Dynamic fracture behavior analysis of functionally graded piezoelectric materials with defects
AN Ni1,2, SONG Tianshu1, ZHAO Ming1
1. College of Aerospace and Architecture Engineering, Harbin Engineering University, Harbin 150001, China;
2. School of Civil Engineering and Architecture, Northeast Electric Power University, Jilin 132012, China
Abstract：Compared with traditional piezoelectric materials, functionally graded piezoelectric materials (FGPMs) have the characteristics of continuous changes in mechanical properties (such as piezoelectric constant, dielectric constant, elastic modulus, mass density, etc.) in a certain direction, which can avoid stress concentration and effectively extend the service life of the components. In actual engineering, various types of defects such as cracks and cavities are often generated at the interface in the material, and the area near the defect is prone to stress concentration and even fracture under the action of external load. At present, the research on the fracture problem of functionally graded piezoelectric materials is limited to single-form defects, that is, there are only cavities or only cracks at the material interface, and there are few studies on composite defects. This paper aims to develop an accurate method for the problem of dynamic stress concentration in the crack tip field of the functionally graded piezoelectric bi-material with hole-initiated interface crack defects under the action of anti-plane shear wave. Green function method, coordinate transformation method, conjunction and crack-deviation techniques are adopted to build mathematical model, so that the crack problem is reduced to solving a set of the first kind of Fredholm’s integral equations and the dynamic stress intensity factors (DSIFs) are expressed theoretically. Finally, numerical results reveal the effect of the geometry of cavity and crack, the characteristics of incident wave and the inhomogeneity of materials on DSIFs. A comparison with a Griffith crack model verifies the validity of the present method.
[1] Sih GC. Stress distribution near internal crack tips for longitudinal shear problems [J]. J. Appl. Mech., 1965, 32(1): 51-58
[2] Wang BL, Han JC, Du SY. Crack problems for functionally graded materials under transient thermal loading [J]. J. Therm. Stresses., 2000, 23: 143-168
[3] Ma L, Wu LZ, Guo LC. Dynamic behavior of two collinear anti-plane shear cracks in a functionally graded layer bonded to dissimilar half planes. Mech. Res., Commun, 2002, 29(4): 207-215
[4] Guo LC, Wu LZ, Ma L. The interface crack problem under a concentrated load for a functionally graded coating-substrate composite system [J]. Compos. Struct., 2004, 63(3/4): 397-406
[5] Guo LC, Wu LZ, Ma L, et al. Fracture analysis of a functionally graded coating-substrate structure with a crack perpendicular to the interface-Part I: Static problem. Int. J. Fracture [J]., 2004, 127(1): 21-38
[6] Guo LC, Wu LZ, Zeng T, et al. The dynamic fracture behavior of a functionally graded coating-substrate system [J]. Compos. Struct., 2004, 64(3/4): 433-441
[7] Guo LC, Noda N, Ishihara M. Thermal stress intensity factors for a normal surface crack in a functionally graded coating structure [J]. J. Therm. Stresses., 2007, 31(2):149-164
[8] Pan HZ, Song TS, Wang ZH. Thermal fracture model for a functionally graded material with general thermomechanical properties and collinear cracks [J]. J. Therm. Stresses., 2016, 39(7-9): 820-834
[9] 仲政, 吴林志, 陈伟球. 功能梯度材料与结构的若干力学问题研究进展. 力学进展, 2010, 40(5): 528-541(Zhong Zheng, Wu Linzhi, Chen Weiqiu. Research progress on some mechanical problems of functionally graded materials and structures [J]. Advances In Mechanics, 2010, 40(5): 528-541 (in Chinese)).
[10] Ghafarollahi A, Shodja HM. Scattering of SH-waves by an elliptic cavity/crack beneath the interface between functionally graded and homogeneous half-spaces via multipole expansion method [J]. J. Sound Vib., 2018, 435: 372-389
[11] 李戎, 杨萌, 梁斌, Noda Nao-Aki. 基于裂纹尖端应力比值的含裂纹功能梯度材料圆筒应力强度因子计算方法. 工程力学, 2020,37(4): 22-29 (Li Rong, Yang Meng, Liang Bin, Noda Nao-Aki. Calculation method of stress intensity factor for cracked functionally graded hollow cylinder based on the ratio of stresses at crack tip [J]. Engineering Mechanics, 2020,37(4): 22-29 (in Chinese))
[12] Guo LC, Wu LZ, Sun YG, et al. The transient fracture behavior for a functionally graded layered structure subjected to an in-plane impact load [J]. Acta Mech. Sinica-Prc., 2005, 21(3), 257-266
[13] Fallahnejad M, Bagheri R, Noroozi M. Transient analysis of two dissimilar FGM layers with multiple interface cracks [J]. Struct. Eng. Mech.,2018, 67(3): 277-281
[14] Bagheri R. Transient behavior of multiple interface cracks in two non-homogeneous half-layers [J]. Iran J Sci Technol Trans Mech Eng., 2020, 44(9): 619–629
[15] Tavakoli A, Pourseifi M, Rezaei S. Stress intensity factors of multiple axisymmetric interface cracks in an isotropic layer with FGM coating under torsional loading [J]. Multidipline Modeling in Materials and Structures, 2019, 15(6): 1352-1365
[16] 程家幸, 盛冬发, 杨天琪, 等. 含微孔洞损伤的压电功能梯度矩形板热屈曲分析 [J]. 应用力学学报, 2018, 35(2): 278-284 (Cheng Jiaxing, Sheng Dongfa, Yang Tianqi, et al. Thermal buckling analysis of functionally graded piezoelectric rectangular plates with micro hole damage [J]. Applied Mechanics, 2018, 35(2): 278-284 (in Chinese))
[17] Pathak H. Crack interaction study in functionally graded materials (FGMs) using XFEM under thermal and mechanical loading environment [J]. Mechanics of Advanced Materials and Structures, 2020, 27(11): 903-926
[18] Fang XQ, Liu JX, Wang DB, et al. Dynamic stress from a subsurface cavity in a semi-infinite functionally graded piezoelectric/piezomagnetic material [J]. Appl. Math. Model., 2010, 34(10): 2789-2805
[19] Wang XH, Fang XQ, Liu JX, et al. Dynamic stress from a circular hole in a functionally graded piezoelectric/ piezomagnetic material subjected to shear waves [J]. Philos. Mag., 2009, 89(33): 3059-3074
[20] 孙建亮, 周振功, 王彪. 功能梯度压电压磁材料中断裂问题分析. 力学学报, 2005, 37(1): 9-14 (Sun Jianliang, Zhou zhengong, Wang Biao. A permeable crack in functionally graded piezoelectric/piezomagnetic materials [J]. Acta Mechanica Sinica, 2005, 37(1): 9-14 (in Chinese))
[21] Bagheri R, Mirzaei AM. Fracture analysis in an imperfect FGM orthotropic strip bonded between two magneto-electro-elastic layers [J]. Iranian Journal of ence and Technology, Transactions of Mechanical Engineering, 2019, 43(2): 253-271
[22] 张超群, 鞠桂玲, 孙炜海. 含耦合弱界面的压电/压磁声子晶体带隙研究. 压电与声光, 2018, 40(6): 835-839,842 (Zhang Chaoqun, Ju Guiling, Sun Weihai. Study on band gap of piezoelectric/piezomagnetic phononic crystal with imperfect interface of magneto-electro-mechanical coupling [J]. Piezoelectrics and Acoustooptics, 2018, 40(6): 835-839,842 (in Chinese))
[23] 夏振庭, 钟轶峰, 黄子昂, 等. 含金属芯压电压磁纤维/聚合物基复合材料时变、非线性和多物理场响应的细观力学模型 [J]. 复合材料学报, 2017, 34 (12): 2747-2755 (Xia Zhenting, Zhong Yifeng, Huang Zixuan, et al. Micromechanics modeling of time-dependent, nonlinear and multiphysics response of metal core piezoelectric and piezomagnetic fibers reinforced polymer matrix composites [J]. Acta Materiae Compositae Sinica, 2017, 34 (12): 2747-275 (in Chinese))
[24] 赵星, 刘响林, 刘赛,等. 非理想界面功能梯度压电/压磁双材料中的SH界面波 [J]. 振动与冲击, 2014, 33(13): 183-183 (Zhao Xing, Liu Xianglin, Liu Sai, et al. SH interfacial wave in a functionally graded piezoelectric/piezomagnetic bi-material with an imperfect interface [J]. Journal of Vibration and Shock, 2014, 33(13):183-183 (in Chinese))
[25] Milan AG, Ayatollahi M. Transient analysis of multiple interface cracks between two dissimilar functionally graded magneto-electro-elastic layers [J]. Arch. Appl. Mech., 2020, 90(8): 1829–1844
[26] Zhao X, Qian Z, Liu J, et al. Effects of electric/magnetic impact on the transient fracture of interface crack in piezoelectric-piezomagnetic sandwich structure: anti-plane case [J]. Applied Mathematics and Mechanics, 2020, 41(1):139-156
[27] Zhao X, Liu JX, Qian ZH et al. Transient fracture of a piezoelectric-piezomagnetic sandwich structure: anti-plane case [J]. Acta Mech, 2019, 230(4): 1233–1246
[28] An Ni, Song Tian-shu, Hou Gangling. Interfacial cracks near an eccentric circular hole in piezoelectric bi-materials subjected to dynamic incident anti-plane shearing [EB/OL]. AIP Advances, 2020. https://doi.org/10.1063/1.5110575
[29] 李冬. 含界面附近多种缺陷压电介质动力反平面行为 [D]. 哈尔滨: 哈尔滨工程大学, 2011 (Li Dong. Dynamic antiplane behaviors on piezoelectric materials with interface defects [D]. Harbin: Harbin Engineering University, 2011 (in Chinese))
[30] Ma L, Wu LZ, Zhou ZG, et al. Scattering of the harmonic anti-plane shear waves by a crack in functionally graded piezoelectric materials [J]. Compos. Struct., 2005, 69(4): 436-441
