On the formation of expanding crack tip precipitates

Abstract

The stress driven growth of an expanding precipitate at a crack tip is studied. The material is assumed to be linearly elastic, and the expansion is considered to be isotropic or transversely isotropic. The extent of the precipitate is expected to be small as compared with the crack length and distance to boundaries. The problem has only a single length scale given by the squared ratio of the stress intensity factor and a critical hydrostatic stress that initiates the growth of the precipitate. Therefore, the growth occurs under selfsimilar conditions. The equations on non-dimensional form show that the free parameters are expansion strain, degree of anisotropy and Poisson's ratio. It is found that the precipitate, once initiated, grows without remote load for expansion strains above a critical value. The anisotropy of the expansion strongly affects the shape

Ab initio thermo-elasticity of δ-MHx (M=Zr, Ti)

“…To model the formation of secondary phases, different types of thermodynamic-based modelling approaches have emerged. Notably, variants of phase-field and continuum modelling have been extensively used to investigate aspects such as hydride formation and reorientation under applied load [16][17][18][19], and formation and fracture in the proximity of stress concentrators [20][21][22][23][24]. The predictability of such modelling relies heavily on the accuracy of the free energy functional and its ability to account for aspects such as e.g.…”