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.     

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.     

Photoelastic stress analysis of a V-shaped die for plastic work

The stress state in the V-shaped die for plastic compression was investigated by using a photoelastic stress analysis in which an Araldite in a glassy elastic state and a softened celluloid were used as model materials for the die and work specimen, respectively. It was found that the direction of the frictional shear stress is reversed at a certain point on the die surface. Because the frictional shear stress of the die mainly depends on the flow speed of the work material, the popular assumption that the coefficient of friction is a constant over the die surface such as in the case of Coulomb friction appears unrealistic.     

The effect of a coupling agent on the viscoelastic properties and internal stresses in high density polyethylene filled with glass spheres

It is shown that covalent bonding between high density polyethylene (HDPE) and glass spheres can have a significant influence on the stress relaxation behaviour and the creep properties of the corresponding composites at room temperature. The bonding is obtained by reacting the glass spheres with an azide functional alkoxysilane which is capable of bonding to the HDPE-chain. The internal stress, evaluated from relaxation experiments, increased markedly as a result of this treatment, and it is suggested that the internal stress level reflects the properties of the interphase region between the filler and the bulk matrix and its effect on the viscoelastic properties.     

Hopf bifurcation analysis of asymmetrical rotating shafts

The Hopf and double Hopf bifurcations analysis of asymmetrical rotating shafts with stretching nonlinearity are investigated. The shaft is simply supported and is composed of viscoelastic material. The rotary inertia and gyroscopic effect are considered, but, shear deformation is neglected. To consider the viscoelastic behavior of the shaft, the Kelvin–Voigt model is used. Hopf bifurcations occur due to instability caused by internal damping. To analyze the dynamics of the system in the vicinity of Hopf bifurcations, the center manifold theory is utilized. The standard normal forms of Hopf bifurcations for symmetrical and asymmetrical shafts are obtained. It is shown that the symmetrical shafts have double zero eigenvalues in the absence of external damping, but asymmetrical shafts do not have. The asymmetrical shaft in the absence of external damping has a saddle point, therefore the system is unstable. Also, for symmetrical and asymmetrical shafts, in the presence of external damping at the critical speeds, supercritical Hopf bifurcations occur. The amplitude of periodic solution due to supercritical Hopf bifurcations for symmetrical and asymmetrical shafts for the higher modes would be different, due to shaft asymmetry. Consequently, the effect of shaft asymmetry in the higher modes is considerable. Also, the amplitude of periodic solutions for symmetrical shafts with rotary inertia effect is higher than those of without one. In addition, the dynamic behavior of the system in the vicinity of double Hopf bifurcation is investigated. It is seen that in this case depending on the damping and rotational speed, the sink, source, or saddle equilibrium points occur in the system.     

Determination of stress intensity factors in three-dimensional problems of fracture mechanics

Dependences of displacements of the surface of a notch on the corresponding stress intensity factors were obtained for axisymmetric bodies with internal and external notches under different deformations (tensile, shear, bending, and torsion). An algorithm is proposed to determine the stress intensity factors of three types (opening mode, longitudinal shear, and transverse shear) from displacements of the notch surface near its tip. The effectiveness of the algorithm is shown, as an example, for numerical analysis of various three-dimensional problems of fracture mechanics.     

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.     

A photoviscoelastic analysis of time-dependent stresses in a polyphase system

The method of photoviscoelastic stress analysis is used to predict time-dependent stress redistributions in a polyphase-material system having a viscoelastic binder and subjected to applied exteernal-loading conditions. The polyphase-material model studied is composed of a photoviscoelastic matrix material and contains rigid inclusions and voids, thus simulating a threephase composite system. In order to perform the study, a photoviscoelastic model material is developed. An epoxy-resin system consisting primarily of Shell Epon 828 and Epon 871, optimized to display the properties desirable for such application, is utilized. The time-dependent stess distributions obtained by the photoviscoelastic analysis are compared with results obtained by applying the “correspondence rule” to a finite-element solution for the elastic stress field of a mathematical model of the three-phase material system. The comparison of results indicates that the technique of photoviscoelastic stress analysis is extremely applicable to complex models such as the one studied. The feasibility of this application to more complex polyphase models with varying loading conditions is indicated.     

Stability of oval cylindrical shells

Elastic buckling under aial compression of finite, oval cylindrical shells with clamped boundaries was investigated experimentally. The determination of the buckling strength was made on a series of oval shells made of Mylar A. The test results indicated that the discrepancy between theoretical and experimental initial buckling loads for the ovals is similar to that of the circular cylindrical shells. However, in contrast to the circular case, a collapse load significantly exceeding the initial buckling load is observed in the case of ovals with moderate-to-large eccentricity.     

Strain gages in cryogenic environment

The increasing use of cryogenics in all fields of endeavor necessitates the use of strain gages for stress analysis of structures under extreme temperatures. This has been a continuing program at the McDonnell Douglas Astronautics Co.'s Strain Gage Engineering Laboratory (Huntington Beach facility). Many characteristics of strain gages were investigated, and a majority of the commercial strain gage types were evaluated. Tests results are presented, as well as composite curves, showing the comparison between various types of strain gages.     

Deformation of melts of mixtures of incompatible polymers in a uniform shear field and the process of their fibrillation

Fibril formation in mixtures of incompatible polymers, in this case polyethylene and polystyrene, has been studied with their melt being deformed in a uniform shear field. It has been found that when polyethylene is present in a smaller amount, it may form very long fibrils 5 to 8 μm in diameter in the deformed mixture. The formation of such fibrils is determined by the relationship between the viscosity ratio of the mixture components and shear stress. Also, just as in the case of a nonuniform shear field in a flow through a duct, fibril formation in melts of mixtures of incompatible polymers in a uniform shear field takes place upon reaching a certain shear stress. The lower the ratio between the viscosities of the fibril-forming polymer and the other component, the lower this shear stress.     

An analytical approach to determine conventional S−N curves from accelerated-fatigue data

This paper describes an analytical method of obtaining conventional S?N curves from the accelerated-fatigue tests, namely the generalized Prot accelerated-fatigue-testing technique in which the stress amplitude increases linearly with respect to cycle. Miner's cumulative-damage theory was applied and an expression for the sum of a series of natural numbers raised to a certain nonintegral power was developed to achieve this. The agreement between analytical prediction and experimental verification is quite reasonable.     

An experimental study of the effects of prestrain on the propagation of small disturbances in neoprene filaments

A small disturbance was caused to propagate along a long, slender, prestrained Neoprene filament. The particle velocity of the pulse was measured at two stations along the length of the filament by means of electromagnetic transducers which operate on the Faraday principle. Particle velocity vs. time data were obtained from oscilloscope photographs of the transducer outputs for each level of prestrain from 0 percent up to 400 percent engineering strain. The two particle-velocity records for each level of prestrain were subjected to linear viscoelastic analysis which employed the use of numerical Fourier transforms of the particle-velocity records. Computer programs were written which allowed computation of the numerical transforms and from them the computation of the phase velocity and attenuation coefficients of the material over the narrow frequency bandwidth of the Fourier spectra of the particlevelocity pulses. Data analysis revealed that, at a given frequency, the phase velocity increases significantly and that the attenuation coefficient decreases significantly with an increase in prestrain level over the range of prestrains of the tests. These material properties, that of a decreasing attenuation and an increasing phase velocity with increasing prestrain, are suggestive of the open possibility of the ability of the material to develop and support a shock wave for a large-amplitude disturbance.     

Propagation of a stress pulse in a viscoelastic rod

Experimental work is reported on the propagation of a stress pulse in a viscoelastic waveguide. The data obtained are compared with results of analysis using one-dimensional wave-propagation theory. The waveguide used in this work is a low-density polyethylene rod 1/2 in. in diameter and 30-in. long. Stress input to the waveguide and the resulting particle velocity at three stations are measured using a crystal stress transducer, two Faraday-principle velocity transducers and a capacitor transducer. The experiment is described mathematically as a boundary-value problem formulated in terms of the one-dimensional equation of motion, the strain-displacement relationship, a hereditary constitutive equation and the stress-boundary condition. Fourier transform and inversion yield an integral expression for velocity which is evaluated numerically at three stations using measured values for the stress-boundary condition, material attenuation and phase velocity. The analytical results compare favorably with the experimental data. The one-dimensional theory appears adequate to describe pulse propagation of this type. The attenuation and phase velocity used here are found to be a linear function and a logarithmic increasing function of frequency respectively.     

The effect of specimen geometry and lateral constraint on the isothermal compressibility of low-strength polymeric materials

Significant errors can be present in the isothermal pressure-volume relationships that have been obtained from laterally constrained compression tests of low-strength polymeric materials. Laterally constrained compression tests on PMMA (polymethylmethacrylate) have shown these errors to result from (1) stress gradients in the specimen caused by constraint friction and (2) unknown volume changes resulting from extrusion of the test specimen. Test-specimen geometry was an important parameter.     

Behavior of surface flaws in reactor pressure vessels under thermal-shock loading conditions

A pressurized-water, nuclear-reactor pressure vessel can be subjected to a severe thermal shock in the event of a loss-of-coolant accident (LOCA). If at the time of the LOCA there is a crack-like defect on the inner surface of the vessel, the crack may propagate as a result of the thermal shock. This paper discusses the conditions necessary for crack propagation during a LOCA, the detailed behavior of the cracks under these specific conditions, and an experimental program designed to determine the validity of the method of analysis (linear-elastic fracture mechanics) used to predict the behavior of flaws under severe thermal-shock loading conditions. A detailed fracture-mechanics analysis of the LOCA thermal shock was performed to help establish the scope of the experimental program. The results of this analysis indicate that present-generation and future PWR vessels will not experience excessive crack propagation. This is also true of earlier PWR vessels, which contain rather high concentrations of copper and, thus, are more susceptible to radiation damage, provided a phenomenon referred to as warm prestressing is effective. Eventually, the experimental program will include investigations of all the major fracture-mechanics phenomena predicted to occur under adverse LOCA-ECC conditions. Two of the experiments conducted thus far were designed for the study of long axial flaws that would penetrate no more than 20 percent of the wall of thick-wall steel test cylinders (533-mm OD×146-mm wall×914-mm length). During one of these experiments, no fast fracture took place, as predicted using LEFM. In the other experiment crack initiation and arrest were expected and took place, with a total penetration of ～16 percent. The agreement between experimental results and the LEFM analysis was very good, indicating that the LEFM analysis is valid at least for shallow flaws in thick-wall steel cylinders subjected to severe thermal shock.     

Photoelastometric recording of stress waves

A very sensitive, fast-responding photomultiplier tube and laser light source were used to record stress-optic data associated with a moving stress wave. By using a “gray-field” (which is halfway between a dark and light field) polariscope, optical-electrical recordings were obtained which were linearly proportional to strain. A discriminatory record results which exhibits a higher signal-to-noise ratio than semiconductor strain gages. Gage length can be varied from 0.005 in. upwards.     

The moiré method for measuring large-plane nonhomogeneous deformations

Moiré-fringe equations have been developed for directly determining the components of Green's and Cauchy's deformation tensors from measurements of fringe pitch and angle. The equations, which were previously verified for large-plane homogeneous deformations, are used to determine the deformation-tensor components for nonhomogeneous strain fields. The results are compared to theoretical values. Specifically, the deformations investigated are pure bending of a rectangular block, and extension of a tapered plane specimen.     

An electromagnetic shear-stress gage for large-amplitude shear waves

In many materials, especially plastics, ceramics and rocks, large-amplitude shear-wave propagation studies could provide valuable information for the development of constitutive equations. A newly developed electromagnetic-gage configuration provides an output voltage which is directly related to the dynamic shear stress in the material. The electromagnetic shear-stress gage has been used to make direct measurements of shear-wave stresses in PMMA and Solenhofen limestone. Large-amplitude shear waves were obtained with a new plate-impact technique which generates shear waves by a controlled-reflection process. The configuration of the stress gage permits it to be used simultaneously with more conventional electromagnetic velocity gages, thus providing both types of data in one experiment.     

The nonlinear vibrations of functionally graded cylindrical shells surrounded by an elastic foundation

This paper reports the result of an investigation on the nonlinear vibrations of functionally graded cylindrical shell surrounded by an elastic foundation, based on Hamilton’s principle, von Kármán nonlinear theory, and the first-order shear deformation theory. Material properties are assumed to be temperature dependent. The surrounding elastic medium is modeled as Winkler foundation model, Pasternak foundation model, and nonlinear foundation model. Galerkin’s method is utilized to convert the governing partial differential equations to nonlinear ordinary differential equations with quadratic and cubic nonlinearities. Considering the primary resonance case, the method of multiple scales is used to study the frequency response of nonlinear vibrations and the softening/hardening behavior. Parametric effects on the nonlinear vibrations are investigated.