多铁性颗粒复合材料内部的平行多裂纹问题
摘要
压电/压磁颗粒复合材料是通过粉末冶金工艺将压电相与压磁相混合烧结形成的复合材料。在文献中,它常常被称为磁电弹材料。磁电弹材料对于应力场、电场、磁场等物理场的变化较为敏感,这三者中任一个发生改变都可能在材料内部引起其余两者变化。由于该类材料为脆性陶瓷,在力电磁载荷作用下,它难免发生开裂。工程中,裂纹的萌生与扩展不仅会降低磁电弹器件的机械强度,而且将显著降低其力电磁耦合效果。在服役过程中,磁电弹材料内部可能同时产生多条裂纹。与单一裂纹的情况相比,多裂纹具有更为复杂的几何排列和相互作用。这使得具有多裂纹的磁电弹材料的断裂行为也将呈现出更复杂的规律。因此,在磁电弹材料的防断裂设计中,有必要研究多裂纹共存的情况及其相互作用规律。与一般的多裂纹问题相比,平行多裂纹问题由于几何构型相对简单,因而在理论分析上具有较强的可行性。不仅如此,平行多裂纹问题还是构造和研究更复杂的多裂纹问题的基础。所以,研究磁电弹材料中的平行多裂纹问题对于磁电弹结构的优化设计具有十分重要的意义。本文采用Green函数与奇异积分方程法,求解电(磁)加载条件下磁电弹条内部的平行多裂纹问题,得到了应力强度因子的数值解,并基于数值结果讨论了平行裂纹之间的相互作用规律,相关结论可为工程中磁电弹材料的防断裂优化设计提供理论参考。
引文
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[2]Li Y D,Lee K Y.Fracture analysis on the arc-shaped interface in a layered cylindrical piezoelectric sensor polarized along its axis[J].Engineering Fracture Mechanics,2009,76(13):2065-2073.
[3]Weertman J.Dislocation based fracture mechanics[M].Singapore:World Scientific Publishing Company,1996:45-99.
[4]Zhang A B,Wang B L.An opportunistic analysis of the interface crack based on the modified interface dislocation method[J].International Journal of Solids and Structures,2013,50(1):15-20.
[5]Chen Y Z,Lin X Y,Wang Z X.Antiplane elasticity crack problem for a strip of functionally graded materials with mixed boundary condition[J].Mechanics Research Communications,2010,37(1):50-53.
[6]Zhong X C,Liu F,Li X F.Transient Response of a Magnetoelectroelastic Solid with Two Collinear Dielectric Cracks under Impacts[J].International Journal of Solids and Structures,2009,46(14-15):2950-2958.
[7]Muskhelishvili N I.Singular Integral Equations[M].The Netherlands:Springer,1977:113-163.
[8]Erdogan F.复变函数技术[M].程沅生译.江苏科学出版社,1982:64-112.
[9]Li X F,Lee K Y.Closed-form Solution for an Orthotropic Elastic Strip with a Crack Perpendicular to the Edges under Arbitrary Anti-plane Shear[J].Zeitschrift fur Angewandte Mathematik und Mechanik,2009,89(5):370-382.
[10]Zhong X C,Li X F,A finite length crack propagating along the interface of two dissimilar magnetoelectroelastic materials[J].International Journal of Engineering Science,2006,44(18-19):1394-1407.