基于相场法的周期性多孔结构断裂行为研究  

FRACTURE BEHAVIOR OF PERIODIC POROUS STRUCTURES BY PHASE FIELD METHOD

作　　者：应宇轩 黄玮[1] 马玉娥[1] 彭帆 Ying Yuxuan;Huang Wei;Ma Yu-E;Peng Fan(School of Aeronautics,Northwestern Polytechnical University,Xi’an 710072,China;School of Science,Chang’an University,Xi’an 710061,China)

机构地区：[1]西北工业大学航空学院,西安710072 [2]长安大学理学院,西安710061

出　　处：《力学学报》2022年第12期3430-3443,共14页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(12172292)。

摘　　要：周期性多孔结构具有质量轻、比密度低、比强度高、隔音等优良特点,同时也能很好地满足结构-功能一体化的需求,在许多领域具有广泛的应用前景.目前,对周期性多孔结构在复杂载荷下的力学响应和断裂行为的研究较少.采用细观力学和相场方法相结合,基于二维代表性体积单元RVE模型,施加能实现比例加载的周期性边界条件,研究周期性多孔结构在复杂多轴比例加载状态下的裂纹萌生位置、断裂模式、承载极限及其变化规律.本文的数值模拟结果表明:首先,周期性多孔结构在竖直方向拉伸载荷作用下,裂纹均从孔边萌生并沿水平方向同步扩展;其次,在双轴载荷作用下,随着水平载荷的增加,结构在竖直方向的极限拉伸载荷逐渐增大;当双轴拉伸载荷等值时,结构的抗拉强度达到最大,此时断裂模式呈现为十字正交型开裂;最后,面内剪切应力的引入会导致结构的拉伸强度极限降低,孔边裂纹的萌生位置和扩展路径发生偏移,裂纹模式从单S型转变为双弧线型,裂纹向水平位置上相邻的孔洞扩展.随着水平载荷的增加,裂纹模式最终转变为斜裂纹,从孔边对角线位置萌生并沿着45°方向扩展.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, cr

关 键 词：周期性多孔结构 相场 断裂 RVE模型 多轴加载 

分 类 号：O346.11[理学—固体力学]