Computational Methods for Debonding in Composites

198 Ernest T.Y. Ng and A. Suleman
overall elastoplastic behavior of multi-phase fiber-reinforced composite materials
based on the von-Mises yield criterion. In this paper, we will employ the combined
TFA-GPM approach but with Gurson-Tvergaard yield criterion instead of
von-Mises yield criterion to predict the overall elastoplastic behavior of n-phase
fiber-reinforced composites with isotropic strain hardening.
Elastoplastic modelling of n-phase fiber-reinforced composites (advanced hybrid
composites) has been proposed by many researchers. One elegant method, namely,
the Transformation Field Analysis (TFA) [7] proposed by Dvorak has shown to
have many advantages over the other models within the context of computational
micromechanics. For instance, the algorithm can take account of the microgeometry
of the fiber phase and is suitable for modelling multi-phase fibrous composites;
it can accommodate with any inelastic constitutive relation, micromechanical model
and uniform overall loading path. More importantly, it is also suitable for 3D modelling
of multi-phase fiber-reinforced composite structures within the finite element
method framework. To determine the concentration factors needed by the governing
TFA equations, we invoke the Eshelby-Mori-Tanaka (EMT) theory [3, 8, 17].
However, the integration scheme employed in the original paper written by Wafa
et al. is explicit [1]. Over the past years, implicit integration has shown to have
more advantages over explicit integration in integrating the constitutive equation
within the context of finite element analysis. Moreover, explicit integration even has
complicated the numerical procedures for analyzing multi-phase fibrous composite
material as discussed in the preceding paper. In this paper, the TFA method is
used to predict the overall elastoplastic behavior of n-phase fiber-reinforced composites
using Gurson-Tvergaard yield criterion. In order to integrate the overall
TFA governing equations, an implicit stress integration scheme called the Governing
Parameter Method (GPM) [15, 16] is used to replace the explicit integration
scheme employed in the original paper by Wafa et al. In short, this paper has the
following contributions:
1. Extend the widely used von-Mises yield criterion to a more general Gurson-
Tvergaard yield criterion in order to account for the effects of void growth in the
matrix phase;
2. Perform the mathematical analysis to obtain the necessary conditions for the
ranges of the change of the mean plastic strain ∆eP m and the change of the effective
plastic strain ∆ēP of the matrix phase within the context of the iterative
algorithm based on the GPM and the Gurson-Tvergaard model;
3. Use the proposed approach to simulate a 4-phase fibrous composite material.
The layout of the paper is as follow: Sect. 10.2 presents the micromechanics
of elastoplastic analysis of multi-phase fiber-reinforced composite materials, this
includes the governing TFA equations and the EMT equations; Sect. 10.3 outlines
the stress integration scheme, this includes a general description to the GPM algorithm,
the procedure to apply the GPM to solving the governing TFA equations;
Sect. 10.4 includes the formulation of Gurson-Tvergaard plasticity within the context
of GPM. More importantly, a necessary condition for the ranges of the change
of the mean plastic strain ∆eP m and the change of the effective plastic strain ∆ēP