The effect of particle clustering on the nucleation, growth and coalescence of voids is studied through modeling of discrete spherical particles in a cubic, three dimensional unit cell using finite element analysis. Void nucleation at discrete particles develops at a traction-separation interface and is stress-controlled. Voids formed at the discrete particle-m atrix interface coalesce through a void sheeting mechanism where matrix damage originating at a secondary population of small void-nucleating particles is modeled using the Gurson-Tvergaard-Needleman (GTN) constitutive equations with strain-controlled nucleation. The effect of various model parameters on the nucleation, growth and coalescence behaviour of the unit cells are studied including cluster type, cluster orientation, cluster density, strain state, stress triaxiality, particle m atrix interface characteristics, and GTN nucleation and coalescence parameters. The study represented by this thesis takes a unique approach to modeling particle clusters in a unit cell and accounts for all stages of ductile damage development. The model also incorporates a comparative length scale in the continuum analysis characterized by the ratio of distance between particles within a cluster to the distance between neighboring clusters.

This thesis demonstrates that a cluster of particles cannot be equated to a single particle with similar dimensions to the cluster but that stresses and strains within inter-particle ligaments play an important role in damage progression. The orientation of an anisotropic cluster is also an important factor in void nucleation and growth with clusters elongated in the direction of major principal strain developing lower damage rates than particle clusters elongated transverse to the major principal strain. In a dual population of particles, the parameters in the GTN constitutive equations which have the greatest effect on strain-to-failure are the volume fraction of void nucleating secondary particles, f_N, and the critical void volume fraction for void coalescence, f_c. It is also shown that coalescence of voids within a particle cluster is a stable event whereas coalescence of voids from one cluster with those of a neighboring cluster leads to imminent material failure.