Modelling Brittle-Ductile Transitions

Abstract

This paper outlines current approaches to modelling fracture and the brittle-ductile transition both in simple materials and in microstructurally complex materials such as steel. The models cover a very wide range of length and time scales, from a few hundreds of atoms and a few hundred picoseconds, to millimetres or more and minutes or hours. The problem and the challenge is to link the most useful features of models at the different scales. The paper describes dislocation based (“mesoscopic”) models that reproduce the rise in cleavage K with temperature of simple single crystals. Such models can take into account experimentally-determined critical variables such as the spacing and activation characteristics of dislocation sources. However, they need as input information, such as K_lc and dislocation mobility as a function of stress and temperature, that cannot at present be predicted (e.g. by atomistic modelling) and must be experimentally determined. In real engineering materials, archetypically steels, the fracture mechanisms are more complex than in the single crystals, even in the low-temperature “cleavage” regime. Failure initiates not from the main crack, but at microcracks associated with brittle particles near the main crack tip. This presents a further challenge to modelling the BDT. Current models for steels are based on Finite Element Modelling of the plastic zone, with a “stress at a particle” failure criterion for determining the BDT curve. They are often statistically-based. The models can be made to fit experimental results, but the “best fit” microstructural parameters in such models (e.g. particle densities and fracture stresses) bear little relation to the real microstructures. This paper outlines an extension to the dislocation-based approach, to model the cleavage portion of the BDT curve in steels, which promises to give justification for the parameters in the statistical models, and possibly to predict BDT behaviour directly.