Phase field approach to bridging between atomistic and macroscopic cohesive laws

Two types of binding relations for both atomistic and macroscopic scale is presented by phase field approach. The length scale in the current phase field model is related to the number of cohesive layers at the crack tip. Then, bridging between atomic and macroscopic scale is derived by analyzing explicit equilibrium stress-strain curve. Independent of which scale is incorp orated, our phase-field theory fundamentally agrees with Griffith’s theory, in which the crack propagates when the elastic energy is large enough to createtwo new surfaces. Because of this, the developed theory is applicable from the atomistic to the macroscopic scales. The finite element method is utilized to solve the complete system of equation including both phase field and equilibrium equations. It is found that the length scale appearing in phase field model plays an important role in the local stress field. For a large but finite number of cohesive layers, the effective asymptotic macroscopic cohesive behavior is reached.

Keywords:

phase field , bridging , crack