A model for damage coalescence in heterogeneous multi-phase materials

Previous models for the deformation of two-phase materials with heterogeneous second phase distributions have been extended to account for damage coalescence. As in the previous work, the model is based on a self-consistent analysis and uses an incremental, tangent modulus approach. Damage coalescence is treated through a micro-crack linkage model that is sensitive to both the local volume fraction of damaged second phase particles and the local stress acting between damaged particles. This work suggests that micro-crack linkage rapidly leads to a loss of global stability and is critical in limiting the ductility exhibited by materials, at least for those exhibiting damage by particle cracking. Thus experimental data for metal-matrix composites agree well with the predictions of the micro-crack linkage model. Ductility predictions resulting from the model are sensitive to both the volume fraction and matrix work hardening exponent. By varying the latter over a range typical of aluminum alloys the model captures the experimentally observed range of ductility for a wide range of Al-based MMCs.