Caustics By Reflection And Their Application To Elastic-Plastic And Dynamic Fracture Mechanics

Abstract

Applications of the method of reflected caustics to the measurement of the J integral in ductile materials are reviewed. It is demonstrated, both numerically and experimentally, that the conditions for accurate interpretation of caustics on the basis of plane stress small scale yielding analyses are often overrestrictive. To overcome these restrictions, we used a three-dimensional, elastic-plastic finite-element calculation to analyze caustics formed by reflection of light from a particular test specimen. Experimental measurements on the same specimen confirm the numerically obtained results. The out-of-plane surface displacements, measured experimentally by interferometry, are in excellent agreement with the corresponding numerical results. In addition, the experimentally obtained caustics agree well with the numerically generated caustics. The excellent agreement between experiment and calculations demonstrates the accuracy of the numerical model and establishes confidence in the interpretation of caustics in the presence of both extensive plasticity and three dimensionality. The analysis of caustics as based on the three-dimensional calculation is applied to the direct optical measurement of the time history of the J integral in a dynamically loaded specimen. The specimen was loaded in a drop weight tower, and the caustics were photographed with a high speed camera.