The Dynamic Energy Release Rate for a Steadily Propagating Antiplane Shear Crack in a Linearly Viscoelastic Body

1987 ◽  
Vol 54 (3) ◽  
pp. 635-641 ◽  
Author(s):  
J. R. Walton
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Shear Crack ◽  
Viscoelastic Body ◽  
Antiplane Shear ◽  
Singular Stress ◽  
Crack Face ◽  
Standard Linear Solid ◽  
Dynamic Energy Release Rate

The steady-state propagation of a semi-infinite, antiplane shear crack is reconsidered for a general, infinite, homogeneous and isotropic linearly viscoelastic body. As with an earlier study, the inertial term in the equation of motion is retained and the shear modulus is only assumed to be positive, continuous, decreasing, and convex. A Barenblatt type failure zone is introduced in order to cancel the singular stress, and a numerically convenient expression for the dynamic Energy Release Rate (ERR) is derived for a rather general class of crack face loadings. The ERR is shown to have a complicated dependence on crack speed and material properties with significant qualitative differences between viscoelastic and elastic material. The results are illustrated with numerical calculations for both power-law material and a standard linear solid.

A Comparison of the Dynamic Transient Anti-Plane Shear Crack Energy Release Rate for Standard Linear Solid and Power-Law-Type Viscoelastic Materials

1991 ◽  
Vol 113 (4) ◽  
pp. 222-229 ◽  
Author(s):  
J. M. Herrmann ◽  
J. R. Walton
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Power Law ◽  
Release Rate ◽  
Shear Crack ◽  
Viscoelastic Body ◽  
Laplace Transforms ◽  
Failure Zone ◽  
Standard Linear Solid ◽  
Standard Linear

The problem of a semi-infinite mode III crack that suddenly begins to propagate at a constant speed is considered for a general linear viscoelastic body. It is shown that the results of an earlier paper for the Laplace transforms of the stress and displacement with the Laplace transform variable s being real and positive are valid, with minor modification, for complex values of s such that Re(s)>0. Therefore, these Laplace transforms can be inverted by means of a Bromwich path integral. Under the assumption that a Barenblatt-type failure zone exists at the crack tip, the energy release rate (ERR) and the work done in the failure zone (WFZ) are calculated through numerical inversion of Laplace transforms. The ERR and WFZ for the standard linear solid and power law material models are contrasted and also compared with the elastic and quasi-static results. The graphs and table illustrate considerable differences in the ERR and WFZ for these different models. These differences may be important to predictions of stable versus unstable crack speeds based upon a critical ERR fracture criterion.

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