Two-Dimensional (2D) Damage Percolation Modeling

Abstract

As discussed in the preceding chapters, the second phase particle field in a dispersion strengthened ductile material can be described as a random distribution displaying a certain level of particle clustering (Pilkey et al. 1995). Ordinary unit cell models such as Gurson’s (1977) analytical model or other numerical unit cell models (e.g. Needleman 1972; Worswick 1988) with a uniformly distributed particle/void field are unable to capture microstructures that are random and/or clustered. In order to overcome this disadvantage of unit cell models when applied to real micro-defects, Benson (1995) used a two-dimensional unit cell calculation to investigate the effect of void cluster size on ductile fracture. In his study, a unit cell with randomly distributed void clusters was modelled. Thomson et al. (1999) proposed a numerical unit cell model that contains a single particle cluster. Unfortunately, this model still possesses a periodic particle field. Real microstructures always display a random particle distribution with some superimposed degree of particle clustering. Therefore, it is doubtful that unit cell calculations are able to capture the onset of ductile fracture in real materials.