THE ENERGY-RELEASE RATE FOR TRANSIENT DYNAMIC-MODE I CRACK-PROPAGATION IN A GENERAL LINEARLY VISCOELASTIC BODY

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), 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) 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].