Anisotropic strain gradient elasticity theory is applied to the solution of a mode III crack in a functionally graded material. The theory possesses two material characteristic lengths, and which describe the size scale effect resulting from the underlining microstructure, and are associated to volumetric and surface strain energy, respectively. The governing differential equation of the problem is derived assuming that the shear modulus is a function of the Cartesian coordinate i.e., where and γ are material constants. The crack boundary value problem is solved by means of Fourier transforms and the hypersingular integrodifferential equation method. The integral equation is discretized using the collocation method and a Chebyshev polynomial expansion. Formulas for stress intensity factors, are derived, and numerical results of for various combinations of and γ are provided. Finally, conclusions are inferred and potential extensions of this work are discussed.
Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials—Part I: Crack Perpendicular to the Material Gradation
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Oct. 18, 2000; final revision, Sept. 6, 2001. Associate Editor: B. M. Moran. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Paulino, G. H., Fannjiang, A. C., and Chan, Y. (August 25, 2003). "Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials—Part I: Crack Perpendicular to the Material Gradation ." ASME. J. Appl. Mech. July 2003; 70(4): 531–542. https://doi.org/10.1115/1.1532321
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