An Antiplane Problem of Magnetoelectroelastic Materials With Nanoscale Lip-Shaped Orifice With 2 Asymmetric Cracks
-
摘要: 基于Gurtin-Murdoch表面弹性理论和磁电弹性(MEE)理论，利用解析函数的保角映射技术，研究了反平面机械载荷和面内电磁载荷作用下，MEE材料中含有纳米尺度唇口次生两不对称裂纹的断裂行为，给出了缺陷(裂纹和唇口孔)周围广义MEE应力场和裂纹尖端MEE场强度因子以及能量释放率的解析解. 在特殊条件下，所得结果退化为已有结果或者给出新的结果. 数值算例揭示了缺陷表面效应对裂纹尖端MEE场强度因子的影响与纳米圆孔半径、唇口孔的大小、唇口次生裂纹大小，以及外加的机-电-磁载荷有关，也揭示了考虑表面效应时，无量纲能量释放率随唇口宽度、无穷远处机械载荷、电载荷和磁载荷的变化而变化.
-
关键词:
- 磁电弹性材料 /
- 表面效应 /
- 唇口次生两不对称裂纹 /
- 场强度因子 /
- 能量释放率
Abstract: Based on the Gurtin-Murdoch surface elasticity theory and the magnetoelectroelasticity (MEE) theory, the fracture behaviors of MEE materials containing nanoscale lip-shaped orifice with 2 asymmetric cracks under anti-plane mechanical loads and in-plane electromagnetic loads were investigated with the analytic function conformal mapping technique. Analytical solutions for the generalized MEE stress fields around defects (the lip-shaped orifice and cracks), as well as the crack tip MEE intensity factors and energy release rates, were given. Under special conditions, the obtained results would degenerate into existing results or offer new insights. Numerical examples reveal that, the defect surface effects on the MEE intensity factors are dependent on the radii of nano-sized circular holes, the size of the lip-shaped orifice, the size of secondary cracks originating from the lip-shaped orifice, and the applied MEE loads. Under the surface effect, the dimensionless energy release rate varies with the lip width, the infinity mechanical load, the infinity electrical load and the infinity magnetic load. -
图 1 MEE材料含纳米尺度唇口次生两不对称裂纹示意图
Figure 1. Schematic diagram of the magnetoelectroelastic material containing a nanoscale lip with asymmetric cracks
表 1 基体材料的MEE常数
Table 1. Magnetoelectroelastic constants of the base material
c44/Pa e15/(C·m-2) κ11/(C2·N－1·m－2) q15/(N·A-1·m-1) α11/(N·s·V-1·C-1) μ11/(N·s2·C-2) 4.53×1010 11.6 8×10－9 550 5×10－12 5.9×10－4 
下载: 导出CSV
表 2 纳米缺陷的表面常数
Table 2. Surface constants of nanodefects
c44s/(N·m－1) e15s/(N·A-1) κ11s/(C2·N-1·m-2) q15s/(N·A-1) α11s/(N·A-1) μ11s/(N·s2·C-2) 6 3.3×10－7 5×10－17 3×10－11 6×10－21 0
下载: 导出CSV
-
[1] SUCHTELEN J V. Product properties: a new application of composite materials[J]. Philips Research Reports, 1972, 27(1): 28-37. [2] VALENTE J, OU J Y, PLUM E, et al. A magneto-electro-optical effect in a plasmonic nanowire material[J]. Nature Communications, 2015, 6: 7021. doi: 10.1038/ncomms8021 [3] LIU L L, FENG W J. Dugdale plastic zone model of a penny-shaped crack in a magnetoelectroelastic cylinder under magnetoelectroelastic loads[J]. Archive of Applied Mechanics, 2019, 89(2): 291-305. doi: 10.1007/s00419-018-1467-6 [4] HU K Q, ZHONG Z, CHEN Z T. Interface crack between magnetoelectroelastic and orthotropic half-spaces under anti-plane loading[J]. Theoretical and Applied Fracture Mechanics, 2019, 99: 95-103. doi: 10.1016/j.tafmec.2018.11.012 [5] XIAO J H, XU Y L, ZHANG F C. Fracture analysis of magnetoelectroelastic solid weakened by periodic cracks and line inclusions[J]. Engineering Fracture Mechanics, 2019, 205: 70-80. doi: 10.1016/j.engfracmech.2018.11.019 [6] AYATOLLAHI M, MONFARED M M, NOURAZAR M. Analysis of multiple moving mode-Ⅲ cracks in a functionally graded magnetoelectroelastic half-plane[J]. Journal of Intelligent Material Systems and Structures, 2017, 28(19): 2823-2834. doi: 10.1177/1045389X17698593 [7] MA P, SU R K L, FENG W J. Moving crack with a contact zone at interface of magnetoelectroelastic bimaterial[J]. Engineering Fracture Mechanics, 2017, 181: 143-160. doi: 10.1016/j.engfracmech.2017.07.012 [8] ZHAO M H, ZHANG Q Y, LI X F, et al. An iterative approach for analysis of cracks with exact boundary conditions in finite magnetoelectroelastic solids[J]. Smart Materials and Structures, 2019, 28(5): 055025. doi: 10.1088/1361-665X/ab0eb0 [9] XIAO J, XU Y, ZHANG F. Surface effects of electroelastic tip fields of multiple cracks emanating from a circular hole[J]. Engineering Fracture Mechanics, 2020, 236: 107219. doi: 10.1016/j.engfracmech.2020.107219 [10] YANG Y, HU Z L, LI X F. Nanoscale mode-Ⅲ interface crack in a bimaterial with surface elasticity[J]. Mechanics of Materials, 2020, 140: 103246. doi: 10.1016/j.mechmat.2019.103246 [11] GURTIN M E, MURDOCH A I. A continuum theory of elastic material surfaces[J]. Archive for Rational Mechanics and Analysis, 1975, 57(4): 291-323. doi: 10.1007/BF00261375 [12] GURTIN M E, MURDOCH A I. Surface stress in solids[J]. International Journal of Solids and Structures, 1978, 14(6): 431-440. doi: 10.1016/0020-7683(78)90008-2 [13] GURTIN M E, WEISSMVLLER J, LARCHÉ F. A general theory of curved deformable interfaces in solids at equilibrium[J]. Philosophical Magazine A, 1998, 78(5): 1093-1109. doi: 10.1080/01418619808239977 [14] DINEVA P, STOYNOV Y, RANGELOV T. Dynamic fracture behavior of nanocracked graded magnetoelectroelastic solid[J]. Archive of Applied Mechanics, 2021, 91(4): 1495-1508. doi: 10.1007/s00419-020-01835-8 [15] YANG D S, LIU G T. Anti-plane fracture problem of three nano-cracks emanating from a magnetoelectrically permeable regular triangle nano-hole in magnetoelectroelastic materials[J]. Modern Physics Letters B, 2021, 35(7): 2150127. doi: 10.1142/S021798492150127X [16] 杨东升, 刘官厅. 磁电弹性材料中含有带四条纳米裂纹的正4n边形纳米孔的反平面断裂问题[J]. 物理学报, 2020, 69(24): 181-190.YANG Dongsheng, LIU Guanting. Anti-plane fracture problem of four nano-cracks emanating from a regular 4n-polygon nano-hole in magnetoelectroelastic materials[J]. Acta Physica Sinica, 2020, 69(24): 181-190. (in Chinese) [17] XIAO J H, FENG G Y, SU M Y, et al. Fracture analysis on periodic radial cracks emanating from a nano-hole with surface effects in magnetoelectroelastic materials[J]. Engineering Fracture Mechanics, 2021, 258: 108115. doi: 10.1016/j.engfracmech.2021.108115 [18] XIAO J H, XU B X, XU Y L, et al. Fracture analysis on a cracked elliptical hole with surface effect in magnetoelectroelastic solid[J]. Theoretical and Applied Fracture Mechanics, 2020, 107: 102532. doi: 10.1016/j.tafmec.2020.102532 [19] GUO J H, HE L T, LIU Y Z, et al. Anti-plane analysis of a reinforced nano-elliptical cavity or nano-crack in a magnetoelectroelastic matrix with surface effect[J]. Theoretical and Applied Fracture Mechanics, 2020, 107: 102553. doi: 10.1016/j.tafmec.2020.102553 [20] LIU Y Z, GUO J H, and ZHANG X Y. Surface effect on a nano-elliptical hole or nano-crack in magnetoelectroelastic materials under antiplane shear[J]. ZAMM Journal of Applied Mathematics and Mechanics, 2019, 99(7): e201900043. doi: 10.1002/zamm.201900043 [21] XIAO J H, XU B X, XU Y L, et al. The generalized self-consistent micromechanics prediction of the magnetoelectroelastic properties of multi-coated nanocomposites with surface effect[J]. Smart Materials and Structures, 2019, 28(5): 055004. doi: 10.1088/1361-665X/ab0b6c [22] WU Z L, LIU G T, YANG D S. Anti-plane fracture behavior of n nano-cracks emanating from a magnetoelectrically semi-permeable regular n-polygon nano-hole in magnetoelectroelastic materials[J]. International Journal of Modern Physics B, 2024, 38(14): 2450170. doi: 10.1142/S0217979224501704 [23] XIAO J H, XIN Y Y. Fracture analysis of circular hole edge arbitrary position crack with surface effects in magnetoelectroelastic materials[J]. Mathematics and Mechanics of Solids, 2023, 28(10): 2202-2214. doi: 10.1177/10812865231156464 [24] 肖俊华, 信玉岩. 磁电弹性体中纳米孔边任意位置贯穿裂纹的解析解[J]. 固体力学学报, 2024, 45(1): 61-73.XIAO Junhua, XIN Yuyan. Analytical solution of an arbitrary-location through crack emanating from a nano-hole in magneto-electro-elastic materials[J]. Chinese Journal of Solid Mechanics, 2024, 45(1): 61-73. (in Chinese) [25] 范天佑. 断裂理论基础[M]. 北京: 科学出版社, 2003.FAN Tianyou. Foundation of Fracture Mechanics[M]. Beijing: Science Press, 2003. (in Chinese) [26] 匡震邦. 只有尖点的平面曲边多角形缺陷的应力分析[J]. 力学学报, 1979, 15(2): 118-128.KUANG Zhenbang. Stress analysis for plane curved polygonal defects containing cusps only[J]. Acta Mechanica Sinica, 1979, 15(2): 118-128. (in Chinese) [27] 刘鑫, 郭俊宏, 于静. 磁电弹性材料中唇形裂纹反平面问题[J]. 内蒙古大学学报(自然科学版), 2016, 47(1): 37-45.LIU Xin, GUO Junhong, YU Jing. Anti-plane problem of a lip-shaped crack in a magnetoelectro-elastic material[J]. Journal of Inner Mongolia University (Natural Science Edition), 2016, 47(1): 37-45. (in Chinese) [28] GUO H M, ZHAO G Z, JIANG L J. Screw dislocation interacting with lip-shaped crack in magnetoelectroelastic media[J]. Chinese Journal of Computational Physics, 2022, 39(1): 33-40. [29] 郭怀民, 赵国忠, 刘官厅, 等. 含唇口次生两不对称裂纹的一维六方压电准晶体的反平面剪切问题[J]. 固体力学学报, 2024, 45(1): 123-134.GUO Huaimin, ZHAO Guozhong, LIU Guanting, et al. The anti-plane shear problem of a lip-shaped orifice with two asymmetric edge rips in the one-dimensional hexagonal piezoelectric quasicrystal material[J]. Chinese Journal of Solid Mechanics, 2024, 45(1): 123-134. (in Chinese). [30] МУСХЕЛИШВИЛИ Н И. 数学弹性力学的几个基本问题[M]. 赵惠元, 译. 北京: 科学出版社, 1958.МУСХЕЛИШВИЛИ Н И. Some Basic Problems of Mathematical Theory of Elasticity[M]. ZHAO Huiyuan, transl. Beijing: Science Press, 1958. (in Chinese) [31] GUO J H, LU Z X. Anti-plane analysis of multiple cracks originating from a circular hole in a magnetoelectroelastic solid[J]. International Journal of Solids and Structures, 2010, 47(14/15): 1847-1856. [32] CHEN T. Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects[J]. Acta Mechanica, 2008, 196(3): 205-217. -
图(13) / 表(2)
计量
- 文章访问数: 109
- HTML全文浏览量: 45
- PDF下载量: 35
- 被引次数: 0
渝公网安备50010802005915号