Numerical modeling of the ductile-brittle transition

Numerical studies of the ductile-brittle transition are described that are based on incorporating physically based models of the competing fracture me chanisms into the material's constitutive relation. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. C leavage is modeled in terms of attaining a temperature and strain rate inde pendent critical value of the maximum principal stress over a specified mat erial region of the order of one or two grain sizes. Various analyses of du ctile-brittle transitions carried out within this framework are discussed. The specimens considered include the Charpy V-notch test and cracked specim ens under mode I or mode II loading conditions. The fracture mode transitio n emerges as a natural outcome of the initial-boundary value problem soluti on.