# A numerical analysis of ceramics strength affected by material microstructure

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## Abstract

To clarify microstructural influences on the ceramic strength, a numerical analysis of the elastic stress distribution around the crack tip for several crack lengths was conducted by using a finite element method (FEM), in which each element was regarded as one grain in a ceramic polycrystal. In the analysis, the anisotropy expected in actual grains was dealt with by randomly assigning different values to the rigidity and the size of each element (i.e., each grain). The FEM results showed that the crack tip stress was dependent on the grain rigidity but was hardly affected by the grain size. A microstructural modification factor *f* _{M} for the stress intensity factor was newly introduced to reflect microstructural influences on ceramic strength. The factor *f* _{M} was defined as the ratio of the crack tip stress obtained by the FEM analysis to the *K*-based stress. Statistical aspects of *f* _{M} were investigated by generating virtual materials with different combinations of grain rigidity and size. When the *f* _{M} distribution was fitted to the two-parameter Weibull distribution function, it was clarified that the distribution shifted toward a lower side with increasing the crack length. The *R*-curve expressed by an exponential form was applied so that the grain bridging effect in ceramics could be included in the analysis of the strength depending on crack length. It was revealed that the estimated scatter band in the relation of the strength versus the crack length represented the central trend of dispersed experimental results.

### Keywords

ceramics fracture mechanics microstructure simulation strength small flaw## Preview

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