Finite element method based micromechanical methodology for homogenizing fiber/fabrics-reinforced composites and their progressive failure

Abstract

The complex microstructure of fabrics makes it challenging to homogenize them using an analytical/semi-analytical micro-mechanics approach like the Mori-Tanaka and the method of cells. Analytical approaches developed for fabrics estimate their elastic constants and do not easily accommodate material nonlinearities. Numerical schemes such as the finite element method (FEM) have been developed to analyze failure in fabrics and not necessarily find moduli of the homogenized material. Here we use the FEM based micro-mechanics approach to both homogenize fiber-reinforced and plain/twill/satin weave, as well as braids/fabrics-reinforced composites using simplified unit cells. The homogenization is based on Hill’s averaging theorem and employs tie constraints to impose periodic displacements and anti-periodic tractions on boundaries of the unit cell. A continuum damage mechanics approach is used to study damage initiation and progression, and degradation of material properties. The predicted elastic constants, failure modes and ultimate strengths of fabrics are found to compare well with their either experimental or computed values available in the literature. We have also analyzed delamination and damage propagation in a laminate with an open hole at the centroid and uniform tensile tractions at its end faces to estimate its ultimate strength that is found to agree well with the experimental value.