An application of holography to complete stress analysis of photoelastic models

A new procedure is proposed by which holographic principles may be extended to include stress analysis of three-dimensional photoelastic models. A sixth independent equation can be obtained to permit a complete stress solution by using the double-exposure hologram technique in conjunction with an immersion tank. The salient feature of the method is that no stress relieving is necessary between exposures of the hologram. Two experiments were performed to compare the stress-relieving method to the immersion method. In both experiments, a two-dimensional model was used to simplify the demonstration of the general techniques, which are also applicable to slices from frozen-stress models.     

The birefringent response of a potential photoelastic material with variable elastic properties

In photoelastic stress analysis, a need sometimes exists for a birefringent material in which the experimenter has the ability to vary its mechanical or elastic properties. It was the intent of this investigation to produce a homogeneous, isotropic solid with variable mechanical properties and which was suitable for photoelastic use. This goal is accomplished through the fabrication of a discontinuous composite where the birefringent constitutents have matched indices of refraction in the unstressed state. The constituents of this composite are solid-glass microspheres embedded in a polyester matrix. Three theories are formulated to define the stress-induced birefringent phenomena found in composites of this nature. Conventional photoelastic techniques were employed to produce data appropriate for comparison to the predictions of these theories.     

Suitability of the photoelastic implementation of polymers with material birefringence

Scattered photoelastic techniques would gain considerable momentum through better understanding of the nature and response of the available photoelastic materials. The influence of the prevailing birefringent effect in the state of load-free polymers on the radiated scattered light energy is investigated. Six different photoelastic materials are considered. The impact of material birefringences on the quality of reading the fringe orders of the scattered radiation in a stressed photoelastic medium is explored. Spectral dependence of the modulation of light vectors in acrylic materials (Plexiglas) is illustrated. The advantage of this characteristic as a convenient means of compensation in scattered photoelasticity is pointed out. Acrylic sheets, a relatively cheap transparent polymer, seem to be suitable for scattered photoelastic analysis. The moiré technique might find application in determining fringe orders in a material such as Homalite-100. Replacing the primary beam by a primary sheet saves the cost and effort consumed in the scanning process. Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

A photoelastic material with variable modulus of elasticity

Instructions are given in this paper to manufacture a photoelastic material (polyurethane rubber) exhibiting a linearly variable modulus of elasticity. In the examples given, the range ofE is of the order of 1 to 2.5. Illustrations of applications in stress analysis are included. The new material should be particularly useful in the solution of soil-mechanics problems and it can be used for its photoelastic properties, or as base for grid and moiré analysis.     

On photoelastic response of composites

Using the theory of the unitary system of retarders, it is shown that two seemingly different theories of photoelasticity (Sampson’s phenomenological theory and Dally and Prabhakaran’s stress-proportioning concept) are identical if the heterogeneous nature of the composites is respected. It is also shown that the optical isoclinic parameter can be accurately predicted even if the initial birefringence is present in the unloaded specimen.     

On the mixing of photoelastic immersion fluids

It is shown that an equation can be used to determine the exact quantities of components to yield a specified refractive index for an immersion fluid. The results obtained from this equation are compared with values obtained experimentally for two different immersion fluids, IMF 163 and Hallowax. The paper also discusses the kinds of errors that are introduced when a mismatch in refractive index occurs between model material and immersion fluid. Graphs are presented which show the effect of temperature on the refractive index, the degree of refraction of the light beam when the refractive indices are different between immersion fluid and birefringent model, and effect of the angle of incidence.     

On the use of photoelastic composite models

Emphasis in the paper is placed on establishing the validity of employing photoelastic composite models to study assumptions used in composite-material analysis. Two approaches for the derivation of material constants for plane-stress layered composite materials are presented. Basic assumptions of the theories are studied. The theoretical and experimental equivalent moduli for test specimens loaded in tension and in shear are also compared.     

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.     

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.     

A holographic method for matching and measuring the refractive index of a photoelastic material

If a wedge-shaped sample of material is immersed in a tank of fluid and a coherent beam of light passed through it, the ensuing wavefront can be made to interfere with a holographically stored wavefront produced with the wedge removed. The interference is measured by the resulting fringes, which can be reduced by varying the fluid mix until the fluid matches the index of refraction of the material. The number of fringes can also be used to determine the difference between the indices of refraction of the fluid and material, and determine the material index from a known fluid index.     

On the role of material dissipation for the crack-driving force

The thermodynamic setting for the formulation of the “crack-driving force” for a singular crack in conjunction with rate-independent material response is discussed. One key ingredient is the introduction of a fixed (absolute) configuration, relative to which both physical and (virtual) configurational and spatial changes can be described. Only quasistatic and isothermal conditions are considered in this paper. A variational framework is established for the rate of global energy dissipation (integrated over the whole material domain) due to the combined action of a (discrete) crack extension and continuum inelasticity, whereby the material time derivative of internal variables and the rate of crack extension are coupled. The classical assumption (previously adopted in the literature) is that there is no coupling, i.e. the internal variables are considered as fixed (material) fields just like an inhomogeneous material property. The other (extreme) assumption is that the internal variables fields are convected with the configurational motion due to the virtual crack extension. Both cases are investigated in this paper for a simple 2D example of an edge crack in a plate in a setting of small strains and hardening plasticity. In particular, we consider convergence issues from mesh refinement.     

Application of the least-squares method to photoelastic analysis

In this paper, the linear and nonlinear leastsquares methods are developed in matrix notation as solution schemes to determine key parameters from whole-field fringe patterns. Examples of the proposed methods to the determination of the photoelastic-fringe constant from a disk in diametral compression and the opening-mode geometric stress-intensity factor from the photoelastic-fringe loops in the neighborhood of a crack tip are presented. In the latter example, the location of the crack tip is treated as an unknown to be determined from the analysis.     

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.