The energy release rate for transient dynamic mode 𝐼 crack propagation in a general linearly viscoelastic body

Herrmann, J. M.; Walton, J. R.

doi:10.1090/qam/1276234

The energy release rate for transient dynamic mode $\textrm {I}$ crack propagation in a general linearly viscoelastic body

Authors: J. M. Herrmann and J. R. Walton
Journal: Quart. Appl. Math. 52 (1994), 201-228
MSC: Primary 73M25; Secondary 73F15
DOI: https://doi.org/10.1090/qam/1276234
MathSciNet review: MR1276234
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Abstract: A mathematical model of a semi-infinite mode I crack that suddenly begins to propagate at constant speed is constructed for a general linear viscoelastic body. Expressions for the Laplace transform of the stress, displacement, and stress intensity factor are derived for general loadings. A Barenblatt type process zone is incorporated into the model and used to determine the total energy flux into the crack tip. This energy release rate, $G\left ( t \right )$, is constructed for two specific loadings: one following the advancing crack tip, the second remaining fixed as the crack tip advances. In each case $G\left ( t \right )$ is analyzed by asymptotic and numerical methods to determine its qualitative form and, in particular its rate of decay to its steady-state value. The effect of such simplifying assumptions as quasi-static propagation or an elastic material is also illustrated. The second loading is intended as an idealized model of the dynamic fracture experiments of Ravi-Chandar and Knauss [13–16].

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