Dynamic photoelastic and dynamic finite-element analyses of dynamic-tear-test specimens

The transient response of the dynamic-tear-test specimen of a brittle material, Homalite-100, was investigated by dynamic photoelasticity and dynamic finite-element method. The dynamic stress-intensity factors obtained from dynamic photoelasticity and dynamic finite-element analyses were in reasonable agreement with each other. The dynamic finite-element analysis also showed that the dynamic-fracture-initiation toughness could be determined from the dynamicstrain response of a strain gage located near the crack tip in conjunction with a simple static analysis. Dynamic-fracture-toughness vs. crack-velocity relation was also obtained.     

A dynamic photoelastic investigation of stress-wave propagation in cones

The embedded-polariscope method was employed to isolate the central plane in cylindrical and conical models subjected to axial loads. Light-field isochromatic-fringe patterns associated with each of the five models studied were recorded by using a multiple-gap camera. Results obtained indicate that the maximum stress decays with distance propagated approximately as indicated by the elementary one-dimensional wave theory.     

A comparison of static and dynamic properties of photoelastic materials

The dynamic values of the modulus of elasticity and photoelastic fringe constant of Homalite 100 and ten epoxy resins were determined. Of those tested, it was found that five exhibited desirable dynamic properties including two materials which exhibited no appreciable change in fringe constant. Included in this group of five materials were three materials which can be purchased in precast shapes; thus, enabling laboratories without casting facilities to obtain suitable materials for dynamic photoelastic experiments.     

A dynamic photoelastic study of stress-wave propagation through an inclusion

A photoelastic study of the elastodynamic-stress fields around a circular, elastic inclusion (Solithane 113) embedded in an elastic plate (Hysol 4485) is presented. The edge of the plate was loaded by an explosive charge, which produced a plane, compressional stress wave of triangular shape. Isochromatic-fringe patterns were obtained, which give the maximum shear stresses, both inside the inclusion and in the surrounding medium. The principal stresses on the axis of symmetry were determined through the use of the oblique-incidence method. It was found that small tensile stresses are generated at the interface on the shadow side of the inclusion. The focusing effect inside the inclusion predicted by ray theory was not observed. Finally, the shape of the wavefront as the wave passes the inclusion was determined.     

A system of modified epoxies for dynamic photoelastic studies of fracture

In order to develop a moderately tough transparent polymer, a three-component modified epoxy was investigated. The polymer system included an epichlorohydrin/bisphenol A epoxy, a polyoxypropyleneamine curing agent and a curing accelerator. Twelve different compositions were prepared and evaluated in a series of static and dynamic tests to determine the material properties important in photoelastic studies of fracture. Static tests showed that the critical strain-energy release rate could be varied from 1.4 to 4.1 lb/in. by changing the constituents in the blending of the epoxy. These results forG _Ic indicate that the modified epoxies are considerably tougher than Homalite 100 (G _Ic =0.33 lb/in.) which is commonly employed as a model material in dynamic photoelastic studies. Dynamic photoelastic tests were conducted with half-plane models in order to determine the dilatational- and distortional-wave velocities,c ₁ andc ₂, as well as dynamic values of the modulus of elasticityE and Poisson's ratio ν at loading times of the order of 10^?5 s. These results indicated that the dynamic modulus of some of the modified epoxies was significantly higher than the static modulus indicating that these polymers are rate sensitive. One of the epoxy materials, Blend No. 3 withG _Ic =2.65 lb/in. (464J/m²), was calibrated dynamically. The material fringe value changed nearly linearly as a logarithmic function of time with an increase of about 100 percent as the loading time decreased from 10⁴ to 10^?4 s. This large variation inf _σ implies that the calibration constant must be adjusted when interpreting dynamic fringe patterns. Two of the epoxy compositions were also characterized in a number of fracture experiments involving crack propagation at velocities ranging from arrest conditions to terminal velocity where branching initiates. Dynamic isochromatic-fringe loops were photographed with a Cranz-Schardin multiple-spark camera. The fringe loops were analyzed to give the instantaneous stress-intensity factorK as a function of crack velocity å. The å vs.K curves appear to be invertedL shapes; however, there appears to be a double branch on the vertical part of theL. Also a slightly higherK is required for accelerating cracks and a lowerK for decelerating cracks. Further investigation is required to identify the basic mechanism involved in this fracture behavior.     

How ‘mixed’ is dynamic mixed-mode crack propagation? — A dynamic photoelastic study

Dynamic photoelastic fringe recordings associated with rapid curved crack propagation, crack division and the interaction between moving cracks and elastic waves show global dynamic mixed-mode crack-tip fringe patterns. When analysed by means of K-determination procedures an ‘apparent’ dynamic mixed-mode ratio K₂/K₁ may be denned which turns out to be a function of the particular selection of measurement data points. This paper compares experimentally recorded fringe data with numerical results in an attempt to resolve the dynamic photoelastic mixed-mode crack problem.     

A photoelastic and FEM analysis of interfacial crack propagation

The linear elastic solution for the bimaterial interface crack is applied to determine the direction of crack propagation during surface-layer removal by scraping. The direction of the load which must be applied to the free end of the surface layer for continued interfacial crack propagation is determined using photoelasticity and finite elements, and results are found to be in good agreement.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

A stress-optic law for photoelastic analysis of orthotropic composites

The feasibility for utilizing transparent filament-resin composites for photoelastic stress analysis was investigated. Satisfactory photoelastic stress patterns were demonstrated in simple models with undirectional and bidirectional fiber orientations. A stress-optic law was formulated, based on the concept that the birefringence components contributed by each component of plane stress are combined according to a Mohr circle of birefringence. Applying this concept, the difference of the physical and optical principal directions was accounted for, and a general method of photoelastic solution for the plane-stress problem in orthotropic sheets was developed. The method of analysis is little more complex than the well-known procedures for isotropic materials, but at least three experimental measurements are required to characterize the optical response of the material to plane stress. Partial confirmation of the proposed stress-optic law was obtained by comparison of the theory to limited experimental data obtained in uniaxial-stress samples. It remains to establish a more positive verification by experiments in a variety of biaxial-stress conditions.     

Optical analysis of photoelastic polariscopes

A full-field interpretation of the photoelastic effect is advanced, supplementing the common pointwise explanation. This “warped-wavefront” viewpoint provides a key for the analysis of resolution, contrast and location of object plane in diffused-light and lens-type polariscopes. The analysis yields quantitative assessment of performance. Two wavefronts with wave normals separated by angle α emerge from the model wherever a gradient of fringe order exists in the interference pattern. It is this angular separation that limits resolution, contrast and object-plane location. Results indicate potentially very high resolution for both types of polariscope, with theoretical resolution being independent of focal length and speed (f-number) of the camera lens. With diffused-light polariscopes, contrast diminishes as fringe gradient increases, but high contrast remains available for common situations. Position and shape of fringes in the isochromatic pattern is affected by location of the plane of focus, which should therefore be fixed in the model. The analysis reveals special considerations applicable to special circumstances, including very high fringe gradients, point-light sources (lasers) and distant model location.     

A three-dimensional photoelastic method for analysis of differential-contraction stresses

The property of homogeneous and isotropic contraction accompanying the slow polymerization of a photoelastic epoxy resin is utilized to produce a photoelastic model of the same size and shape, at the elevated cure temperature, as the container in which it was cast. Reducing the temperature of the bonded model-container composite structure through the epoxy material transition-temperature range results in frozen-stress photoelastic patterns which correspond to the forces of mutual elastic restraint of differential thermal contraction. The requirements for model-prototype similarity and the model-calibration method are discussed. Particular experiments with calibration specimens and with more complex structures in two and three dimensions are described. The validity of the technique is further demonstrated by correlation with a three-dimensional numerical solution. The properties of a material that was specially developed for use in this new technique are given.     

The determination of the refractive index of a photoelastic specimen by immersion technique

Conventional methods for determining the refractive index demand specimens of optical quality, the preparation of which is often very difficult. An indirect determination by matching the refractive indices of specimen and immersion liquid is a practical alternative for photoelastic specimen of nonoptical quality. An experimental arrangement used for this technique and observations made while matching the refractive indices of three different specimens are presented.     

Complete automatic analysis of photoelastic fringes

TV technology combined with a modern video-frame store is used to store the complete fringe pattern in digitized form in real time. A minicomputer connected to the store has direct access to any picture point in the store. In this manner, it is possible to evaluate the photoelastic-fringe pattern in the computer by special developed software.     

Polarimetry for spatiotemporal photoelastic analysis

This paper describes a new photoelastic technique for the spatiotemporal stress analysis. In a polarimeter developed, an elliptically polarized signal beam of light, modulated in state of polarization by two-dimensional principal-stress distributions interferes with a reference beam of light consisting of orthogonal linearly polarized two components. A time-sequential series of two-dimensional interference patterns are received one after another by a MOS video camera, followed by a computer. Of the elliptically polarized signal beam, the orthogonal field components along the directions of the principal stresses in a two-dimensional photoelastic sample can be computed from a recorded interference pattern, which offer the data needer for mapping the spatiotemporal principal-stress distribution over the sample. Not only each of the two orthogonal principal stresses but also the principal-stress difference are mapped in a time-sequential diagram. No use of any movable polarization element such as a rotating analyzer allows us to follow a rapid change in stress distribution within the maximum frame rate 2066 s⁻¹ of the MOS video camera.     

An approximate method of orthotropic photoelastic analysis

An approximate strain-optic law has been derived for photoelastic analysis of orthotropic model materials. Principal-strain difference and the direction of major principal strain can be obtained from only two photoelastic measurements (isochromatic-fringe order and isoclinic angle) by means of this strain-optic law. Limited experiments on models subjected to uniaxial and biaxial stresses indicate good agreement between the experimental results and predictions of the strain-optic law. A parametric study demonstrates that the direction of major principal strain can be predicted to within a few degrees of the exact value and that the principalstrain difference can be predicted within ±20 percent for most practical values of degree of orthotropy and ratio of principal strains. The error levels are quite acceptable considering the significant ease in analysis provided by the new law and the fact that such error levels are not uncommon in experimental investigations.     

A composite three-dimensional photoelastic method

Care must be taken in preparation and testing of three-dimensional composite photoelastic models. Some problems encountered in modeling the prototype and during model testing are: model-material failure, loss of fringe pattern in slicing, inherent shrinkage response in freezing, inadequate bonding between materials, and modular ratio difficulties. The selection of the correct plastic can eliminate the first four problems, but the correct modular ratio between the matrix and the insert has to be obtained. This investigation illustrated the behavior of commercially manufactured plastics as inserts, with a matrix material of Epon 828 epoxy. The effective moduli of elasticity of these plastics are reported for pure tension and for flexure. Since the manufactured plastics produced varying results, the use of Epon 828 epoxy as an insert was investigated. The inserts were cast in tygon tubing and their curing cycle was altered from that used for the matrix material to produce a different effective modulus of elasticity. The Epon 828 inserts gave excellent results in the beams. The use of the same material for matrix and insert eliminates many of the problems associated with composite three-dimensional photoelasticity.     

A recording photoelastic stress meter

An instrument for automatically making photoelastic measurements of stress is described. It may be used for recording transient stresses at a point or for scanning spatial stress distributions. Its use is illustrated by an application entailing the measurement of transient thermal stresses in a viscoelastic material.     

Three-dimensional photoelastic analysis of a fiber-reinforced composite model

A three-dimensional photoelastic analysis using the “stress-freezing” technique was conducted to determine the stress distributions in the matrix of a unidirectionally fiber-reinforced composite model subjected to matrix shrinkage and normal transverse loading. The model, consisting of a square array of polycarbonate rods in an epoxy matrix, simulated a boron-filament-reinforced plastic composite with a fiber-volume fraction of 0.50 at the critical temperature of the matrix epoxy. The effects of matrix shrinkage were separated from those of external loading by analyzing two identical models, one loaded and the other unloaded. The Lamé-Maxwell equations of equilibrium were used to separate stresses along axes of symmetry on interior transverse slices. Axial stress components were obtained by subslicing. Results are presented in dimensionless form by dividing the stresses by the average stress through the section. A comparison with theoretical results for a boron-epoxy composite shows excellent agreement, although Poisson's ratio of the model matrix is appreciably different from that of the prototype (0.5 compared to 0.35). One significant result was that the maximum stress occurs in the middle of the matrix section between fibers which is at variance with the theoretical prediction of maximum stress at the interface. Stress-concentration factors vary from 1.80 at the interface to 2.0 at the midpoint of the matrix section between fibers.     

A photoelastic fiber-optic strain gage

This paper reports on the development of a photoelastic fiber-optic strain gage sensitive to transverse strain. The sensing element is made from an epoxy resin which is stress frozen to passively achieve the quadrature condition. Light, emitted from an LED operating at 820 nm, is transmitted to and from the sensing element via multi-mode fibers and the signal is detected using a dual-channel operational photodiode/amplifier.This unique combination of optics and electronics produces a fiber-optic sensor having a high signal to noise ratio and a measurement system which is lead-in/out insensitive. Results show that strains on the order of 1 microstrain can be measured over an 800 microstrain range when a dummy gage is used for compensation.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.