Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (4): 44601-044601.doi: 10.1088/1674-1056/22/4/044601

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

The influence of defects on the effective Young’s modulus of a defective solid

沈伟a, 范群波b, 王富耻b, 马壮b   

  1. a Central Iron and Steel Research Institute，Beijing 100081, China;
    b School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2012-07-06 修回日期:2012-08-27 出版日期:2013-03-01 发布日期:2013-03-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 50801005).

The influence of defects on the effective Young’s modulus of a defective solid

Shen Wei (沈伟)a, Fan Qun-Bo (范群波)b, Wang Fu-Chi (王富耻)b, Ma Zhuang (马壮)b   

  1. a Central Iron and Steel Research Institute，Beijing 100081, China;
    b School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China
  • Received:2012-07-06 Revised:2012-08-27 Online:2013-03-01 Published:2013-03-01
  • Contact: Shen Wei E-mail:wells.shen@gmail.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 50801005).

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摘要： It is difficult to establish structure-property relationships in defective solid because of its inhomogeneous-geometry microstructure caused by defects. In the present research, the effects of pores and cracks on Young's modulus of defective solid are studied. Based on the law of the conservation of energy, mathematical formulations are proposed to indicate how the shape, size, and distribution of defects affect the effective Young's modulus. In this approach, detailed equations are illustrated to represent the shape and size of defects on the effective Young's modulus. Different from the results obtained from the traditional empirical analyses, mixture law or statistical method, for the first time, our results from the finite element method (FEM) and strict analytical calculation show that the influence of pore radius and crack length on the effective Young's modulus can be quantified. It is found that the longest crack in a typical microstructure of ceramic coating dominates the contribution of the effective Young's modulus in vertical direction of the crack.

关键词: defects, effective Young's modulus, conservation of energy, pore radius and crack length

Abstract: It is difficult to establish structure-property relationships in defective solid because of its inhomogeneous-geometry microstructure caused by defects. In the present research, the effects of pores and cracks on Young's modulus of defective solid are studied. Based on the law of the conservation of energy, mathematical formulations are proposed to indicate how the shape, size, and distribution of defects affect the effective Young's modulus. In this approach, detailed equations are illustrated to represent the shape and size of defects on the effective Young's modulus. Different from the results obtained from the traditional empirical analyses, mixture law or statistical method, for the first time, our results from the finite element method (FEM) and strict analytical calculation show that the influence of pore radius and crack length on the effective Young's modulus can be quantified. It is found that the longest crack in a typical microstructure of ceramic coating dominates the contribution of the effective Young's modulus in vertical direction of the crack.

Key words: defects, effective Young's modulus, conservation of energy, pore radius and crack length

中图分类号:  (General theory of continuum mechanics of solids)

  • 46.05.+b
62.20.de (Elastic moduli)