The Dynamic Energy Release Rate for a Steadily Propagating Mode I Crack in an Infinite, Linearly Viscoelastic Body

1990 ◽  
Vol 57 (2) ◽  
pp. 343-353 ◽  
Author(s):  
J. R. Walton
Keyword(s):  
Steady State ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Viscoelastic Body ◽  
Mode I ◽  
Mode I Crack ◽  
Failure Zone ◽  
Special Cases

An analysis is presented for the dynamic, steady-state propagation of a semi-infinite, mode I crack in an infinite, linearly viscoelastic body. For mathematical convenience, the material is assumed to have a constant Poisson’s ratio, but the shear modulus is only assumed to be decreasing and convex. An expression for the Stress Intensity Factor (SIF) is derived for very general tractions on the crack faces and the Energy Release Rate (ERR) is constructed assuming that a fully developed Barenblatt type failure zone with nonsingular stresses exists at the crack tip and the loadings have a simple exponential form. For comparative purposes, expressions for the ERR are derived for the special cases of dynamic steady-state crack propagation in elastic material and quasi-static crack propagation in viscoelastic material, both with and without a failure zone. Sample calculations are included for power-law material and a standard linear solid in order to illustrate the combined influence of inertial effects, material viscoelasticity, and a failure zone upon the ERR.

On The Response Of Dynamic Cracks To Increasing Overload

1995 ◽  
Vol 409 ◽  
Author(s):  
P. Gumbsch
Keyword(s):  
Steady State ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Mechanical Energy ◽  
Terminal Velocity ◽  
Brittle Crack ◽  
Dislocation Generation ◽  
Stable Crack Propagation

AbstractOne of the most interesting questions in the dynamics of brittle fracture is how a running brittle crack responds to an overload, i.e. to a mechanical energy release rate larger than that due to the increase in surface energy of the two cleavage surfaces. To address this question, dynamically running cracks in different crystal lattices are modelled atomistically under the condition of constant energy release rate. Stable crack propagation as well as the onset of crack tip instabilities are studied.It will be shown that small overloads lead to stable crack propagation with steady state velocities which quickly reach the terminal velocity of about 0.4 of the Rayleigh wave speed upon increasing the overload. Further increasing the overload does not change the steady state velocity but significantly changes the energy dissipation process towards shock wave emission at the breaking of every single atomic bond. Eventually the perfectly brittle crack becomes unstable, which then leads to dislocation generation and to the production of cleavage steps. The onset of the instability as well as the terminal velocity are related to the non-linearity of the interatomic interaction.

Numerical Estimation of Energy Release Rate of Mode I Crack by Load Displacement Procedure in LEFM and SSY Regimes: A Review

2013 ◽  
Vol 275-277 ◽  
pp. 203-207
Author(s):  
Sai Guru Govind.P ◽  
Raju Karthikx Raju Karthik Mohan ◽  
Sunil Bhat
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Finite Element Solution ◽  
Mode I ◽  
Mode I Crack ◽  
Element Solution ◽  
Alloy Plate ◽  
Load Displacement

Energy release rate, G, of a Mode I crack is estimated numerically by load displacement procedure in the paper. A, through, edge crack is considered in a thin aluminum 2024-T3 alloy plate. The cracked plate is modeled by finite element method. Values of applied load and crack size are suitably selected to simulate LEFM and SSY regimes. Load line displacements are measured from finite element solution. Values of G are compared with J integral values that are obtained from finite element solution using stress and displacement fields near the crack tip.

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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