**2. Damage modeling approaches for fabric composites**

Preparatory to discussing the damage mechanisms of woven and non-woven fabrics, a definition for an appropriate damage model should be provided. Generally, a comprehensive and accurate damage model for a given material would embrace three features:


The studies investigating damage in woven and non-woven fabric materials can be classified in different ways. One categorization may be with respect to the group of studies on each of the three aforementioned features of a damage model. Another classification is based on the investigations methodology. Researchers have performed analytical, numerical, and experi‐ mental methods in order to study the damage behavior of fabric composite materials. The numerical and analytical studies are in turn divided to micro, meso, and macro. The latter type of classification is the one opted here for the subsequent review sections.

#### **2.1. Damage models for woven fabric composites**

#### *2.1.1. Micro/meso level analyses*

Despite the fact that composite materials are predominantly regarded as homogeneous orthotropic materials, notably in industrial projects, they are not as homogeneous as conven‐ tional materials such as metals. Composites are comprised of fibers and matrix constituents and therefore the mechanical properties of different points of the material medium are not necessarily the same. In fact, it is this specific feature of composite materials that distinguishes their global behavior. As an illustration, when a visible macro-damage is observed in a composite specimen under loading, failure has already initiated and propagated in the micro/ meso level of the specimen before it appears at macro level. As a consequence, one of the ways to study the failure mechanism of fabric composite materials is to conduct an investigation into the micro/meso levels. However, studying full scale structures/specimens at these levels is more arduous and expensive in comparison to the macro level. In order to carry out the micro/meso level analyses of composite materials in a cost-effective manner, the smallest segment of a whole specimen is sometimes defined such that it is the representative of the whole specimen. That is, the whole specimen should be reproducible by repeating this representative volume element (RVE). Homogenization—the main basic rule in the RVE approach—is then employed to define the effective mechanical properties of the RVE based on the mechanical properties of its constituents, namely fibers and matrix. The effectiveness of the micro/meso-level investigation for woven composite materials is deemed to be more, when compared to unidirectional composites, in that the micro-structure of woven architec‐ tures is more complicated and may not be idealized at macro-levels.

to complex reinforcement architecture in woven composites, new enhanced damage models need to be driven. In order to further underscore this need, some recent experimental evidences by the authors regarding the influence of in-plane and out-of-plane waviness of yarns upon the mechanical behavior of a typical woven composite is presented. The last section of the chapter outlines the main conclusions and the anticipated future work developments.

Preparatory to discussing the damage mechanisms of woven and non-woven fabrics, a definition for an appropriate damage model should be provided. Generally, a comprehensive

**•** Damage initiation: Exploiting precise and reasonable failure criteria to predict the onset of

**•** Degradation of material properties: On account of any damage in a material, it cannot provide stiffness and strength as high as its undamaged state. Anticipating a reasonable pattern to reduce the mechanical properties of the material upon damage is another critical

**•** Damage propagation: How an induced damage grows is perhaps the most controversial part of any damage model. Forecasting the rate of damage growth with an acceptable accuracy imparts the post-damage behavior and tolerance of a manufactured structure/

The studies investigating damage in woven and non-woven fabric materials can be classified in different ways. One categorization may be with respect to the group of studies on each of the three aforementioned features of a damage model. Another classification is based on the investigations methodology. Researchers have performed analytical, numerical, and experi‐ mental methods in order to study the damage behavior of fabric composite materials. The numerical and analytical studies are in turn divided to micro, meso, and macro. The latter type

Despite the fact that composite materials are predominantly regarded as homogeneous orthotropic materials, notably in industrial projects, they are not as homogeneous as conven‐ tional materials such as metals. Composites are comprised of fibers and matrix constituents and therefore the mechanical properties of different points of the material medium are not necessarily the same. In fact, it is this specific feature of composite materials that distinguishes their global behavior. As an illustration, when a visible macro-damage is observed in a composite specimen under loading, failure has already initiated and propagated in the micro/ meso level of the specimen before it appears at macro level. As a consequence, one of the ways

and accurate damage model for a given material would embrace three features:

**2. Damage modeling approaches for fabric composites**

various failure modes is the primary part of any damage model.

of classification is the one opted here for the subsequent review sections.

**2.1. Damage models for woven fabric composites**

aspect of a full-scale damage model.

product during service.

236 Non-woven Fabrics

*2.1.1. Micro/meso level analyses*

The woven composite RVEs can be mainly studied in two ways. The first method is to model yarns in warp as well as fill directions and matrix in a detailed numerical model with shell or solid elements. In this approach, the yarns and matrix are considered explicitly. In one of the first study of this kind, Blackketter et al. presented a meso-level model for woven composite materials using solid elements [4]. In their simulations, the mechanical properties of yarns, which included fibers and resin, were found based on the micromechanical homogenization approach and the mechanical properties of constituents. The volume fraction of fibers in the yarns and in the unit cell was selected 70% and 60%, respectively. The failure occurrence in the matrix, which was considered isotropic, was based on a maximum stress criterion. In addition, damage degradation was taken into account by decreasing the corresponding Young's modulus of the Gaussian integration points in an element by 99%. Regarding the yarns modeled as orthotropic materials, two failure modes in the longitudinal and transverse directions were assumed. The results of experimental and numerical studies were rather comparable.

In another study, Tang and Withcomb assumed a failure criterion and a linear degradation model for different woven architectures in order to compare their damage mechanisms [5]. They modeled warps, wefts, and matrix pockets of an RVE in a detailed 3D fashion. The maximum stress failure criterion was utilized. The obtained results showed that the weave architecture can have a considerable impact on the composite's progressive damage behavior, even if the volume fraction of fibers, tow waviness, and tow cross-sections of the specimens were the same. Jia et al. established a micro-meso scale model for the repeating unit cells of a 3D woven composite material, in which there were yarns in three principal directions [6]. The yarns in the meso level simulation were composed of repeating micro representative unit cells (RUC) consisting of fibers and matrix. The maximum strain and stress values were monitored as the failure criteria for the damage in the matrix and fibers. As to post-damage behavior, they presumed that the corresponding stress becomes zero instantly. A quadrilateral cross section was employed for the yarns. The results for one tensile testing demonstrated that there is an agreement regarding the ultimate strength prediction by the model; however, there were disagreements between numerical and experimental results at each time step (i.e., different stages of deformation before the final failure). In another research project by the same authors, the behavior of woven composite materials under three-point bending was investigated at a multi-scale (micro-meso-macro) level [7].

In each of the aforementioned studies, only a fabric cell was modeled, as a periodic boundary condition was used instead of repeating cells to create the whole specimen geometry. In general, there are two types of periodic boundary conditions known as parallel and series models. In a parallel model, it is assumed that the displacement of all constituents (cells) is the same and the load is shared between them. On the other hand, the stress is presumed to be the same in all cells in a series model, and the general displacement is the sum of that of each cell. In order to avoid such boundary assumptions, some researchers have opted to create the whole specimen meso-model by reproducing a large number of cells adjacent to each other. A good example of such approach is the simulation conducted by Chandekar and Kelkar [8]. Making use of LS-DYNA, they investigated the low velocity impact of glass and carbon woven composite materials [8]. The mosaic pattern was chosen to repeat the unit cells so as to produce the whole plate geometry. Although comparable results were observed between numerical and experimental results, running such simulations normally takes a considerable time, comprising their effectiveness for large scale industrial simulations.

In order to reduce computational time in meso-level modeling of woven composites, a second RVE methodology has been introduced. In this approach, the RVE is divided into several subcells, instead of a great number of elements. Where one level of homogenization was consid‐ ered in the first RVE modeling approach, two levels of homogenizations are performed in the second approach; the first of which is to find the general mechanical properties of sub-cells and the second is to determine the general mechanical behavior of the whole cell. The first research in this area was performed by Ishikawa and Chou [9]. Employing the classical laminate theory, they studied the elastic behavior of woven fabric materials in three models, including mosaic, undulation, and bridging models [9]. In the mosaic pattern, the fiber continuity and its crimping were not taken into account. However, these factors were consid‐ ered in the undulation model. One of the main limitations of this model was that two UD layers were assumed instead of one interlaced layer. After this work, some researchers attempted to conduct investigations into the failure behavior of woven fabric materials using the subconstituents method [10–12]. In one of the latest papers in this area, Li et al. predicted the stiffness matrix, strength, and damage evolution of woven fabric materials using Abaqus [13]. They used parallel-series assumption for the two-level homogenization. Six failure variables referring to six failure modes, including longitudinal, transverse, and out-plane failures, besides shear failure in 12, 23, and 13 directions, were taken into account. The maximum stress was chosen as the failure criterion of both fibers and matrix. The numerical results were comparable with the experimental data of tensile tests on a glass epoxy woven composite.

Although using RVEs as representatives of woven fabric materials could help designers predict the general behavior of these materials with some accuracy, this method relies on some limiting assumptions. For instance, a common assumption is that fibers and matrix have perfect contact with each other. In other words, the interface between yarns and matrix is assumed to be bonded perfectly under arbitrary deformation conditions. In reality, however, voids which arise during manufacturing processes are inevitable. On top of that, even by assuming perfect curing/consolidation, the genuine contact between fibers and matrix is similar to a 'tiebreak' contact, rather than a tied contact. In a tiebreak contact, components are bonded to each other until an ultimate interface stress is reached [14], which debonds fibers and matrix. As stated earlier, another drawback of the RVE approaches may be that the simulations in micro as well as meso levels normally takes a great amount of time/cost; therefore, they are not always feasible to use for industrial applications. The last, and perhaps the most debatable, point is that in reality the failure starts in one point of a specimen and propagates to other points, whereas it is assumed in the RVE approach that when a failure mode occurs within one RVE, it arises in all the RVEs. In other words, damage localization cannot be captured in most RVE approaches. The most useful information that can be obtained from such analysis, however, is the extent of stress concentration in the meso/micro level due to the specific architecture of woven fabric materials; specially knowing that the stress applied to the composite constituents can be much higher than the global stress applied to the specimen at macro level [15].
