Stress field near the crack tip of a semi-infinite crack inside a current-carrying plate at the moment while the current is switching on

With the Maxwell's equations for an elastic body and the boundary and initial conditions, the equations for determination of electrical current density near a crack tip are obtained. The tip of the semi-infinite crack is located inside an infinite thin current-carrying plate. All the equations hold at the moment while the current is switching on. From these equations the temperature and stress expressions at the crack tip are obtained too. The numerical examples show that under the Joule heat source provided by electric current, the temperature around crack tip grows up instantly and the compressive stresses appear too. Consequently, propagation of the crack could be arrested.