Theory Of Ultrasonic Wave On Measurement Of Texture And Residual Stress In Metals

The stress in a body changes the speeds of elastic waves propagating in the body.This phenomenon is called the acoustoelastic effect. The possibility of using theacoustoelastic effect for nondestructive evaluation of stress has been the impetus formuch of the research in acoustoelasticity during the last four decades. In thedevelopment of acoustoelasticity as a tool for the nondestructive evaluation of stress,it has become increasingly apparent that the characterization of the structuralmaterials being examined as isotropic is overly simplistic. Most of these materials areactually polycrystalline aggregates whose manufacturing procedures (rolling, drawing,and forging, etc.) make grains have certain preferred orientation which causes theaggregates to be anisotropic.Empirical experiments and computational results suggest that the influence ofthe certain preferred orientation on ultrasonic wave speeds is stronger than that ofinitial stresses. To determine the initial stresses in the polycrystalline, we have to findthe constitutive relation of the polycrystalline with effects of certain preferredorientation and initial stresses. Over the years, various ultrasonic techniques havebeen developed to measure the wave speed changes due to the microstructure andinitial stress. Electromagnetic transducers (EMAT) and piezoelectric transducers(PZT) have been used to generate and detect polarized waves in a polycrystalline.Knowing the path length and the time interval required for the waves to pass, one candetermine wave speeds. Our work mainly includes:1) In classic linear elasticity, one often takes a constitutive relation as linearfunction of strains. When initial stresses are very high, the classicconstitutive relation is challenged and the nonlinear effect of theconstitutive relation has to be considered. Barsch (1968) gave the nonlinearconstitutive relation for isotropic materials based on Vogit's model. Herein,we will derive a general constitutive relation on nonlinearly elasticpolycrystals.2) Man(1998) gave the constitutive relation of a weak-textured orthorhombicaggregate of cubic crystallites with effects of the microstructure and initialstresses. Man's constitutive relation contains twelve material constants andseven texture coefficients. In this paper, we obtain a general constitutive relation of a weakly-textured anisotropic polycrystals based on theory ofnonlinear elasticity.3) The surface-impedance tensors and Green's function of isotropic andtransversely isotropic materials are obtained by Tanuma (1994) by themethod of Stroh's eigenvalues. Here, we study the surface-impedancetensors and Green's function for weakly anisotropic materials via theintegration expressions introduced by Barnett and Lothe.4) Tanuma and Man (2002) derived an angular dependence of Rayleigh-Wavevelocity in prestressed polycrystalline medial with monoclinic texture byStroh's formalism. By the acoustoelastic tensor we obtained in section 4, wederive Rayleigh-Wave velocity with the effect of material anisotropic andresidual stress.