An automated process for three-dimensional photoelastic analysis

The use of two monochromatic light sources to obtain two isochromatic patterns permits a fully automated shear-difference analysis of the stress distribution in a three-dimensional photoelastic model. A development is given of the logic necessary to process the data taken from an automated polariscope as well as the design details of the polariscope.     

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.     

Computer aided photoelasticity by an optimum phase stepping method

In this paper an automated photoelastic method based on the phase stepping technique is described. It provides full-field maps of the isoclinic parameter and the relative retardation. The technique is based on processing six images of a photoelastic specimen acquired using plane and circularly polarized light. The number of acquisitions and the type of polariscope used in this approach have been chosen with the aim at reducing the influence of quarter wave plate errors and obtaining raw photoelastic data in a periodic form suitable for easy applications of automatic unwrapping routines.     

Load and stress distribution in screw threads

The load distribution and the normalized stress distribution in the threads of an ISO metric nut and bolt were found by frozen-stress photoelastic analysis employing a fringe-multiplying polariscope in conjunction with a recording microdensitometer. Previous investigators assumed that these distributions were identical, whereas the present study shows that this is not the case. It has been further shown that deducing the load distribution from measurements of the nut deformation is unsatisfactory. The results of the reported method correlate closely with Sopwith's theoretical load distribution. Three recent finite-element analyses of nut-bolt systems have been compared indirectly to the experimental load distribution. That of Bretl and Cook was found to give the best comparison.     

Stresses in hollow hexagons under external pressure

A two-dimensional photoelastic study was made of the stresses produced in a regular hexagon with a central, circular hole when subjected to external pressure. Four sizes of the hole were tested, and three types of loading were used. This paper describes the pressure-loading fixtures and the procedure which was used to calibrate them. An experimental confirmation of the theoretical solution of Kawaguchi¹ is given, and typical stress patterns and boundary stress distributions are included.     

Stress field tomography based on 3D photoelasticity

A tomographic method for identification of stress fields based on 3D photoelasticity has been developed. A second order tensor field tomographic method based on the general inverse problem of 3D photoelasticity, previously developed by the authors, is found to be highly sensitive to errors in photoelastic observations. In this study a new tomographic method for stress field with fairly high robustness to errors in photoelastic observations has been developed by introducing both equilibrium condition and linear elasticity to the previously developed general tensor field tomographic method. This new stress field tomographic method expands unknown 3D stress distributions as a linear combination of independent set of basis functions and a new inverse problem is posed: identify the amplitudes of basis functions based on photoelastic observations. Just as the inverse problem of 3D photoelasticity, this newly posed inverse problem is also nonlinear and ill posed. Unlike conventional approaches to 3D photoelasticity, both these nonlinearity and ill-posedness are properly treated using a load incremental approach. Load incremental approach chops the nonlinear solution space into segments with unique solutions by conducting photoelastic observations at sufficiently small increments in external load. Validating both numerically and experimentally, it is shown that this new stress field tomographic method has sufficient robustness against errors in photoelastic observations and is applicable to experimental stress measurements.     

Computer-aided photoelastic analysis of orthogonal 3D textile composites: Part 1. Whole-field determination of isochromatics and isoclinics

Two correlative methods are developed for the computer-aided photoelastic analysis of orthogonal 3D textile composites comprising 6 mm×6 mm highly heterogeneous unit cells in-plane. The first method, presented in Part 1, is used for the whole-field determination of isochromatics and isoclinics; the second method, presented in Part 2, is applied for subsequent photoelastic stress analysis. Part 1 delineates precisely how one circular polariscope and two plane polariscope photoelastic images are implemented to extract the isochromatic parameterR and isoclinic parameter α using the digital image processing technique. The photoelastic experiments were performed with orthogonal 3D textile composite as well as aluminum plates containing a hole under the uniaxial tension loading. The obtained values ofR and α, for the case of the aluminum plate, are smoothly distributed over the field and show consistent agreement with those computed from finite element analysis (FEM). In the case of the composite plate, the global distribution ofR and α also agree well with FEM results employing the homogenized composite properties. However, bothR and α exhibit local variations according to the 3D fabric structure, and the varying amplitude of α is relatively larger than that ofR.     

Stresses in spheres with concentric spherical cavities under diametral compression by three-dimensional photoelasticity

This paper presents the experimental solution of the problem of a sphere with a concentric spherical cavity under diametral compression using the three-dimensional photoelastic method and calculations of the complete stress distributions along lines of interest using Golecki's analytical series solution. The experimental procedure, the stress distributions along different lines as well as the comparison with the theoretical results and a discussion of Golecki's solution are included.     

Thermal stresses in infinite circular cylinder subjected to rotation

The present investigation is concerned with the effect of rotation on an infinite circular cylinder subjected to certain boundary conditions.An analytical procedure for evaluation of thermal stresses,displacements,and temperature in rotating cylinder subjected to thermal load along the radius is presented.The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface is maintained at zero temperature are discussed.Such situation can arise due to melting of insulating material deposited on the surface cylinder.A solution and numerical results are obtained for the stress components,displacement components,and temperature.The results obtained from the present semi-analytical method are in good agreement with those obtained by using the previously developed methods.     

Separation of principal stresses by SOR technique over arbitrary boundaries

A computerized method is presented that generates a grid mesh within the digitized boundary of a photoelastic specimen as it appears in the single viewing through an overhead polariscope. The second-order partial differential equation for the first linear invariant of stress which satisfies the Laplace equation is solved from the boundary values for the digitized domain by the finite-difference method. Connectivity and the weighting functions that are required for the iterative solution of the systems of linear equations are generated from the digitized information along the boundary. Isochromatic values at each nodal point within the boundary are estimated from the digitized fringe patterns by a scanning technique, and the individual values of principal stresses are determined. To enhance convergence, the method of successive over relaxation is applied with an optimum accelerating factor determined in the course of the solution process. The accuracy and the speed of the solution are tested with three different examples. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

Optimization of hole shapes in circular cylindrical shells under axial tension

Hole shapes are optimized in circular cylindrical shells subjected to axial load considering only the predominantly large membrane stresses present around the holes. Two-dimensional photoelastic isochromatics obtained with a special-purpose polariscope are utilized for the optimization process. The process leads to a significant decrease in the membrane stress-concentration factor and a modest decrease in weight, thus yielding a considerable increase in strength-to-weight ratio. This paper presents results for certain typical ratios of hole diameter to shell diameter. Previous theoretical and experimental studies for the circular hole have also been verified     

An electromagnetic,plane stress-wave generator

This paper describes a unique device that has been developed for the transient loading of models along straight and curved boundaries and that operates by discharge of a high-energy, high-voltage capacitor bank. In its present configuration, this device can generate uniform pressures from 1500 psi (10 MPa) to pressures that approach 100,000 psi (690 MPa) and that rise from zero to maximum pressure in 2 μs and decay to approximately zero in another 2 μs. The transient stress-wave patterns in photoelastic models loaded with this device have been recorded by a dynamic polariscope. The dynamic polariscope presently in use is identical to a static polariscope except that the light source is of a short enough duration (½ μs) to photographically stop the movement of the photoelastic-fringe patterns caused by the stress wave. With the stress-wave generator and the dynamic polariscope, transient photoelastic patterns have been recorded in a number of models. These patterns indicate that the scatter from duplicate shots performed with this technique is on the order of 3 percent. This represents considerable improvement over the 15-percent scatter normally experienced with sheet-explosive loading techniques. This improvement and the rapid turnaround between shots (approximately 5 min) are distinct advantages this system has over other methods of dynamic loading.     

Another method to separate principal strains in photoelastic coatings

It is shown that the combination of a prism and a reflection polariscope provided with a Babinet-Soleil compensator offers a simple practical solution to the problem of separation of the principal strains in photoelastic coatings.     

用动态光弹性法研究炮身膛线的脱落问题

本文利用动态光弹性法研究了炮膛膛线脱落的机理。用包含五条膛线的部分炮筒横截面或扇形平面模型,在六种不同的载荷状态下进行了实验。得到了不同载荷状态下,不同瞬时的等差线条纹图的系列照片,以及膛线根部不同瞬时的应力分布曲线。结果表明:当一条或相邻数条膛线顶端受到足够大的均布冲击载荷时,将在承载膛线两侧根部的应力极值点出现膛线脱落的起裂点,而形成八字形脱落;而对非均布的其它几种冲击载荷,膛线都不会出现八字形脱落。     

用光弹性法测定复合应力强度因子

工程结构裂纹尖端应力强度因子(SIF)由于形状、荷载的复杂性及边界条件的不确定性,难以用解析法得到,数值计算也有困难,而光弹性法弥补了上述方法的不足。本文用环氧树脂制作圆轴模型,采用机加工的方法制作圆轴模型裂纹,然后将加载模型进行应力冻结,通过光弹性实验研究分析了圆轴裂纹尖端应力分布。由于带环形裂纹的圆轴在弯扭组合变形时,离中性轴最远的裂纹尖端处于复合裂纹状态,而三维光弹性应力冻结法是测定复杂三维问题复合裂纹的有效方法。本文用双参数法测定I型应力强度因子,用切片逐次削去法测定Ⅲ型应力强度因子,实验误差较小。     

The effect of out-of-plane restraint on plane-stress solutions near straight boundaries

The existence of out-of-plane displacement restraint where thin photoelastic plates are bonded to relaively rigid boundaries or inclusions will induce transverse stress components whose presence can cause the in-plane stresses to deviate significantly from the plane-stress solution. The extended generalized planestress formulation, which was developed in a previous paper to study the effect of out-of-plane restraint on the through-the-thickness averages of the in-plane stresses and displacements in thin plates, is applied here to obtain correction factors by which the photoelastically determined in-plane stress components at a straight restrained boundary can be multiplied to recover the desired twodimensional solution. Cases of mechanical and thermal loadings which vary sinusoidally in the direction parallel to the restrained boundary are treated. The stress-field alterations due to out-of-lane restraint are shown to depend strongly on Poisson's ratiov and the ratioL/H of the half-wavelength of the load variation to the plate thickness, and can be minimized by choosing a photoelastic material with the smallest values ofv andH possible. The simple asymptotic form of the stress-field alterations for large values ofL/H has enabled us to prescribe simple correction factors in this range. Finally, it is observed that, although the normal stress component which is parallel to the restrained boundary is altered to a greater degree than are the other in-plane stress components, the effect on this stress component penetrates into the plate a distance of only about one plate thickness, whereas the effect on the other components penetrates a distance of approximately one half-wavelength of the load variation.     

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.     

Stress waves in pyramids by photoelasticity

The propagation of stress waves in pyramids was studied photoelastically with the application of a laser-photomultiplier tube system and an internal polariscope for recording moving fringes. Dispersion and attenuation of stress waves were considered in a straight bar, a 5-deg pyramid, and a 20-deg pyramid made of Hysol 4290 epoxy plastic. In the straight bar and 5-deg pyramid, longitudinal waves propagate without any dispersion even though the waves attenuate as they progress down the models; in the 20-deg pyramid, however, the dispersion of the stress waves is quite significant. The distributions of the axial and radial stresses and the photoelastic fringe patterns obtained on the 20-deg pyramid show that the stress wave front is spherical with the maximum stress along the central axis of the pyramid. A one-dimensional theory of wave propagation without correction factors in a small-angle infinite cone compares well with the experimental results.     

Stress analysis of an orthotropic material under diametral compression

The diametral compression test is commonly used to determine the tensile strength of brittle materials. For isotropic materials a simple relation based on specimen geometry and the applied load at failure is used to calculate the tensile strength. Previous to this work the effect of material orthotropy and material orientation on the specimen stress state had not been completely determined. In this study, both isotropic and orthotropic specimens were analyzed using a finite element analysis and experimentally verified by strain gage and photoelastic measurements. Further, this work investigated the effect of the applied load area on the specimen stress state. Results of this work show that there is a significant difference between the theoretical calculations based on the assumption of material isotropy when compared to an orthotropic material. This difference can be as much as 45 percent depending on the degree of orthotropy and the orientation. It was also determined that the applied load area and material orientation significantly influence the specimen stress state. An applied load area of 8 percent of the circumference was found to reduce the stresses in the applied load region.     

光弹法实测正交异性双材料界面裂纹断裂参数

采用光弹贴片法实测正交异性双材料界面裂纹尖端区域的应力应变场, 进而求出界面裂纹的断裂力学参量. 将正交异性双材料板加工成拉伸试件,在聚碳酸酯贴片 的单侧表面镀金属铝膜,以提高贴片的反射效率. 沿贴片后的双材料界面预制裂缝,逐渐加 大载荷,得到一系列清晰的等差线条纹图. 利用正交异性双材料界面裂纹尖端应力分量表达 式计算出应力强度因子. 实验表明,光弹贴片法可有效地分析正交异性双材料界面裂纹问题.