The traditional approach to modeling ductile fracture involves homogenizing the microstructure of a material into a simple, equivalent geometry from which the relevant constitutive laws can be derived. While attractive from a modeling perspective, critical details of the microstructure are lost in this homogenization process such as the particle size, shape, orientation, distribution and degree of clustering. Since void initiation and evolution is a highly localized phenomenon originating within heterogeneous particle clusters, these models fail to accurately predict fracture. These limitations can be overcome using a promising new technique known as damage percolation modeling that requires no idealizations or approximations of the microstructure. In this approach, digital imaging techniques or x-ray microtomography can be used to obtain the particle distribution in a material. Using this information, micromechanical models are applied to characterize void and crack formation leading to failure at the individual particle scale. The damage percolation model represents the future in material modeling as it directly relates changes in the local microstructure to the overall material behaviour.

In this research, the first fully-coupled multi-scale damage percolation model has been developed to predict fracture in advanced materials with heterogeneous particle distributions. In the first phase of this work, a sophisticated damage percolation model is developed using the latest micromechanical models to characterize void nucleation, growth, and coalescence in three-dimensions for general loading conditions. A novel strategy is proposed to determine the stress state within the reinforcing particles and inclusions to facilitate the development of a void nucleation model based solely upon the particle properties.

The percolation model was implemented into a commercial finite-element code using so-called “percolation elements” to capture the complex stress- and strain- gradients that develop during deformation. A particle field generator is developed and integrated into the finite-element code to create representative particle distributions within the percolation elements to provide stochastic predictions of fracture that reflect the experimental variation. Finally, the percolation model is validated numerically and experimentally for an automotive-grade aluminum alloy in a notched tensile test used for material characterization. The complete multi-scale percolation model predicts fracture as a direct consequence of the stress state, material properties and the local conditions within the microstructure.