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.     

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.     

A dual-observation method for determining photoelastic parameters in scattered light

A dual-observation method is developed for determining photoelastic parameters in scattered light. Using this method, the intensities of scattered light along two directions of observation, making an angle of 45 deg in a plane normal to the beam, are recorded simultaneously without rotation of either the beam or the model. Photoelastic parameters are evaluated from these records. The theory of the method, the apparatus and techniques, as well as an illustrative experiment, are reported.     

New method for determining strain on the surface of a body with photoelastic coatings

An experimental method has been developed for determining the strains at all points on the surface of a structure. Narrow epoxy-resin strips on a thin film are cemented to the surface of the body under study. Photoelastic studies show that the birefringent pattern of these strips is dependent only on the longitudinal strain parallel to their axes. When the strips are used in conjunction with a continuous photoelastic coating, the surface strain can be determined at all points from direct observation of the fringe patterns. Paper was presented at 1964 SESA Annual Meeting held in Cleveland, Ohio, on October 28–30.     

Accuracy of compensation methods in photoelastic fringe-order measurements

A complete photoelastic stress analysis depends, in the majority of cases, on the accuracy of the fractional-fringe-order measurements. The error involved due to an error in the measurement of the isoclinic angle has been studied. It was found that the Tardy method was more accurate than the Sénarmont method, assuming negligible errors in the optical elements.     

Determination of the stress distribution in assemblies of photoelastic particles

An optical measuring method and a calculation procedure for determining the distribution of the stress tensor in a plane-strained three-dimensional assembly of random-shaped photoelastic particles are described. The stress tensor at an arbitrary point of the model is determined by an integration procedure, based on the equations of equilibrium of stresses. The distribution of the principal-stress direction and the relative principal-stress difference and at least two normal stresses in a plane have to be known to perform the integration. The distribution of the principal-stress directions and their difference are measured optically by scanning the model with an optical filter system with a single rotating polarizer.     

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.     

Computer-aided photoelastic analysis of orthogonal 3D textile composites: Part 2. Combining least squares and finite-element methods for stress analysis

An approach combining least squares methods and finite element methods (FEM) is presented for subsequent photoelastic stress analysis of orthogonal 3D textile composites withR and α obtained in Part 1. Through this approach, these photoelastic stresses are obtained over a region of interest as if the composites were homogeneous materials. The least squares method is used for requiring the solution strain fields to best correlate with the distribution of the two photoelastic strain data of ɛ _x − ɛ _y and γ _xy calculated directly from the measuredR and α. The FEM uses the homogenized composite properties to construct the nodal force equilibrium equations as constraints in the least squares formulation. As a result of combining this least squares method and FEM with lagrange multipliers, a linear system of equations is formulated with the unknown nodal displacements. Once these nodal displacements are solved, the strains and stresses can be calculated through FEM formulations. This approach is tested with the two experimental results completed in Part 1 for the aluminum and composite plates. The stresses obtained for the aluminum plate show close agreement with those obtained with the plain FEM computation. In the case of the orthogonal 3D composite plate, the local variations as observed inR and α are already necessarily eliminated from these solved photoelastic stresses. Furthermore, these stresses also match well with those computed with the plain FEM from the homogenized composite properties.     

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.