The combined effects of finite deformation and material inertia have been analyzed for fast crack growth under antiplane loading conditions. A steady-state dynamic solution has been obtained for the finite strain on the crack line, from the moving crack tip to the moving transition boundary with the zone of small strains. The crack propagates in a material with a response curve in uniform shear that is linear at small strains, and which remains constant once a critical strain has been exceeded. The corresponding quasi-static solution is given in the full zone of large deformation. For the dynamic formulation, an explicit expression for the crack-line strain has been obtained by expanding the displacement in a power series in the distance to the crack line, with coefficients that depend on the distance to the moving crack tip. Substitution in the equation of motion yields a nonlinear ordinary differential equation for the relevant coefficient, which can be solved rigorously. The finite deformation crack-line fields have been matched to appropriate small-strain fields at the transition boundary. The principal result is that the dynamic strain remains bounded at the crack tip, apparently due to the effect of material inertia. The crack-line strain has been plotted for several crack-tip speeds. It decreases with higher crack-tip speed. An explicit expression has been given for the extent of the zone of finite deformation, as a function of the crack tip speed and the far-field loading.
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June 1985
Research Papers
Effect of Inertia on Finite Near-Tip Deformation for Fast Mode-III Crack Growth
J. D. Achenbach,
J. D. Achenbach
Department of Civil Engineering, Northwestern University, Evanston, Ill. 60201
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N. Nishimura
N. Nishimura
Department of Civil Engineering, Northwestern University, Evanston, Ill. 60201
Search for other works by this author on:
J. D. Achenbach
Department of Civil Engineering, Northwestern University, Evanston, Ill. 60201
N. Nishimura
Department of Civil Engineering, Northwestern University, Evanston, Ill. 60201
J. Appl. Mech. Jun 1985, 52(2): 281-286 (6 pages)
Published Online: June 1, 1985
Article history
Received:
March 1, 1984
Revised:
July 1, 1984
Online:
July 21, 2009
Citation
Achenbach, J. D., and Nishimura, N. (June 1, 1985). "Effect of Inertia on Finite Near-Tip Deformation for Fast Mode-III Crack Growth." ASME. J. Appl. Mech. June 1985; 52(2): 281–286. https://doi.org/10.1115/1.3169041
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