A homogenized model for porous materials with an inhomogeneous matrix: Application to the modelling of strain hardening
Résumé
A homogenized model is proposed for describing ductile porous materials in which voids are embedded in an inhomogeneous isotropic matrix. First, limit analysis is used to derive yield criteria for spherical voids in a matrix material with an inhomogeneous yield stress. A three-parameter yield stress spatial distribution is considered, which generalizes special cases already considered in the literature. Three distinct yield criteria are derived, that correspond to void growth/low stress triaxiality, void growth/large stress triaxiality, and void necking coalescence. These criteria are combined using a regularized multi-surface plasticity framework. Evolution laws are proposed for the spatial distribution of yield stress as a function of the material’s hardening behaviour. The model is evaluated against a comprehensive database of porous unit cell FFT simulations for axisymmetric loading conditions, validating the yield criterion and demonstrating the model’s ability to reproduce stress–strain curves and porosity evolution. The model’s key output is that it greatly improves the predictions for stress triaxiality values relevant in the presence of cracks, surpassing the standard approach used in the literature. The model is used to perform non local finite element simulations of the ductile tearing of Compact Tension samples for different hardening behaviour, demonstrating its potential application in structural calculations. Finally, the implications of the power law regularization used to combine the yield criteria are discussed, as well as the model’s potential for physical modelling of void nucleation.
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