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

• Published in: Chinese physics B Vol. 22; no. 4; pp. 307 - 311
• Main Author: 沈伟 范群波 王富耻 马壮
• Format: Journal Article
• Language: English
• Published: 01.04.2013
• Subjects: Ceramic coatings; Cracks; Defects; Energy conservation law; Finite element method; Mathematical analysis; Microstructure; Modulus of elasticity; Porosity; 体弹性模量; 几何结构; 微观结构; 数学公式; 杨氏模量; 缺陷分布; 能量守恒定律; 裂纹长度
• ISSN: 1674-1056; 2058-3834; 1741-4199
• DOI: 10.1088/1674-1056/22/4/044601

It is difficult to establish structure-property relationships in a defective solid because of its inhomogeneous-geometry microstructure caused by defects. In the present research, the effects of pores and cracks on the Young’s modulus of a 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 the vertical direction of the crack.