Computer modelling of plastic deformation and fracture in heterogeneous systems.

The results from a computational investigation of plastic deformation and fracture in austenitic steel are presented. A lattice model representing the continuum mechanical behaviour in three-dimensions is developed. The model is shown to recover the governing equations for continuum elasticity theory and is extended to include plasticity through the localised reduction of elastic moduli, and the application of internal forcces in order to maintain stress continuity. The properties of the bonds constituting the lattice are varied in different regions in order to simulate multi-phase materials. The resulting system of equations retains its linearity and is, therefore, solvable using a conjugate gradient algorithm. Fracture is introduced through the iterative removal of bonds, where clusters of bonds normal to a potential fracture plane are considered. The model gives reasonable agreement with theoretical predictions for the elastic fields generated by a spherical inclusion, although for small particle sizes the discretisation of the underlying lattice causes some departures from the predicted values. Results are presented for a spherical inclusion in a plastic matrix and are found to be in good agreement with predictions of Wilner.The deformation and fracture of inclusions due to particles characteristically embedded in austenitic steel are considered. The deformation fields within spherical particles are found to depart from uniformity in the presence of plasticity in the matrix, and their decohesion is in accord with experimental expectations. The model accounts for the internal fracture characteristics of elongated manganese sulphide particles when orientated parallel to the tensile direction. The interaction between two iron carbide particles or two voids are also investigated, and found to be potentially detrimental. Random voidal microstructures are simulated, with subsequent results analysed using Weibull statistical analysis. The maximum stress levels, with respect to the applied stress, are considered and the system size dependence is found to be characteristic of a Weibull distribution. The effects of varying the volume fraction of voids is observed to have a deleterious effect on both the strength and toughness of the simulations.