反平面电弹性断裂动力问题的拟应力解  

QUASI-STRESS SOLUTION OF THE ANTIPLANE PROBLEM FOR ELECTRO ELASTIC DYNAMIC FRACTURE

作　　者：侯密山[1] 边文凤[2] 

机构地区：[1]石油大学建筑工程系,山东东营257062 [2]哈尔滨工业大学威海分校机械工程系,威海264209

出　　处：《机械强度》2001年第3期326-328,315,共4页Journal of Mechanical Strength

基　　金：山东省自然科学基金资助项目 (Y99A0 2 )~~

摘　　要：对反平面问题 ,压电材料的动态电弹性控制方程是波动与调和方程的耦合方程。本文通过耦合方程的解耦 ,建立了相应的拟应力问题 ,并对几个典型的压电材料反平面断裂动力问题进行了研究。研究表明 ,介质内的耦合场与裂纹扩展速度有关 ,在裂纹尖端有r- 1 2 阶的奇异性 ;电位移强度因子与机械载荷无关 。Dynamic control equations of the electric-elastic antiplane problem for piezoelectric materials are coupled wave motion equation and Laplace equation. Two independent quasi-stress dynamic problems are presented by eliminating the coupled effects of wave motion equation and Laplace equation by introducing electric displacement potential (Bleustein J. L., Applied Physics Letters, 1968, 13: 412 [similar to] 413). They can be solved independently by the corresponding boundary conditions and the initial value conditions of the quasi-stress dynamic problem. The solution form of quasi-stress is consistent with that of pure stress problem. A few type problems of dynamic fracture for the piezoelectric materials, such as anti-plane self-similar crack growth, anti-plane moving crack and anti-plane center crack subjected the impact loading, have been studied. The dynamic stresses and electric displacement around the crack-tip are obtained. It is shown from the above examples that the coupled field inside piezoelectric medium depends on the speed of the crack propagation, and the intensity factors of stress, strain and electric displacement have singularity of 1/2 order at the crack tip. Moreover, the intensity factor of the electric displacement is independent of the mechanical load. With a = vt standing for the length of transient crack, the electric displacement intensity factor is the same as the static results (Pak Y. E., Journal of Applied Mechanics, 1990, 57: 647 [similar to] 653). If the piezoelectric constant e15 = 0, the results of electro-elastic dynamic fracture fore mentioned can degenerated as the results of the corresponding problems of the elasto-dynamic problem.

关 键 词：压电材料 断裂动力学 扩展裂纹 强度因子 反平面问题 

分 类 号：TB34[一般工业技术—材料科学与工程] O346.1[理学—固体力学]