**3.1. The in-plane waviness effect**

to fully predict damage propagation of non-woven felts due to the presence of more random‐ ness than, e.g., woven composites. Furthermore, on account of existence of voids, various fiber concentrations, and non-uniform fiber orientations at different points of a non-woven fabric, the homogenization rule may not be fully valid. In other words, the micro behavior of representative volume cells should be very cautiously extended to the macro behavior of nonwoven felts. Therefore, some researchers decided to sacrifice computational time for accom‐ plishing more reliable results by modeling the entire specimen at the micro/meso level instead of a single unit cell. Although this method is computationally expensive and may not be directly applied to large scale structures, small laboratory-scale specimens can be modeled and compared to experiments. In this type of modeling, however, simulation of bonding between fibers is controversial. In some studies, rigid contacts were defined between fibers. The first group of analyses that implemented this assumption was performed by Britton et al. [59–61]. Although they considered rigid contacts in bonds, they took into account bonding breakage. For the determination of bonding failure, they assumed when the force of a fiber exceeds a certain value, the fiber is debonded from the bond point. In another study, Wu and Dzenis considered the elastic behavior of planar fiber networks numerically [62]. In their simulations, slippage of fibers on each other and their angular displacement were overlooked. Constitutive equation was found based on the average of dissipated energy in each fiber. The numerical results were fairly comparable with analytical predictions. To make use of more advanced fiber contact models, Grindstaff and Hansen used springs to model bonds between fibers [63]. In order to determine the stiffness of springs, tensile tests were carried out on one single bond. One of the other advanced contact simulations was performed by Ridruejo et al. [64]. They simulated the behavior of glass fiber non-woven fabrics by explicitly introducing the fiber bundles using a random distribution. The implemented mechanical behavior and geometrical parameters of fibers were measured by removing a single fiber from the fabric and applying tensile test on it. In order to model a realistic contact, tiebreak contact was utilized in which fibers were jointed at their crossovers until bonding failure occurs. Although fibers do not move together after debonding, there was a pre-defined friction between them due to the use of this type of contact, which brought another capability of the model to consider fibers sliding. Experimental results of that study demonstrated that the main and first induced failure mode in non-woven fabrics under tension is bonding failure which propagates and creates a wide band. There was a good agreement between numerical and experimental results. Farukh et al. simulated thermally bonded nonwovens with a new insight into the bonding issue [65]. It has been reported that during the manufacturing process, high temperature and pressure at bond points can cause changes in molecular arrangement of fibers [66]. Additionally, stress concen‐ tration exists in fiber crossover points of nonwovens, similar to woven composites. As a result, the mechanical behavior of fibers in a fibrous network is different between an original fiber before the fabrication process and a fiber removed from the fabricated fabric sample. Hence, they extracted a fiber from the fabric sample in a way that the fiber was jointed to bonds at both ends. Their tensile tests showed that the ultimate strength and strain of fibers within fabrics are less, in comparison with those of unprocessed fibers. The numerical simulation was able to predict the general behavior of non-woven felts under tension with a reasonable

accuracy.

250 Non-woven Fabrics

A detailed experimental investigation was carried out into the mechanical behavior of a consolidated polypropylene/glass twill lamina under uniaxial tensile loading in warp and weft directions. Digital image correlation (DIC) and microscopy were employed in order to find the effect of in-plane waviness of fibers on the material response at each stage of tension. All the tests were performed based on ASTM D3039. Three test repeats were performed for each direction (warp and weft) in order to ensure the repetitiveness of results, as also confirmed by related statistical tests [67]. Figure 5 illustrates the presence of in-plane waviness in the studied specimens. In practice, in addition to out-of-plane waviness through the thickness of a woven specimen due to the interlacement of yarns in weaving process, the warp yarns of consolidat‐ ed specimens through vacuum infusion technique were wavy in the plane of lamina, whereas the weft yarns were almost straight; this clearly indicated that the manufacturing/lamination process itself can add additional complexities to the mechanical behavior of woven compo‐ site structures.

**Figure 5.** Example of in-plane waviness of warp yarns in a woven cured composite (notice that the weft yarns are near‐ ly straight in the plane of fabric) [67].

Figure 6 shows the example of stress-strain behavior of the twill fabric samples obtained in the warp and weft directions. As depicted, the tensile behavior in the weft direction of the samples is almost linear up to the final failure with a sudden drop, which is analogous to that of most UD composites. On the other hand, the specimen responded non-linearly under the warp direction loading and then encountered failure in multiple steps with small falls at each. The results of DIC and microscopy pointed out that the main reason of such differences is the existence of in-plane waviness in the warp yarns. In fact, when the twill composite specimen was subjected to tension in the warp direction, the warp yarns which inherently had more inplane waviness than weft (fill) yarns due to weaving process, moved similar to 'snakes sliding' on a ground of matrix, hence changing the global stiffness of the sample. Although matrix cracking followed by fiber breakage arose in the samples of both directions, as illustrated in Figure 7, performing analytical and statistical analyses on the obtained results from DIC, a high resolution stereotype microscope, and visual observations of tested samples demonstrat‐ ed that the reason of matrix cracking is totally different between the warp and weft directions. Namely, the matrix experienced shear failure in warp direction whereas matrix tensile failure occurred in the weft direction. This difference in failure mode of matrix causes a sooner matrix crack initiation in specimens under tension in the warp direction. Not only does in-plane waviness affect the local damage behavior of woven composites in different directions, but also it can change the effective (global) mechanical properties such as Young's modulus, ultimate strength, and ultimate strain.

**Figure 6.** A comparison between the stress-strain behavior of the cured PP/glass twill lamina in the warp and weft directions: (A) Matrix cracking initiation, (B) Fiber fracture onset [67].

#### **3.2. The out-of-plane waviness effect**

In-plane waviness discussed in the previous section could mainly affect the tensile behavior of woven composites, rather than their bending behavior. On the other hand, undulation is the cause of less stiffness of woven composites in comparison with comparable UD composites with the same fiber/matrix constituents. Expectedly, fiber crimping should make the behavior

(a) Before damage initiation (b) Matrix cracking onset (c) Final failure (fiber fracture)

Figure 6 shows the example of stress-strain behavior of the twill fabric samples obtained in the warp and weft directions. As depicted, the tensile behavior in the weft direction of the samples is almost linear up to the final failure with a sudden drop, which is analogous to that of most UD composites. On the other hand, the specimen responded non-linearly under the warp direction loading and then encountered failure in multiple steps with small falls at each. The results of DIC and microscopy pointed out that the main reason of such differences is the existence of in-plane waviness in the warp yarns. In fact, when the twill composite specimen was subjected to tension in the warp direction, the warp yarns which inherently had more inplane waviness than weft (fill) yarns due to weaving process, moved similar to 'snakes sliding' on a ground of matrix, hence changing the global stiffness of the sample. Although matrix cracking followed by fiber breakage arose in the samples of both directions, as illustrated in Figure 7, performing analytical and statistical analyses on the obtained results from DIC, a high resolution stereotype microscope, and visual observations of tested samples demonstrat‐ ed that the reason of matrix cracking is totally different between the warp and weft directions. Namely, the matrix experienced shear failure in warp direction whereas matrix tensile failure occurred in the weft direction. This difference in failure mode of matrix causes a sooner matrix crack initiation in specimens under tension in the warp direction. Not only does in-plane waviness affect the local damage behavior of woven composites in different directions, but also it can change the effective (global) mechanical properties such as Young's modulus,

**Figure 6.** A comparison between the stress-strain behavior of the cured PP/glass twill lamina in the warp and weft

In-plane waviness discussed in the previous section could mainly affect the tensile behavior of woven composites, rather than their bending behavior. On the other hand, undulation is the cause of less stiffness of woven composites in comparison with comparable UD composites with the same fiber/matrix constituents. Expectedly, fiber crimping should make the behavior

ultimate strength, and ultimate strain.

252 Non-woven Fabrics

directions: (A) Matrix cracking initiation, (B) Fiber fracture onset [67].

**3.2. The out-of-plane waviness effect**

Figure 7. Different steps of mechanical behavior of twill composite specimen under warp tension (the white region in the red ellipse of panel (b) that does not exist in panel (a) points to the matrix **Figure 7.** Different steps of mechanical behavior of twill composite specimen under warp tension (the white region in the red ellipse of panel (b) that does not exist in panel (a) points to the matrix cracking in macro level) [67].

of woven composites quite distinct from UDs under bending. To divulge this, the damage mechanism of oven-vacuum bagged twill glass/PP composite specimens under three-point bending was investigated [68]. The specimens were comprised of six twill layers with 6.18 mm of total thickness. Other dimensions of the specimens and deformation rate of loading were selected based on ASTM D7264. DIC was exploited to precisely observe the failure mechanisms of the woven composite samples step-by-step. The effect of surface quality was also examined in order to take into account the effect of the manufacturing process itself. In fact, due to the existence of crimping in woven composites, each studied specimen had two different surface conditions on its sides; one of which was almost flat as it was adjacent to the metallic mould during vacuum process. As a consequence, it was under more pressure, causing the undulation of the layer to fade. The other surface (open side) that was inherently not subject to the same processing pressure was wavy, with an average amplitude of 0.4 mm. Figure 8 demonstrates these two surfaces. As a result, two groups of samples were considered in the subsequent statistical analysis of the study. Namely, the specimens were subjected to loading in two conditions in which either the smooth or the curvy surface had direct contact with the loading nose. during vacuum process. As a consequence, it was under more pressure, causing the undulation of the layer to fade. The other surface (open side) that was inherently not subject to the same processing pressure was wavy, with an average amplitude of 0.4 mm. Figure 8 demonstrates these two surfaces. As a result, two groups of samples were considered in the subsequent statistical analysis of the study. Namely, the specimens were subjected to loading in two conditions in which either the smooth or the curvy surface had direct contact with the loading cracking in macro level) [67]. **3.2. The out-of-plane waviness effect**  In-plane waviness discussed in the previous section could mainly affect the tensile behavior of woven composites, rather than their bending behavior. On the other hand, undulation is the cause of less stiffness of woven composites in comparison with comparable UD composites with the same fiber/matrix constituents. Expectedly, fiber crimping should make the behavior of woven composites quite distinct from UDs under bending. To divulge this, the

(a) Bottom view (smooth surface)

of woven composites.

nose.

(b) Upper view (rough/wavy surface)

Figure 8. Different surfaces of an open-molded (oven vacuum bagged) twill specimen [68].

Figure 9. Although for both loaded surfaces, the bending response is linear until the first failure mode—fiber compression failure—and for the final failure—fiber tensile failure—significant differences can be observed between the two curves in Figure 9, proving the effect of surface quality (manufacturing) and eventually out-of-plane waviness of fibers on the bending behavior

 Figure 9. Comparison between the bending responses of two woven composite specimens with different loaded surfaces. For *flat surface loaded sample:* Point A: Initiation of fiber micro buckling in the first (top) layer, Point B: Completion of failure in the first layer, Point F:

(c) Side view (showing both surfaces at the same time)

Typical bending responses of samples under the two surface conditions are presented in Figure 9. Although for both loaded surfaces, the bending response is linear until the first failure mode —fiber compression failure, significant differences can be observed between the two curves in Figure 9, proving the effect of surface quality (manufacturing) and eventually out-of-plane waviness of fibers on the bending behavior of woven composites.

**Figure 9.** Comparison between the bending responses of two woven composite specimens with different loaded surfa‐ ces. For *flat surface loaded sample:* Point A: Initiation of fiber micro buckling in the first (top) layer, Point B: Completion of failure in the first layer, Point F: complete compression failure in the second layer, Point C and G: Delamination occurrence, Point H: Onset of fiber tensile failure in the lowest layer (6th), Point I: Complete fiber breakage in 5th layer. For *curvy surface loaded sample*: Point A: Initiation of fiber micro buckling in the first (top) layer, Point B: Completion of failure in the first layer, Point C: Complete compression failure in the second layer, Point D: Nucleation of fiber break‐ age in the lowest layer, Point E: Complete failure in the lowest layer, Point F: Complete fiber tensile failure in the 5th layer [68].

Figure 10 further investigates the failure mechanisms of specimens in each loading condition. The DIC results informed that crimping can cause fiber compression failure not to occur exactly in the middle of the beam specimen where the applied (global) bending moment is maximum. In fact, due to the crimping, yarns in woven composites are comparable to sinusoidal beams with various amplitudes of waviness over their longitudinal axis, as illustrated in Figure 11. The higher the amplitude at a point, the less the buckling force of that location of yarn, and hence, a higher chance of failure initiation at that point. Consequently, the location in which fiber compression failure begins depends not only on the amount of applied bending moment, but also on the crimping amplitude of that point—which in effect changes the critical force of micro-buckling. However, delamination, the most common disadvantage of UD composites under bending due to the significant mismatch between layers of UD laminates, occurred only when the flat surface of the woven samples was under loading. However, concurrently taken photos by DIC and the force-displacement curves obtained by Instron machine divulged that delamination is not so influential to substantially drop the global force, point C and G in "loaded flat surface" curve as shown in Figure 9. The given interpretation for this observation may be that the debonded area is restricted between cells in woven composites, as shown in Figure 12(a). Hence, it cannot grow through the whole interface between the two layers, while the delamination area is much larger in UDs because it can propagate substantially [41]. Supporting this hypothesis, the actual micrograph in Figure 12(b) showed that matrix cracking has in the red regions of Figure 12 (a) where there is no fibers to resist the loading. These matrix cracks then resulted in debonding between the two layers. It is to note that along with the effect of out-of-plane waviness on the damage mechanism of woven composites, this type of waviness can affect the bending material parameters such as maximum force, ultimate deflection, and absorbed energy. For instance, the ultimate deflection was different by 37% between the two samples as seen in Figure 9.

Typical bending responses of samples under the two surface conditions are presented in Figure 9. Although for both loaded surfaces, the bending response is linear until the first failure mode —fiber compression failure, significant differences can be observed between the two curves in Figure 9, proving the effect of surface quality (manufacturing) and eventually out-of-plane

**Figure 9.** Comparison between the bending responses of two woven composite specimens with different loaded surfa‐ ces. For *flat surface loaded sample:* Point A: Initiation of fiber micro buckling in the first (top) layer, Point B: Completion of failure in the first layer, Point F: complete compression failure in the second layer, Point C and G: Delamination occurrence, Point H: Onset of fiber tensile failure in the lowest layer (6th), Point I: Complete fiber breakage in 5th layer. For *curvy surface loaded sample*: Point A: Initiation of fiber micro buckling in the first (top) layer, Point B: Completion of failure in the first layer, Point C: Complete compression failure in the second layer, Point D: Nucleation of fiber break‐ age in the lowest layer, Point E: Complete failure in the lowest layer, Point F: Complete fiber tensile failure in the 5th

Figure 10 further investigates the failure mechanisms of specimens in each loading condition. The DIC results informed that crimping can cause fiber compression failure not to occur exactly in the middle of the beam specimen where the applied (global) bending moment is maximum. In fact, due to the crimping, yarns in woven composites are comparable to sinusoidal beams with various amplitudes of waviness over their longitudinal axis, as illustrated in Figure 11. The higher the amplitude at a point, the less the buckling force of that location of yarn, and hence, a higher chance of failure initiation at that point. Consequently, the location in which fiber compression failure begins depends not only on the amount of applied bending moment, but also on the crimping amplitude of that point—which in effect changes the critical force of micro-buckling. However, delamination, the most common disadvantage of UD composites under bending due to the significant mismatch between layers of UD laminates, occurred only when the flat surface of the woven samples was under loading. However, concurrently taken photos by DIC and the force-displacement curves obtained by Instron machine divulged that delamination is not so influential to substantially drop the global force, point C and G in "loaded flat surface" curve as shown in Figure 9. The given interpretation for this observation may be that the debonded area is restricted between cells in woven composites, as shown in Figure 12(a). Hence, it cannot grow through the whole interface between the two layers, while the delamination area is much larger in UDs because it can propagate substantially [41].

waviness of fibers on the bending behavior of woven composites.

layer [68].

254 Non-woven Fabrics

Figure 10. Damage mechanisms in two woven three-point bending specimens; left photos (a), (c), (e), and (g) correspond to the specimen loaded on a flat surface; right images (b), (d), (f), and (h) are for the specimen loaded on a curvy surface. (a) and (b): Specimens before any damage onset; (c) and (d): Initiation of fiber micro buckling; (e) and (f): Propagation of fiber buckling; **Figure 10.** Damage mechanisms in two woven three-point bending specimens; left photos (a), (c), (e), and (g) corre‐ spond to the specimen loaded on a flat surface; right images (b), (d), (f), and (h) are for the specimen loaded on a curvy surface. (a) and (b): Specimens before any damage onset; (c) and (d): Initiation of fiber micro buckling; (e) and (f): Prop‐ agation of fiber buckling; (g) and (h): Fiber breakage initiation [68].

(g) and (h): Fiber breakage initiation [68].

**Figure 11.** Schematic of varying bending moment and waviness amplitude in different locations of a yarn, especially in the open-side of the molded specimen (i.e., the highest layer of laminate). Figure 11. Schematic of varying bending moment and waviness amplitude in different locations

of a yarn, especially in the open-side of the molded specimen (i.e., the highest layer of laminate).

Figure 12. Restricted matrix crack in the woven composite specimen. (a) Schematic diagram; (b) Actual micro-image of cracks from the sample under three-point bending [68]. **Figure 12.** Restricted matrix crack in the woven composite specimen. (a) Schematic diagram; (b) Actual micro-image of cracks from the sample under three-point bending [68].

#### Based on the conducted review, the interlaced fiber architecture of woven composites, the **4. Conclusion and anticipated future developments**

**4. Conclusion and anticipated future developments** 

main reason of their superb behavior, causes a series of complexities such as in-plane as well as out-of-plane misalignment effect in the laminated parts, along with a coupling between warp and weft yarns, all of which having a different effect under different deformation modes. As an example, recent experimental results show that not only the in-plane waviness inherited from the waving process is one of the reasons of non-linearity in uniaxial tensile behavior of woven composites, but it also leads to a significant unbalance in the damage tolerance measure in warp and weft directions. In effect, material properties such as Young's modulus, ultimate strength, and ultimate strain of the two principal directions of woven laminates should be expected to be statistically different in the presence of processing-induced in-plane waviness, despite the fact that as-received fabric preforms are often assumed balanced. In addition, evidence in the literature demonstrates that out-of-plane waviness can yield unusual failure modes in openmolded woven composites under three-point bending mode, similar to the propagation of "Plate Based on the conducted review, the interlaced fiber architecture of woven composites, the main reason of their superb behavior, causes a series of complexities such as in-plane as well as outof-plane misalignment effect in the laminated parts, along with a coupling between warp and weft yarns, all of which having a different effect under different deformation modes. As an example, recent experimental results show that not only the in-plane waviness inherited from the waving process is one of the reasons of non-linearity in uniaxial tensile behavior of woven composites, but it also leads to a significant unbalance in the damage tolerance measure in warp and weft directions. In effect, material properties such as Young's modulus, ultimate strength, and ultimate strain of the two principal directions of woven laminates should be expected to be statistically different in the presence of processing-induced in-plane waviness, despite the fact that as-received fabric preforms are often assumed balanced. In addition, evidence in the literature demonstrates that out-of-plane waviness can yield unusual failure modes in open-molded woven composites under three-point bending mode, similar to the propagation of "Plate Tectonics" in Geology. So dominant is the effect of yarn crimping that a change in the loaded surface of a sample can lead to a significant decrease in the bending resistance of the open-molded woven laminates. Moreover, it was observed that in converse

with UD composites, in which interlaminar failure grows instantly, delamination can be well confined between the cells of a weave architecture and not extended to the entire sample, hence inducing higher damage tolerance.

Owing to the aforementioned complexities in the response of woven fabrics, earlier micro, meso, and macro level damage models of UDs may not be fully compatible to predict the behavior of woven structures under various loading regimes, while fulfilling high accuracy and minimum computational cost. To meet the two latter practical requirements, the most appropriate way to analyze woven composites and to predict their damage is believed to be the phenomenological approach, along with required experimental analyses. Currently, there is no comprehensive experimental study revealing the effect of woven architecture of fibers in a multitude of deformation modes, classifying the dominant failure modes specifically to these composites, and eventually presenting an explicit, short, and easy-to-implement phenomeno‐ logical model for the damage nucleation stage and finally growth. Moreover, different stressstrain behaviors of textile composites with non-linear functions have been employed in the previous macro-level research investigations, while there have been no sufficient mirco/meso level evidence on the roots of this non-linearity. As reviewed in this chapter, the determination of the sources behind material non-linearity is crucial to propose accurate damage models. Furthermore, with the exception of a few recent works, past researches have not paid close attention to combined loading effects—which are very likely in practical applications—on the behavior of woven composites. Recent experimental works reveal that the interaction between warp and weft yarns has a significant effect on both dry and coated fabrics under combined loadings; however, to the best of authors' knowledge, no detailed study of this kind has been reported for consolidated laminates. In addition, the characterization of loading-unloading behavior of woven composites in quasi-static and high strain rate regimes (e.g., for application in inflatable fabric tube, or impact design of structures), particularly after arising some first damage, have not received sufficient consideration.

**Figure 11.** Schematic of varying bending moment and waviness amplitude in different locations of a yarn, especially in the open-side of the molded specimen (i.e., the highest layer of laminate). Figure 11. Schematic of varying bending moment and waviness amplitude in different locations of a yarn, especially in the open-side of the molded specimen (i.e., the highest layer of laminate).

(a) (b)

**Figure 12.** Restricted matrix crack in the woven composite specimen. (a) Schematic diagram; (b) Actual micro-image of

**4. Conclusion and anticipated future developments** 

**4. Conclusion and anticipated future developments**

cracks from the sample under three-point bending [68].

256 Non-woven Fabrics

Figure 12. Restricted matrix crack in the woven composite specimen. (a) Schematic diagram; (b) Actual micro-image of cracks from the sample under three-point bending [68].

main reason of their superb behavior, causes a series of complexities such as in-plane as well as out-of-plane misalignment effect in the laminated parts, along with a coupling between warp and weft yarns, all of which having a different effect under different deformation modes. As an example, recent experimental results show that not only the in-plane waviness inherited from the waving process is one of the reasons of non-linearity in uniaxial tensile behavior of woven composites, but it also leads to a significant unbalance in the damage tolerance measure in warp and weft directions. In effect, material properties such as Young's modulus, ultimate strength, and ultimate strain of the two principal directions of woven laminates should be expected to be statistically different in the presence of processing-induced in-plane waviness, despite the fact that as-received fabric preforms are often assumed balanced. In addition, evidence in the literature demonstrates that out-of-plane waviness can yield unusual failure modes in openmolded woven composites under three-point bending mode, similar to the propagation of "Plate

Based on the conducted review, the interlaced fiber architecture of woven composites, the main reason of their superb behavior, causes a series of complexities such as in-plane as well as outof-plane misalignment effect in the laminated parts, along with a coupling between warp and weft yarns, all of which having a different effect under different deformation modes. As an example, recent experimental results show that not only the in-plane waviness inherited from the waving process is one of the reasons of non-linearity in uniaxial tensile behavior of woven composites, but it also leads to a significant unbalance in the damage tolerance measure in warp and weft directions. In effect, material properties such as Young's modulus, ultimate strength, and ultimate strain of the two principal directions of woven laminates should be expected to be statistically different in the presence of processing-induced in-plane waviness, despite the fact that as-received fabric preforms are often assumed balanced. In addition, evidence in the literature demonstrates that out-of-plane waviness can yield unusual failure modes in open-molded woven composites under three-point bending mode, similar to the propagation of "Plate Tectonics" in Geology. So dominant is the effect of yarn crimping that a change in the loaded surface of a sample can lead to a significant decrease in the bending resistance of the open-molded woven laminates. Moreover, it was observed that in converse

Based on the conducted review, the interlaced fiber architecture of woven composites, the

Regarding the analysis of non-woven fabrics, in addition to the aforementioned complexities in woven composites, more complexities such as non-uniform fiber architecture, fiber sliding, and complex bonding behavior between fibers need to be addressed. As a consequence, the analysis of non-woven felts is deemed more complicated than woven composites, despite several general similarities seen in damage modeling approaches taken for both types of fabric materials.

Finally, it is noticed that statistical analysis has taken little part in the past characterization efforts on fabric reinforced composites. This is despite the fact that uncertainties underlying the soft reinforcing materials in the dry form [69], along with process-induced uncertainties and risk during matrix curing/manufacturing stages, may have an enormous effect on the variation of parameters needed for damage modeling. Subsequently, the application of hypothesis testing and black-box optimization methods in the field of damage modeling of composites is believed to be vital in future studies to ensure the reliability and applicability of the identified models.
