Predicting the ductility of two-phase alloys and metal matrix composites has been an outstanding problem in materials science for many years. One of the most challenging aspects of this problem involves the final coalescence of damage leading to component failure. This is a largely stochastic process and not readily amenable to analytical modeling approaches. In recent years we have developed a series of models for the development of damage - in the form of particle cracking - and its influence on tensile deformation. The approach we have used is based on self-consistent methods using an incremental effective medium approach. These models have tended to correlate well with measured tensile curves but overpredict the onset of tensile instability and thus material ductility. More recently we have added a microcrack coalescence step to the models. This is based on a localized version of the Considere criterion in which coalescence is assumed to occur once the local ligament stress falls below the global work hardening rate of the alloy or composite. The material is assumed to contain a random distribution of particles which crack according to Weibull statistics. Thus both the stochastic nature of particle damage and of coalescence and incorporated into the averaging process. The model gives rather good predictions of ductility.
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