Page 115 - 3D Fibre Reinforced Polymer Composites

104 3D Fibre Reinforced Polymer Composites

A “cross-over model” was proposed by Ramakrishna (1997a) for expressing the
crossing over of looped yarns of knitted fabric. This model considers the three-
dimensional orientation of yams in the knitted fabric composite. Each impregnated
yam is idealised as a curved unidirectional lamina. The effective elastic properties of the
yams were estimated using the laminated plate theory. The elastic properties of the
composite were determined by combining the elastic properties of yarns and the resin-
rich regions. The analytical model was extended to predict the elastic properties of
knitted-fabric composite with different fibre volume fraction (Ramakrishna, 1997b).
The predicted tensile properties compared favourably with the experimental results.

4.6 FAILURE STRENGTH PWDICTION

The failure mechanisms and procedures of a 3D textile composite material at the
micromechanical scale vary with type of loading and are intimately related to the
properties of the constituents, i.e., fibre, matrix and interface-interphase, and the micro
architectures of fibre yarns as well as yarn-matrix interphase. Strength predictions are
based on micromechanical analyses and point-based failure criteria, and may be
accurate with regard to failure initiation at critical points. However, such predictions
are only approximate in the context of global failure of the composite material.
Due to the complexity and irregularity of fibre distributions and the limitation of
measurement facilities, there is a lack of detailed knowledge and understanding of
failure mechanisms for 3D textile composites. It is difficult, if not impossible, to
perform thorough micromechanical analyses to obtain reliable strength predictions for
3D textile composites under a general type of loading. For this reason, it may be
preferable to carry out the strength predictions by treating fibre yams as an anisotropic
property, comprising of unidirectional fibres and matrix, and embedded in an isotropic
matrix. Similar to mechanical property predictions, a textile composite material may be
idealised as fibre yams of different architectures embedded in a matrix. In this
approximation, failure may occur in the yarns, matrix and the interfaces amongst yarns
and matrix in a textile composite subject to a general type of loading.
The strength of a yarn along an arbitrary direction may be correlated with the basic
strength parameters. Similar to a unidirectional lamina, a yarn may be characterized by
a number of basic strength parameters with respect to its principal material directions
from the macro-mechanical point of view. For example, the first principal material
direction, axis 1, is chosen as along the fibre direction or the tangential direction at any
point along the yarn centreline path, while the second and third principal material
directions, axis 2 and 3, are selected to be two orthogonal axes within a plane
perpendicular to the first principal material direction. In general, there are three tensile
and three compressive strength parameters in the three principal material directions, and
three shear strengths in the mutually orthogonal planes passing through any two
principal material axes. However, for a unidirectional yarn, it is desirable to reduce the
number of independent strength parameters from nine to six. This is because the tensile
and compressive strength parameters in direction 2 can be assumed to be the same as
those in direction 3, and the shear strength parameter in the plane going through axis 1
and 2 can be assumed to be identical to that going though axis 1 and 3. When all the
basic strength parameters are known, the maximum stress criterion and maximum strain
criterion (see Jones, 1975; Christensen, 1979) may be used in conjunction with stresses