A computational framework for predicting the fracture toughness of metals as function of microstructure

Abstract

We present a simplified computational framework based on the cohesive finite element method (CFEM) for predicting the macroscale fracture measures such as KIC and JIC of ductile metals as functions of microstructural attributes. Currently, no systematic approach exists to explicitly quantify the effects of grain and grain boundary behavior on the fracture measures of polycrystalline materials. Our computational approach involves embedding a microstructure region around the crack tip in a compact tension specimen subjected to mode-I loading and explicitly resolving fracture processes in the microstructure. To track how the interplay between intergranular and transgranular fracture mechanisms affect the fracture processes and consequently KIC and JIC, a grain boundary misorientation dependent interfacial separation model is used. The framework allows exploration of the effects of microstructure on the macroscopic fracture measures via the manifestation of different fracture mechanisms. Calculations carried out for Mo capture and delineate the competing effects between (a) intergranular and transgranular fracture and (b) constituent plasticity and fracture on the overall fracture toughness of the material. The use of statistically equivalent microstructure sample sets (SEMSS) allows the statistical distributions of KIC to be predicted for Mo with different grain sizes. The results indicate that, as the minimum grain boundary interfacial strength decreases and the grain yield strength increases, intergranular fracture becomes more pronounced over transgranular fracture. Consequently, the plastic dissipation primarily associated with transgranular fracture is suppressed, resulting in lower overall fracture toughness. Microstructures with intermediate levels of grain size exhibit the toughest material response via a combination of tortuous crack paths and plastic dissipation. Finally, the results are analytically quantified in a manner that takes into account the effects of grain boundary characteristics, constituent plasticity, and stochasticity via the use of the SEMSS. Although the calculations here are performed on Mo in a simplified setting, the approach can be extended and applied to other material systems.