平行微裂纹削弱的弹性体的各向异性有效性能与双周期裂纹模型

EFFECTIVE MODULI OF AN ELASTIC SOLID WEAKENED BY A PARALLEL ARRAY OF MICROCRACKS

平行微裂纹损伤模型被用于构建各向异性损伤理论.当施加在代表性体积单元上的边界条件满足Hill条件时,基于平均场理论论证了由平行穿透裂纹损伤的弹性体仅有6个独立有效弹性常数.除了原各向同性基体的2个弹性常数外,与损伤相关的另外4个常数中,3个描述有效弹性常数的折减,1个描述损伤导致的拉剪耦合效应.结合单胞模型和有限元方法分析了双周期阵列平行裂纹问题,数值结果显示:裂纹呈一般双周期阵列时,拉剪耦合参数相比其它模量小很多;当裂纹密度一定时,改变裂纹的排列形式,面内剪切模量和面外剪切模量的折减呈现出不同的规律.

The model about parallel microcracks is used to develop the anisotropic damage theory. An elastic body weakened by parallel microcracks is studied based on the average field theory when the boundary conditions imposed on the RVE meet the Hill condition. It is shown that such a damaged anisotropic e- lastic body has only 6 independent elastic constants. Besides two elastic constants of the original isotropic matrix there are four elastic constants related to the damage, among them three describe the reduction of the effective elastic constants, and one describe the damage induced tension-shear coupling. After that, an infinite solid containing a doubly periodic array of cracks is analyzed based on the unit cell model and the fi- nite element method. The numerical results reveal that the tension-shear coupling coefficients is much smal- ler than the other elastic constants for an elastic body with a general doubly periodic array of cracks,and the variation of the in-plane and out-plane shear moduli with the cracks array parameters changing are not the same.