Theoretical and Numerical Derivation of Stress Tensor From Thick Steel Plates Using Acoustoelasticity

In this paper the interaction between nonlinear ultrasonic characteristics and stress state of complex loaded thick steel plates using fundamental theory of nonlinear ultrasonics is investigated in order to measure the stress state at a given cross section. The acoustoelasticity is the relationship between stress and ultrasonic velocity when higher order terms in the strain equation are considered. The measurement concept is based on phased array placement of ultrasonic transmitter-receiver to scan three angles of a given cross section using Rayleigh waves. The change in the ultrasonic data in thick steel plates is influenced by normal and shear stresses; therefore, three measurements are needed to solve the equations simultaneously. For the thick cross section, shear stress becomes influential if the depth of penetration of Rayleigh wave is greater than the half of the thickness. The influences of plate thickness and ultrasonic frequency on the identification of stress tensor are numerically studied in 3D structural geometry and Murnaghan material model. The theoretical component of this study focuses on including the shear stress in the existing equation of motion in order to account its effect on the acoustoelasticity coefficients.