Digital Gradient Sensing (DGS): A Full-Field Optical Technique to Measure Angular Deflections of Light Rays and Its Applications to Failure Mechanics

Abstract

Optical transparency is an essential characteristic of solids used in many engineering applications such as automotive windshields, electronic displays, aircraft windows and canopies, hurricane resistant windows, bullet resistant enclosures, personnel helmet visors, and transparent armor used by the military. In some of these applications, the ability of a structure to continue to remain transparent and bear load after impact is also critical for personnel safety. Motivated by these, an optical, full-field measurement technique called Digital Gradient Sensing (DGS) has been introduced in this dissertation for measuring angular deflections of light rays propagating through transparent solids subjected to non-uniform quasi-static and dynamic stress fields. The technique is based on the elasto-optic effect exhibited by transparent materials due to the imposed stresses that cause light rays to deflect. The working principle of the method is explained, and the governing equations derived. DGS employs 2D Digital Image Correlation (DIC) technique to quantify the angular deflections, which can then be related to spatial gradients of stresses under plane stress conditions. The new method is first demonstrated by performing validation experiments to capture angular deflections of light rays in two orthogonal directions produced by a thin plano-convex lens. The feasibility of this method to study material failure/damage is demonstrated on transparent planar sheets of PMMA subjected to both quasi-static and dynamic line-load acting on an edge. In the latter case, ultra high-speed digital photography is used to perform time-resolved measurements. The quasi-static measurements are successfully compared with those based on the Flamant’s solution for a line-load acting on a half-space in regions where plane stress conditions prevail. The dynamic measurements, prior to material failure, are also successfully compared with finite element computations. The measured stress gradients near the impact point after damage initiation are also presented and failure behavior is discussed. DGS is next extended to study fracture mechanics and impact mechanics problems, where stress gradients near crack and punch tips in transparent PMMA sheets are quantified. Both quasi-static and dynamic mode-I crack problems are studied. The crack-tip stress intensity factors measured under quasi-static and dynamic loading conditions using DGS are in good agreement with the analytical and finite element results. The problem of a square-punch impacting the edge of a PMMA sheet is also studied using DGS by exploiting punch-tip – crack-tip analogy. The dynamic punch-tip stress intensity factors are extracted from the optical measurements and are again in good agreement with the ones from the finite element counterparts. The DGS method is finally extended to study deformation of thin structures in reflection mode. After suitably modifying the governing equations, full-field surface slopes of specularly reflective thin plates (silicon wafers) subjected to out-of-plane displacements are quantified for the case of a clamped plate subjected to central deflection. The full-field plate curvatures are also evaluated from surface slope fields in view of the direct dependency of stresses on curvatures in thin structures. Both surface slope and curvature fields are successfully compared with the analytical solutions. The dissertation also explores a few promising commercial applications of transmission mode DGS including inspection of defects and inhomogeneities in transparent media such as a glass pane. Quantification of process-induced stresses by reflection mode DGS is demonstrated by evaluating slopes and curvatures of a silicon wafer coated with a polymer film as it cures in situ.