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Chin. Phys. B, 2013, Vol. 22(4): 044601    DOI: 10.1088/1674-1056/22/4/044601

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

Shen Weia, Fan Qun-Bob, Wang Fu-Chib, Ma Zhuangb
a Central Iron and Steel Research Institute,Beijing 100081, China;
b School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China
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.
Keywords:  defects      effective Young's modulus      conservation of energy      pore radius and crack length     
Received:  06 July 2012      Published:  01 March 2013
PACS:  46.05.+b (General theory of continuum mechanics of solids) (Elastic moduli)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 50801005).
Corresponding Authors:  Shen Wei     E-mail:

Cite this article: 

Shen Wei, Fan Qun-Bo, Wang Fu-Chi, Ma Zhuang The influence of defects on the effective Young’s modulus of a defective solid 2013 Chin. Phys. B 22 044601

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