Segregation effects on intergranular fracture: an atomistic simulation study of Ni-Cu alloys

Abstract

The effects of segregation on the cohesive energy or ideal fracture toughness of a Σ5 [001] twist boundary in Ni-Cu alloys have been examined for a wide range of temperatures and compositions within the solid solution region of the phase diagram. The cohesive energy 2γint is defined as the difference between the free energies of the surfaces created and the grain boundary destroyed when a crack propagates along a grain boundary. Atomistic simulations of the Σ5 [001] twist boundary and (001) surfaces were performed within the framework of the free energy simulation method that is based upon minimizing an approximate free energy functional with respect to both atom positions and solute concentration profile. Three different types of cohesive energies (2γint)μ, (2γint)Γ, and (2γint)C have been evaluated; (2γint)μ is the cohesive energy for slow fracture, (2γint)Γ is the cohesive energy for fast fracture, and (2γint)C is the cohesive energy of the unsegregated boundary. In the normal situation (where the solute segregates more strongly to the surface than the boundary), the inequality (2γint)μ ≤ (2γint)Γ ≤ (2γint)C is always satisfied, and for anomalous segregators (where the solute segregates more strongly to the boundary than the surface), (2γint)C ≤ (2γint)μ ≤ (2γint)Γ is satisfied. For all Ni-Cu alloy bulk compositions (0.05 ≤ C ≤ 0.95) and temperatures (400 ≤ T(K) ≤ 1000) examined, Cu segregates strongly to both the grain boundary and the free surface. Nonetheless, segregation only results in a small reduction (10 pct) in 2γint compared with the unsegregated case. The difference between the fast fracture (2γint)Γ and slow fracture (2γint)μ cohesive energies is very small. Therefore, at least in the Ni-Cu system, the two theoretical bounds on 2γint are tight.