功能梯度材料有限宽板的反平面断裂问题研究

李永东; 贾斌; 张男; 戴耀; 唐立强

功能梯度材料有限宽板的反平面断裂问题研究

1.
解放军装甲兵工程学院机械工程系工程力学教研室,北京 100072;2.哈尔滨工业大学航天学院,哈尔滨 150001;3.哈尔滨工程大学建筑工程学院,哈尔滨 150001

基金项目: 国家自然科学基金资助项目(90305023)

详细信息

作者简介:
李永东(1971- ),男,四川眉山人,副教授,博士(联系人.Tel/Fax:+86-10-66719259;E-mail:lydbeijing@163.com).

中图分类号: O346.1
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出版历程
- 收稿日期: 2005-04-08
- 修回日期: 2006-02-12
- 刊出日期: 2006-06-15

Anti-Plane Fracture Analysis of a Functionally Gradient Material Infinite Strip With Finite Width

1.
Division of Engineering Mechanics, Department of Mechanical Engineering, Academy of Armored Force Engineering, Beijing 100072, P. R. China;

摘要

摘要: 研究了功能梯度材料有限宽板中与板边平行的III型裂纹问题．假设材料的剪切模量沿板宽度方向呈指数规律变化，利用Fourier变换将问题描述为奇异积分方程，并进一步将未知的位错密度函数表示为Chebyshev多项式的级数式，从而将奇异积分方程化为线性代数方程组进行配点数值求解．基于数值结果，讨论了材料非均匀性参数、板和裂纹的几何参数等对应力强度因子（SIF）的影响．研究表明，SIF随裂纹长度的增大而增大，随裂纹所在区域材料刚度的增大而减小；板越窄，SIF对非均匀性参数的变化越敏感，且变化规律也越复杂．随着非均匀性参数的增大，SIF既可能增大也可能减小还可能基本保持不变，这主要取决于板的相对宽度和裂纹的相对位置．当裂纹位于板的中央或当板较宽时，SIF对非均匀性参数的变化都不太敏感．
- 功能梯度材料 /
- 反平面断裂 /
- 应力强度因子 /
- Fourier变换 /
- 奇异积分方程 /
- 有限宽板
Abstract: The special case of a crack under mode conditions was treated,lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges.By using Fourier transforms the problem was formulate dinterms of a singular integral equation.It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations.The stress intensity factor (SIF)results were discussed with respect to the influences of different geometric parameter sand the strength of the non-homogeneity.It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack.The SIF of narrow strip is very sensitive to the change of the non-homog eneity parameter and its variation is complicated.With the increase of the non-homogeneity parameter,the stress intensity factor may increase,decrease or keep constant,which is mainly determined by the strip width and the relative crack location.If the crack is located at the midline of the strip or if the strip is wide,the stress intensity factor is not sensitive to the material non-homogeneity parameter.
- functionally gradient material /
- anti-plane fracture /
- stress intensity factor /
- Fourier transform /
- singular integral equation /
- finite-width strip

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参考文献(12)

[1]	李永东，张丙喜.压剪载荷作用下界面裂纹尖端场的研究[J]. 力学学报，2003，35(1):85—89.
[2]	唐立强，李永东，刘长海.弹性-幂硬化蠕变性材料Ⅱ型界面裂纹准静态扩展的渐近分析[J].应用数学和力学，2004,25(2):206—212.
[3]	Erdogan F. Fracture mechanics of functionally graded materials[J].Composites Engineering,1995,5(7):753—770. doi: 10.1016/0961-9526(95)00029-M
[4]	Chen Y F, Erdogan F. The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate[J].Journal of Mechanics and Physics of Solids,1996,44(7):771—787. doi: 10.1016/0022-5096(96)00002-6
[5]	Sang-Pyo J, Yoshinobu T.Axisymmetrical elastic behavior and stress intensity factor for a nonhomogeneous medium with a penny-shaped crack[J].JSME International Journal Series A,1998,41(4):457—464. doi: 10.1299/jsmea.41.457
[6]	HUANG Gan-yun, WANG Yue-sheng, YU Shou-wen. Fracture analysis of a functionally graded interfacial zone under plane deformation[J].International Journal of Solids and Structures,2004,41(3/4):731—743. doi: 10.1016/j.ijsolstr.2003.08.007
[7]	Erdogan F. The crack problem for bonded nonhomogeneous materials under antiplane shear loading[J].Journal of Applied Mechanics,1985,52(4):823—828. doi: 10.1115/1.3169153
[8]	Erdogan F, Ozturk M. Periodic cracking of functionally graded coatings[J].International Journal of Engineering Science,1995,33(15):2179—2195. doi: 10.1016/0020-7225(95)00065-6
[9]	Chan Y S,Paulino G H,Fannjian A C.The crack problem for nonhomogeneous materials under antiplane shear loading—a displacement based formulation[J].International Journal of Solids and Structures,2001,38(17):2989—3005. doi: 10.1016/S0020-7683(00)00217-1
[10]	HUANG Gan-yun,WANG Yue-sheng, Dietmar G.Fracture analysis of functionally graded coatings: antiplane deformation[J].European Journal of Mechanics A/Solids,2002,21(3):391—400. doi: 10.1016/S0997-7538(02)01223-8
[11]	WANG Bao-lin, MAI Yiu-wing,SUN Yu-guo. Anti-plane fracture of a functionally graded material strip[J].European Journal of Mechanics A/Solids,2003,22(3):357—368. doi: 10.1016/S0997-7538(03)00048-2
[12]	Erdogan F,Gupta G D. On the numerical solution of singular integral equations[J].Quarterly of Applied Mathmatics,1972,29(4): 525—534.

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功能梯度材料有限宽板的反平面断裂问题研究

作者简介:
李永东(1971- ),男,四川眉山人,副教授,博士(联系人.Tel/Fax:+86-10-66719259;E-mail:lydbeijing@163.com).

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Anti-Plane Fracture Analysis of a Functionally Gradient Material Infinite Strip With Finite Width

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留言板

功能梯度材料有限宽板的反平面断裂问题研究

作者简介: 李永东(1971- ),男,四川眉山人,副教授,博士(联系人.Tel/Fax:+86-10-66719259;E-mail:lydbeijing@163.com).

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出版历程

Anti-Plane Fracture Analysis of a Functionally Gradient Material Infinite Strip With Finite Width

计量

出版历程

目录

作者简介:
李永东(1971- ),男,四川眉山人,副教授,博士(联系人.Tel/Fax:+86-10-66719259;E-mail:lydbeijing@163.com).