Model design and fabrication for stress analysis in multilaminar composites

Steps in preparing fiber composite models for scattered-light photoelastic analysis are presented. They include dimensional analysis, mold design, and material preparation and handling. Techniques are applied to produce two-layer and four-layer models.     

Scattered-light rosette

A newly developed concept, called thescattered-light, rosette, is used to determine the state of stress on a free surface. Three simultaneous, polarized-light beams intersecting at a surface point yield sufficient scattered-light photoelastic data to evaluate the stresses at a surface point. After initial calibration, the surface-stress analysis consists of a series of photographs, one photograph for each point of interest. General equations are derived which are valid for any three light beams intersecting at a surface point on a stressed, photoelastic material. Simplifications of the general equations and techniques are also noted. Stresses obtained from the scattered-light-rosette analysis are compared with the known solutions for two problems.     

A class of zero-birefrngent polymers

A class of photoelastically insensitive materials consisting of a blend of rigid and flexible polyesters is described. The mechanical and optical response of these polymers is viscoelastic in character. For a wide range of the compositions, the birefringence changes from positive to negative under constant load or constant displacement. The influence of composition, time under load, and principal stress difference on the birefringence is studied. Isochromatic-fringe development in a diametrally loaded disk shows that a major region of the stressed body becomes optically insensitive after a reasonable period of time under load and remains insensitive for a time sufficiently large for associated photoelastic operations. A typical operating-time band is presented during which the optical response of a model characterized by the fringe order per unit thickness is reasonably small. It appears that this class of photoelastically insensitive materials can be employed to produce composite models with glass-fiber reinforcements. Compared to other zero-birefringent polymers, the present material has the advantage of easier processing (casting and curing), improved adhesion to glass fibers and closer matching of the refractive index with that of glass.     

Instrumentation improvements for scattered-light photoelasticity

Devices which simplify the collection and improve the quality of scattered-light photoelastic data are described. These devices include electromechanically controlled optics for varying the polarization of the incident-light beam and a photometric scanner for observing the scattered-light fringes.     

Integrated-plane photoelastic method—Application of photoelastic isodynes

It has been shown by Pindera and Mazurkiewicz that a new type of scattered-light modulation in the plane of a two-dimensional photoelastic object can be obtained when the stationary integrated photoelastic method developed by Pindera and Straka is applied in a scanning mode and when the transfer function of the photoelastic system satisfies certain conditions. The new type of light modulation, called field of isodynes by the authors, carries information on stress components normal to the direction of propagation of primary beam, and on corresponding total-force component. The points where this stress component is equal to zero can be easily determined. The classical scattered-light modulation along a chosen line represents a cross section of a corresponding isodynes field. It is shown that these features of the method of isodynes make it possible to easily determine the distribution and values of normal stress components at any arbitrary rectilinear cross section, and to check immediately the accuracy of measurements. The experimental determination of contact stresses and contact regions using the method of isodynes is especially simple and elegant.     

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.     

Analysis of behavior near a cylindrical glass inclusion by scattered-light photoelasticity

Application of scattered-light photoelastic techniques to the determination of the normal-stress differences and shearing stresses in the matrix near an Eglass rod embedded in a polyester-resin matrix under tension is discussed. The rod is semi-infinite, that is, it extends from the center of the test section through one of the grip ends. Specific methods for making the three-dimensional scattered-light observations on the composite specimen under load are described in detail. Some typical fringe patterns are presented. Results will be useful in predicting the behavior of fibrous-glass-reinforced plastic composites since both matrix and inclusion are made of prototype materials. The system is modeled in geometric scale only.     

Scattered-light flow-optic relations adaptable to three-dimensional flow birefringence

The scattered-light method has been studied with the aim of developing a flow-optic relation which can be used for the analysis of three-dimensional flow problems of Newtonian fluids utilizing flow birefringence. A set of flow-optic relations which potentially can be adapted to three-dimensional scattered-light birefringent analysis has been developed on a phenomenological basis for the aqueous suspensions of Milling Yellow. Good agreement with theoretical solutions was obtained when these relations were applied to flows through channels of three different geometries.     

Linear limit stresses of some photoelastic and mechanical model materials

Certain laws of similarity must be observed in structural-model analyses. In this paper, one aspect of model similarity—that of linearity—is examined quite extensively. Most model analyses assume that both prototype and model materials obey Hooke's law. But the plastics often used for structural or photoelastic models are viscoelastic or photoviscoelastic. The stress-strain and stress-birefringence relations are time dependent and may be nonlinear. Through careful calibration of model materials and proper design of model tests, potential errors due to the time dependence of material properties can usually be avoided. If the results of the test are to be interpreted conveniently and accurately, the stresses in the model material must be within the linear range. This range is limited and time dependent for most plastics. The linear range may extend only to stresses considerably below the ultimate or fracture strength of the material. Hence, analyses based don linearity may be in error if the initial stresses are too high and/or if given stresses are sustained too long before desired information is collected. The stresses which limit the linear range, called linear limit stresses, were determined for both stress-strain and stress-birefringence relations for four commonly used plastics: CR-39 (Cast Optics Co.), PS-1 and PS-2 (Photolastic, Inc.) and P6-K (B.A.S.F., Germany). A graphical presentation of the time-dependent photoelastic and mechanical properties is employed. It was concluded that linear limit stresses for birefringence are approximately equal to those based on strain and can therefore be used to establish, within reasonable bounds of accuracy, the linear range of behavior of the material.     

Experimental analysis of plates using the method of model curing

The method of model curing is applicable to the analysis of plates. When the polymerization process is complete and model is unloaded, the deflection and the birefringence remain permanent. The stereometric method is used for evaluation of bending and torsion moments, and photoelastic method is used as a control method. The example given of the method of curing is a square plate supported at three points and loaded by a concentrated load.     

Study of basic patterns of light scattering in aqueous solution of milling yellow

Basic characteristics of light scattering in an aqueous solution of milling yellow are presented in a form of relations between the scattered radiant power, states of polarization of primary radiation and scattered radiation, observation angle and azimuthal angle.It is found that the state of polarization of the scattered light in milling-yellow solution can be utilized as a foundation of reliable photoelastic scattered-light techniques for flow analysis. However, Rayleight's model of scattering is nnt directly applicable.Paper contains data on major parameters of light scattering, knowledge of which is necessary to correctly design flowbirefringence experiments. In particular, these data can be used to develop a set of conditions and constraints for designing of particular scattered-light flow-birefringence experiments, and of corresponding transfer functions.     

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.     

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.     

Stress-concentration factors for fatigue configurations

Stress concentrations in thin-plate configurations commonly used in fatigue bending tests were determined by photoelastic means. The test configurations were rectangular and tapered plates with a centrally located hole. These configurations were machined from plates constructed by cementing together two sheets of similar photoelastic material. A reflective-type cement was used. In this manner, photoelastic measurements for the bending case were indicative of the average between maximum fiber stress and the stress at the reflective surface. The maximum fiber stress was then computed assuming that plane sections remain plane. Although bending was of primary concern, tension tests were also performed. The measured stress concentrations are compared with available analytical solutions. In the case of bending, the results are compared with infinite-plate solutions since the perforated finite-width plate bending problem has not been solved.     

Photoelastic model measurement with rotated principal axes by scattered-light photoelasticity

The method of measurement of a three-dimensional photoelastic model with rotated principal axes has not yet been fully experimentally established. It is known that a three-dimensional photoelastic model can be reduced to an optically equivalent model. In this paper, the optically equivalent model is realized from a stratified model consisting of two layers of the frozen stress model. The secondary principal stress direction and the relative phase retardation of the frozen disk model in the stratified frozen stress model are determined for the entire field from Stokes parameters obtained by scattered-light photoelasticity using unpolarized light. The accuracy of these values is confirmed by a comparison with results only from the frozen stress disk model.     

Three-dimensional scattered-light stress analysis of discontinuous fiber-reinforced composites

This paper reports an investigation of three-dimensional stresses in models of composite materials with discontinuous fibers using the scattered-light photoelastic method. A special scattered-light polariscope with loading system was designed and constructed for this research. Two models were used in this investigation. The first was a cylindrical tension model with a single discontinuous axially aligned aluminum fiber surrounded by a polyester matrix. The second was a five-fiber cylindrical compression model with a central discontinuous fiber surrounded by four continuous ones and polyester matrix. The experimentally determined stress distribution from each model along chosen lines was presented. The stress distribution on the same lines in the single-fiber case was calculated using the finite-element method. The calculated result showed fair agreement with the experimentally determined results.     

The double-light-beam method in three-dimensional scattered-light photoelasticity

This paper presents a new scattered-light photoelasticity technique which may be called the double-light-beam measurement method. Principal-stress directions and relative retardations related to the principal-stress differences can be measured at any point within an ordinary three-dimensional photoelastic model by this method. This method does not need double loading and the quantities to be measured depend only on the relative light intensity. Moreover, the output signals alternate, providing improved accuracy and stability. If supported by an appropriate program-control and digital processing system, the double-light-beam method can be used to quickly determine the internal stress distribution in ordinary three-dimensional photoelastic models.     

A measurement method of scattered light photoelasticity using unpolarized light

This paper describes an automatic measurement method for the stress analysis of a three-dirnensional photoelastic model having the rotation of the principal stress by scattered-light photoelasticity using unpolarized light. The relative phase retardation and the principal stress directions of a linear retarder for a distance in the solid model are expressed in terms of measurable Stokes parameters. The method was used for measurements on a frozen stress sphere under diametral compression.