An atomistic-statistical thermodynamic evaluation of grain boundary embrittlement

Abstract

A theory of intergranular brittle fracture at low temperature is presented. The intergranular crack nucleation process is modelled by utilizing the stress-concentrating effect of the double slip bands coincident on the boundary plane. The criterion of propagation is based upon an examination of such nucleated crack against blunting by nucleated dislocations. The resulting nucleation stress and the propagation stress are shown to depend critically upon the interfacial cohesion γ. The interfacial cohesion is expressed in terms of the interfacial cohesion of the boundary in pure state, γ 0, and a term involving a statistical-thermodynamic decohesion parameter Λ which is a measure of the ratio of the fracture surface activities to the grain boundary surface activities due to the segregant. γ 0 is determined by an atomistic model while Λ is obtained from experimental data. The model is applied to the analysis of coincidence tilt boundaries in Cu and Al. The internal energies, entropies, free energies, and the interfacial cohesions of these boundaries at temperatures of 1200 K for Cu and 1073 K for Al are presented and discussed. The calculated specific surface energies are in reasonable agreement with measured values. The separation process of these boundaries at 300 and 0 K has also been simulated for the analysis of the observed low temperature intergranular fracture stress. The predicted variation of fracture stress with the bulk concentration of Bi for the Cu Bi alloys is in good agreement with the experimental observations.