the central zone. Blue circles represent the onset of yarn breakage in the specimen.   69 4.3.4.1 Remark 2: Local tensile and shear forces along the yarns in the MBBE test It may be of interest to obtain the local tensile and shear forces in the gauge section while testing the material using the biaxial bias extension test. An attempt has been made to resolve the applied global forces to forces parallel and along the tows in the gauge section of the specimen [33]; however, two important issues have not taken into account in the latter study.  Firstly, the applied force to the region of interest does not totally transfer to the rectangular region of interest and some of the applied force is used to shear the material in region B and bottom part of region A. More importantly, yarns in the gauge section are free-ended and hence the amount of tension is less likely to be significant within region A (Figure 4.4), though the borders between regions b and D might act as week pivot points; and as a result some, slight tension may be applied to the tows. Observing Figure 4.13 would justify this assumption as the normalized shear forces in the longitudinal and transverse directions are relatively equal at low-medium shear angles. Nevertheless, future studies should be undertaken as to accurately obtain the amount of local tensile forces along the tows in the region of interest via optical measurements and/or energy based approaches.    4.3.5 Some practical considerations During forming of fiber textile reinforcements, the fabric is often submitted to various loading modes. Tensile forces developing due to friction between the fabric and blank holder can depend on the blank holding pressure imposed to ensure formability. Care must be taken to reduce the chance of arising forming-induced defects while the fabric is being deformed over the mould contour. Based on the performed wrinkling/de-wrinkling characterization tests at the 2D level, the following may be suggested:   A sound routine for installation of fabric into the moulding setup must be developed in order to reduce the chance of misalignment. As discussed in section 4.4.1.1, even some degrees of misalignment would spur the yarns to wrinkle at very low fabric shear angles due to unbalanced boundary conditions; consequently, blank holder pressure should be optimized in the regions that are vulnerable to such compressive forces. These regions depend on the geometry of the part which may possess irregular curvatures. The ply  70 orientation with respect to the blank-holder also needs to be wisely selected before being sheared over the mould contour.   On account of the obtained trend of de-wrinkling forces, a correlation is anticipated between 2D characterization and the actual 3D forming of woven fabrics, which can be further implemented in numerical simulations to devise de-wrinkling strategies based upon the blank holder pressure, modification of the mould, or the blank holder geometry (which will be presented in more details in Chapter 5). Care must be taken, however, not to induce extra tension onto the wrinkled region as it can cause slippage (and subsequently excessive space between the yarns) or yarn tearing. This notion will also become more apparent in 3D experiments in Chapter 5.  The investigation of the full fiber paths under tension provided some valuable information regarding their contribution to the de-wrinkling mechanism. In the practical stamping operations, depending on mould shape/size/tooling, some full fiber paths similar to the de-wrinkling test in this Chapter may be present. Even in the absence of full fiber paths, some small regions of fibers close to the region of interest (like the zone D triangles in Figure 4.4) may experience tensioning. The presence of full fiber path slowed down the de-wrinkling process due to the formation of pivot points (Figure 4.12), while in either case the induced tension in zone D caused cross-over tow slippage. Further numerical study on this subject is deemed worthwhile.   The bending rigidity of fabrics has a direct influence on the size and shape of wrinkles. This should be taken into account in numerical modeling approaches while the relationship between the forming temperature and bending rigidity is also taken into account.   4.4 Summary of findings One of the principal goals of optimizing textile composite structures is to improve the forming of the material by mitigating wrinkles and other forming-induced defects in the final product. This chapter presented an experimental investigation into the wrinkling and de-wrinkling mechanisms of a typical plain weave. Namely, a multi-step biaxial bias extension (MBBE) test was introduced to form and then flatten wrinkles, comprised of different sizes and shear angles, making it possible to investigate wrinkles with shear angles both lower and higher than the locking angle (wrinkles 1, 2, 3). Employing 3D scanning technique, geometrical properties of  71 the defect during the wrinkling and de-wrinkling tests were examined and the influence of nonlinear contact forces was deemed to be significant when removing the wrinkles, especially at high shear angles. In addition, the source of initiation of compressive forces at low shear angles was deemed to be the inherent misalignments/non-uniformities within the dry fabric and/or the global misalignment caused due to small mishandling during mounting, therefore this may need to be taken into account when selecting a protocol for ply orientation during draping. along with other factors such as yarns crimp variations, etc. In essence, any noise source causing some local fabric regions not to perfectly follow the global shear flow of the fixture may yield wrinkling at some point far before the locking point, depending on the applied boundary conditions (e.g., constrained fiber ends as in PF test, or free fiber ends as in BE test) along with the magnitude of frictional contact at cross-over points relative to the s-shape bending of yarns that needs to be accommodated during shearing of woven fabrics [36]. Comparison between the normalized shear forces in the longitudinal and transverse directions of the MBBE tests suggested that the transverse shear deformation predominantly controls the de-wrinkling mechanism, yet future work is required for the detailed normalization of such irregular bias extension test. Furthermore, contribution of tensioned yarns to slippage was highlighted in the context of 2D characterization of the de-wrinkling. The influence of transverse pre-loading on delaying the onset of wrinkling was apparent, while the limiting effect of high pre-tension load on causing small drapablity window was also noticed.     72 Chapter 5: Experimental Investigation of Tension-Assisted 3D Forming   5.1 Overview The intent of experimental forming trials is often to verify and improve the analytical/numerical models, as well as to predict the influence of various processing conditions on the formability of reinforcing composite sheets. Nonetheless, as mentioned in Chapter 1, the scope of the current thesis has been limited to small (lab) scale forming experiments as to link the findings from Chapters 3 and 4 on 2D fabric characterization. To this end, in this chapter, a series of single-ply and double-ply hemisphere forming trials using asymmetrical blank holding pressures will be first presented, reporting the distribution of shear angle and quantifying defects across deformed layers. Finally, a new idea of blank holder geometry modification based on the findings obtained in Chapters 3 and 4 will be introduced and verified.   5.2  Experimental forming test setup Figure 5.1a shows the employed experimental setup for hemisphere geometry, formed from the initially flat woven fabric. An Instron 5969 tensile device was used as the forming machine. The fabric was subjected to a hemispherical punch under semi-constrained boundary condition imposed from the blank holder. Symmetric part geometry was used in order to apply a relatively uniform loading in all directions within the fabric plane under the punch. Subsequently, a more genuine influence of boundary condition could be assessed by means of altering the pressure distribution/geometry of the blank holder, whereby the wrinkles could also be imposed artificially. The preform fabric sample size was 300 by 300 mm2. Clamps were placed on the draw-in ring (Figure 5.1a) to apply pressure on the blank holder at specified locations (e.g., by means of C-clamps as shown in Figure 5.3). A torque meter set at 3 lbf.in was used to reach the same tightness at each spot. This clamping condition did not fully restrain the fabric from sliding, hence the draw-in could be taken place progressively. Two series of experiments were carried out; namely single layer forming and double layer forming. In the former case, the fabric was positioned with 0° orientation with respect to the supporting bar, while in the latter two layers of fabrics with a 45° orientation were clamped onto the blank holder. In both cases (including single layer forming) the fabric layers were partially pre- 73 consolidated using a hot press, similar to Chapter 4. In the upper layer, the yarn warp and weft directions were parallel to the supporting bar edges whereas the bottom layer was positioned at 45° relative to the upper fabric (Figure 5.1b). The punch was mounted on the tensile machine and brought down at constant rate of 100 mm/min, taking 35 seconds to finish the whole stamping process. The diameters of the punch and blank holder were 120 mm and 150 mm, respectively. Once the fabric reached a certain displacement, the test was stopped and the force–displacement curves were extracted. For each preform, three samples were tested and sample-to-sample variations were found to be within a reasonable range (less than 5%) given the high precision of the Instron 5969 tensile machine. In the following discussions of test results, the average values are reported. A ‘backlighting’ technique was also implemented in the forming setup. Namely, after deliberately taking out the punch, a headlight was placed at the top of the preform, allowing more closely identifying the shear angles and defects across the deformed preform, especially on its backside.    (a) (b) Figure 5.1    (a) Experimental setup employed for stamping operation; (b) Ply orientation during the double layer forming experiments. In single forming experiments, the 0° ply was used.  5.3 Results and discussion 5.3.1 Correlation of 2D characterization to 3D forming 5.3.1.1 3D hemisphere forming without the blank holder geometry modification The forming process of fabric reinforcements is anticipated to somewhat mimic the bias extension test as the yarns move more freely with the punch at the bottom and constrained to  74 the blank holder at the top. Furthermore, since the force direction induced by the punch is in vertical direction, wrinkles are lengthened along the same direction. It was of interest to correlate the results of the 2D characterization from Chapter 4 to the actual 3D forming trials in this section. Figure 5.2 further illustrates how this correlation may be substantiated. Assuming a strip along the longitudinal circumference of the hemisphere (shown in red in Figure 5.2a), a bias extension test would occur along the strip path, making it possible to investigate the shear deformation of the fabric reinforcement in 3D.   Figure 5.2    Correlation between the 2D bias extension test and the actual 3D forming trial  Figure 5.3 depicts the open die forming process of the fabric reinforcement using the hemisphere punch for both single and double layer preforms. As the punch moved down against the preform, in-plane and out-of-plane deformation modes took place, including yarn slippage, yarn bending, transverse compression, fiber distortions, and particularly trellising shear. The trellising/shear was observed to be the main deformation mechanism during forming. The local shear angles at specific spots were measured with the aid of backlighting method and image analysis. The unbalanced clamping (see the C-clamp locations in Figure 5.3) led to irregular shear distribution especially on the high curvature zones near the equator of the punch. Note that the weight of the blank holder on the draw-in ring imposes a uniform pressure, but the additional pressure due to C-clamps makes the resultant distribution asymmetric.  75       (a) (b) Figure 5.3    The deformed hemisphere via unbalanced clamping pressure. (a) Single ply forming; (b) Double ply forming with a 45° relative orientation. Shear angles at some select regions are shown. The unbalanced clamping condition on the blank holder was imposed by use of C-clamps at select locations.   Due to imposing unsymmetrical boundary conditions, the shear angles were distributed non-uniformly in the hemisphere part. For both single and double forming trials, the maximum shear angle did not exceed 60°. Ply deformation was decreasing from the top to bottom region (with visually distinguishable regimes of high shear, medium shear, and low shear as shown in Figure 5.3). The highly sheared regions were in the neighborhood of C-clamped corners where a more displacement controlled/severe deformation would be present (as one end of yarns are nearly fixed and the other end moves with the punch). In addition, the lines of backlit pattern remained parallel and straight, indicating a uniform shear at the less curved areas of the punch. Moreover, a highly stretched region was formed at the top of the hemisphere (apex), where the yarns remained essentially perpendicular to each other (similar to region C of bias- 76 extension test in Figure 4.4); a similar nearly un-deformed region was also noted at the bottom area (shear<2o). In the case of double ply forming, defects could be identified across the preform both on the upper and bottom plies. However, similar to single ply forming, most of the defects occurred around the periphery of the blank. In Figure 5.3 wrinkles can be seen around the outer edge as the fabric accommodates large shear deformation in those regions. Yarn transverse compression is known to be one of the main deformation modes during resin infusion processes due to the applied vacuum and pressure [78]; herein, analogously, the non-uniform holding force would have caused localized in-plane compressive deformations in between corner areas, where regions of tow waviness are observed.  Based on more detailed view of the defects in the current experiments (see unmodified BH cases in Figures 5.6 & 5.7), additional marginal defects were observed in the case of double-ply forming compared to the single layer draping, while the deformation behavior was almost identical for inside and outside layers. The maximum shear angle at highly sheared regions in both plies was slightly increased to 60° (compared to 58° in the case of single ply forming, which is likely to be due to the presence of non-uniform inter-ply frictional forces at some regions caused by the asymmetric blank holding pressure). Overall, with increased relative orientation of the layers, the number and intensity of defects would rise, as reported earlier for carbon plain woven fabric reinforcements in [65] and for thermoplastic reinforcements in [79]. The 45° relative ply orientation would induce the most severe defect cases in multi-layer forming trials [62, 65, 79]. 5.3.1.2 3D hemisphere forming with a blank holder geometry modification In this section, a new method (namely the blank holder geometry modification) is proposed as a possible strategy to mitigate defects, especially around the blank holder boundaries, during forming of fabric reinforcements. Figure 5.4 shows the proposed experimental setup in which this geometry modification is implemented. As shown in Figure 5.4a, a half-cone shape was 3D printed and placed at the top of the draw-in ring. The preform was laid down and subsequently clamped via the blank holder system. During forming, the extra flange on the cone part in the blank holder imposes extra tension to the fabric boundaries while the other regions of the preform being sheared at the far bottom of the hemisphere. Given most of the  77 defects often occur around the periphery of the punch edges, it would be rational to modify the geometry of the blank holder in a sense that such vulnerable regions could undergo tension instantly from the beginning of the forming; and hence, the chance of developing compressive stresses and subsequently wrinkling would be lessened. Initial trails of the experiments showed that employing the proposed modified blank holder suppressed most of the defects across the preform. Subsequently a more fine-tuned design of modified blank holder was proposed (Figure 5.5; to be discussed in more detail in the next section). Figures 5.6 and 5.7 represent the detailed views of defects in the single and double ply forming cases with and without the final geometry modification, respectively. Examining the final shapes, defects such as tow waviness, yarn jamming, and wrinkling have been noticeably mitigated using the modified blank holder. At the meso-level, this may be attributed to exerting tensile forces along the bias directions during forming, and hence assisting in increasing tow cross-over contact forces and postponing wrinkling (the same wrinkle delaying trend was observed in 2D characterization trials in Section 4.3.4). Under the the modified blank holder setup, the preform also possessed no other local defects such as tow jamming. These observations imply that using the modified blank holder could be an appropriate process optimization route for forming complex composite parts.   (a)         (b) Figure 5.4    Implementation of blank holder geometry modification in the 3D forming trials (a) Forming test configuration; (b) front and bottom views of the setup. The added conical part of blank holder has fillets around its flange, reducing the chance of damaging fibers while inducing tension-assisted forming of the fabric.       78 5.3.1.2.1 Further geometrical modification: Considering implementation issues Applying excessive tension via increased blank holding pressure, or here via blank-holder geometry modification, can lead to high membrane forces at the extremities of the fiber yarns to the extent that weave pattern heterogeneity or tow sliding may take place (Figure 5.5a), as also discussed in [69]. This local weave pattern heterogeneity is caused by a relative slip of the warp and weft yarns and results into a low local yarn density (and hence low local fiber volume fraction in the final part), which is another undesired defect for the preform. It was interesting that a very similar phenomenon was observed during the de-wrinkling of the test fabric at 2D scale. Namely, as discussed in Section 4.4.1.3.1, the neighboring tensioned yarns caused the tows to slide. Consequently, in the 3D forming case, it was deemed that the extra force supplied by the conical flange could be adjusted depending on the geometry of the part and the base blank holder pressure distribution so as to prevent excessive tension and tow sliding across the useful regions of the preform. The flange of the 3D printed part was modified accordingly as to not apply extra tension to those areas vulnerable to sliding (namely, regions were c-clamps were used and imposed expressive pressure). The results is shown Figure 5.5 in which the slippage and large fiber branching have been clearly avoided. It should be noted that other processing factors such as pressure points on the blank holder, forming rate, and ply orientation were kept constant, in order to specifically observe the effect of blank holder geometry customization. An inner view of the quality of the formed part under customized blank holder is also compared to the original forming case in Figure 5.8, where the defects have been clearly alleviated.                 (a)                                                                                                                  (b) Figure 5.5    (a) Outer view of weave pattern heterogeneity near the part edges using the modified forming setup with no customization of conical part in the blank holder system; (b) the tow sliding was prevented by further customizing the conical part and hence removing excessive tension imposed to the fabric during forming.   79   Figure 5.6    Detailed view of defects in single ply forming using the final modification shown in Figure 5.5.   80  Figure 5.7    Detailed view of defects in double ply forming using the final modification shown in Figure 5.5.   81  Figure 5.8    Comparison between the inner views of the formed fabric with and without the final blank holder geometry modification. The general deformation zones in both images are quite similar, owing to repeatability of the forming test. Notice that the local defects have been alleviated with the modified blank holder.  Figure 5.9 shows typical force-displacement curves recorded in the forming experiments for both single and double ply forming cases. In both cases, using the final modified blank holder exhibited a substantial increase in the forming load. However, as shown earlier the inspection of final parts after forming revealed no yarn damage or fabric tearing across the preform due to the increased force magnitudes (Figures 5.6 and 5.7). Hence, it can be concluded that such increase in the force should not be of concern in for manufacturing designers as long as there is no forming defects or fiber damage in the final part (it should also be noted that the 3D printed conical part of blank holder system had fillets all around its flange, reducing the chance of damaging the fibers). Finally, from comparison of Figures 5.9a and b, it can be noticed that in the case of double forming the required forming force is not necessarily double of the case of single ply forming and factors such as ply orientation and punch geometry could affect the resultant force.    82   (a) (b) Figure 5.9    Force-displacement curve response for (a) single ply forming and; (b) double ply forming; the preforms are made using the final geometry modification process described in section 5.3.1.2.1.  5.4 Summary of findings This chapter aimed to qualitatively correlate the findings obtained in 2D characterization of tension-shear coupling (Chapter 3) and wrinkling (Chapter 4) to the actual 3D forming trials. Single-ply and double-ply forming trials were conducted using unbalanced blank holder pressure conditions as to artificially generate wrinkles and other forming-induced defects such as tow slippage and yarn jamming. The shear angle distribution was evaluated in formed parts and their quality was inspected, for both single and double-ply cases. Observing the influence of tension at tow extremities and its contribution to delaying the onset of wrinkling, the idea of modifying the blank holder geometry was proposed as to apply an optimum amount of de-wrinkling force to the preform during forming. The repetitive forming results showed that the modified blank holder can effectively mitigate the defects, thanks to the induced tension-assisted shearing condition for the fabric. Yet more extensive research is needed to correctly predict the optimum configuration of the modified blank holders according to given mould shapes, fabric architectures, number of plies, processing temperatures, etc.       83 Chapter 6: Conclusions and Future Work Recommendations  6.1 Summary  The use of textile reinforcing fabrics provides massive potential in design of lightweight composite structures with complex shapes. Nonetheless, the deformation mechanisms during fabric forming are complex and far from being fully understood to date. The complexity of interactions between different elements at different scales (micro, meso, and macro) makes the behavior of such reinforcements complicated to characterize using conventional mechanical tests and simplified numerical models. One of the principal goals of optimizing textile composite structures is to improve the forming of the material by mitigating wrinkles and other forming-induced defects in the final product. Hence, fundamental deformation mechanisms must be characterized correctly and more advanced material models are required such that forming simulations can optimized at minimal cost, and ultimately provide manufacture of defect-free parts.  The work presented in this thesis aimed to arrive at an enhanced understanding of the mechanisms behind wrinkling of woven fabrics, and to primarily seek for methods to cope with this forming-induced defect by means of an inherent tension shear-coupling in the material. To this end, in the first stage, an investigation into the interaction between tension and shear responses of a typical glass/PP weave was undertaken. Dependence of shear rigidity of fabrics on yarns pre-tension had been reported in the literature, however some conflicts regarding the trend of this effect was identified. Sources of the conflicts were discussed and resolved in Chapter 3 using a new characterization framework and custom-design combined loading fixture.   Next, in Chapter 4 it was deemed of high interest to designers to predict the minimum magnitude of forces required to mitigate wrinkles/defects in useful regions of final products, possibly through applying optimum boundary conditions by blank holders during forming. With that goal in mind, for the de-wrinkling force prediction, a new characterization technique, namely a multi-step biaxial bias extension (MBBE) test, was proposed to determine the amount of required longitudinal and transverse forces to form and then flatten wrinkles of different  84 sizes, respectively. The underlying deformation mechanisms and the wrinkling/de-wrinkling response of the fabric were investigated, resulting into some potential design considerations for future applications.  Lastly, based on the findings in Chapter 3 and 4, tension-assisted forming trials of the plain woven composite was conducted by performing 3D stamping tests at room temperature. Blank holder geometry modification idea was found to be an effective method to mitigate defects such as yarn jamming and wrinkling around the periphery of the preform, making it a potential processing route for forming complex composite parts in the future. Overall, this study would be a preliminary step for optimization of tension-assisted processing of fabrics, providing the ground for conducting more elaborated numerical research and eventually arrive at new manufacturing guidelines to eliminate defects.  The summary of specific conclusions drawn from the phases of the study is as follows:  Investigation of the two-way tension-shear coupling  Advantages of using needles over fully clamped boundary condition in characterizing the shear response of fabric reinforcements became evident through real-time monitoring of the yarns tensile load. Employing needle-type clamps freely allowed the filaments relative movement, causing a uniform deformation close to the jaws.  In particular, using needles is highly recommended when investigation the tension-shear coupling of textile reinforcements using displacement-control devices since during the course of PF test the pre-tension effect abates; unless a highly sophisticated mechanism is used where the jaws can follow the shear deformation of the arms concurrently.    It was shown that, the analysis of global force results cannot provide a reliable characterization of the tension-shear coupling, given that the global measured parameters are inter-dependent due to a kinematic coupling in the device mechanism, and hence not a true representative of local forces as experienced by the woven yarns. Thus an analytical approach was needed to transform the global force-displacement  85 measurements to the fabric local coordinates while considering the aforementioned kinematic coupling and its effect on the net shear force and deformation.   Comparison between the picture-frame experiments with two different pre-tension levels pointed to a consistent impact of in-plane tension on the shear resistance of the fabric at both low and high shear angles. This observation stands on the hypothesis that imposing yarn tension increases the compression contact forces at cross-over points as well as between filaments, and hence the friction forces, which in turn increases the fabric shear rigidity   Analyzing local force responses between the biaxial and simultaneous (biaxial-shear) loading tests suggested that the less interaction between non-orthogonal yarns due to the fabric shearing is perhaps the cause of a more compliant tensile behavior under simultaneous loading mode. However, under this loading mode, the shear resistance of the fabric amplified notably.   It was perceived that the fabric even in the dry form at room temperature can show a sizable visco-elastic behaviour which, in addition to the studied two-way tension-shear coupling effect, may be taken into account in future implementation of fabric constitutive models.   It was perceived that using needle clamps, satisfactory test repeatability can be achieved even without pre-conditioning of the fabric. This observation suggests that modifying boundary conditions of tooling to needle clamping may rectify the need for preconditioning.  Characterization of wrinkling and de-wrinkling behavior of woven fabrics  Multi-step biaxial bias extension test method can provide valuable information regarding the material’s behavior during formation of wrinkles as well as their de-wrinkling process.   86  Analysis of the wrinkling and de-wrinkling results showed a sound fabric positioning (installation) routine needs to be developed to reduce the chance of expediting the formation of defects; e.g. even a slight amount of misalignment could spur the yarns to buckle at low shear angles due to induced unbalanced loading/boundary conditions. Consequently, in practice, blank holder systems can be optimized in the regions that are more vulnerable to severe compressive forces. These regions depend on the geometry of a given part, or distribution of pressure under blank holder. The ply orientations with respect the blank holder also need to be optimally selected before draping over complex 3D contours.   On account of the obtained de-wrinkling forces, a qualitative correlation was found between 2D characterization and the actual 3D forming of woven fabrics, which can be further expanded and implemented in numerical simulations to devise de-wrinkling strategies based upon on the blank holding pressure and modification of blank holder geometry. Care must be taken however, as to not induce extra tension to the wrinkling regions as it can cause fiber slippage (and hence excessive space between the yarns in the final part) or even yarn tearing.    The investigation of the full fiber paths under tension (section 4.4.1.3.1) during trellising was a preliminary step towards understanding the influence of adjacent yarns to wrinkles and their contribution to de-wrinkling. In the practical stamping operations, based on the mould shape/size some full fiber paths similar to the performed de-wrinkling test setup may be present. Regardless, even in the absence of such full fiber paths, in some regions closer to the blank holder, some yarns may experience tension.   The bending rigidity of the fabric has a direct influence on size and shape of wrinkles. This should be taken into account in modeling approaches and the relationship between bending rigidity and the forming temperature and forming rates should also be investigated.    87  The influence of nonlinear contact forces was speculated to be significant when flattening wrinkles at high shear angles. In addition, the source of initiation of compressive forces at low shear angles was deemed to be possibly due to the fabric misalignments.  Experimental forming trials using blank holder geometry modification  Using the proposed blank holder modification, defects such as tow waviness, yarn jamming, and wrinkling were noticeably mitigated. This was attributed to exerting forces along the bias tow direction, assisting in overcoming tow cross-over forces, and hence postponing wrinkling. Less compressive forces were developed along the tow directions using the modified blank holder, and the deformed part possessed higher quality compared to the formed sample without the blank holder modification.   6.2 Contributions to knowledge  Sources of some conflicts in the literature regarding the effect of membrane stresses on the shear response of woven fabrics were discussed and resolved using a new analytical characterization framework which transfers the global measured data to the local normalized forces and displacements within the region of interest of the test sample.   A two-way tension shear coupling was detected in woven fabrics through development of a custom design combined loading fixture; it was shown that the effect of shear loading on yarns’ tensile behavior is quite significant. This new effect is deemed vital in design considerations as the mechanical properties of the final part become closely linked to the forming operation.   The need to pre-conditioning fabrics to get repeatable results between tests among laboratories has been a highly debated topic in the fabric forming community; since the reinforcement often is not pre-conditioned on the actual manufacturing floors. Removing the need for pre-conditioning using needle-type boundary condition during the tests was yet another novelty throughout this study.   88  A new characterization technique, namely a multi-step biaxial bias extension (MBBE) test, was proposed to determine the amount of required longitudinal and transverse forces to form and flatten wrinkles of different sizes, respectively. The underlying deformation mechanisms and the wrinkling/de-wrinkling response of the fabric were investigated, resulting into some potential design considerations for future applications.   The idea of modifying the blank holder geometry was proposed as to apply an optimum amount of de-wrinkling force to the preform during forming. The repetitive forming results showed that the modified blank holder can effectively mitigate the defects, thanks to the induced tension-assisted shearing condition for the fabric. The modification method would be fairly easy to implement in practice and would not oblige manufacturers to alter their thermoforming setup drastically. Implementation of modified blank holders in RTM processes is anticipated to be easier and more cost effective compared to segmented blank holders or rollers which necessitate sophisticated devices to control the pressure around the mould circumferences.  6.3 Future work The following recommendations are proposed as possible future research directions in the field:   Further exploring the validity of above-mentioned blank holder modification idea under part geometry conditions closer to industrial thermo-forming case studies, the investigation of fabric behavior under general in-plane loadings at elevated temperatures or during curing process of the composite part.    Similar characterization approaches such as investigation of tension-shear coupling and wrinkling/de-wrinkling can be conducted on other types of fabric architectures and fiber materials to examine the generalization of present conclusions.   The significance of coupling factor in meso-level is dependent on the weave architecture and geometrical parameters such as yarn width and spacing. Hence, some sensitivity  89 analyses on the effect of these parameters on the coupling factor can be performed, similar to [46, 47]. A deeper understanding of the effect of coupling in predicting the shape and size of wrinkles (e.g. similar to [48]) can be another worthwhile study.   More sophisticated testing devices can be designed as to decouple the effect of processing conditions and the loading modes on the tension-shear coupling characterization of fabrics.    Future numerical studies on the MBBE test would be valuable to validate the hypothesis made here based on experimental results. In particular, examining the deformation of fiber slippage regions and their relation to tension-shear coupling is deemed to be of significant importance for forming simulations.   Future implementation of the blank holder geometry modification in numerical simulations is expected to enable the manufacturer and adjust the optimum blank holder boundary conditions to accurately mitigate wrinkling in the useful regions of the parts, with no excessive pressure to damage the fibers or cause undesired slippage, waviness or yarn jamming. As discussed in Chapter 5, defects due to intentionally posed asymmetric blank holding conditions may provide the worst case scenario for lab-scale research, upon which the feasibility of geometry modification of blank holders may be examined. Nevertheless, real-life forming applications involve more complex geometrical shapes, and additional 3D forming experiments are recommended to verify this investigation.   Finally, the idea of blank holder geometry modification may be adapted to unidirectional (UD) composites. A main source responsible for the formation of defect for UD laminates has been shown to be the interaction between the tool surface and the ‘curing’ composite plies [80]. For instance, as shown in Figure 6.1, adding an extra flange to the mould may prevent the layers to slide over each other and hence mitigate defects such as in-plane misalignment and wrinkling, both of which known to cause noticeable reduction in the mechanical properties of the final part [81].  90  Figure 6.1    The proposed geometry modification (shown in green). Shear slip will result in the formation of an S-shaped wrinkle in a 90 or ± 45 ply (adapted from [80]).                       91 Bibliography or References   [1] F. Abbassi, I. 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