Thermodynamics of crack healing under electropulsing
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Shengxia Su Department of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, People’s Republic of China (Received 21 September 2001; accepted 22 May 2002)
The effect of electropulsing on the evolution of an elliptical cylinder microcrack was studied from a thermodynamic point of view. An analytical expression for the healing driving force with respect to the passing electric current density, crack geometric shape, Young’s modulus, and sample size was derived. The critical current density for crack healing was calculated and agreed with the experimental results very well. The heterogeneous temperature rise due to Joule heat was calculated and proved ideal to the crack healing. Earlier experimental results can be fully understood within the present theoretical frame.
I. INTRODUCTION
Crack healing in metallic materials is currently an important engineering issue. Biomimetics study reveals that the method for crack healing should meet the demands of (i) enough strong healing effect on crack, (ii) negligible small side effect on the microstructure and mechanical properties of matrix, (iii) short duration, and (iv) engineering practicable. Our earlier theoretical study showed that electropulsing could meet the above-listed needs.1 Recently, experiments on 1045 steel have successfully healed cracks by electropulsing treatment.2,3 The effect of electric current on the fatigue life of metallic materials has been studied since the 1970s. Karpenko et al. first found that, the low cycle fatigue life of low-carbon steel was increased by the application of a direct current of only 7 A/cm2) during the fatigue test.4 Conrad et al. applied high-density electropulsing (about 104 A/cm2) during the fatigue test of polycrystalline copper in rotating and bending and noticed that the fatigue life was increased 2–3 times.5 Shen et al. observed a result similar to the work of Conrad et al. in fatigue tests of low-carbon steel.6 Zhou et al. observed the structural transition on the rim of crack in 1045 steel induced by electropulsing2 and more recently realized the crack healing.3 There have been a few theoretical explanations for the above-listed observations. For example, Joule heat,2 pinch force,4 electromigration, and electroplastic effect,5 and so on. However, to the authors’ knowledge, all those previous theoretical works were qualitative and in the 2048
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J. Mater. Res., Vol. 17, No. 8, Aug 2002
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kinetic point of view. No equations describe the relationship among healing driving force, current density, and geometric shape of the crack. Due to the well-known low reproducibility of electropulsing experiments, a quantitative theoretical description is even more important. In this paper, the effect of electropulsing on the evolution of a crack was studied thermodynamically. The healing driving force and its relationship with respect to electric current density and geometric shape of the crack was derived. The heterogeneous rise of temperature around cracks
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