磁电弹性体中唇形运动裂纹问题分析  

Analysis for a Lip-Shaped Moving Crack in a Magnetoelctroelastic Body

作　　者：郭怀民[1] 高明[1] 赵国忠[1] 

机构地区：[1]包头师范学院数学科学学院,内蒙古包头014030

出　　处：《力学季刊》2017年第3期518-526,共9页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11761054);内蒙古自然科学基金(2015MS0108);内蒙古自治区高等学校科学青年科技英才支持计划(NMYT-15-A07);包头师范学院阴山学者培养计划;内蒙古自治区高等学校科学研究项目(NJZY16235)

摘　　要：本文通过共形映射公式,利用复变函数方法研究了磁电弹性体中的唇形运动裂纹问题.对裂纹面上受反平面剪应力和面内磁电载荷共同作用情况,导出了磁电全非渗透型边界条件下运动裂纹尖端场应力强度因子和机械应变能释放率的解析解.当运动速度为零时这两解都退化成了静止状态下的解.通过算例,与具有相同尺寸的带双裂纹的椭圆孔口问题进行了比较,给出了两种裂纹尖端点处应力强度因子和机械应变能释放率随孔口高度h与裂纹半长a之比h/a的变化规律曲线图,得出了两种孔口裂纹问题在应力强度因子和能量释放率两方面的异同点,结果表明采用唇形孔口裂纹比采用带双裂纹的椭圆孔口能降低裂纹的扩展,这在工程建设及构件的制造上有一些指导作用.By using conformal mapping formula as well as the complex function method, the problem of a lip-ship crack in a magnetoelectroelastic body under the anti-plane shear stress and in-plane electric and magnetic loads was analyzed. The analytical solutions of the field intensity factors and the energy release rate were presented with the assumption that the surface of the crack was electrically and magnetically impermeable. When the velocity tends to zero, the analytical solutions can be degraded into a stationary state solution. Through numerical examples, the lip-ship crack problem was compared with the problem of elliptical hole with double cracks in the same size. The curves of the stress intensity factors and the energy release rates of two cracks along with the change of h/a were plotted. The similarities and differences between the two crack problems in terms of stress intensity factor and the energy release rate were given. As the results indicate, the lip-ship crack results in less crack extension than the elliptical hole with double cracks, which provides some guidance in the engineering construction and the manufacture of components.

关 键 词：磁电弹性复合材料 唇形运动裂纹 复变函数法 应力强度因子 机械应变能释放率 

分 类 号：TB330.1[一般工业技术—材料科学与工程] O346.1[理学—固体力学]