Remarks on properties of photoviscoelastic model materials

One of the basic problems of structural-model analysis, model photoelasticity and photoelastic coatings in the problem of mechanical and optical creep, relaxation and related phenomena. It is pointed out that, in spite of creep or relaxation, it is possible to achieve physical similarity between model and object if the model material behaves in a certain range as a linear viscoelastic material. Such a material is called a “momentarily linear material.” Several model materials behave in this way in a certain range of stress and time. Because of creep and relaxation, the common tensile tests are, in general, not quite adequate for evaluation of physical properties of plastics used for models. Also the bending test is not always adequate. It is shown how to obtain sufficiently accurate relations between stress, strain, birefringence and time, using tapered specimens. The problem of biaxial creep of model materials is discussed, and a simple method of evaluating the suitability of a given plastic as a model material is shown. Some conclusions concerning time-dependent factors are formulated, and some possible areas of investigation are shown.     

Photoelastic concrete similutide with CR-39 reinforced with epoxy and glass

This investigation was undertaken to study the similitude of models for reinforced concrete beams by photoelasticity. All previous attempts of model analysis have not maintained the correct modular ratio of reinforcing rod to the beam material. The material problem of obtaining the necessary rods was solved. The material exploratory investigation revealed suitable reinforcing plastics that have opened a wide range of model analyses for reinforced concrete. The models fabricated provided a study in correlation of models and prototype. A sample of the stresses obtained with a photoelastic interferometer is given to demonstrate the practical application of the model analysis.     

Photoelastic stress freezing analysis of total shoulder replacement systems

Photoelastic stress freezing analyses in the orthopaedic literature have, in the past, been limited to studies where bone-on-bone, bone-on-metal or ultra-high molecular weight polyethylene (UHMWPE)-on-metal constructs are modeled. In these cases photoelastic plastics are used to simulate either bone or UHMWPE as it interacts with a metal implant. In joints such as the shoulder, a UHMWPE component is often cemented directly into the scapula's glenoid concavity using polymethylmethacrylate (PMMA). While a photoelastic material can be used to simulate bone with proper load scaling, UHMWPE and PMMA have very different mechanical properties at elevated stress freezing temperatures as compared within vivo body temperature. In this study, materials were identified such that proper scaling of elastic properties at elevated temperatures was utilized to simulate the metal-UHMWPE-PMMA-bone construct. Stresses on orthogonal planes throughout the glenoid were compared for two different UHMWPE component anchoring geometries (keeled and pegged). High stresses were found at the neck of the glenoid and also at the component-bone interface beneath simulated PMMA inclusions.     

General stress-strain relations in non-linear theory of viscoelasticity for large deformations

Conclusion General phenomenoligical stress-strain relations in non-linear theory of visco-elasticity for large deformations have been presented.In the first place, according to V. V. Novozhilov 1 we express the generalized equilibrium equation for large deformations in the Lagrange representation, and we apply the generalized Hamilton's principle to the equation of energy conservation, which denotes that the sum of the elastic energy and the dissipative energy is equal to the work done by the body force and the surface on the substance; so that we obtain the required general stress-strain relations in comparison with the above two equations.On the condition that the elastic potential is a function only of the strain, and the dissipation function is a function of the rate of strain and of strain; such a substance is reduced to the Voigt material necessarily, and the stresses which act on the substance are given by the sum of elastic- and viscous stresses, and the stress-strain relations are reduced to the so-called Lagrangian form.If elongations, shears and angles of rotation are small and also the strains and rates of strain are sufficiently small, the stress-strain relations are expressed by a linear Voigt model constituting a Hookian spring in parallel with a Newtonian dashpot.Non-linearity in the theory is classified into two groups i. e. the geometrical non-linearity and the physical non-linearity. The former is introduced into the theory through the definition of the generalized strain and of the generalized stress and through the equilibrium equation for large deformation, and the latter through the general stress-strain relations.The main result of this paper is that the general stress-strain relations in viscoelasticity are deduced necessarily from the physically appropriate assumptions.     

Optical and mechanical properties of birefringent polymers

The stress-strain behavior and corresponding birefringence of several polymers have been investigated within a limited range of temperatures (from ?65 to 70°F) and strain rates (from 0.0027 to 0.1613 sec^?1). One of these materials, a polyethylene resin, has been studied in more detail to ascertain the existence of a simple relationship between stress history, temperature, strain rate and birefringence. When the results were compared with the photoviscoelastic relations developed by E. H. Dill for a simple rheological material, it was concluded that the polyethylene tested does not completely satisfy this model. Polyethylene as well as the other materials investigated—nylon, a polyester, cellulose acetate butyrate, cellulose nitrate—exhibits a linear relation between birefringence and strain, independent of rate within the limits of the present experimental range.     

Measurement of favorable residual stresses in polycarbonate

Research in this laboratory has been directed toward the production and effects of beneficial residual stresses in plastics. Such stresses have been shown to have a dramatic effect on the impact strength and fatigue life of polycarbonate samples. For example, thermal quenching, in water or liquid nitrogen, of samples heated above their glass-transition temperature, resulted in an increase in the mean fatigue life of the material by as much as 20 times over that of annealed material. This increase is attributed in large part to the introduction of compressive stresses on the surfaces of the samples. This paper concentrates on methods used to measure residual stresses in the surface of the material and on the variation of these stresses with time after treatment. Three measurement techniques are described: (1) material slicing, (2) photoelastic fringe displacement and (3) the ASTM hole-drilling method. The advantages, limitations and comparative results of these three methods are described and analyzed. Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics held in New Orleans, LA on June 8–13.     

A generalized method for photoelastic studies of transient thermal stresses

This paper describes the apparatus and experimental method which was developed for generalized studies of transient thermal stresses in photoelastic models of many different shapes under a variety of steady-state or transient temperature conditions. It explains how the desired temperature gradients are established in the models and how rapidly changing temperature and stress profiles are monitored during a test. The experimental method is used to study the stresses in a three-dimensional photothermoelastic model subjected to three different temperature sequences. These are: symmetrical cooling of both faces of a thick plate initially at a uniform temperature; heating of one face only of a thick plate initially at a uniform temperature; and heating of only the cold face of a thick plate with an initial linear temperature gradient through its thickness. The last sequence generated temperature profiles which relate to conditions where internal heating is present. The resultant temperature and stress histories for each case are presented graphically and similarity scales are applied to give correct time-stress relations for a typical steel prototype. The magnitude and time of occurrence of the peak stresses on the boundary, as well as in the interior of the plate are found. These stresses are very high and occur comparatively late in each test, at a time when the temperature of the central plane has already started to respond to the changing conditions at the surface. The model was of the sandwich-type construction used by previous investigators, which has a built-in polariscope to isolate a transverse plane for viewing.     

Inelastic deformations of stainless steel leaf springs-experiment and nonlinear analysis

A stainless steel leaf spring is designed and constructed followed by its performance evaluation by experiment and non-linear analysis so that an insight into the optimum use of material can be made. Cantilever beams of uniform strength, popularly termed as leaf springs, undergo much larger deflections in comparison to a beam of constant cross-section; that needs inclusions of geometric non-linearity for rigorous analysis. This study deals with such a cantilever beam, but takes into account the material non-linearity as well. Experiments were conducted for such a cantilever beam, with highly non-linear stress-strain curves. In addition to the experiment, a computer code in ‘C’ has been developed using the Runge-Kutta technique for the purpose of simulation. Effective modulus-curvature relations are obtained from the non-linear stress-strain relations for different sections of the beam and used for the analysis. It is seen that non-linear stress-strain curve governs the bending of the beam. Importantly, non-linear analysis shows the stresses are not so high as predicted by the linear theory without end-shortening. Moreover, the tensile and compressive stresses are different in magnitude and both decrease along the span. Experimental load-deflection curves are found to be initially concave upward but, non-linear and convex upward at a high load. Comparison of the numerical results with the available experimental results from another research group and theory shows excellent agreement verifying the soundness of the entire numerical simulation scheme.     

A three-dimensional photoelastic method for analysis of differential-contraction stresses

The property of homogeneous and isotropic contraction accompanying the slow polymerization of a photoelastic epoxy resin is utilized to produce a photoelastic model of the same size and shape, at the elevated cure temperature, as the container in which it was cast. Reducing the temperature of the bonded model-container composite structure through the epoxy material transition-temperature range results in frozen-stress photoelastic patterns which correspond to the forces of mutual elastic restraint of differential thermal contraction. The requirements for model-prototype similarity and the model-calibration method are discussed. Particular experiments with calibration specimens and with more complex structures in two and three dimensions are described. The validity of the technique is further demonstrated by correlation with a three-dimensional numerical solution. The properties of a material that was specially developed for use in this new technique are given.     

Three-dimensional photoelastic and finite-element analysis of a propellant grain

The results of a three-dimensional photoelastic analysis of a propellant-grain model are compared with the results obtained from a three-dimensional finite-element analysis of the same model. The loading considered was differential thermal expansion between the case and the grain model. The model analyzed was the Stage I Minuteman propellant grain which consists of a six-point-star configuration with a head-end web. Stresses and strains determined from the two analyses in the star valley are compared. The excellent correlation between the stresses determined from the photoelastic analysis and the stresses calculated by the three-dimensional finite-element computer program established the validity of the computer program.     

Linear and Nonlinear Algorithms for Stress Separation in Photoelasticity

An experimental-numerical hybrid method for the stress separation in photoelasticity is proposed in this study. In the proposed method, boundary conditions for a local finite element model, that is, tractions along boundaries are inversely determined from photoelastic fringes. Two algorithms are proposed for determining the boundary condition. One is a linear algorithm in which the tractions are obtained by the method of linear least-squares from both principal stress difference and principal direction. Another is the nonlinear algorithm in which the tractions are determined only from the principal stress difference. After determining the boundary conditions for the local finite element model, the stresses can be obtained by finite element direct analysis. The effectiveness is demonstrated by applying the proposed method to a perforated plate under tension and contact problems. Results show that the boundary conditions of the local finite element model can be determined from the photoelastic fringes and then the individual stresses can be obtained by the proposed method. Furthermore, the stresses can be evaluated even if the boundary condition is complicated such as at the contact surface. It is expected that the proposed method can be powerful tool for stress analysis.     

Photoelastic investigation of large deflections by low-modulus photoelastic materials

Information is given to enable the experimental analysis of large deformations by application of photoelastic techniques. Promising photoelastic materials having low elastic modulus and high optical sensitivity were obtained for practical use at room temperature. The time and temperature dependence of the stress-fringe order and stress-strain relations of one of these viscoelastic materials is discussed. Photoelastic investigations of large deflected straight and circular beams are reported. Photoelastic technique seems to be a useful method for analysis of large deformations of models with complicated shapes.     

On the studies of residual stresses in glass plates

The theoretical foundation of the photoelastic methods being presently used for measuring and analyzing residual stresses in glass is insufficient for studying development of transient viscoelastic stress states in glass plates during tempering process and for an explanation of the actual material behavior. It is shown that the basic knowledge of photoviscoelastic effect in glass over a wide range of electromagnetic radiation and temperature is necessary for such on analysis. Some photoelastic properties of plate glass are presented.     

Half-fringe photoelasticity: A new approach to whole-field stress analysis

This paper presents a new method for whole-field stress analysis based on a symbiosis of two techniques—classical photoelasticity and modern digital image analysis. The resulting method is called ‘half-fringe photoelasticity (HFP)’. Classical photoelasticity demands materials with high birefringence, which leads to extensive use of plastics as model materials. Since the behavior of these materials is often different from that of the prototype materials, their use distorts the similitude relationships. In many contemporary problems this distortion is untenable. HFP offers a way out of this dilemma. It permits materials and loads to be chosen so that no more than one half of a fringe order appears in the area of interest. Thus, for example, glass, which behaves linearly up to high stress levels and over a wide range of temperatures, could be used as model material. Alternatively, models from polymeric materials could be used under very low load in order to stay within the linear part of the stress-strain diagram and to prevent large deformations. The half-fringe-photoelasticity system, which is described here, utilizes the resulting low levels of birefringence for effective stress analysis. This paper describes the system. It outlines a calibration routine and illustrates its application to two simple problems using glass models.     

Woven fabric composite material model with material nonlinearity for nonlinear finite element simulation

The objective of the current investigation is to develop a simple, yet generalized, model which considers the two-dimensional extent of woven fabric, and to have an interface with nonlinear finite element codes. A micromechanical composite material model for woven fabric with nonlinear stress-strain relations is developed and implemented in ABAQUS for nonlinear finite element structural analysis. Within the model a representative volume cell is assumed. Using the iso-stress and iso-strain assumptions the constitutive equations are averaged along the thickness direction. The cell is then divided into many subcells and an averaging is performed again by assuming uniform stress distribution in each subcell to obtain the effective stress–strain relations of the subcell. The stresses and strains within the subcells are combined to yield the effective stresses and strains in the representative cell. Then this information is passed to the finite element code at each material point of the shell element. In this manner structural analysis of woven composites can be performed. Also, at each load increment global stresses and strains are communicated to the representative cell and subsequently distributed to each subcell. Once stresses and strains are associated to a subcell they can be distributed to each constituent of the subcell i.e. fill, warp, and resin. Consequently micro-failure criteria (MFC) can be defined for each constituent of a subcell and the proper stiffness degradation can be modeled if desired. This material model is suitable for implicit and could be modified for explicit finite element codes to deal with problems such as crashworthiness, impact, and failure analysis under static loads.     

Three-dimensional photoelasticity of the rotating body

Report covers the stress distribution of a hydraulically loaded pump impeller obtained with the aid of the stress-freezing method. The similarity of stress distribution of an actual metallic impeller and the photoelastic model is discussed dynamically and hydrodynamically. From the experiments by freezing stresses under centrifugal force and hydraulic forces, the stress distribution of the actual metallic impeller has been estimated on the basis of similarity.     

An experimental study of thermal stress in porous materials by methods of holography and photoelasticity

In heat-loaded structures of energy equipment at the moment of crisis of heat exchange in working elements, the ultimate state of the material occurs. Thermal stresses were studied experimentally in a bulk porous material with a groove on the surface with a view to finding out the distribution of deformations and thermal stresses due to the location of the heat source. It appeared efficient to apply optical methods. Using holographic interferometry, a pattern of distribution of thermal deformations over the surface of the specimens was obtained. Using the photoelastic method to investigate a grooved porous structure, a physical pattern of the distribution of thermal stresses inside the block and in the groove was obtained. Ways are outlined for designing and reducing the probability of occurrence of destructive cracks. A similarity is observed in the distribution of strains and stresses that indicates the interrelatedness of surface and internal processes. The application of optical methods made it possible to discover a physical pattern of destruction. The results are expected to be used in the future to investigate other porous materials.     

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.     

A 3/D finite element approach for metal matrix composites based on micromechanical models

Based on analytical considerations by Dvorak and Bahel-El-Din, a 3/D finite element material law has been developed for the elastic-plastic analysis of unidirectional fiber-reinforced metal matrix composites. The material law described in this paper has been implemented in the finite element code ABAQUS via the user subroutine UMAT. A constitutive law is described under the assumption that the fibers are linear-elastic and the matrix is of a von Mises-type with a Prager-Ziegler kinematic hardening rule. The uniaxial effective stress-strain relationship of the matrix in the plastic range is approximated by a Ramberg-Osgood law, a linear hardening rule or a nonhardening rule. Initial yield surface of the matrix material and for the fiber reinforced composite are compared to show the effect of reinforcement. Implementation of this material law in a finite element program is shown. Furthermore, the efficiency of substepping schemes and stress corrections for the numerical integration of the elastic-plastic stress-strain relations for anisotropic materials are investigated. The results of uniaxial monotonic tests of a boron/aluminum composite are compared to some finite element analyses based on micromechanical considerations. Furthermore a complete 3/D analysis of a tensile test specimen made of a silicon-carbide/aluminum MMC and the analysis of an MMC inlet inserted in a homogenous material are shown.