A solid mechanics approach to the modeling of hydride formation and cracking in zirconium alloys

A solid mechanics approach is used to investigate hydride formation and cracking in Z r-2.5Nb alloys used in the pressure tubes of CANDU nuclear generating stations. The forming hydride is assumed to be purely elastic and its volume dilatation is accommodated by elastoplastic deformation of the surrounding matrix material. 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energy of formation and the interaction energy associated with an external stress using Eshelby's methodology are no longer valid.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 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 probabilistic hydride formation coupled with the elastoplastic deformation of the material are modeled at a blunting crack tip under mode I plane strain loading, zero flux condition at the crack surfaces and the outer boundary, and a uniform initial hydrogen concentration below the stress free terminal solid solubility. A full transient finite element analysis allows for numerical monitoring of the development and expansion of the hydride zone 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 the zirconium alloy and quantify the fracture toughness dependence on temperature, initial concentration and the loading rate. (author)