*5.2.7. Three-dimensional axial braided fabric structure*

Kuo [143] investigated topology of 3D braided fabrics by using pultruded rods as axial reinforcements. The effect of yarns size and spacing as well as the pitch length on the final preform geometry was examined. Structural analysis of 3D axial braided preforms revealed that braider yarn orientation and yarn volume fraction can be predicted from the measured values of yarn sizes, preform contour sizes, pitch length and number of axial and braider yarns [144]. Li [145] studied the structural mechanics of 3D braided preforms. It was observed that the load in the axial direction was mostly carried by axial yarns whereas the braider yarns carry the transverse loads. Therefore, it was desirable for the orientation angle of the braiders to be large.

#### *5.2.8. Three-dimensional nonwoven fabric structure*

The 3D nonwovens are anisotropic materials in which the fiber strength and modulus, fiber length and thickness, fiber volume fraction and fiber angle in the in-plane and out-of-plane directions are important preform properties [56]. The general stress–strain relationship is given by:

$$
\sigma = \mathbb{C} : \mathfrak{x} \tag{11}
$$

where *σ* is the stress, a second order tensor, *ε* is the strain, also a second-order tensor, and *C* is the stiffness constant, a fourth-order tensor [56]. For two-dimensional nonwovens, the inplane directional stiffness of the nonwoven is given in Eqs. (12) and (13) based on fiber web theory [56].

$$C\_{11} = E\_f \int\_0^\pi \cos^4 f\left(\theta\right) \,d\theta \tag{12}$$

$$C\_{12} = E\_f \left[ \cos^2 \theta \sin^2 \theta \, f(\theta) \right] d\theta \tag{13}$$

where *C11* is the stiffness constant in the x-direction on the plane perpendicular to the x-axis, *C12* is the stiffness constant in the y-direction on the plane perpendicular to the x-axis, *Ef* is the fiber modulus and *f (θ)* is the distribution of fiber orientation.

Directional stiffness constants of a web can be obtained, given the fiber modulus and the fiber orientation distribution in the web. The fiber web theory can be applied to the 3D nonwoven preform in which some amount of z-fiber is oriented in the thickness direction of the web [102, 146]. It was claimed that there is a good agreement between the fiber web theory and the experimental measurement of needle punched web where the fibers between two bonded points are straight and that fibers are rigidly bonded. It is tedious and time consuming to determine the fiber orientation distribution in a web. However, several practical methods have been developed to measure the fiber orientation as X-ray diffraction, laser light diffraction, light reflection and refraction intensity [147].

#### *5.2.9. Three-dimensional knitted fabric structure*

braided layer. The unit cell structure has a fine intertwine in the 1×1 pattern, whereas it has a coarse intertwine for other braid patterns. When the influence of number of layers is consid‐ ered, it was found that, for all braid patterns, the unit cell thickness increases when the number of layers is increased in 3D braided and 3D axial braided structures. Furthermore, for the same number of layers, the unit cell thickness in the 1×1 pattern is less when compared to other patterns. This showed that all braid patterns except 1×1 resulted in a coarse form of unit cell

Byun and Chou [141] examined the process-microstructure relationships of 2-step and 4-step braided composites by geometrical modeling of unit cells. The effect of process parameters such as braid pattern and take-up rate on the microstructural properties like braid yarn angle and fiber volume fraction was investigated. They also studied the fabric jamming phenomen‐ on. Three-dimensional braided composites were characterized by using the fabric geometry model (FGM). This model uses the processing parameters as well as the properties of the fibers and the matrix. It basically relies on two parameters such as the fabric geometry and the fiber volume fraction. Fabric geometry is a function of the take-up rate, whereas row and column motions determine the yarn displacement values, which are expressed as number of yarns. The yarn orientation in a 3D preform is dependent upon fabric shape and construction as well

Kuo [143] investigated topology of 3D braided fabrics by using pultruded rods as axial reinforcements. The effect of yarns size and spacing as well as the pitch length on the final preform geometry was examined. Structural analysis of 3D axial braided preforms revealed that braider yarn orientation and yarn volume fraction can be predicted from the measured values of yarn sizes, preform contour sizes, pitch length and number of axial and braider yarns [144]. Li [145] studied the structural mechanics of 3D braided preforms. It was observed that the load in the axial direction was mostly carried by axial yarns whereas the braider yarns carry the transverse loads. Therefore, it was desirable for the orientation angle of the braiders

The 3D nonwovens are anisotropic materials in which the fiber strength and modulus, fiber length and thickness, fiber volume fraction and fiber angle in the in-plane and out-of-plane directions are important preform properties [56]. The general stress–strain relationship is given

> e

where *σ* is the stress, a second order tensor, *ε* is the strain, also a second-order tensor, and *C* is the stiffness constant, a fourth-order tensor [56]. For two-dimensional nonwovens, the inplane directional stiffness of the nonwoven is given in Eqs. (12) and (13) based on fiber web

= *C* : (11)

s

structure [70].

124 Non-woven Fabrics

to be large.

by:

theory [56].

as the dimensions of the braiding loom [142].

*5.2.7. Three-dimensional axial braided fabric structure*

*5.2.8. Three-dimensional nonwoven fabric structure*

The properties of 3D knitted structures including multilayered weft or warp knitted fabrics and 3D multiaxis warp knitted preforms were studied by various researchers. The fiber volume fraction of the 3D multilayered weft knitted structure was proposed by Eq. (14):

$$V\_f = \frac{n\_k \ D\_y \ L\_s \ \gets W}{\text{9 } \ \rho\_f \ A \ t} \times 10^{-5} \tag{14}$$

where *nk* is the number of plies of the fabric in the composite, *Dy* is the yarn linear density, *Ls* is the length of yarn in one loop of the unit cell, *C* is the course density, *W* is the wale density, *ρ<sup>f</sup>* is the density of fiber and *A* is the planar area over which *W* and *C* are measured, and t is the structure thickness.

It was concluded that the fiber content of weft knitted fabric composites can be increased by increasing *D*y using the coarser yarns [36]. In general, the coarser yarns are difficult to knit and the coarsest yarn knittable is dependent on the yarn type and knitting needle size. In addition, the maximum Vf is limited by the knitting needles used in the knitting machine based on the relation *N* = *C/W*, where N is the stitching density. Hence, Vf is proportion‐ al to the structure parameters of Ls and N. The maximum Vf can be achieved by increas‐ ing the stitch density or the tightness of the knitted fabric. It was claimed that the attainable volume fraction of knitted fabric composite can be 40% [36, 79]. It was stated that the failure mechanisms for weft knitted structures were dependent on both the wale and the course directional crack propagations, and demonstrated better interlaminar fracture toughness properties due to the 3D loop structure [49]. It was found that the failure process of weft knitted structures under tensile load includes crack branching, loop to loop friction, yarn bridging and fiber breakages. It was also shown that an increase in loop length or stitch density has opposite effects on the tensile strength and impact performance of the weftknitted composites. The plain weft knitted structure exhibited good energy absorption capacity. Matrix cracking, matrix/fiber debonding, and fiber breakage were the major damage mechanisms [36, 49, 109]. The 3D loop structure was studied, and it was pro‐ posed that the loop structure was constituted by sets of arcs. Adoption of the arc shape loop geometry into micromechanical technique considers the influence of knitting parame‐ ters and the estimation of elastic properties of knitted composites [148].
