Determination of Elastic Constants and Damage in Ceramic Matrix Composites Using Ultrasonic Wave Speed Measurements

Abstract

MATLAB programs were developed to compute the elastic constants and damage of ceramic matrix composites using ultrasonic wave speed measurements. The matrix of elastic stiffnesses, C, relates the material stresses and strains. The ultrasonic wave velocities are related to the elastic constants through the Christoffel equation. The immersion ultrasonic wave speed measurement method has been used extensively to determine elastic constants of anisotropic media. The computer programs contained herein are designed to recover the elastic stiffnesses and damage magnitudes for materials of orthotropic symmetry (i.e. having nine independent elastic stiffnesses) from data generated from the ultrasonic wave speed measurements. The elasticity matrix, C, is recovered using three methods: minimization of the least-squares of the Christoffel equation, minimization of the sum of squares of the deviations between experimental velocities and the solution of the Christoffel equation, and use of the rotation of axes equation for fourth-order tensors. Damage is defined in the macroscopic sense as the normalized variation of the elastic stiffnesses under loading.