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We study the stress field near a crack tip in a random heterogeneous domain under remote anti-plane loading using tensor-valued random fields (TRFs). Specifically, we investigate interpenetrating phase composites (IPCs) and generate micromechanically consistent, statistically homogeneous and isotropic stiffness and compliance TRFs that capture the full spatial correlation structure. We focus on the mode III stress intensity factor ( K I I I ), which depends on the mesoscale size δ , phase contrast k , and the specific realization of the material microstructure. For stiffness TRFs, the distribution of K I I I is approximately Gaussian with a mean exceeding the homogeneous value; the probability of exceedance is greater than 0.5, while the variance increases with k while decreasing with increasing δ . For compliance TRFs, the K I I I distribution is positively skewed, yielding a more conservative response. Taken together, the stiffness- and compliance-based stochastic boundary value problems bound the true mechanical response and provide a practical range for estimating failure probabilities. These results demonstrate that mesoscale variability and phase contrast influence both the mean and scatter of K I I I , underscoring the limitations of homogenized medium assumptions for fracture assessment.