A hierarchical multiscale cohesive zone model and simulation of dynamic fracture in metals

In this work, a hierarchical higher order multi-scale cohesive zone model (MCZM) is developed to simulate the fracture and crack propagation in crystalline solids. The main novelties of the present work are: (1) the hierarchical cohesive zone model is developed, and higher order Cauchy-Born rules (up to the third order) are employed to model different orders of the process zones; (2) the finite element bubble mode is added into the lower order element to capture high-order strain gradient effects in the conventional bilinear quadrilateral element; (3) Barycentric finite element method is used to construct shape functions for hexagonal shaped cohesive zones, and (4) realistic EAM potential is implemented to simulate fracture in metals. Numerical simulations of fracture and crack propagation in both monocrystalline solids and polycrystalline solids are performed. Results show that the crack propagation velocity is in general agreement with that of a corresponding molecular dynamics simulation. Moreover, the transition from intergranular fracture to transgranular fracture in polycrystalline solids is found to be sensitive to both the grain size and the relative grain strength. Finally, it is revealed that the proposed multiscale model can capture the spall fracture in a copper plate under high-speed impact.