A residual stress-dependent mixed-mode phase-field model: Application to assessing the role of tailored residual stresses on the mechanical performance of ceramic laminates

Ceramics offer several attractive properties of industrial relevance, e.g. high strength and hardness, thermal conductivity, and chemical inertness in critical environments. There is thus interest among researchers to improve the fracture toughness of ceramics, which is generally low and considered a major drawback. Numerous experimental studies in the literature report on the enhancement of mechanical performance ceramic laminates, especially fracture toughness, by tailoring the residual stress, resulting in crack deflection or bifurcation. However, there is a dearth of computational models that can reliably predict the crack path accurately quantify the improved fracture toughness. In this article, we propose a residual stress-dependent mixed-mode phase-field model within a small deformation set-up. The proposed model is efficient in including any energy dissipation effect in a consistent manner. The model can be exploited as a tool to study the effect of tailored residual stresses on the fracture toughness of ceramic laminates. We have validated our proposal by reproducing the results for a few problems that require the incorporation of residual stresses within formulation. By conducting a set of four-point bending tests on notched composite beams made of alternating layers of Al2O3 with 5% tetragonal ZrO2 (ATZ) and Al2O3 with 30% monoclinic ZrO2 (AMZ), we demonstrate how tailored residual stresses could indeed influence the mechanical performance of ceramic laminates.