ABSTRACT of the Doctoral Thesis
The aim of the present study is the modeling of the successive brittle failure of particles embedded in a ductile matrix subjected to global uniaxial tensile loading. The work is based on three-dimensional multi-particle unit cells and uses the Finite Element method. Micro-geometries are generated by appropriately arranging a number of spherical particles within the unit cell. On the one hand so called Randomly Pruned Cube (RPC) arrangements are employed, in which the unit cell is split into a number of cube-shaped subvolumina some of which are randomly selected to contain a centered particle. On the other hand periodic pseudo-random particle arrangements are generated by a modified Random Sequential Adsorption (RSA) algorithm. Elastic material properties are used for the particles and the matrix is described by J2 plasticity.
Predefined fracture surfaces, which are assumed to be oriented perpendicularly with respect to the direction of the overall uniaxial stress state, are provided for within the reinforcements. Brittle failure of the reinforcements, which is modeled as instantaneous cleavage at these surfaces, is implemented by a node release technique. Failure in a given particle is controlled by Weibull-type fracture probabilities in combination with a Monte Carlo algorithm. The fracture probabilities are evaluated for the whole particle on the basis of the current stress distribution.
Within the modeling assumptions used, which do not account for other local failure mechanisms such as ductile damage of the matrix and decohesion at the interface between the constituents, successive particle cleavage and the resulting stress redistribution effects are simulated for two types of materials, a particle reinforced aluminium matrix composite and a high speed tool steel. Results are presented in terms of predictions for the overall stress vs. strain behavior and for damage relevant fields at the microscale for the above types of composite, which represent materials with highly ductile and rather hard matrices. Special consideration is given to influences of the material properties and the relative sizes of the particles on the predicted fracture behavior.