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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 vary 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 the cracks surfaces. To solve dual integral equations, the jumps of displacements across cracks surfaces are directly expanded in a series of Jacobi polynomials. it’s 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.