Higher sensitivity Digital Gradient Sensing configurations for quantitative visualization of stress gradients in transparent solids

Abstract

Two modified full-field Digital Gradient Sensing (DGS) methods of higher measurement sensitivity relative to the prevailing ones are described for quantifying small angular deflections of light rays caused by stresses in transparent solids. These methods are devised by combining or altering previously proposed reflection-mode DGS (r-DGS) [1] and transmission-mode DGS (t-DGS) [2] methods. The concept involves increasing the optical path within the stressed medium by introducing an additional reflective surface behind the transparent solid, either as a separate reflector or as a rear surface reflective film deposition. The former approach is designated as t2-DGS method whose measurement sensitivity is twice that of t-DGS. The latter method results in an even higher sensitivity and is called the transmission-reflection DGS or tr-DGS method by making the back surface of a transparent planar solid reflective. The governing equations of tr-DGS are introduced first followed by a comparative demonstration of t2-DGS and tr-DGS methods by measuring the stress gradients in the crack-tip region during dynamic and static fracture experiments, respectively. Results show that tr-DGS is approx. 1.5 times more sensitive than t2-DGS, and at least three times more sensitive than t-DGS approach. Together as a family of DGS methods, these methods are used to extract the crack-tip stress intensity factors of PMMA beams under quasi-static loading conditions. The measured stress intensity factors are in good agreement with the predictions.