Asymptotic analysis for temperature fields induced by dynamic crack growth in pressure-sensitive materials

Abstract

In this paper the thermic effects of a rapidly propagating crack are investigated. In the case of a dynamic crack propagation, a large portion of the work of inelastic deformation near the crack tip is dissipated as heat. As a result of the rapid propagation the heat conduction from the crack tip is negligibly small. In this paper, the induced asymptotic temperature crack tip fields for fast running cracks in an elastic-plastic and particularly pressure-sensitive material are determined. The calculation of the temperature field (thermal problem) follows from the corresponding asymptotic stress and velocity fields (mechanical problem). Therefore, the mechanical problem has to be solved before the thermal problem. The asymptotic stress and velocity fields were calculated from a corresponding boundary value problem considering the mathematical consequences of a mode I-loading and associated symmetry effects. Then, the asymptotic temperature field can be calculated directly from the received results of the stress and velocity fields. For the calculation of the crack tip fields an asymptotic analysis is used as shown in [1‐8]. Further, for the calculation of the asymptotic crack tip fields the incremental theory of plasticity was applied and stationary crack growth under mode I-loading and plane stress conditions have been adopted. The modelling of the pressure-sensitive properties of the material [9‐11] was performed by the Drucker-Prager yield function. Studies concerning pressure-sensitive materials and asymptotic analysis have been performed in [1, 2] using the assumptions of the HRR-field theory. In [3, 4] the stress and velocity fields for a quasistatic crack growth under mode I-loading conditions are investigated.