A stochastic XFEM model for the tensile strength prediction of heterogeneous graphite based on microstructural observations

A stochastic XFEM model based on microstructural observations has been developed to evaluate the tensile strength of NBG-18 nuclear graphite. The nuclear graphite consists of pitch matrix, filler particles, pores and micro-cracks. The numerical simulations are performed at two length scales due to large difference in average size of filler particles and pores. Both deterministic and stochastic approaches have been implemented. The study intends to illustrate the variation in tensile strength due to heterogeneities modeled stochastically. The properties of pitch matrix and filler particles are assumed to be known at the constituent level. The material models for both pitch and fillers are assumed to be linear elastic. The stochastic size and spatial distribution of the pores and filler particles has been modeled during the micro and macro analysis respectively. The strength of equivalent porous pitch matrix evaluated at micro level has been distributed stochastically in the elemental domain along with filler particles for macro analysis. The effect of micro-cracks has been incorporated indirectly by considering fracture plane in each filler particle. Tensile strength of nuclear graphite is obtained by performing the simulations at macro-level. Statistical parameters evaluated using numerical tensile strength data agree well with experimentally obtained statistical parameters available in the literature.