By means of the combined model, i.e., the phase-field model with finite interface dissipation in combination with the modified Cahn–Hilliard model, together with the materials parameters comprehensively verified in monolithic c-TiAlN coatings, the microstructure evolution in multilayer c-Ti[Formula: see text]Al[Formula: see text]N/TiN coatings annealed at [Formula: see text]C was quantitatively simulated by directly comparing with the experimental data. The sharp interface between c-TiN and c-Ti[Formula: see text]Al[Formula: see text]N layers in the as-deposited state was found to change into a diffuse one, which can act as highly effective obstacles against dislocation motion. Moreover, the simulations indicate that the spinodal decomposition occurs in the Ti[Formula: see text]Al[Formula: see text]N layer and the decomposed layer becomes thinner, which is in good agreement with the experimental observation. In addition, the effect of modulation period and modulation ratio on microstructure evolution in c-Ti[Formula: see text]Al[Formula: see text]N/TiN coating was further studied. The relatively smaller modulation period can generate more layers in the real scale of coatings, which can help to strengthen the coatings due to refinement of grains and restriction of dislocations. As for the modulation ratio, when the value decreases from 5:1 to 1:1, Ti atoms in the decomposed layer disappear faster. A further extension into a larger-sized simulation was also performed.
On constitutive assumptions in phase field approaches to brittle fracture
