Phase-field modeling the effect of misfit on the precipitation of the second-phase particles and grain coarsening

• The model overcomes the artificial second-phase particles set beforehand.
• The increasing misfit restrains the precipitation of the second-phase particles.
• Large elastic modulus leads to particles coarsening fast along the soft direction.
• The rod-like particles make the grain size more uniform.
• The rod-like particles accelerate the coarsening.

A modified phase-field model has been used to study the precipitation of the second-phase particles and the coarsening of grains under the influence of lattice mismatch. The elastic strain energy caused by misfit is taken into account, and the force equilibrium equation is solved using the iterative-perturbation method. The simulations show that the morphology of the second-phase particles is significantly influenced by the misfit, and the elastic stress blocks the precipitation of the particles. With the increase of the elastic modulus, the process of grain coarsening changes, and the morphology of the second-phase particle gradually transforms from globular to square and rod. The interactions between solute concentration and the misfit are cooperative, which together control the size of grains.