Chandru Periasamy

Full-field digital gradient sensing method for evaluating stress gradients in transparent solids

A full-field digital gradient sensing method is proposed for measuring small angular deflections of light rays due to local stresses in transparent planar solids. The working principle of the method is explained, and the governing equations are derived. The analysis shows that angular deflections of light rays can be linked to nonuniform changes in thickness and refractive index of the material. In mechanically loaded planar solids, the angular deflections can be further related to spatial gradients of first invariant of stresses under plane stress conditions. The proposed method is first demonstrated by capturing the angular deflection fields in two orthogonal directions for a thin plano-convex lens. The measured contours of constant angular deflection of light rays are in good agreement with the expected ones for a spherical wavefront. The method is also successfully implemented to study a stress concentration problem involving a line load acting on an edge of a large planar sheet. Again, the stress gradients, measured simultaneously along and perpendicular to the loading directions, are in good agreement with the analytical predictions. The measured stress gradients have also been used to estimate stresses in the load point vicinity where plane stress results hold.

Visualization and Quantification of Quasi-Static and Dynamic Surface Slopes Using a Reflection-Mode Digital Gradient Sensor

A full-field, reflection-mode Digital Gradient Sensing (DGS) technique capable of measuring small angular deflections of light rays reflected off specularly reflective planar surfaces is developed. The method is aided by 2D digital image correlation principle to quantify angular deflections of light rays. In this paper, the principle of the method is described and the governing equations relating light ray deflections to surface slopes are presented. The method is demonstrated by simultaneously mapping orthogonal surface slopes of a circumferentially clamped silicon wafer subjected to a central deflection. The curvature fields, proportional to stresses in thin plates, as well as surface topography are evaluated from the measured slopes. Subsequently, the method is demonstrated for studying a stress-wave dominant problem of a free, thin, compliant plate subjected to impact by a rigid spherical ball.

A digital gradient sensor for nondestructive evaluation and stress analysis

Optical transparency is an essential characteristic of many solids that are used in transportation, defense, and safety applications. Such transparent materials are used, for example, in automotive windshields, electronic displays, aircraft windows and canopies, hurricane resistant windows, bullet resistant enclosures, personnel helmet visors, and transparent armor. In some of these situations, the capacity of the structure to remain transparent and bear load during service, resisting shock and impact, is critical for human safety. We have developed a new full-field measurement technique called digital gradient sensing (DGS) that can be used to detect the angular deflections of light rays propagating through optically transparent solids that are subjected to nonuniform mechanical stress fields, applied either quasi-statically or dynamically.1 This transmission mode technique has a relatively simple experimental setup (see Figure 1) and is based on the elasto-optic effect exhibited by optically transparent objects, where imposed stresses deflect light rays. In DGS, we employ the 2D ‘Digital Image Correlation’ (DIC) technique to quantify optical angular deflections that can be as small as 1 10 5 radians. The angular deflections are related to the spatial gradients of stresses, under plane stress conditions, that are encountered when thin (relative to the planar dimensions) sheets of material have mechanical stresses imposed upon them. We have demonstrated the feasibility of the method by examining the situation where a line-load acts on the edge of a relatively large planar sheet and produces severe local stress concentrations (see Figure 2). The spatial gradients of the measured stress can also be used to estimate the applied stresses. We have also demonstrated the viability of using DGS to study material failure or damage on transparent planar Figure 1. Schematic of the experimental setup for the transmission mode digital gradient sensing (DGS) method. L and : Distances. F: Force. ıx and ıy : Displacement components. x and y : Angular deflections in the x-z and x-y planes. B: Plate thickness.

A digital gradient sensing method for evaluating orthogonal stress gradients in transparent solids subjected to mechanical loads

An optical, full-field measurement technique called Digital Gradient Sensing (DGS) has been developed for measuring angular deflections of light rays propagating through transparent planar solids subjected to non-uniform stresses. The technique is based on the elasto-optic effect exhibited by transparent materials due to an imposed stress field that cause light rays to deflect. The working principle of the method and the governing equations are presented. DGS relies on 2D Digital Image Correlation (DIC) approach to quantify the angular deflections, which can then be related to spatial gradients of stresses under plane stress conditions. 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 lineload acting on an edge. In the latter case, ultra high-speed digital photography (200,000 frames/sec) is used to perform time-resolved measurements. The quasi-static measurements are successfully compared with those 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.

Dynamic Response of Homogeneous and Functionally Graded Foams When Subjected to Transient Loading by a Square Punch

In this work, failure response of structural syntactic foams subjected to dynamic square punch impact loading is studied. Experiments are being carried out on homogeneous and compositionally graded syntactic foam sheets. The former are made of hollow microballoons dispersed uniformly in an epoxy matrix at different volume fractions whereas in the latter the volume fraction of microballoons is spatially varied in the impact loading direction. An experimental set-up comprising of a long-bar apparatus is developed in conjunction with a gas-gun for subjecting unconstrained syntactic foam sheets to transient stress wave loading. Digital image correlation method and high-speed photography are used to measure time-resolved, inertia induced, in-plane deformations near the vicinity of the punch. The effects of volume fraction and spatial variation of microstructure on punch tip deformations are currently being studied. Feasibility of characterizing punch tip deformations using an analogous crack tip model is explored. Complementary finite element computations are also carried out using measured particle velocity in the long-bar as input boundary conditions.

Dynamic Compression of an Interpenetrating Phase Composite (IPC) Foam: Measurements and Finite Element Modeling

Dynamic compression response of Syntactic Foam (SF)–aluminum foam Interpenetrating Phase Composites (IPC) is measured. By infusing uncured syntactic foam (epoxy filled with hollow microballoons) into an open-cell aluminum network, a 3D interpenetrating structure is obtained. The uniaxial compression responses are measured at ~1500 /sec using a split Hopkinson pressure bar set up. The effect of volume fraction of microballoons on the compression response of IPC is examined in terms of yield stress, plateau stress and energy absorption. The response of IPC samples are also compared with those made using syntactic foam alone. For all volume fractions of microballoons, the IPC samples have better compression characteristics when compared to the corresponding syntactic foam samples. The failure modes of SF and IPC foams are examined both optically (using high-speed photography) and microscopically. The measured dynamic responses of SF are used in a finite element model based on a Kelvin cell representation of the IPC structure. Using infinite elements and measured particle velocity histories as input boundary conditions, the compression response of IPC foams have been successfully captured