On the steady-state propagation of an anti-plane shear crack in an infinite general linearly viscoelastic body
Author:
Jay R. Walton
Journal:
Quart. Appl. Math. 40 (1982), 37-52
MSC:
Primary 73M05; Secondary 73F99
DOI:
https://doi.org/10.1090/qam/652048
MathSciNet review:
652048
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The steady-state propagation of a semi-infinite anti-plane shear crack is considered for a general infinite homogeneous and isotropic linearly viscoelastic body. Inertial terms are retained and the only restrictions placed on the shear modulus are that it be positive, continuous, decreasing and convex. For a given integrable distribution of shearing tractions travelling with the crack, a simple closed-form solution is obtained for the stress intensity factor and for the entire stress field ahead of and in the plane of the advancing crack. As was observed previously for the standard linear solid, the separate considerations of two distinct cases, defined by parameters $c$ and $c*$, arises naturally in the analysis. Specifically, $c$ and $c*$ denote the elastic shear wave speeds corresponding to zero and infinite time, and the two cases are (1) $0 < \upsilon < c*$ and (2) $c* < \upsilon < c$, where $\upsilon$ is the speed of propagation of the crack. For case (1) it is shown that the stress field is the same as in the corresponding elastic problem and is hence independent of $\upsilon$ and all material properties, whereas, for case (2) the stress field depends on both $\upsilon$ and material properties. This dependence is shown to be of a very elementary form even for a general viscoelastic shear modulus.
- C. Atkinson, A note on some dynamic crack problems in linear viscoelasticity, Arch. Mech. (Arch. Mech. Stos.) 31 (1979), no. 6, 829–849 (English, with Russian and Polish summaries). MR 583773
C. Atkinson and C. J. Coleman, J. Inst. Maths. Applics. 20, 85–106 (1977)
C. Atkinson and C. H. Popelar, Antiplane dynamic crack propagation in a viscoelastic layer, J. Mech. Solids 27, 431–439 (1979)
- F. D. Gakhov, Boundary value problems, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966. Translation edited by I. N. Sneddon. MR 0198152
J. R. Willis, Crack propagation in viscoelastic media, J. Mech. Phys. Solids 15, 229–240 (1967)
C. Atkinson, A note on some dynamic crack problems in linear viscoelasticity, Arch. Mech. Stos. 31, 829–849 (1979)
C. Atkinson and C. J. Coleman, J. Inst. Maths. Applics. 20, 85–106 (1977)
C. Atkinson and C. H. Popelar, Antiplane dynamic crack propagation in a viscoelastic layer, J. Mech. Solids 27, 431–439 (1979)
F. D. Gakov, Boundary value problems, Pergamon, London, 1966
J. R. Willis, Crack propagation in viscoelastic media, J. Mech. Phys. Solids 15, 229–240 (1967)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73M05,
73F99
Retrieve articles in all journals
with MSC:
73M05,
73F99
Additional Information
Article copyright:
© Copyright 1982
American Mathematical Society