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

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 ( t ) 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 ( t ) 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].