Photoelastic model

The distribution of stresses in a joint can also be revealed in photoelastic models of joint assemblies made from a transparent material that becomes bire-fringent when subjected to stress. If a beam of polarized white light is directed through a stressed component, colored fines appear as a result of interference effects when the object is viewed through a second polarization filter. These lines mark regions of equal stress. If the loading level is increased, the se-... 

Figure 6-8. Polariscope for two- and three-dimensional photoelastic model analysis. (Courtesy of Measnrements Group, Inc.).

Of these. No. 1 is the most restrictive. Not only must the elastomers be transparent and preferably colorless, the molds must have a mirror finish to prevent distortion of the light beam. In addition, the experimental stress analyst is usually examining a complex shape and his photoelastic models must be cast because rubbers cannot be readily machined to shape. 

The microductile/compliant layer concept stems from the early work on composite models containing spherical particles and oriented fibers (Broutman and Agarwal, 1974) in that the stress around the inclusions are functions of the shear modulus and Poisson ratio of the interlayer. A photoelastic study (Marom and Arridge, 1976) has proven that the stress concentration in the radial and transverse directions when subjected to transverse loading was substantially reduced when there was a soft interlayer introduced at the fiber-matrix interface. The soft/ductile interlayer allowed the fiber to distribute the local stresses acting on the fibers more evenly, which, in turn, enhanced the energy absorption capability of the composite (Shelton and Marks, 1988). 

Materials Photoacoustic measurements were made on a component-assembled PAS spectrometer consisting of a 9W argon ion laser (Spectra Physics), a 0.5 cc internal volume PAS cell equipped with a sensitive electret microphone (Radio Shack, 3.2 mV/Pa). Circular polarization modulation was achieved with a special low frequency (220 Hz) photoelastic modulator (15) (Hinds International). Signals were detected and processed with a vector tracking lock-in amplifier (PAR model 5204), and intensity modulation was done with a 30-slot blade mechanical chopper (Ortec). Syntheses of all compounds were by well established literature methods. 

Polarization-modulation infrared reflection-absorption spectroscopy (PM-IR-RAS) spectra were recorded with a Bruker ITS 66/S Fourier transform infrared spectrometer equipped with a PMA 37 polarization modulation module and a ititrogen-cooled MCT detector. The infrared beam was first p-polarized with a ZnSe wire grid polarizer (Specac) before passing through a photoelastic modulator (Hinds Instruments, PEM-90), which modulated at a frequency of 74 kHz. A lock-in ampHfier (Stanford model SR-830) was used to obtain the PM-IRRAS spectra. The half-wave retardation frequency was set at 4000 cm . The PM-IR-RAS spectra were recorded as S= R -Rs)/(R +Rg). A total of 250 scans at a resolution of 4 cm were collected for each measurement at an angle of incidence of 82.5° with respect to the normal to the sample surface. 

It is also useful to be able to study stress distributions experimentally. Some materials, especially glasses and polymers, are photoelastic, i.e., they undergo a change in refractive index under the application of mechanical stress. When viewed under polarized light, meehanical models made from these materials give rise to an optieal pattern that can be related quantitatively to the principal stress distribution in the loaded body. Figure 4.26 shows a phototelastic fringe pattern... 

This being so the engineer who has a problem to solve may have to resort to a model merely to obtain a solution from the deductive calculus of the theory. The use of photoelasticity is an example. Consider a photoelastic specimen used to model the theory of simple beam behaviour. This is for illustration purposes only, of course, since the deductive calculus of a simple elastic beam is easily solved. Both model and theory assume at least the following Newtonian mechanics elastic behaviour of materials symmetrical bending and no resultant forces on the system. The theoretical derivation of the elementary equations of... 

Photoelastic analysis, one of several related testing techniques, is easy to use and usually a more economical and positive method than computer analysis. From the information it provides, the test can lead to better-designed, lower-cost products. Traditionally used to test the integrity of metal parts, photoelastic analysis is now being used to physically test thermoplastics as well as thermosets. For transparent plastics, the analysis can be made directly on the plastic. For nontransparent plastics, a transparent coating is used. Actual parts and representative models can be tested by a simple procedure. The former may be stressed under actual use conditions, whereas models are tested under simulated conditions. 

Volkersen s theory predicts that the shear stresses in the adhesive layer reach a maximum at each end of the overlap, when the bonded plates are in pure tension. Photoelastic analyses of these composite structures show that stresses are uniform in the central part of the model adhesive, but high near the edges of the steel plate used in the analysis (Figure 7.2). Stress distributions at the end were found to be independent of the length of the overlap, when its length was at least three times the thickness of the adhesive layer. " ... 

Recently, new models were proposed which can indeed be used to characterize the structure of real elastomeric networks in view of their mechanical properties 6, 7 However several parameters are necessary to describe the relationship between molecular and macroscopic deformations and therefore stress-strain measurements are generally not sufficient to conclude without any ambiguity on the validity of these elaborated theories- Another possible test consists in measuring molecular orientation in stretched rubbery networks- With this in view, the photoelastic properties of rubbers have been widely investigated However birefringence data... 

In recent years, epoxy resins have become the polymer of choice for three-dimensional photoelastic investigations. Further, the phenomena of birefringence has been used to study plasticity and viscoelasticity effects in materials through the use of extensions to the photoelastic method called photoplasticity and photoviscoelasticity (see Brill (1965) and Brinson (1965, 1968), respectively). Brill used polycarbonate, a thermoplastic polymer, as a model material for his work on photoplasticity and Brinson used an epoxy, a thermosetting polymer, as a model material for his work on photoviscoelasticity. Later, it will become clear why thermoplastic materials are used for photoplasticity while thermosetting materials are used for photoviscoelasticity. 

The remaining part of this chapter will review the three most common direct methods for measuring fiber-matrix adhesion, focusing on the sample preparation and fabrication, the experimental protocols and the underlying theoretical analyses upon which evaluation of these methods are based. In addition, finite-element nonlinear analyses and photoelastic analyses will be used to identify differences in the state of stress that is induced in each specimen model of the three different techniques. In order to provide an objective comparison between the three different techniques to measure the interfacial shear strength for the prospective user, data and a carbon fiber-epoxy resin system will be used as a baseline system throughout this chapter, However, these methods and procedures can be applied for adhesion measurements to any fiber-matrix combination. 

A. Drescher and G. de Josselin de Jong. Photoelastic verification of a mechanical model for the flow of a granular material. Journal of the Mechanics and Physics of Solids, 20(5) 337-340, 1972. 

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