Experimental verification of Hudson and Eshelby-Chen’s effective crack theory

Abstract

Physical modeling of cracked / fractured media in downscaled laboratory experiments has served as a great alternative for understanding the anisotropic media behavior. In this work, it was performed ultrasonic measurements on samples with low crack densities and different aspect ratios. The main goal was to investigate the experimental behavior of elastic parameters, such as: waves velocities and Thomsen parameters ε and 𝛾 and elastic stiffness coefficients for transverse isotropic media. Comparison of the results with the predictions made by the effective models of Hudson (1981) and Eshelby-Cheng (1993), it was also investigated in this work. Twelve samples were prepared with two types of cracks density, 5 and 8%. The cracks that have three different aspect ratios (0.133, 0.1778 and 0.2667) were formed by rubber inclusions in a homogeneous isotropic matrix resin. Moreover, an isotropic matrix sample was constructed by only epoxy resin. Among all samples, six (three for each density) have only one aspect ratio type (samples with single crack), while another six (three for each density) have three types of different aspect ratio (mixed samples). Among the predictions of the models, the Eshelby-Cheng (1993) shows a better fit in relation to the experimental results for samples with single crack (for the two densities of inclusions). However, none of the models predicts accurately with minimal tendency for the mixed samples.