A study of crack propagation in precipitate hardened materials using Discrete Dislocation Plasticity

Abstract

The analysis of cracks in ductile micro-crystals has been a major research topic in the past few years. At this scale, the material behavior demonstrates a significant length-scale dependence, mostly observed to be a “smaller is stronger” size-effect. Different approaches and plasticity theories have been formulated and applied, in order to investigate the microscopic plastic material behavior. Continuum level theories are mostly length-scale independent while atomistic or molecular level theories are computationally intensive. In between these scales, Discrete Dislocation Plasticity (DDP) theory was also introduced, that can solve small scale plasticity problems by taking into account the collective motion of a large number of discrete dislocations. The lattice resistance to dislocation motion, nucleation, interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Although this approach has been applied in crack study of micro-crystals, but research has been mostly limited to homogeneous materials, whereas materials such as electronic devices e.g. NEMS/MEMS, which contain heterogeneity, have not received significant attention. In this study, Discrete Dislocation Plasticity (DDP) simulations are used to study the behavior of a crack in an Aluminum matrix, that is incorporated with elastic precipitates of SiC. An inhouse MATLAB code is used to build the DDP model. Three specimen cases with different number of precipitates are taken, that are of square geometry, with overall constant volume fraction in each case. The Al crystal has FCC like orientation and contains three slip systems in plane-strain. The crack, that is of mode-I, is incorporated with the crack-tip placed at the center of the specimen and is considered stationary throughout the loading. Symmetry is considered around crack path while incorporating precipitates. The crack and precipitate boundaries are both impenetrable to dislocations. The results of the cracked specimen are compared with the same specimen that is not cracked. The results and calculations predict increase in strength with increasing precipitates, attributed to the precipitate boundaries acting as effective barriers to dislocation motion. In addition, the configuration or placement of precipitates relative to the crack is also found to significantly affect the material response. The results of this study provide an increased understanding of enhancing the fracture resistance of precipitate hardened materials.