**1. Introduction**

Several decades ago, composite materials were introduced with a great potential to replace conventional monolithic materials, primarily metals, due to two main features:

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Since the dawn of composite materials (1937), "unidirectional" (UD) fiber reinforced composite materials caught most of the designers' attention for several years, primarily due to their high specific stiffness ratios as well as simplicity in their analyses/design. Nevertheless, woven fiber reinforced composites gradually became a decent alternative to traditional UD composites in specific industries [1]. Woven fabric reinforcement in essence can be defined as interlaced warp and weft fibers in a repetitive pattern or weave style such as plain, twill, satin, etc. Woven composites can enjoy numerous inherent characteristics—all of which arising from their interlaced fibrous structure [1]:

In addition to woven fabrics, there exists another main type of fabric reinforcement known as 'non-woven' fabrics, which also include 'felts'. Non-woven fabrics are sheets or web structures comprised of chopped or long fibers or filaments arranged in a rather disordered architecture and consolidated by bonds of different nature, such as chemical, mechanical (e.g., stitching), or thermal bonding, rather than geometrical weaving or knitting. According to this definition, the distinct differences between woven and non-woven fabrics are the fibers arrangement at the microstructural level and the type of bonding. Woven fabrics have an ordered architecture of fibers interlaced to one another, whereas there is more randomness in the fibrous architec‐ ture of non-woven fabrics. Recently, in light of lower processing cost of non-woven composites, and easier recyclability in some cases, the use of these materials is being increased in several industrial applications such as fireproof layers, thermal insulations, ballistic protections, liquid-absorbing textiles, and geotextiles for soil reinforcement [2]. Owing to the aforemen‐ tioned inherent geometrical differences between woven and non-woven fabrics, their me‐ chanical performances are also expectedly different. In general, woven composites enjoy higher stiffness and strength in comparison with non-woven felts. However, the ultimate deformation and absorbed energy values in non-woven fabrics are often higher than woven fabrics [2].

Thanks to defined standards by most governments and related safety authorities, risk-sensitive industries in general, and aerospace and transportation in particular, as the main sectors of the composite world, are expected to satisfy certain requirements before a product can be brought to service. By flourishing the use of composites more and more, so crucial is the possession of a comprehensive knowledge on their underlying damage mechanisms upon which the ultimate load bearing capacity and deformation of structures can be predicted. As a matter of fact, the design of a composite structure with highest safety and at the same time the lightest possible *weight* cannot be accomplished without a profound knowledge on its damage behavior. Regarding the damage modeling of composite materials, to date there have been much more research activities in the area of UD composites, rather than woven and nonwoven fabrics. As an example, according to the World Wide Failure Exercise [3], there are nearly 20 failure theories derived for UD composite materials, while there is a very limited explicit failure criterion specifically developed and standardized for woven composites. Actually, using some assumptions and modifications, the common failure models of UD composite materials, for example the maximum stress criterion, are being used by some practitioners for the damage analysis of woven materials. This practice is despite the fact that none of such failure theories has been originally developed to mimic the woven nature of reinforcing material in consolidated laminate. The fact is, although woven composites are endowed with some advantages in comparison with UDs on account of their enhanced fibrous architectures, some intrinsic complications can cause their analysis to be cumbersome and very different from UDs. These complexities are briefly introduced in this section and will be further discussed in the next sections of the chapter. One of these difficulties is the change in crosssection of woven yarns over their longitudinal axes. Another one is that fibers are not straight in woven yarns similar to fibers in UD tows. In fact, yarns can have in-plane waviness (misalignment) and out-of-plane waviness (crimping) in woven laminates, which considerably affect their tensile and bending behaviors. Moreover, interaction between the warp and weft yarns may affect the effective mechanical behavior of woven laminates, especially under multidirectional/combined loading modes, similar to its significant effect on the mechanical behavior of dry fabrics. Furthermore, owing to a cellular reinforcement architecture, failure modes such as matrix cracking is restricted between weave cells in woven composites and cannot propagate as fast as it would in UDs. Another point is that the interlacement of yarns can cause local stress concentrations at meso-level. More severe complications come in the behavior of non-woven fabrics due to their rather random architecture and complex contact between fibers. Fiber re-orientation, fiber sliding, non-linear bond failure, fiber fracture, and continuous rearrangement of fibrous network are among other difficulties encountered in the analysis of non-woven fabrics [2].

Since the dawn of composite materials (1937), "unidirectional" (UD) fiber reinforced composite materials caught most of the designers' attention for several years, primarily due to their high specific stiffness ratios as well as simplicity in their analyses/design. Nevertheless, woven fiber reinforced composites gradually became a decent alternative to traditional UD composites in specific industries [1]. Woven fabric reinforcement in essence can be defined as interlaced warp and weft fibers in a repetitive pattern or weave style such as plain, twill, satin, etc. Woven composites can enjoy numerous inherent characteristics—all of which arising from their

**•** Laminated composites comprised of UD architecture are often inclined toward experiencing delamination, which in turn can decrease their stiffness and yield low damage tolerance. Instead, interlaced yarns in two directions of woven fabric reinforced composites can decrease the mismatch between laminate layers, and hence helping the material system

**•** The undulation of yarns, resulting from the interlacing yarns, induces an out-of-plane reinforcement state in woven textile composites, whereas UD composites generally suffer

**•** The manufacturing process of woven fabric composites is generally easier than the UDs. This is mainly because of the yarns entanglement, easing the draping and molding process

**•** Woven fabric plies, due to their bi-directional reinforcement, can show a much more

In addition to woven fabrics, there exists another main type of fabric reinforcement known as 'non-woven' fabrics, which also include 'felts'. Non-woven fabrics are sheets or web structures comprised of chopped or long fibers or filaments arranged in a rather disordered architecture and consolidated by bonds of different nature, such as chemical, mechanical (e.g., stitching), or thermal bonding, rather than geometrical weaving or knitting. According to this definition, the distinct differences between woven and non-woven fabrics are the fibers arrangement at the microstructural level and the type of bonding. Woven fabrics have an ordered architecture of fibers interlaced to one another, whereas there is more randomness in the fibrous architec‐ ture of non-woven fabrics. Recently, in light of lower processing cost of non-woven composites, and easier recyclability in some cases, the use of these materials is being increased in several industrial applications such as fireproof layers, thermal insulations, ballistic protections, liquid-absorbing textiles, and geotextiles for soil reinforcement [2]. Owing to the aforemen‐ tioned inherent geometrical differences between woven and non-woven fabrics, their me‐ chanical performances are also expectedly different. In general, woven composites enjoy higher stiffness and strength in comparison with non-woven felts. However, the ultimate deformation and absorbed energy values in non-woven fabrics are often higher than woven

Thanks to defined standards by most governments and related safety authorities, risk-sensitive industries in general, and aerospace and transportation in particular, as the main sectors of the composite world, are expected to satisfy certain requirements before a product can be

balanced behavior than the UDs under complex loading modes in service.

resist de-bonding and its propagation in a superior manner.

from a weak resistance through the thickness direction.

of the material for producing near-net shapes.

interlaced fibrous structure [1]:

234 Non-woven Fabrics

fabrics [2].

The rest of this chapter attempts to review the methods employed by different researchers to investigate the mechanical behavior of woven and non-woven fabric composites in general, and their damage mechanisms in particular. Benefits as well as disadvantages of each approach are discussed by relating to the above-described inherited complexities in fabric composites. In addition, the validity of presumed assumptions for each approach is argued. For woven composites, different approaches will be discussed in sub-sections 2.1.1–2.1.3, and the ap‐ proaches employed to predict the mechanical behavior of non-woven fabrics, which are methodically similar to those of woven composites, are reviewed in section 2.2. Thereafter, the above-addressed incompatibility of previous damage models of UDs to accurately anticipate the mechanical behavior of fabric composites is assessed. In particular, it is argued that owing 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.