Angular Deflections Of Light Rays Research Articles

Enhanced Digital Gradient Sensing Using Backlight Digital Speckle Target.

Digital gradient sensing (DGS) is a non-contact and full-field optical measurement technique, which assesses mechanical behaviors of transparent materials or specular structures by measuring angular deflections of light rays. However, owing to the poor light-gathering capability of its imaging system, the dynamic performance of DGS is heavily restricted. Here, a method of enhancing the dynamic performance of DGS by improving its speckle target is proposed. The method employs the technique of backlight illumination, which significantly increases the utilization efficiency of light, shortens the exposure time, and enhances the dynamic performance of DGS. Additionally, it also uses the optimized digital speckle pattern to improve the measurement precision and accuracy. For validation, a comparison experiment was conducted, proving that the proposed method can improve the utilization efficiency of light by about 80 times and improve the quality of the speckle images by about 40%. Real tests, including a uniaxial tension test using transmission-mode DGS (t-DGS) and a three-point bending test using reflection-mode DGS (r-DGS), were also carried out, showing the efficacy and high compatibility of the proposed backlight digital speckle target. In summary, this simple method greatly improves the performance of DGS, which can be used as a standard method in both t-DGS and r-DGS.

Fracture behavior of carbon fiber reinforced polymer composites: An optical study of loading rate effects

Crack initiation and growth in single-edge notched unidirectional T800s/3900-2 CFRP laminates are studied under stress wave and quasi-static loading conditions. An optical technique called reflection-mode Digital Gradient Sensing is also extended to study fracture mechanics of CFRP by using it in conjunction with ultrahigh-speed photography to perform full-field measurement of crack-tip deformations in the pre- and post-crack initiation regimes. DGS is capable of measuring two orthogonal surface slopes in the crack-tip vicinity as angular deflection of light rays. A method for extracting crack-tip parameters – the instantaneous crack speed and stress intensity factor (SIF) histories – associated with the stationary and propagating cracks using measured surface slopes is presented. The effect of fiber orientation in the range 0°–60° relative to the initial notch and two loading rates are investigated. Nominally mode-I fracture occurs when the fiber orientation is 0° whereas mixed-mode fractures ensue in others. Besides crack initiation occurrence at higher loads as fiber orientation increases, the SIF histories imply strong fiber bridging at low fiber orientations under quasi-static conditions. Furthermore, this CFRP shows significant loading rate dependence during crack growth. Unlike stress wave loading conditions, an increasing crack growth resistance immediately after crack initiation is seen under quasi-static conditions.

Measurement of Sub-micron Deformations and Stresses at Microsecond Intervals in Laterally Impacted Composite Plates Using Digital Gradient Sensing

Visualization and quantification of surface topography and stresses from measured slope data is of considerable importance to study many engineering problems including response of structural plates to stress wave loading. In this work, a full-field optical technique called Digital Gradient Sensing (DGS) is implemented in the reflection-mode to quantify time-resolved surface slopes in composite plates at microsecond intervals as they are impact loaded. The method being capable of determining two orthogonal surface slopes by measuring angular deflections of light rays, as small as a few micro-radians, surface topography can be quantified using a Higher-order Finite-difference-based Least-squares Integration (HFLI). Numerical differentiation of surface slopes, on the other hand, provides all three curvatures enabling estimation of stresses. Carbon fiber reinforced composite plates of different layups are subjected to dynamic impact loading using a Hopkinson pressure bar. Ultrahigh-speed digital photography is used to record deformations using DGS. The out-of-plane deformations are obtained by post-processing data from DGS at each time instant using HFLI whereas stresses are estimated by evaluating instantaneous curvatures obtained by differentiating measured slopes.

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

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.

Dynamic mixed-mode fracture behaviors of PMMA and polycarbonate

Mixed-mode dynamic crack initiation and growth in polymethymethacrylate (PMMA) and polycarbonate (PC) are studied experimentally. A simple specimen geometry in conjunction with a dynamic loading configuration to generate different mode-mixities at crack initiation is demonstrated. A Hopkinson pressure bar is used to rapidly load free-standing edge cracked samples in a reverse impact configuration. By eccentrically loading the specimen relative to the crack line, various mode-mixities at crack initiation are achieved by increasing the initial crack length while keeping all other experimental parameters the same. A relatively new full-field optical technique, Digital Gradient Sensing (DGS), along with high-speed photography is used to perform full-field measurements. DGS measures instantaneous angular deflections of light rays representing two orthogonal stress gradients under plane stress conditions. The mode-I and -II stress intensity factor histories are evaluated via over-deterministic least-squares analysis of optically measured data. By quantifying the critical stress intensity factors evaluated at crack initiation, dynamic fracture envelopes are developed for both the polymers. The results are studied comparatively and relative to the brittle fracture criteria. From measured stress intensity factors and crack speeds in the post-initiation regime, energy release rate vs. velocity plots for different mixed-mode configurations are produced for both the polymers.

Stress field at V-notch tip in polymer materials using digital gradient sensing

ABSTRACTThe digital gradient sensing (DGS) technique was used to study the stress field at the V-notch tip of polymer materials. First, DGS governing equations at the V-notch tip were deduced using the elastic singular stress fields. Then, theoretical angular deflections of light rays at the V-notch tip were simulated, and the effect of notch angle on the angular deflections was analyzed. Finally, the DGS experiments were conducted, and the angular deflection contours were obtained. The results show that the stress intensity factors at the V-notches extracted from the angular deflections agree well with the results calculated from the finite element method.

Surface profile and stress field evaluation using digital gradient sensing method

Shape and surface topography evaluation from measured orthogonal slope/gradient data is of considerable engineering significance since many full-field optical sensors and interferometers readily output such a data accurately. This has applications ranging from metrology of optical and electronic elements (lenses, silicon wafers, thin film coatings), surface profile estimation, wave front and shape reconstruction, to name a few. In this context, a new methodology for surface profile and stress field determination based on a recently introduced non-contact, full-field optical method called digital gradient sensing (DGS) capable of measuring small angular deflections of light rays coupled with a robust finite-difference-based least-squares integration (HFLI) scheme in the Southwell configuration is advanced here. The method is demonstrated by evaluating (a) surface profiles of mechanically warped silicon wafers and (b) stress gradients near growing cracks in planar phase objects.

Evaluating angular deflections from the digital gradient sensing method with rigid-motion deleted

The digital gradient sensing method is used for measuring small angular deflections of light rays due to local stresses in transparent planar solids. The method is based on two-dimensional (2D) digital image correlation (DIC) to measure the angular deflection of light rays; however, when a specimen is subjected to loading, deformation measurement from DIC is not perfect because of the existence of small in-plane and out-of-plane motions of the test sample surface that occurred after loading. These disadvantages will lead to errors in the measured angular deflections. The influence of unavoidable in-plane and out-of-plane motions was discussed, and a method to eliminate the influence to show the pure stress gradient of polymethy methacrylate is demonstrated.

Experimental Investigation on Curing Stress in Polymer Composite Using Digital Gradient Sensing Technique

Abstract The curing stress and deformation of epoxy resin and aramid fiber/epoxy composites was measured using Digital Gradient Sensing (DGS) technique. First, the working principle of the DGS method was explained, and the governing equations were derived based on angular deflections of light rays. Then the angle deflection of light rays due to curing stress of epoxy resin was measured, and the effect of the fiber bundle and aramid fiber fabric on the stress distribution during formation was analyzed. The experimental results show that angular deflections of light rays can be related to nonuniform distribution of curing stress in epoxy. The fiber bundles and fabric style have important effects on the curing stress distribution. These results play an important role for predicting curing stress and deformation of fiber reinforced composites.

A generalized DGS method for studying the deformation field around a crack tip

A generalized method for calculating the stress intensity factor from angular deflection of light rays is proposed. The method is based on 2D digital image correlation (DIC) to measure angular deflection of light rays, however, when a specimen is subjected to loading, deformation measurement from DIC is not perfect because of the existence of small in-plane and out-of-plane motions of the test sample surface that occurred after loading. These disadvantages will lead to errors in the measured angular deflections and fracture parameters. The influence of unavoidable in-plane and out-of-plane motions is discussed, and a generalized method to eliminate them to show the pure stress gradient of the crack tip of Polymethyl Methacrylate (PMMA) is demonstrated. At the same time, the fracture parameter of stress intensity was calculated. The experimental angular deflection of light rays was compared with the theoretical angular deflection predicted by generalized model using data points in an array around the crack tip region. To show the potential and efficacy of the method, K values were obtained from experimental data during tests conducted in a PMMA three-point-bend specimen. Results show an excellent level of agreement with K values predicted from FEM, highlighting the potential of the proposed methodology.

A full-field reflection-mode digital gradient sensing method for measuring orthogonal slopes and curvatures of thin structures

A full-field optical technique capable of measuring angular deflections of light rays reflected off specularly reflective planar surfaces is developed. The method is aided by 2D digital image correlation to measure angular deflection of light rays. The principle of the method is described and the governing equations that relate light ray deflections to surface slopes are presented. The method is demonstrated by measuring the orthogonal surface slopes of a circumferentially clamped silicon wafer subjected to a central load and are shown to be in good agreement with the analytical solutions. The curvature fields are also computed by taking advantage of differentiation schemes integral to digital image correlation algorithms. The method is utilized to successfully quantify relatively small surface slopes of the order of 10−5 rad caused by a curing layer of spin-coated epoxy on a thin (100 µm) silicon wafer.

Nondestructive evaluation of transparent sheets using a full-field digital gradient sensor

Abstract A full-field, non-contact, optical inspection tool for transparent materials is demonstrated. The technique is sensitive to refractive index and thickness variations caused by inhomogeneities and defects in an otherwise uniform sheet stock. The technique utilizes a 2D digital image correlation method to visualize and quantify angular deflections of light rays in two orthogonal directions to assess the uniformity. The principle of the method and its feasibility is demonstrated by visualizing the heat affected zone in a uniform borosilicate sheet sample.

Measurement of crack-tip and punch-tip transient deformations and stress intensity factors using Digital Gradient Sensing technique

The optical method of Digital Gradient Sensing (DGS) is extended to the study of fracture mechanics and impact mechanics problems. DGS is based on the elasto-optic effect exhibited by transparent materials subjected to non-uniform state of stress causing the angular deflection of light rays propagating through the material. Under plane stress conditions, the deflections of light rays can be related to two orthogonal in-plane stress gradients. In this paper, the principle of the method is presented first, followed by crack and punch experiments on PMMA plates for quantifying stress gradients near stress risers. The crack-tip stress intensity factors under both quasi-static and dynamic loading conditions are extracted from DGS measurements and are in good agreement with analytical and finite element results. The problem of a square-punch impacting the edge of a PMMA sheet is also studied using the new method 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 a complementary finite element analysis of the problem.

Measurement of Orthogonal Stress Gradients Due to Impact Load on a Transparent Sheet using Digital Gradient Sensing Method

A full-field optical method called Digital Gradient Sensing (DGS) for measuring stress gradients due to an impact load on a planar transparent sheet is presented. The technique is based on the elasto-optic effect exhibited by transparent solids due to an imposed stress field causing angular deflections of light rays quantified using 2D digital image correlation method. The measured angular deflections are proportional to the in-plane gradients of stresses under plane stress conditions. The method is relatively simple to implement and is capable of measuring stress gradients in two orthogonal directions simultaneously. 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 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.

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.

Quantitative Evaluation of Flow Computations by Rainbow Schlieren Deflectometry

Rainbow schlieren deflectometry, a line-of-sight optical measurement technique, was used to evaluate computations of steady nonreaeting and reacting flows in axisymmetric systems. The nonreacting flow was that of an isothermal helium jet discharged vertically in air, and the reacting flow was that of a hydrogen jet diffusion flame. The computed results were processed to obtain a color schlieren image for direct visual comparison with the corresponding experimental color schlieren image. The computed and measured angular deflections of light rays were also compared. In addition, the computed field distributions of scalar flow properties including the refractive index, species concentration, and temperature were compared quantitatively by inverting the experimental schlieren measurements. The results demonstrate the effectiveness of the rainbow schlieren technique in evaluating the physical models used for flow computations

Measurement of interfacial fracture parameters using coherent gradient sensing (CGS)

AbstractAn optical interferometry called coherent gradient sensing (CGS) has been extended for mapping interface crack tip fields and for evaluating fracture parameters. The optical technique is a double grating shearing interferometer with an on line spatial filtering arrangement. The method offers real time full field measurements and can be used both in transmission made and reflection mode. The interferometer measures small angular deflections of light rays which can be further related to in plane gradients of s̀x + s̀y in transmission through elasto‐optic relations. Direct interfacial crack tip measurements in a high stiffness mismatch PMMA‐aluminium bimaterial system are performed. A variety of crack tip mode mixities are studied using asymmetric four point bend specimens subjected to different far field mechanical loads. The. complex stress intensity factors and the associated phase angles are measured from CGS patterns using an asymptotic expansion field. The measurements are compared with finite element results.

Integrated Photoelasticity Of Axisymmetric Bodies

The paper reviews integrated photoelastic methods for stress determination in axisymmetric bodies. The specimens are put in an immersion bath and viewed in a common transmission polariscope. If birefringence of the specimen is high, integral fringe pattern as well as quasi-isoclinics may be photographed. By point-by-point technique the characteristic directions as well as the characteristic phase retardation on a number of light rays are measured. This experimental data, often combined with the application of the equilibrium equations and macrostatic equilibrium conditions, permit one to determine stress distribution in the specimen. Investigation of stresses in isotropic speci-mens as well as in cubic single crystals is considered. A new method of determining stress in cylinders, including measurement of the angular deflec-tion of light rays, is described.