Phase structural ordering kinetics of second-phase formation in the vicinity of a crack

摘要

The formation of a second phase in presence ofa crack in a crystalline material is modelled and studied fordifferent prevailing conditions in order to predict and a posterioriprevent failure, e.g. by delayed hydride cracking. Tothis end, the phase field formulation of Ginzburg-Landauis selected to describe the phase transformation, and simulationsusing the finite volume method are performed fora wide range of material properties. A sixth order Landaupotential for a single structural order parameter is adoptedbecause it allows the modeling of both first and second ordertransitions and its corresponding phase diagram can beoutlined analytically. The elastic stress field induced by thecrack is found to cause a space-dependent shift in the transitiontemperature, which promotes a second-phase precipitationin vicinity of the crack tip. The spatio-temporal evolutionduring nucleation and growth is successfully monitoredfor different combinations of material properties andapplied loads. Results for the second-phase shape and sizeevolution are presented and discussed for a number of selectedcharacteristic cases. The numerical results at steadystate are compared to mean-field equilibrium solutions anda good agreement is achieved. For materials applicable tothe model, the results can be used to predict the evolution ofan eventual second-phase formation through a dimensionlessphase transformation in the crack-tip vicinity for givenconditions.