压电材料反平面Ⅲ型裂纹电塑性区的分析  

ANALYSIS OF THE ELECTRIC YIELDING ZONE OF THE ANTI-PLANE MODE Ⅲ CRACK PROBLEM IN PIEZOELECTRIC MATERIALS

作　　者：薛存 周又和[1] 雍华东[1] 

机构地区：[1]兰州大学西部灾害与环境力学教育部重点实验室,兰州大学土木工程与力学学院力学与工程科学系,兰州730000

出　　处：《固体力学学报》2012年第5期449-455,共7页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(11032006和11121202)资助

摘　　要：论文对反平面Ⅲ型裂纹电塑性区进行了分析.采用条带模型得到了电塑性区大小的表达式.对于电塑性区的边界条件采用了两种处理方式,一是采用机械位移连续性边界条件,另一种是假设电塑性区的切应力保持为常数的假设.其中后一种处理方式消除了电场和应力在裂纹尖端的奇异性,与实际情况相符合.两种处理方式得到了相同的电塑性区的大小的表达式,并根据两种处理方式计算了能量释放率.类比Irwin的应力松弛模型,论文采用电位移松弛模型同样得到了电塑性区的大小.将条带模型得到的结果与电位移松弛模型得到的结果进行比较发现,在小范围塑性变形条件下,两种方法所得的结果比较接近,从而说明这两种方法的有效性,得到了比较满意的结果。The yielding zone of the anti-plane mode Ⅲ crack problem in piezoelectric materials is ana- lyzed in this paper. Based on the strip model, the expression of the electric yielding zone is derived. The boundary conditions along the yielding segments have two types：one is the mechanical displacement conti nuity condition and the other one is that the stress is assumed to be constant in the electric yielding zone. The latter eliminates the singularity of the electric field and the stress at the crack tip,which is coincident with the reality. The two different conditions have the same results. The energy release rates of the two types are also derived in this paper. The electric yielding zone is also obtained based on the electric displace- ment relaxation model which is similar to the stress relaxation model by Irwin. Comparing the results of the two different models, the yielding zone size obtained by the strip model is approximately equal to the result of the electric displacement relaxation model. Therefore, under the condition of the small deformation,the results are effective.

关 键 词：裂纹 压电材料 条带模型 电位移松弛 

分 类 号：O346.1[理学—固体力学]