The nonlocal theory solution of a Mode-I crack in functionally graded materials  

作　　者：LIANG Jun Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150001, China 

出　　处：《Science China(Technological Sciences)》2009年第4期1101-1111,共11页中国科学（技术科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 90405016, 10572044);the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20040213034);the Program for New Century Excellent Talents in University (Grant No. NCET-05-0346)

摘　　要：The behavior of a Mode-I finite crack in functionally graded materials is investigated using the non-local theory. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate vertical to the crack. The problem in this paper can be solved through the Fourier transform with the help of two pairs of dual integral equations, in which the unknown variables are jumps of dis- placements across crack surfaces. To solve dual integral equations, the jumps of displacements across crack surfaces are directly expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solu- tions yield a finite stress at crack tips, thus allowing us to use the maximum stress as a fracture crite- rion. Numerical examples are provided to show the effects of the crack length, the parameter describ- ing the functionally graded materials, the lattice parameter of materials and the materials constants upon the stress fields near crack tips.The behavior of a Mode-I finite crack in functionally graded materials is investigated using the non-local theory. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate vertical to the crack. The problem in this paper can be solved through the Fourier transform with the help of two pairs of dual integral equations, in which the unknown variables are jumps of displacements across crack surfaces. To solve dual integral equations, the jumps of displacements across crack surfaces are directly expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. Numerical examples are provided to show the effects of the crack length, the parameter describing the functionally graded materials, the lattice parameter of materials and the materials constants upon the stress fields near crack tips.

关 键 词：CRACK functionally GRADED materials the NON-LOCAL theory MECHANICS of SOLIDS 

分 类 号：TB34[一般工业技术—材料科学与工程]