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黏弹性功能梯度材料裂纹问题的有限元方法

彭凡 马庆镇 戴宏亮

彭凡, 马庆镇, 戴宏亮. 黏弹性功能梯度材料裂纹问题的有限元方法[J]. 力学学报, 2013, 45(3): 359-366. doi: 10.6052/0459-1879-12-264
引用本文: 彭凡, 马庆镇, 戴宏亮. 黏弹性功能梯度材料裂纹问题的有限元方法[J]. 力学学报, 2013, 45(3): 359-366. doi: 10.6052/0459-1879-12-264
Peng Fan, Ma Qingzhen, Dai Hongliang. FINITE ELEMENT METHOD FOR CRACK PROBLEMS IN VISCOELASTIC FUNCTIONALLY GRADED MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 359-366. doi: 10.6052/0459-1879-12-264
Citation: Peng Fan, Ma Qingzhen, Dai Hongliang. FINITE ELEMENT METHOD FOR CRACK PROBLEMS IN VISCOELASTIC FUNCTIONALLY GRADED MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 359-366. doi: 10.6052/0459-1879-12-264

黏弹性功能梯度材料裂纹问题的有限元方法

doi: 10.6052/0459-1879-12-264
基金项目: 湖南省自然科学基金资助项目(11JJ3001).
详细信息
    通讯作者:

    彭凡,教授,主要研究方向:复合材料疲劳与断裂.E-mail:fanpeng@hnu.edu.cn

  • 中图分类号: O034

FINITE ELEMENT METHOD FOR CRACK PROBLEMS IN VISCOELASTIC FUNCTIONALLY GRADED MATERIALS

Funds: The project was supported by the Natural Science Foundation of Hunan Province (11JJ3001).
  • 摘要: 针对组分材料体积含量任意分布的黏弹性功能梯度材料裂纹问题建立有限元分析途径. 通过Laplace变换,将黏弹性问题转化到象空间中求解,基于反映材料非均匀的梯度单元和裂纹尖端奇异特性的奇异单元计算象空间中的位移、应力和应变场,应用虚拟裂纹闭合方法得到应变能释放率,分别由应力和应变能释放率确定应力强度因子. 给出这些断裂参量在物理空间和象空间之间的对应关系,由数值逆变换求出其在物理空间的相应值. 文中分析两端均匀受拉的黏弹性边裂纹板条,首先针对松弛模量表示为空间函数和时间函数乘积的特殊梯度材料进行计算,结合对应原理验证方法的有效性. 然后分析组分材料体积含量具有任意梯度分布的情形,由Mori-Tanaka方法预测象空间中的等效松弛模量. 计算结果表明,蠕变加载条件下,应变能释放率随时间增加,其增大程度与黏弹性组分材料体积含量相关. 由于梯度材料的非均匀黏弹性性质,产生应力重新分布,导致应力强度因子随时间变化,其变化范围与组分材料的体积含量分布方式有关.

     

  • Delale F, Erdogan F. The crack problem for a nonhomogeneous plane. ASME Journal of Applied Mechanics, 1983, 50(3): 609-614  
    Jin ZH, Noda N. Crack-tip singular fields in nonhomogeneous materials. ASME Journal of Applied Mechanics, 1994, 61(3): 738-740  
    Wang BL, Han JC, Du SY. Cracks problem for nonhomogeneous composite material subjected to dynamic loading. International Journal of Solids and Structures, 2000, 37(9): 1251-1274  
    黄干云, 汪越胜, 余寿文. 功能梯度材料的平面断裂力学分析. 力学学报, 2005, 37(1): 1-8 (Huang Ganyun, Wang Yuesheng, Yu Shouwen. A new multi-layered model for in-plane fracture analysis of functionally graded materials. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(1): 1-8 (in Chinese))
    程站起,高丹盈,仲政. 任意梯度分布功能梯度涂层平面裂纹分析. 固体力学学报, 2011, 32(4): 426-431 (Cheng Zhanqi, Gao Danying, Zhong Zheng. Plane crack problem for functionally graded strip with arbitrarily distributed material properties. Chinese Journal of Solid Mechanics, 2011, 32(4): 426-431 (in Chinese))
    Kim JH, Paulino GH. Finite element evaluation of mixed mode stress intensity factors in functionally graded materials. International Journal for Numerical Methods in Engineering, 2002, 53(8): 1903-1935  
    Oral A, Lambros J, Anlas G. Crack initiation in functionally cracked materials under mixed mode loading: Experiments and simulation. ASME Journal of Applied Mechanics, 2008, 75(5): 0511101-0511108
    张艳艳, 果立成, 白晓明等. 热载荷作用下含裂纹功能梯度板的有限元分析. 哈尔滨工业大学学报, 2011, 43(1): 12-15 (Zhang Yanyan, Guo Licheng, Bai Xiaoming, et al. Finite element analysis of functionally graded plate with a crack under thermal load. Journal of Harbin Institute of Technology, 2011, 43(1): 12-15 (in Chinese))
    Paulino GH, Jin ZH. Correspondence principle in viscoelastic functionally graded materials. ASME Journal of Applied Mechanics, 2001, 68(1): 129-132  
    Paulino GH, Jin ZH. Viscoelastic functionally graded materials subjected to antiplane shear facture. ASME Journal of Applied Mechanics, 2001, 64(2): 284-293
    李伟杰, 王保林, 张幸红. 功能梯度材料的黏弹性断裂问题. 力学学报,2008,40(3): 402-406 (Li Weijie, Wang Baolin, Zhang Xinghong. Viscoelastic fracture of a functionally graded material strip. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(3): 402-406 (in Chinese))
    梁军, 杜善义. 粘弹性复合材料力学性能的细观研究. 复合材料学报, 2001, 18(1): 97-100 (Liang Jun, Du Shanyi. Study of mechanical properties of viscoelastic matrix composite by micromechanics. Acta Materiae Compositae Sinica, 2001, 18(1): 97-100 (in Chinese))
    Dave EV, Paulino GH, Buttlar WG, et al. Viscoelastic functionally graded finite-element method using correspondence principle. Journal of Materials in Civil Engineering, 2011, 23(1): 39-48  
    Santare MH, Lambros J. Use of graded finite elements to model the behavior of nonhomogeneous materials. ASME Journal of Applied Mechanics, 2000, 67(4): 819-822  
    Eischen JW. Fracture of non-homogeneous materials. International Journal of Fracture, 1987, 34(1): 3-22
    Irwin GR. Analysis of stresses and strains near the end of a crack traversing a plate. ASME Journal of Applied Mechanics, 1957, 24(3): 354-361
    Jin ZH, Batra RC. Some basic fracture mechanics concepts in functionally graded materials. Journal of Mechanics and Physics of Solids, 1996, 44(8): 1221-1235  
    解德, 钱勤, 李长安. 断裂力学中的数值方法及工程应用. 北京:科学出版社, 2009 (Xie De, Qian Qing, Li Changan. Numerical Method in Fracture Mechanics and Engineering Application. Beijing: Science Press, 2009 (in Chinese))
    Rybicki EF, Kannimen MF. A finite element calculation of stress intensity factors by a modified crack closure integral. Engineering Fracture Mechanics, 1977, 9(4): 931-938  
    Raju IS. Calculation of strain-energy release rates with high-order and singular finite-elements. Engineering Fracture Mechanics, 1987, 28(2): 251-274
    Bellman R, Kalaba RE, Lockett J. Numerical Inversion of the Laplace Transform. New York: Americal Elsevier Publish Corporation, 1966
    Swanson SR. Approximate Laplace transform inversion in dynamic viscoelasticity. ASME Journal of Applied Mechanics, 1980, 47(6): 769-774
    张淳源. 黏弹性断裂力学. 武汉:华中理工大学出版社, 1994 (Zhang Chunyuan. Viscoelastic Fracture Mechanics. Wuhan: Huazhong University of Science and Technology Press, 1994 (in Chinese))
    Mukherjee S, Paulino GH. The elastic-viscoelastic correspondence principle for functionally graded materials, revisited. ASME Journal of Applied Mechanics, 2003, 70(3): 359-363  
    彭凡, 顾勇军, 马庆镇. 热环境中黏弹性功能梯度材料及其结构的蠕变. 力学学报, 2012, 44(2): 308-316 (Peng Fan, Gu Yongjun, Ma Qingzhen. Creep behavior of functionally graded materials and structures in thermal environment. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(2): 308-316 (in Chinese))
    Yin HM, Paulino GH, Buttlar WG, et al. Micromechanics-based thermoelastic model for functionally graded particulate materials with particle interactions. Journal of Mechanics and Physics of Solids, 2007, 55(2): 132-160
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出版历程
  • 收稿日期:  2012-09-25
  • 修回日期:  2013-01-25
  • 刊出日期:  2013-05-18

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