For homogeneous materials, the ultrasonic immersion method, associated with a numerical optimization process mostly based on Newton's algorithm, allows the determination of elastic constants for various synthetic and natural composite materials. Nevertheless, a principal limitation of the existing optimization procedure occurs when the considered material is at the limit of the homogeneous hypothesis. Such is the case of the woven bidirectional SiC matrix and SiC fibre composite material.

In this study, we have developed two numerical methods for the determination of the elastic constants of the 2D SiC or SiC composite material (2D SiC/SiC). The first one is based on Newton's algorithm: the elastic constants are obtained by minimizing the square deviation between experimental and calculated velocities. The second method is based on the Levenberg–Marquardt algorithm. We show that these algorithms give the same results in the case of homogeneous anisotropic composite materials. For the 2D SiC/SiC composite material, the two methods, using the same measured velocities, give different sets of elastic constants. We then note that the Levenberg–Marquardt algorithm enables a better convergence towards a global set of elastic constants in good agreement with the elastic properties, which can be measured using classical quasi-static methods.

source:iopscience

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