Three-dimensional photoelastic analysis of a fiber-reinforced composite model

A three-dimensional photoelastic analysis using the “stress-freezing” technique was conducted to determine the stress distributions in the matrix of a unidirectionally fiber-reinforced composite model subjected to matrix shrinkage and normal transverse loading. The model, consisting of a square array of polycarbonate rods in an epoxy matrix, simulated a boron-filament-reinforced plastic composite with a fiber-volume fraction of 0.50 at the critical temperature of the matrix epoxy. The effects of matrix shrinkage were separated from those of external loading by analyzing two identical models, one loaded and the other unloaded. The Lamé-Maxwell equations of equilibrium were used to separate stresses along axes of symmetry on interior transverse slices. Axial stress components were obtained by subslicing. Results are presented in dimensionless form by dividing the stresses by the average stress through the section. A comparison with theoretical results for a boron-epoxy composite shows excellent agreement, although Poisson's ratio of the model matrix is appreciably different from that of the prototype (0.5 compared to 0.35). One significant result was that the maximum stress occurs in the middle of the matrix section between fibers which is at variance with the theoretical prediction of maximum stress at the interface. Stress-concentration factors vary from 1.80 at the interface to 2.0 at the midpoint of the matrix section between fibers.     

Constant-acceleration stresses in a composite body

This paper is a contribution to the experimental stress analysis of composite structures subjected to gravitational forces. It is proved, generally, that the immersion analogy can be used to analyze these stresses in composite bodies provided all the materials of such bodies have the same weight per unit volume. Applications are described in two-dimensional problems immersing urethane-rubber models bonded to epoxy shells in a thallium-formate solution. Photoelasticity is used to determine stresses. The method increases the response obtained and will have application in the solution of problems where constant-acceleration stresses are important, as in dams and solid-propellant rocket grains.     

Influence of concentrated lateral loads on the elastic stability of cylinders in bending

The character of the instability and the degradation of the moment-carrying capacity are found by Mylar model experiments for cylinders in bending when subjected to concentrated lateral loads. Lateral loads can seriously degrade the moment capability of cylinders. Critical combinations of moment and lateral load cause two distinct modes of failure—collapse and snapping. Collapse modes exhibit buckles which cover the compression half of the cylinder and are critical for large values of moment and small values of lateral load. Snapping modes of failure involve a single dimple and exist for smaller values of moment and larger values of lateral load.     

Epon 828 epoxy: A new photoelastic-model material

The photoelastic properties of Epon 828 are discussed. The epoxy is evaluated experimentally for its time-edge effect, optical creep, stress-optic relations, and mechanical properties at room and elevated temperatures. Epon 828 is extremely clear, has good transparency, and can be use for photoelastic stress analysis at room and elevated temperatures. It has a low-fringe constant at room temperature as well as at elevated temperatures coupled with a high critical modulus of elasticity. Epon 828 can easily be cast stress-free and has relatively small amounts of optical and mechanical creep. The machining characteristics of Epon 828 are excellent and it cements easily with itself and other epoxy materials.     

Experimental analysis of slow viscous flow using photoviscosity and bubbles

Photoelasticity in solids is a well-developed technique for stress and strain analysis. Less progress has been made in applying a similar effect, photoviscosity, to flow analysis. This paper has three objects: (1) to simplify photoviscous methods; (2) to compare velocity profiles obtained from photoviscosity with those obtained by the double-exposure bubble technique; (3) to determine the principal strain rates and the maximum shear stress from photoviscotity. The problem of slow viscous flow about a cylindrical obstacle in a rectangular channel was selected for the comparison. The fluid was a suspension of milling yellow dye in water. Strain rates and stresses averaged over the path of ligh can be obtained easily using photoviscosity. The bubble technique is shown to be a very powerful tool that permits the determination of the velocity field in three-dimensional problems.     

Investigation of the Dynamic Response of Swirling Flows Based on LES and Experiments

The dynamic response of a swirling flow undergoing vortex breakdown is investigated via Large Eddy Simulation (LES) and experiments in a water flow facility. The investigation is carried out following previous work on the link between thermoacoustic combustion instabilities and coherent structures in lean premixed gas turbine combustors. The velocity field transfer function is obtained in LES from the Unit Impulse Response determined via application of a low intensity broadband noise perturbation of the inflow mass flow rate and the Wiener-Hopf filtering method. In the experiments, harmonic fluctuations in the water flow rate through the swirler are generated via a piston mounted on the side wall of the test facility and activated with a low frequency linear motor. The velocity field transfer function is then obtained via phase averaging applied to Particle Image Velocimetry snapshots which are collected at prescribed values of the harmonic phase. The analysis, which is carried out in terms of coherent structures identified via Proper Orthogonal Decomposition, gives numerical transfer functions with amplitude and phase consistent with the experimental ones.     

The size of plastic zones in cracked plates made of polycarbonate

The influence of the thickness of a cracked plate, made of Polycarbonate of Bisphenol A, on the plastic zones developed at the crack tip was studied. The three-dimensional character of yielding at the vicinity of the crack tip is revealed. The study of the thickness variation in the plastic zones is made by applying the shadow-moiré method. It has been derived that the thickness variation in the plastic zones is discontinuous with successive dimples of different thickness. The influence of the overall thickness of the specimen on the size and length of the plastic zone was studied for different crack lengths. Irwin's theory for small yielding, as well as the simple and modified Dugdale-Barenblatt models, were applied for the study of plastic zones. By comparing the plastic-zone lengths in relation to their shape, with those given by the above theories, it may be concluded that, for small loads where the applied stress σ is not exceeding 0.40 of the yield stress \(\sigma _o \) in tension and small values of the ratio of crack lengtha to plate thicknesst, (a/t<4) a state of plane strain dominates at the vicinity of the crack tip, while, by increasing the load and ratioa/t, the plastic zones approach in shape and size those given by the modified Dugdale-Barenblatt model.     

Strain-induced low-frequency relaxation in colloidal DGEBA/SiO2 suspensions

Diglycidyl ether of bisphenol A (DGEBA) is widely exploited as an epoxy resin in adhesives and coatings. In this paper, it is used as an oligomer matrix for silica-filled nanocomposites. Rheological measurements show that the pure matrix obeys power-law relaxation dynamics in the vicinity of the dynamic glass transition of this low-molecular-weight glass former. In the filled systems, a low-frequency relaxation appears additionally to the structural α-process of the matrix. Considering the nanocomposites as Newtonian hard-sphere suspensions at low angular frequencies (or high temperatures), the modified terminal regime behavior of the matrix can be linked to strain-induced perturbations of the isotropic filler distributions. While in the low-frequency regime hydrodynamic stresses relax instantaneously, the Brownian stress relaxation is viscoelastic and can be evidenced by dynamic rheological measurements. At higher angular frequencies, the α-process of the matrix superimposes on the Brownian stress relaxation. In particular, we were able to depict the low-frequency anomaly for concentrated, semi-dilute, and even for dilute suspensions.     

A composite three-dimensional photoelastic method

Care must be taken in preparation and testing of three-dimensional composite photoelastic models. Some problems encountered in modeling the prototype and during model testing are: model-material failure, loss of fringe pattern in slicing, inherent shrinkage response in freezing, inadequate bonding between materials, and modular ratio difficulties. The selection of the correct plastic can eliminate the first four problems, but the correct modular ratio between the matrix and the insert has to be obtained. This investigation illustrated the behavior of commercially manufactured plastics as inserts, with a matrix material of Epon 828 epoxy. The effective moduli of elasticity of these plastics are reported for pure tension and for flexure. Since the manufactured plastics produced varying results, the use of Epon 828 epoxy as an insert was investigated. The inserts were cast in tygon tubing and their curing cycle was altered from that used for the matrix material to produce a different effective modulus of elasticity. The Epon 828 inserts gave excellent results in the beams. The use of the same material for matrix and insert eliminates many of the problems associated with composite three-dimensional photoelasticity.     

Mechanism of transverse structure formation in supersonic flow past a body

Direct numerical simulation within the framework of the Navier-Stokes equations is applied to study the mechanism of the generation of transverse structures (streamwise vortices) in the problem of supersonic M = 6 flow over a flat plate, when a shock wave is incident on it. The vortices formed at the lateral edges of the plate are shown to be the sources of streamwise streaky structures in the zone of separation of the boundary layer from the plate. Their interaction with the Kelvin-Helmholtz vortices in the region of incidence of the shock on the plate leads to the formation of mushroom-shaped structures (streamwise vortices) similar with the azimuthal Λ-structures in subsonic jets. The plate width effect on the formation and turbulization of the mushroom-shaped structures is considered.     

Dynamic geometrically nonlinear analysis of transversely compressible sandwich plates

In order to construct a plate theory for a thick transversely compressible sandwich plate with composite laminated face sheets, the authors make simplifying assumptions regarding distribution of transverse strain components in the thickness direction. The in-plane stresses and σ_yy (Fig. 1) are computed from the constitutive equations, and the improved values of transverse stress components and σ_zz need to be computed by integration of pointwise equations of motion in a post-process stage of the finite element analysis. The improved values of the transverse strains can also be computed in the post-process stage by substituting the improved transverse stresses into the constitutive relations. A problem of cylindrical bending of a simply supported plate under a uniform load on the upper surface is considered, and comparison is made between the displacements, the in-plane stress and the improved transverse stresses (obtained by integration of the pointwise equations of motion), computed from the plate theory, with the corresponding values of exact elasticity solutions. In this comparison, a good agreement of both solutions is achieved. In the finite element analysis of sandwich plates in cylindrical bending with small thickness-to-length ratios, the shear locking phenomenon does not occur. The model of a sandwich plate in cylindrical bending, presented in this paper, has a wider range of applicability than the models presented in literature so far: it can be applied to the sandwich plates with a wide range of ratios of thickness to the in-plane dimensions, with both thin and thick face sheets (as compared to the thickness of the core) and to the sandwich plates with both transversely rigid and transversely compressible face sheets and cores.     

Stress distributions in a semi-infinite plate due to a pin determined by interferometric method

The stress distributions in a semi-infinite plate due to a loaded pin of the same material as the plate are systematically investigated by an interferometric method which has been developed by the authors. For the experiments, a finite plate of diallylphthalate with a circular hole is used. It is supported at one side and loaded in the direction normal to the opposing straight edge by a pin which just fits the hole. The ratio of the distancee between the hole center and the straight edge to the diameterd of the hole is varied in steps from 4.0 to 1.0. At each step, the distributions of principal stresses σ₁ and σ₂ along the hole edge, line of symmetry and straight edge, which have not been fully investigated especially whene/d is small, are obtained separately from the isopachic and isochromatic fringes of the interfero-stress patterns. The relations between the maximum values of these stresses and the shape factore/d are determined.     

The water rise in front of a model planing hull

It is known that the water “splashes-up” or rises above the undisturbed surface immediately in front of a planing surface. This rise is greatest in front of a flat planing plate and a number of attempts have been made to reduce the experimental measurements of this phenomenon to some kind of order. Since it was first independently proposed by both Schnitzer and Smiley in 1952, all attempts to correlate the flat plate splash-up have started with the assumption that splash is only a function of the immersed length of the plate and is independent of trim angle at least below about 20°. In part, this was because the three early studies which compared this hypothesis with experimental data omitted those portions of the data which did not support the hypothesis. The present paper concludes that this forty year old hypothesis is fallacious and that the water rise in front of any prismatic planing surface is best approximated by $$\frac{d}{{\sqrt {bl} }} = k\sin ^2 {\mathbf{\tau }}$$ whered is the vertical water rise at the water/keel intersection;b is the beam;l is the submerged length of the keel;τ is the trim angle;k: is a constant determined from experiment, approximated by,k = 2e ^?2.5β , whereβ is the deadrise angle in radians. It might be thought that this is a slight contribution, of little practical import, but for one thing. Starting in the 1950's most towing tank experimenters in the United States abandoned the difficult measurement of model draft and obtained only the “actually wetted length” from underwater photographs. But theoretical planing force calculations require a knowledge of the relationship between a hull and the undisturbed water plane. Thus if modern experimental data is to be compared with theory, it is necessary to estimate what the undefined splash-up or water rise was during each experiment, in order to estimate the model's true position in space. The paper concludes by criticizing the format of some modern reports of experiments with model planing hulls and suggests that, in addition to the usual graphical presentations, measured data should always be reported numerically. Also, that when relevant data is omitted from a plot, the facts of such omission should be clearly stated.     

The gamma-ray-irradiation method applied to three-dimensional thermal photoelasticity

It has recently been shown that a gamma-ray irradiation fixes the birefringence in photoelastic models of Araldite B. The method has hitherto only been used to fix the birefringence in specimens subjected to constant forces. This work applies the irradiation method to determine the thermal stresses in a thick-walled cylinder with a temperature gradient along the radius. The model behaved in the following way during the experiment. The material relaxed when the temperature gradient was applied, and the model was irradiated when it was stress free. Real stresses, which were equal to the thermal stresses but with opposite sign, appeared when the temperature gradient was removed. As the problem is mathematically two-dimensional, it is possible to determine the birefringence by means of the slicing technique. Good agreement was obtained between the stress determined experimentally and those calculated analytically. The irradiation sensitivity of a number of materials has been determined, and some new materials have been used that are superior in two important ways to that used earlier in that they require a much lower irradiation dose and their mechanical properties are considerably better.     

Photoelastic optimization of the profiles of Wildhaber-Novikov gears

Wildhaber-Novikov gears having circular flanks hold out a very promising future in the field of gearing for power transmission in very heavily loaded machineries. In order to optimize the profile parameters of these gears, a photoelastic investigation was carried out. Models of Wildhaber-Novikov gears made of photoelastic material, Araldite-D, were used in the investigation. Included were the models with various profile radii and fillet radii at different pressure angles. The flank and bending stresses of these gears were determined in each case and were compared with those of involute gears. From this investigation, it was concluded that the load-carrying capacity of circular-arc gears is 3.5 times that of involute gears. It was found that with profile radius up to 1.5 module, the bending stresses of these gears are lower than those of corresponding involute gears, under identical conditions of loading. It was observed that high pressure angles, when used for Wildhaber-Novikov gears having comparatively smaller profile radii, produce high flank stresses. Gears with larger profile radii, at smaller pressure angles were seen to have a high value for the ratio of flank stress to the bending stress. On the other hand, gears with smaller profile radii, at higher pressure angles, were observed to have a smaller value for this ratio of stresses.     

Natural convective heat transfer in water enclosed between pairs of differentially heated vertical plates

This paper presents the results of an experimental study of buoyancy-driven convective heat transfer between three parallel vertical plates, symmetrically spaced with water as the intervening medium. The centre plate was electrically heated, while the other side plates were water-cooled forming two successive parallel vertical channels of dimensions 20 cm × 3.5 cm × 35 cm (length W, gap L, height H) each. Top, bottom and sides of the channels were open to water in the chamber which is the novel aspect of this study. Plate surface temperature and bath temperature at different levels of height from the bottom of channel were measured by K-type thermocouples. Experimental data have been correlated as under:

Miniature piezoresistive transducers for transient soft-body contact-stress problems

Assessment of contact-stress distributions between irregular bodies of high compliance has often proven difficult because of the lack of suitable sensing elements. Miniature transducers using piezoresistive elastomers appear to provide a means for making such measurements. A protocol for fabrication of the transducers is presented. Bench tests of the load/response characteristics reveal that the devices are capable of measuring static contact stresses up to at least 5.0 MN/m², but that the resistance changes are a nonlinear function of both load magnitude and current throughput. The dynamic range depends strongly upon mechanical preconditioning. For 10⁴ preloading cycles, the transducers can reproduce loading signals at frequencies up to at least 15 Hz. The transducers exhibit high output (>90-percent resistance changes over the range of load sensitivity) but present some difficult problems in the area of quality control.     

Effect of Gas Diffusion Layer Properties on Breakthrough Time and Pressure

The gas diffusion layer (GDL) plays an important role in the removal of product water from the catalyst layer to the flow plate in a fuel cell. Numerous studies have reported water management, especially in the GDL, as the limiting factor hindering convective and diffusive transport of reactants which results in lowering power density. In this paper, an experimental technique is presented to study the GDL water transport properties associated with the breakthrough conditions which are critical to overall water management. Fluorescence microscopy technique is used to measure the pressure and time required for water to penetrate and break through the surface of the GDL. The results obtained for GDLs produced by different manufacturers confirm that the breakthrough time and pressure are larger for PTFE treated hydrophobic GDLs. The results are analyzed in terms of the contact angle, thickness, and SEM images to see the effects of different structural properties. The changes in morphology due to compression are also presented. In addition, the changes in breakthrough conditions when samples are reused are presented. The results provide basic insights into the water transport properties of the GDL, leading to the design of new materials with enhanced water management.     

Analysis of scattered-light methods in photoelasticity

The use of scattered light for nondestructive analysis of general photoelastic models is becoming quite common and, during the last few years, several methods have appeared in the literature to determine the directions of the secondary principal stresses and their differences at any general point. Among the methods suggested, some are mentioned as “exact” and some “approximate”. Even the exact methods have limitations in their applicability for a generally stressed model. The present discussion attempts to bring out the inaccuracies involved in the various exact methods. Also, a few modifications to improve the accuracy and a new method called the Mini-max method are proposed. References 1, 2 and 3 give the general methods and the derivations of equations used in the present analysis.     

A simple testing technique for fracture under biaxial stresses

Evidence is accumulating to suggest that the fracture toughness of and cyclic crack-propagation rates in a material may be affected by stresses acting parallel to the crack plane. This effect contradicts the justifiable assumption, implicit in fracture-mechanics theory, that only loads causing a stress singularity at the tip of a crack can affect its behavior. More extensive investigation of this important problem involves the development of special testing equipment and specimens. This article offers a simple design for such a system, which has proved in practice to be highly reliable and of adequate accuracy. Preliminary tests on polymethylmethacrylate (PMMA) under biaxial fatigue and ramp loading are described, to demonstrate the technique itself and the phenomena under investigation. The results suggest that, for this material at least, the effects of transverse stresses are indeed slight.