Electric Current Induced Stresses Around the Crack Tip in Conductors

Abstract

Electric current can have a variety of effects on the mechanical behavior of conductors, especially when flaws are present in the materials. Two of the effects, namely the magnetic effect and the thermal effect, on the stress distribution around a crack tip in a conducting material have been investigated. The conductor is assumed to be linearly elastic with constant values of mechanical and physical properties. However, the stresses is proportional to the square of the current in some cases, according to Lorentz's law and Joule's law. Static analysis as well as dynamic analysis are carried out to reveal the effects of the electric current on the stress distribution around the crack tip.

General solutions are derived for the static analyses of the thermal effect and the magnetic effect caused by an externally applied magnetic field. Analytical analyses are carried out to reveal the characteristics of stress distribution around the crack tip for these two cases. For the static analysis of magnetic effect caused by the self-induced magnetic field, a numerical analysis procedure is developed. Similar numerical procedures are also developed to analyze the effects of the electric current, both thermal and magnetic, under dynamic conditions.

Although the electric current is singular around the crack tip, the analysis results reveal that, under static conditions, the stresses caused by the electric current around the crack tip remain the original singular order of -1/2. Under dynamic conditions, however, the stress distribution does not have a consistent singular order due to the complicated temperature distribution. It is concluded that the fracture criteria based on the stress intensity factors may not be applicable because of the complicated stress distribution. A criterion in terms of critical stress at a critical distance ahead of the crack tip is used in an attempt to correlate analysis results with some existing experimental observations. The major trends are consistent between the analysis results and the experimental observations. By utilizing the analysis results, the electric current could be used to actively control the damage propagation in conductors, hence catastrophic failure could be avoided.