通过构造新保角映射,利用stroh公式研究了远场受反平面剪应力和面内电载荷共同作用下无限大压电复合材料中幂函数型曲线裂纹的断裂行为。给出了电不可渗透边界条件下裂纹尖端场强度因子和机械应变能释放率的解析解。该解析解在幂函数的幂次为零时,可退化为已有文献中无限大压电复合材料含直线裂纹的结果,证明了其合理性。由解析解可知,裂纹几何形状一定时,电场分布将不受机械载荷的影响。最后,通过数值算例讨论了幂函数的幂次、系数及其在X1轴上的投影长度对机械应变能释放率的影响。结果表明,当压电体仅受X2方向载荷作用时,对于给定幂次与开口的曲线裂纹,在X1轴上的投影长度存在一临界值使其最容易开裂;而对于给定投影长度与幂次的曲线裂纹,开口越大裂纹越容易扩展。
By proposing a new conformal mapping and using the Stroh formula the fracture problem of a power function curved crack in an infinite piezoelectric coposite is studied under anti-plane shear stress and in-plane electric load at infinity The analytical solutions of the field intensity factors and the mechanical strain energy relrase rate are presented with the assumptio that the surface of the crack is electrically impermeable When the power of the curve is zero the present results can be reduced to the solutions of a Griffith crack in an infinite piezoelectric comosite Based on the analytical solutions it is found that the distribution of electric field is independent on the mechanics load under a fixed shape of the curve,Numerical examples are finally conducted to analyze the influences of the projected length along the X1-axis power and coefficient of curved cracks on the mechanical strain energy release rate The results show that if the plezoelectrlc composlte is subjected to the only load along the direction ot X2-axis there exists a critical projected length along the X1-axis which can promote the crack growth easily for given power and coefficient of curved cracks Moreover for given values of projected length and power of curved cracks the smaller coefficient of curved crack is,the easier crack propagates.
参考文献
[1] | 方岱宁,刘金喜.压电与铁电体的断裂力学[M].北京:清华大学出版社,2008. |
[2] | 王保林.压电材料及其结构的断裂力学[M].北京:国防工业出版社,2003. |
[3] | Zhang T Y,Zhao M H,Tong P.Fracture of piezoelectricceramics[J].Adv Appl Mech,2002,38:147-289. |
[4] | Zhang T Y,Gao C F.Fracture behaviors of piezoelectricmaterials[J].Theo Appl Fract Mech,2004,41(1-3):339-379. |
[5] | Kuna M.Fracture mechanics of piezoelectric materials:Whereare we right now[J].Engineering Fracture Mechanics,2010,77(2):309-326. |
[6] | Guo Junhong,Liu Ping,Lu Zixing,et al.Anti-plane analysisof semi-infinite crack in piezoelectric strip[J].Appl MathMech:English Edition,2011,32(1):75-82. |
[7] | Guo Junhong,Lu Zixing,Han Haitao,et al.Exact solutionsfor anti-plane problem of two asymmetrical edge cracksemanating from an elliptical hole in a piezoelectric material[J].International Journal of Solids and Structures,2009,46(21):3799-3809. |
[8] | Guo Junhong,Lu Zixing,Han Haitao,et al.The behavior oftwo non-symmetrical permeable cracks emanating from anelliptical hole in a piezoelectric solid[J].European Journal ofMechanics A:Solids,2010,29(4):654-663. |
[9] | Guo Junhong,Lu Zixing,Feng Xiang.The fracture behaviorof multiple cracks emanating from a circular hole inpiezoelectric materials[J].Acta Mechanica,2010,215(1):119-134. |
[10] | 侯密山,钱秀清.含曲线裂纹的压电材料反平面应变问题[J].石油大学学报,2001,25(2):95-99,105. |
[11] | 胡元太,赵兴华.沿抛物线分布的各向异性曲线裂纹问题[J].应用数学与力学,1995,16(2):107-114. |
[12] | Pak Y E.Crack extension force in a piezoelectric material[J].ASME Journal of Applied and Mechanics,1990,57(3):647-653. |
[13] | Wang B L,Mai Y W.Impermeable crack and permeable crackassumptions,which one is more realistic[J].ASME Journalof Applied Mechanics 2004,71(4):575-578. |
[14] | Park S B,Sun C T.Fracture criteria for piezoelectric ceramics[J].Am Ceram Soc,1995,78(6):1475-1480. |
[15] | 郭俊宏,卢子兴.含周期性裂纹正交各向异性板平面问题的应力场分析[J].复合材料学报,2010,27(1):162-166. |
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