Elastoplastically accommodated hydride formation and embrittlement

In a previous work (Lufrano et al., 1996), the authors investigated stress driven diffusion of hydrogen in a hydride forming system whose constitutive response was modeled as linearly elastic. In the present work the more realistic constitutive assumption of a purely elastic hydride that is accommodated elastoplastically by the surrounding matrix is used. Due to the nonlinearity in the material deformation, the classical description and calculation of the accommodation energy of formation and the interaction energy associated with an external stress using Eshelby's methodology are no longer valid. The elastoplastic deformation of the matrix due to the volume dilatation induced by the hydride, and the interaction of this deformation with externally applied stresses, are studied. The energetics of the hydride formation is revisited and the terminal solid solubility of hydrogen in solution is defined on the basis of the total elastoplastic work done on the system by the forming hydride and the external loads. Hydrogen diffusion and hydride formation coupled with the elastoplastic deformation of the material are modeled at a blunting crack tip in the case of the niobium-hydrogen system. Nonlinear finite element analysis is used to monitor the local distribution and time evolution of hydrogen concentration, hydride volume fraction, stress, and strain as the externally applied loads increase. A Griffith fracture criterion allows the calculation of a critical hydride size, in the neighborhood of the crack tip, at which cracking of the hydride particle by the local stresses is energetically favorable. Using this criterion for fracture initiation, one can predict the reduced fracture resistance of hydride forming systems quantitatively and investigate the fracture toughness dependence of the material on initial concentration and loading rate.