THE EFFECTS OF HYPERBOLIC HEAT-CONDUCTION AROUND A DYNAMICALLY PROPAGATING CRACK-TIP

Using infrared detectors, Zehnder and Rosakis (1991, J. Mech. Phys. Solids 39(3), 385), Zehnder and Kallivayalil (1991, SPIE ISS4A, 48) and Mason and Rosakis (1992, SN Report 92-2), have recorded the temperature field around a dynamically propagating crack tip travelling at constant velocity in several metals. At the same time, Tzou (1990a, J. Heat Transfer 112, 21, 1990b, Inst. Heat Mass Transfer 33(5), 877) has suggested that the temperature field around a propagating crack tip might exhibit some of the characteristics of hyperbolic heat conduction. In this paper a corrected solution of the hyperbolic heat conduction equation for a travelling point source is derived. Then an experimental estimate of the active plastic zone (heat generating zone) at a crack tip is used for various experimental conditions to examine the possible effects of hyperbolic heat conduction around a propagating crack tip. Finally, using the actual experimental conditions of Zehnder and Rosakis (1991), Zehnder and Kallivayalil (1991) and Mason and Rosakis (1992) it is shown that no effects of hyperbolic heat conduction are observed around a propagating crack tip. It is seen that, due to adiabatic conditions at the crack tip during these experiments, the solution of the hyperbolic heat equation is indistinguishable from the solution of the parabolic heat conduction equation for crack propagation in steel.