Damage Evolution in Composites with a Homogenization-based Continuum Damage Mechanics Model

Abstract

This paper develops a 3D homogenization-based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage. Micromechanical damage in the representative volume element (RVE) is explicitly incorporated in the form of fiber—matrix interfacial debonding. The model uses the evolving principal damage coordinate system as its reference in order to represent the anisotropic coefficients. This is necessary for retaining accuracy with nonproportional loading. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as macroscopic internal variable. Damage in 3D composites is accounted for through functional forms of the fourth order damage tensor in terms of macroscopic strain components. The HCDM model parameters are calibrated by using homogenized micromechanical (HMM) solutions for the RVE for a few strain histories. The proposed model is validated by comparing the CDM results with HMM response of single and multiple fiber RVEs subjected to arbitrary loading history. Finally the HCDM model is incorporated in a macroscopic finite element code to conduct damage analysis in a structure. The effect of different microstructures on the macroscopic damage progression is examined through this study.

Foundational aspects of a multi-scale modeling framework for composite materials

“…For predicting damage in composites at the macroscales, Ghosh and coworkers have developed anisotropic HCDM models in [25][26][27]. This model can avoid the need to perform micromechanical analysis at each load increment and is computationally very efficient.…”

“…However, when the strains are represented in a coordinate system that corresponds to the principal damage axes, the coupling terms in the stiffness C ijkl reduce to near vanishing values and the initial symmetry properties are retained. Hence, the homogenized stiffness matrix has been represented in the PDCS in [25][26][27]. Determination of the continuously evolving principal damage coordinate system requires the determination of the second-order damage tensor D ij and subsequent evaluation of its eigen-vectors at each step of the incremental loading process.…”

“…The HCDM model proposed in [25][26][27] introduces a damage evolution surface to delineate the interface between damaged and undamaged domains in the strain (e ij )-space as…”

“…In such cases, a concurrent multi-scale model as developed by the authors in [21,22] is desirable. The author has developed 3D HCDM model in [25][26][27] in a principal damage coordinate system (PDCS), which evolves with the load history. These are essential steps in developing rigorous multi-scale models of damage and failure in heterogeneous materials.…”

A nonlinear cumulative evolution model for corrosion fatigue damage

“…Corrosion fatigue phenomenon is very common in marine and aerospace engineering, but there are many other issues which still do not have good solutions to this problem. With the flourish of damage mechanics (Lemaitre, 1985;Lemaitre and Chaboche, 1990;Fatemi and Vangt, 1998;Jain and Ghosh, 2008;Besson, 2010;Ohata et al, 2010), some researchers tried to study corrosion fatigue behavior of metals from the perspective of damage evolution, and proposed some corrosion fatigue damage evaluation methods (Kotsikos et al, 1999;Kermanidis et al, 2005).…”