基于相场法的周期性多孔结构断裂行为研究

Periodic porous structures have excellent characteristics such as low mass, low density, high specific strength, sound insulation, and they are also well satisfy the needs for structural-functional integration, which have a wide range of applications in many fields. At present, the mechanical response and fracture behavior of periodic porous structures under complex loads have been poorly investigated. In this paper, we use a combination of micro-mechanics method and phase field method to investigate the crack initiation location, crack propagation path, fracture mode and the ultimate strength of periodic porous structures under combined multiaxial loading based on a two-dimensional representative volume element (RVE) model with the periodic boundary condition (PBC) that can implement multiaxial proportional loading. Numerical simulation results in this paper show that all cracks in the periodic porous structure established in this paper initiate from the edge of the holes and propagate consequently along the horizontal direction under the uniaxial tensile loading in the vertical direction. Secondly, under the biaxial loadings in both vertical and horizontal directions, the ultimate strength of the periodic porous structure gradually increases with the increase of the horizontal tensile loading. When the horizontal load is equal to the vertical load, the fracture pattern exhibits as orthogonal cross-type cracking and the ultimate strength reaches the maximum value. Thirdly, the in-plane shear stress simultaneously acted on the RVE model of the periodic porous structure results in a significant decrease of the ultimate strength and the variations of initiation location and propagation trajectory of the hole-edge cracks. Hence, the fracture pattern of periodic porous structure subjected to combined multiaxial loadings changes from the single S-type cracking to the double arc-type cracking, and cracks extend toward adjacent holes in horizontal direction. Finally, with the increase of the horizontal tensile loading, cracks initiate diagonally at the edge of the holes and propagate along the 45-degree direction which lead to the oblique cracking of periodic porous structure.