A numerical study of intergranular fracture and oxygen embrittlement in an elastic-viscoplastic solid

We present results from a numerical investigation of fracture along an embrittled surface embedded in an elastic-viscoplastic solid, an idealized model for high-temperature intergranular fracture in nickel-base superalloys. The formulation includes coupled models for the mechanical response, stress-assisted diffusion of oxygen, and a moving cohesive interface that determines crack initiation, growth and arrest. The entire system is formulated in a frame that translates with the crack tip and is implemented in an adaptive, space-time finite element code that supports both transient and direct steady-state calculations. We present a criterion for stable crack growth specific to the moving cohesive interface model and apply it to studies of fracture along a planar grain boundary with uniform cohesive properties. No stable solutions were found for the steady case. In the transient case, the stability criterion resolves a lack of uniqueness in the incremental solutions for growing cracks. Results are reported for monotonie loading to failure, linear ramp to sustained hold at a peak load level and cyclic loading. We investigate the sensitivity of the response to the loading rate, the cohesive interface properties and the degree of overload past crack initiation. Finally, we extend the cohesive interface model and the stability criterion with a phenomenological model for oxygen embrittlement and report the effects of embrittlement on steady-state response.