Estimation of the Stress State Within Particles and Inclusions and a Nucleation Model for Particle Cracking

Abstract

Despite great strides in developing physically motivated models for void growth, shape evolution and coalescence, a suitable treatment for void nucleation remains an open question. Accurate modeling of void nucleation is difficult within a Gurson-based framework due to the intrinsic assumption that the material does not contain any second-phase particles. Consequently, the nucleation models employed in these constitutive models are overly simplistic as the particle shape, composition, stress state and load-sharing are neglected, lumped into a single calibration parameter (Beremin 1981) or indirectly accounted for in a phenomenological manner (Chu and Needlman 1980). The lack of progress in developing physically sound nucleation models has not been for lack of effort but a result of the inherently complex nature of the nucleation process. Void nucleation is very difficult to capture experimentally since it is a relatively random and instantaneous event that cannot be captured in-situ without the aid of high resolution x-ray tomography. Additionally, the local stress state near a particle of interest is typically unknown, as well as the particle composition and mechanical properties. The nucleation mechanism can occur by debonding or particle cracking and is influenced by the particle size, shape, composition, distribution, strain rate and temperature. From an engineering perspective, one can clearly see the attraction in adopting a phenomenological nucleation model whose parameters can be adjusted to give good agreement with the experiment data. Nevertheless, there is ample opportunity to improve the physical foundation of the current nucleation models, especially in regards to percolation modeling.