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Ab initio calculation of traction separation laws for a grain boundary in molybdenum with segregated C impurites
We have determined the influence of carbon on mechanical properties such as grain boundary energy, work of separation (WoS) and fracture strength of the sum 5(3 1 0)[0 0 1] symmetrical tilt grain boundary (STGB) in molybdenum with ab initio methods. From our ab initio results, we derived traction–separation laws that can be used in continuum simulations of fracture employing cohesive zones. Our results show that with an increasing number of C atoms at the grain boundary, the energy of the grain boundary is lowered, indicating a strong driving force for segregation. Uni-axial tensile tests of the grain boundary reveal that there is only a small effect of segregated C atoms on the cohesive energy orWoS of the grain boundary, while the strength of the sum 5(3 1 0)[0 0 1] STGB increases by almost 30% for a complete monolayer of C. This increase in strength is accompanied by an increase in grain boundary stiffness and a decrease of the interface excess volume. The characteristic parameters are combined in the concentration-dependent traction–separation laws. A study of the scaling behaviour of the different investigated systems shows that the energy–displacement curves can be well described by the universal binding energy relationship even for different C concentrations. These findings open the way for significant simplification of the calculation of ab initio traction separation laws for grain boundaries with and without impurities.