On determination of orthotropic material moduli from ultrasonic velocity data in nonsymmetry planes

Abstract

This paper reports analysis of the reconstruction of elastic constants from ultrasonic velocity measurements in nonsymmetry planes of unidirectional composite materials. It is shown that the nonlinear least-square optimization method is stable to initial guess selection and data scatter and can be used routinely to measure the full set of nine elastic constants for orthotropic materials. Simple analytical expressions are derived for phase velocities in arbitrary directions in an orthotropic material with low transverse-to-fiber anisotropy. Using these, coefficients of sensitivity of phase velocities to elastic constants are obtained in closed form and used to find the optimal wave propagation directions for elastic constant measurement. The changes in velocity due to elastic constant variation calculated by the exact theory agree well with the predictions from the sensitivity coefficients. When all nine elastic constants are reconstructed from velocity data in nonsymmetry planes, the inversion is highly dependent on the initial guesses and susceptible to random data scatter. When seven elastic constants are found from velocity data in planes of symmetry, the remaining two (C12 and C66) can be found from nonsymmetry-plane data independently of initial guesses and scatter levels. This is especially important since the elastic constants C12 and C66 cannot be determined from immersion velocity measurements in two accessible planes of symmetry.