Experimental analysis of rolling contact stresses in a viscoelastic strip

An experimental approach to two-dimensional, viscoelastic, steadily moving rolling contact is described. The photoviscoelastic technique is employed for the analysis of rolling contact stresses between a viscoelastic plate and a rigid rolling cylinder in which the principal axes of stress, strain and birefringence are not coincident with each other. Using an elliptically polarized white light, the distribution of isochromatic fringe order and the principal axes of birefringence at an instant are determined from a single photoviscoelastic image. The time variations of the differences of the principal stresses and strains, as well as their directions, are obtained by use of the optical constitutive equations of photoviscoelasticity. The experimental results involving the time variation of the stresses around the contact surface and their distributions are analyzed.     

Photoviscoelastic stress analysis of a plate with a central hole

An epoxy resin containing excessive plasticizer was developed and characterized. The material, which deforms viscously at room temperature, has optical properties that depend on stress and strain. A tensile specimen was prepared from the epoxy resin so that the mechanical and optical properties of the epoxy resin could be characterized. The elastic and plastic behavior was determined at 37°C using tensile stresses between 4 and 26 MPa. The birefringence was also recorded as a function of time and stress. From these results, a photoviscoelastic constitutive equation was constructed to describe the dependence of the birefringence on stress and strain. The constitutive equation was then applied to study the deformation of a tensile specimen containing a central circular hole. By using the isochromatic fringes in combination with the isoclinic, the time-dependent variation of the stress field in the specimen was solved.     

Tricolor photoviscoelastic technique and its application to moving contact

A new technique for simultaneous determination of both fringe order and principal direction of birefringence in practical photoviscoelastic analysis using white incident light with a set of the primary colors, called tricolor photoviscoelasticity, is described. This method can determine both the fringe order and principal direction of birefringence from a single-color photoviscoelastic image under plane polarization. Then, the authors evaluate time dependent stresses and strains around a contact region in a viscoelastic strip plate under nonproportional loading condition. The variations of the principal stresses and strains are easily obtained over a wide time range by use of the optical constitutive equations of photoviscoelasticity and the characteristic material property functions.     

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.     

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.     

Viscoelastic analysis of residual stress in quenched thermosetting resin beams

The residual stress generated by the molding process of thermosetting resins exerts serious influences upon their mechanical properties. This residual stress is generally classified by two groups: one produced by shrinkage in the curing reaction of monomers, the other produced by the nonuniformity of the temperature distribution in the cooling process. This paper is concerned with the theoretical and experimental analysis of the generation of residual stress of the latter type, using examples of rectangular beams of thermosetting resins quenched on both the upper and lower surfaces. First, a viscoelastic model is applied to make a qualitative prediction of the residual stress in quenched beams. Second, using linear-viscoelastic theory, fundamental equations are derived for the residual stress in a viscoelastic rectangular beam, where an unsteady and nonuniform temperature distribution is assumed in the direction of depth. The theoretical values of the residual stress in rectangular beams are calculated under various quenching conditions for two resins having different viscoelastic characteristics, i.e., epoxy and unsaturated polyester. The theoretical residual-stress distributions agree fairly well with the residual stress measured experimentally at every quenching condition for both resins. The qualitative prediction that the residual stress in quenched beams is compressive in the vicinity of the upper and lower surfaces and is tensile in the inner parts is confirmed. The relaxation modulus of epoxy resin changes more greatly with time and temperature than that of unsaturated polyester resin. The theoretical and experimental analysis shows that the residual stress for the former resin is larger than that for the latter. Therefore, it is concluded that the generation of residual stress is more significant where the relaxation modulus of resin changes greatly with time and temperature.     

Transient thermal stress analysis of a functionally graded magneto-electro-thermoelastic strip due to nonuniform surface heating

This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic strip due to unsteady and nonuniform surface heating in the width direction. We analyze the transient thermal stress problem for a functionally graded strip constructed of the anisotropic and linear magneto-electro-thermoelastic materials using a laminated composite mode as one of theoretical approximation. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the solution for the simply supported and functionally graded magneto-electro-thermoelastic strip under a plane strain state. As an illustration, we carried out numerical calculations for a functionally graded strip composed of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄, and examined the behaviors in the transient state for temperature change, stress, electric potential and magnetic potential distributions. Furthermore, the effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential are investigated.     

Photoviscoelasticity on a microsecond time scale

A previous paper¹² has described the optical calibration of photoviscoelastic materials on a microsecond time scale. In this paper, attention is given to the experimental determination of the two-dimensional plane-stress field in a body subjected to arbitrary loads. Symmetry of load and geometry is not assumed. Since the stress state depends on the history of fringe order and isoclinic angle, these basic data must be recorded. Due to nonlinearity in the material studied, the photoviscoelastic data were limited to fractional fringe orders. This introduced problems of initial birefringence and polariscope imperfections. Techniques are described which correct for these imperfections and allow for acquiring and analyzing the basic photoviscoelastic data.     

Photoviscoelastic behavior and residual thermal birefringence in optical-grade polycarbonates

The stress-optical coefficient functions of two optical-grade polycarbonates (PCs) have been obtained by simultaneous measurements of the relaxation modulus and strain-optical coefficient functions. Nonlinear behavior of the relaxation modulus and strain-optical coefficient was observed at small strains at room temperature. Comparison of these functions in the linear region with those of a commercial grade PC was made. These functions have been incorporated to linear viscoelastic and photoviscoelastic constitutive equations to calculate residual thermal birefringence in freely quenched PC plates. The numerical results have been compared with the measurements indicating a fair agreement between them.     

Residual stress prediction and determination in 7010 aluminum alloy forgings

Precipitation-hardened aluminum alloys gain their high strength through heat treatment involving a severe quenching operation, which can have the adverse effect of introducing residual stresses. The finite element code ABAQUS is used to simulate the quenching of aluminum alloy 7010 in an attempt to predict the residual stress distribution that develops in simple shapes. The rate of heat transfer from the material is determined using the finite element method to predict the heat transfer coefficient from surface cooling curves achieved experimentally. The flow stress of the material is assumed to be strain rate dependent and to behave in a perfectly plastic manner. The predicted residual stress magnitudes and directions are compared to values determined using the holedrilling strain gage method and the X-ray diffraction technique.     

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.     

Considerations of the “freezing-in” of flow-induced orientation in polymer melts by vitrification with application to processing

We develop the implications of the experimentally tested hypothesis that (i) birefringence developed during flow is quantitatively frozen-in during vitrification of glass-forming polymer melts and (ii) that the rheo-optical law may be combined with a knowledge of the stress field existing immediately prior to vitrification to yield birefringence distributions. This hypothesis is applied to various problems including multiaxial stretching of sheets, melt spinning, tubular film extrusion and injection molding. Special problems concerned with internal temperature distributions are discussed. We examine difficulties which may arise in application of the hypothesis due to residual thermal stresses. Comparisons are made to other methods of representing orientation development during flow.     

The transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply

This paper is concerned with the theoretical treatment of the transient piezothermoelastic problem involving a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply in the width direction. The thermal, thermoelastic and piezoelectric constants of the strip are assumed to vary exponentially in the thickness direction. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the exact solution for a simply supported strip under the state of plane strain. Some numerical results for the temperature change, the displacement, the stress and electric potential distributions are presented in figures and table. Furthermore, the influence of the nonhomogeneity of the material and that of the electric boundary conditions are investigated.     

A simplified optical method for measuring residual stress by rapid cooling in thermosetting resin strip

This paper presents a simplified optical method for measuring the residual stresses by rapid cooling in thermosetting resin strips. First, the fundamental equations for calculating the residual stress from the residual birefringence were obtained by the linear photoviscoelastic theory. The specimens were then subjected to rapid cooling. After rapid cooling, the residual stress was measured by two methods, the simplified optical method mentioned above and the well-known layer-removal method. The effectiveness of the simplified optical method was discussed by comparing results of the two methods.     

Curved thermal crack growth in nonhomogeneous materials with different shaped external boundaries II. Experimental results

Curved thermal cracks are considered running along special principal stress trajectories in self-stressed two-phase solids with different cross sections. The resulting mixed boundary-value problems of the stationary plane thermoelasticity are solved by applying the finite element method. Moreover, using appropriate directional criteria established for crack path prediction, the further extension of thermal cracks starting at the external surfaces of different shaped two-phase solids has been determined. Furthermore, the corresponding fracture mechanical data like crack edge displacements, strain energy release rates and stress intensity factors, respectively, have been calculated. Finally, the theoretical investigations given in part I of the paper are compared with experiments using differing optical methods of the experimental stress analysis. The experimental results reported in part II of the paper and the theoretical calculations show a reasonable agreement.     

Experimental investigation on fracture of viscoelastic materials under biaxial-stress fields

Fracture behavior of viscoelastic materials under various biaxial-stress fields was studied experimentally in a specially developed apparatus. The biaxial stresses were applied at various time rates of stress to study the effects of rate of loading on fracture behavior. Examination of experimental data indicated that a simple relationship could be established between octahedral shear stress and octahedral shear strain at fracture corresponding to various biaxial stresses. Finally, a criterion of failure based on the total strain energy at fracture was suggested. The strain energy at fracture predicted from the linear viscoelastic theory agrees reasonably well with that determined experimentally.     

Heuristic approach to thermal shock damage due to single and multiple crack growth

Multiple cracking caused by thermal shock of smooth specimens is predicted qualitatively by invoking time dependent energy release rates. The results suggest that the experimentally observed final crack pattern may have developed stably from an intermediate transient state of unstable crack growth initiated from preexisting flaws. In this way, thermal shock damage and its dependence on the temperature difference in quenching and on initial strength are explained.     

Multi-Functional Measurement Using a Single FBG Sensor

This paper describes the measurement of average strain, strain distribution and vibration of a cantilever beam made of Carbon Fiber Reinforced Plastics (CFRP), using a single Fibre Bragg Grating (FBG) sensor mounted on the beam surface. Average strain is determined from the displacement of the peak wavelength of reflected spectrum from the FBG sensor. Two unstrained reference FBG sensors were used to compensate for temperature drift. Measured strains agree with those measured by a resistance foil strain gauge attached to the sample. Stress distributions are measured by monitoring the variation in the full width at half maximum (FWHM) values of the reflected spectrum, using a proposed optical analytical model, described in the paper. FWHM values were measured for both the cantilever test beam and for a reference beam, loaded using a four-point bending rig. The trend of the stress distribution for the test beam matches with our analytical model, however with a relatively large noise present in the experimentally determined data. The vibration of a cantilever beam was measured by temporal analysis of the peak reflection wavelength. This technique is very stable as measurements are not affected by variations in the signal amplitude. Finally an application of FBG sensors for damage detection of CFRP plates, by measuring the natural frequency, is demonstrated. With small defects of different sizes applied to the CFRP plate, the natural frequency decreased with damage size.     

Quasi-static properties of a photoviscoelastic material

This paper describes the results of mechanical and optical measurements in plasticized polyvinyl chloride under conditions of creep and relaxation at room temperature. It covers one task of a broader investigation aimed at developing experimental methods for viscoelastic stress analysis. The moiré method of strain analysis was found well suited for continuous recording of axial and transversal deformation in creep tests. The material exhibits linear viscoelastic behavior, both mechanical and optical. Strain, stress and birefringence measured from creep and relaxation tests gave straightline plots on log-log scale and, thus simple empirical formulas were possible to derive. The theoretical prediction that birefringence in a linear viscoelastic material not exhibiting flow can be expressed as a linear relationship of stress and strain was satisfactorily substantiated.     

The suppression of a dynamic instability of an elastic body using feedback control

A theoretical and experimental study is made to determine the feasibility of controlling a thin cantilevered beam subject to a (nonconservative) follower force. A theoretical model is developed using the equations for a thin beam under initial stress and Galerkin's method. An experiment is constructed with the capability of using a variety of feedback loops to control a thin aluminum beam with a tip jet mounted parallel to the chord. A particular control system is chosen for study and an increase of follower force required to destabilize the beam of over 65 per cent is recorded. The theoretical results show good correlation with the experimentally determined stability boundaries and frequency variations with follower force.