Assessment of Localized Plastic Deformation during Fatigue in Polycrystalline Copper by Nonlinear Ultrasonic
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INTRODUCTION
Nonlinear ultrasonic (NLU) is becoming a potential nondestructive technique for materials degradation study especially for fatigue damage assessment. When a purely sinusoidal acoustic wave propagates through a degraded material, it distorts and generates harmonics of the fundamental waveform because of the nonlinearity of the propagation medium.[1–8] A quantitative measure of the wave distortion is the ‘‘acoustic’’ nonlinearity parameter (b). This nonlinearity parameter AVIJIT METYA, Project Assistant, N. PARIDA and S. PALIT SAGAR, Scientists, are with the Material Science and Technology Division, National Metallurgical Laboratory, Jamshedpur - 831 007, India. Contact e-mail: [email protected] or sarmishtha.sagar@gmail. com D.K. BHATTACHARYA, Head, is with the Analytical Facility Division, Central Glass and Ceramic Research Institute, Kolkata - 700 032, India. N.R. BANDYOPADHYAY, Director and Professor, is with the School of Materials Science and Engineering, Bengal Engineering and Science University, Shibpur - 711 103, India. Manuscript submitted January 25, 2007. Article published online November 6, 2007 METALLURGICAL AND MATERIALS TRANSACTIONS A
is proportional to the ratio of the amplitude of the second harmonic to the square of the amplitude of the fundamental of the transmitted ultrasonic signal. Recent experimental studies and new physical models[9,10] are strong evidence that the parameter b is highly dependent on fatigue degradation. The enhancement in generation of higher harmonics with fatigue has been shown by Morris et al.[11] in their experiment on highstrength aluminum alloy. The increased nonlinearity during material degradation was examined by Nagy,[5] who applied cyclic bending to generate fatigue damage in a great variety of materials including plastics, metals, composites, and adhesives. Experimental results were presented by him to illustrate that the NLU parameters are more sensitive indicators of fatigue damage than their linear counterparts. The magnitude of the higher order harmonic component appears differently in normal and degraded materials, when the same amplitude of wave and the same propagation distance are used. This tendency was shown by Jhang and co-workers[4,12,13] in their research work on biomaterials. The experiment by Cantrell and Yost[6] suggested that the cyclic loading in metal fatigue promotes the formation of dislocation dipoles as a result of the mutual trapping of dislocations moving to and fro in response to the cyclic stress. These dislocation dipole substructures formed during fatigue produce a substantial distortion of ultrasonic waves propagating through the fatigued material. They have explained the interaction of the acoustic wave with dislocation dipoles and other substructures formed during fatigue using a quasi-isotropic model.[9] Substantial second harmonic generation, which is dependent on the dislocation arrangement, was predicted by this model. There was much research done regarding the source of nonlinearity that produced the second harmonic
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