In this paper, a crack in a strip of a viscoelastic functionally graded material is studied under antiplane shear conditions. The shear relaxation function of the material is assumed as where h is a length scale and f(t) is a nondimensional function of time t having either the form for a linear standard solid, or for a power-law material model. We also consider the shear relaxation function in which the relaxation time depends on the Cartesian coordinate y exponentially. Thus this latter model represents a power-law material with position-dependent relaxation time. In the above expressions, the parameters β, δ, q are material constants. An elastic crack problem is first solved and the correspondence principle (revisited) is used to obtain stress intensity factors for the viscoelastic functionally graded material. Formulas for stress intensity factors and crack displacement profiles are derived. Results for these quantities are discussed considering various material models and loading conditions.
Viscoelastic Functionally Graded Materials Subjected to Antiplane Shear Fracture
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, Feb. 24, 2000; final revision, July 13, 2000. Associate Editor: M.-J. Pindera. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, 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., and Jin, Z. (July 13, 2000). "Viscoelastic Functionally Graded Materials Subjected to Antiplane Shear Fracture ." ASME. J. Appl. Mech. March 2001; 68(2): 284–293. https://doi.org/10.1115/1.1354205
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