LAUSR

A theoretical model is established to address the effect of nanoscale twinning near a second-phase particle on crack growth in fine-grained magnesium alloys. The numerical solutions of singular integral equations are obtained by the considering complex variable method of Muskhelishvili, the superposition principle of elasticity, and the distributed dislocation technique. The expressions of stress intensity factors near the left crack tip are derived, and the energy release rate (ERR) characterizing the condition for crack propagation is also calculated. The influences of relevant parameters such as the location of nanoscale twin, the size of particle, and the relative distance between the inhomogeneity and the left crack tip on the ERR are examined in detail. The results indicate that the ERR is strongly influenced by the nanoscale twinning and the second-phase particle. The hard inhomogeneity decreases the ERR while the soft inhomogeneity increases the ERR when nanoscale twinning is not taken into account. At the same time, there is competition between the effects of the hard particle and nanoscale twinning on the ERR, and the nanoscale twin band with an optimum size displays the best toughening effect.