Concepts of the photoelastic stress gage

With the photoelastic stress gage birefringence readings are made with light that traverses a path parallel to the surface of the workpiece. Individual stresses are determined in the elastic range of deformation, rather than stress or strain differences. The theory of a circular and linear stress gage is developed, including the influence of Poisson's ratio, and stress gradients. Stresses in the surface of the workpiece are expressed in terms of measured birefringence. Instrumentation is extremely simple. High sensitivity is derived from the relatively long optical-path length through the transducer. Applications should include stress analysis, load analysis and transducer design.     

Determination of strains in photoelastic coatings

Photoelastic coatings can be cemented directly to actual structural components and tested under field conditions. This important advantage has made them relatively popular in industry. The information obtained, however, may be misinterpreted and lead to serious errors. A correct interpretation requires the separation of the principal strains and, so far, this operation has been found very difficult. Following a previous paper by one of the authors, it is proposed to drill small holes in the coating and record the birefringence at points removed from the edge of the holes. The theoretical background of the method is reviewed, the technique necessary to use it is explained and two applications are described. The precision of the method is evaluated and found satisfactory in contradiction to information previously published in the literature.     

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.     

Crushing of particles in idealised granular assemblies

Four idealised assemblies of equally sized spherical particles are subjected to a range of macroscopic compressive principal stresses and the contact forces on individual particles are determined. For each set of contact forces the stress fields within individual particles are studied. A failure criterion for brittle materials is imposed and indicates that crushing (or rupture) occurs when the maximum contact force reaches a threshold particle strength value, irrespective of the presence and magnitude of other lesser contact forces acting on the particle and the material properties of the particle. Combining the crushing mechanism with an assembly instability mechanism enables failure surfaces to be drawn in the three-dimensional stress space. A simple spatial averaging technique has been applied to the failure surfaces to remove the effects of assembly anisotropies. Sections of the failure surfaces on π planes have similarities to those commonly used in sand modelling.     

Determination of fracture toughness by photoelastic coating

The photoelastic-coating method was applied to the determination of fracture toughness in aluminum plates. The specimens were plates with a central transverse crack. Determinations were made first by the compliance method. The specimens were loaded statically to failure. The opening displacement across the crack was measured with a clip gage. In using this photoelastic-coating method, the stress-intensity factor was obtained in terms of the radius and fringe order of various isochromatic fringe loops using an extrapolation law. An apparent stress-intensity factor was obtained from several isochromatic fringe patterns away from the crack tip and then extrapolated to the crack tip to determine the true value. Results obtained by the photoelastic-coating method are higher than those obtained by the compliance method for all loads, due to the bluntness of the crack tip in the first set of specimens. Theoretical predictions fall between the compliance method and photoelastic-coating results. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Scattered-light photoelastic stress analysis of a solid-propellant rocket motor

Scattered-light photoelasticity, a nondestructive technique, is used to determine the stress distribution in a three-dimensional, solid-propellant rocket motor. The model is a case-bonded solid propellant with a stargrain internal boundary. Stresses are induced by internal pressure. The pressure load simulates part of the stresses developed in firing a rocket. The model material is polyurethane rubber which is similar to the binder material in actual rockets. The model construction and data analysis are discussed in detail, and the results are presented in graphical form.     

Dynamic photoelastic study of wave fields in elastic plates with stress concentrators

The method of dynamic photoelasticity is used to study the dynamic failure of structural members in the form of plates with a curvilinear (circular or elliptic) hole and an isolated crack under impulsive loading. The time-dependences of the stress intensity factors and the crack tip velocity are investigated for two types of models __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 84–92, December 2005.     

Particle shape consideration in numerical simulation of assemblies of irregularly shaped particles

The mechanical behavior of granular materials depends much on the shape of the constituent particles. Therefore appropriate modeling of particle, or grain, shape is quite important. This study employed the method of direct modeling of grain shape (Matsushima & Saomto, 2002), in which, the real shape of a grain is modeled by combining arbitrary number of overlapping circular elements which are connected to each other in a rigid way. Then, accordingly, a discrete-element program is used to simulate the assembly of grains. In order to measure the effects of grain shape on mechanical properties of assembly of grains, three types of grains—high angular grains, medium angular grains and round grains are considered where several biaxial tests are conducted on assemblies with different grain types. The results show that the angularity of grains greatly affects the behavior of granular soil.     

Graphical methods for determining the resulting photoelastic effect of compound states of stress

The aim of this work is to give a simplified representation of an interesting subject, namely, the calculation of the photoelastic effect behind a system in which the principal stresses or secondary principal stresses rotate about the direction of the propagation of light. The methods are described in a popular form for understanding the essential features and the necessary graphical operations for solving these complicated problems. Further, the relations between the different methods are shown. Thej-circle technique is improved in order to simplify the operations and a new possibility in applying Wulff's grid is introduced in photoelasticity. The graphical tools can then be applied as so-called “rotation rules.” Some examples related to recent papers which present theoretical results or new methods are given in order to study the function of these “rotation rules” and to recognize the power of these methods.     

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.     

Dynamic photoelastic investigation of interaction of stress waves with running cracks

Dynamic photoelasticity in conjunction with high-speed photography was utilized in experiments to study the interaction of stress waves with a running crack. Experimental data were analyzed to study the effect of wave scattering about a moving crack tip. The results indicated a strong influence of stress waves on crack-propagation behavior and crack branching.     

Obtaining stress maps from photoelastic data using a digital computer

A general procedure for the analysis of photoelastic isochromatic and isoclinic photographs by digital computer to produce plots of coordinate normal and shear stresses is presented. The solution for normal stresses, involving a finite-difference iterative harmonization of the Laplace equation, is discussed, including treatment of the boundaries and selection of an appropriate network grid. The results of a classical problem, solved by this technique, are included.     

Hybrid stress analysis by digitized photoelastic data and numerical methods

A method is presented that determines photoelastic isochromatic values at the nodal points of a grid mesh which in turn is generated by a computer program that accepts digitized input. Values of σ₁ - σ₂ are computed from the digitized fringe orders. The Laplace equation is solved to separate the principal stresses at each nodal point. The method is extended to digitize isoclinics. Subsequently, σ _x - σ _y and τ _xy are calculated to be used as starting values for the solution of the pertaining partial differential equations to enhance convergence. For further accelerating the rate of convergence, superfluous boundary conditions are added from the digitized data; significant improvement is demonstrated. Estimated values of σ _x - σ _y from the digitized data are further used in conjunction with the solution of the Laplace equation to determine the state of stress without solving the boundary value problems. Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles

In the present article, we study the effect of inherent anisotropy, i.e., initial bedding angle of particles and associated voids on macroscopic mechanical behavior of granular materials, by numerical simulation of several biaxial compression tests using the discrete element method (DEM). Particle shape is considered to be irregular convex-polygonal. The effect of inherent anisotropy is investigated by following the evolution of mobilized shear strength and volume change during loading. As experimental tests have already shown, numerical simulations also indicate that initial anisotropic condition has a great influence on the strength and deformational behavior of granular assemblies. Comparison of simulations with tests using oval particles, shows that angularity influences both the mobilized shear strength and the volume change regime, which originates from the interlocking resistance between particles.