Stress Measurement in Circular Cylinders

A general procedure is presented whereby all the internal stresses in a glass cylinder can be calculated from birefringence observations. The method applies to circular cylinders, either rods or tubes, where the stress distribution may be any arbitrary function of the radial coordinate and where the observation path is far enough from the ends of the cylinder so that end effects are negligible. The method is applied to an oil-tempered solid glass rod and the calculated stress is compared with that expected from a constant cooling rate.     

Residual birefringence in modified polycarbonates

The residual birefringence in quenched and injection‐molded specimens of bisphenol‐A polycarbonate (BAPC) homopolymer and its copolymers with substituted bisphenol‐A is investigated. The chemical modifications lead to a different stressoptical behavior in the melt and glass state, which generates differences in the residual birefringence of molded specimens. In this way the origins of the residual birefringence can be interpreted in a better way. In quenched samples it is found that the level of birefringence depends on the stress‐optical coefficient in the glassy state, but the unbalance of the birefringence distributions scales with the stress‐optical coefficient in the melt state. This supports the idea that transient thermal stresses present during vitrification induce molecular orientation, which is responsible for the unbalance of the distributions. The residual birefringence distributions in injection‐molded specimens all display a broad plateau in the core, as is usually observed in BAPC. The level of the plateau is found to scale with the stress‐optical coefficient of the melt state. This is a proof for the interpretation of this plateau being induced by transient thermal stresses during vitrification and not by residual stresses. It cannot be eliminated by optimizing molding conditions but only by drastically reducing the stress‐optical coefficient in the melt state.     

Modeling birefringence in SiO2 glass fiber using surface stress relaxation

The retardance of silica glass fibers was evaluated using photoelastic techniques. Here, surface birefringence in glass fibers is shown to be a consequence of surface stress relaxation for as-received fibers drawn from Suprasil II. The surface features of the birefringent fibers were compared to a model of the residual axial stress profile resulting from a diffusion-controlled surface stress relaxation. Additionally, a uniform birefringence in the fiber equivalent to a constant tensile stress was recognized and attributed to structural anisotropy produced during fiber drawing. The contribution of structural anisotropy to the observed birefringence remained constant as the surface features were successively etched away. Surface compressive stress generation was also observed, as retardance corresponding to a surface compressive stress was found to increase with applied tensile stress during short heat treatments. Significant features of the retardance profile in as-received silica glass fibers, with a thin surface compressive stress layer and compensating interior tensile stress, agreed with the residual stress profiles predicted by the surface stress relaxation model after correcting for this observed structural anisotropy.     

Birefringence and interface in sequential co‐injection molding of amorphous polymers: Simulation and experiment

Modelings of the interface distribution and flow‐induced residual stresses and birefringence in the sequential co‐injection molding (CIM) of a center‐gated disk were carried out using a numerical scheme based on a hybrid finite element/finite difference/control volume method. A nonlinear viscoelastic constitutive equation and stress‐optical rule were used to model the frozen‐in flow stresses in disks. The compressibility of melts is included in modeling of the packing and cooling stages and not in the filling stage. The thermally induced residual birefringence was calculated using the linear viscoelastic and photoviscoelastic constitutive equations combined with the first‐order rate equation for volume relaxation and the master curves for the relaxation modulus and strain‐optical coefficient functions of each polymer. The influence of the processing variables including melt and mold temperatures and volume of skin melt on the birefringence and interface distribution was analyzed for multilayered PS‐PC‐PS, PS‐PMMA‐PS, and PMMA–PC–PMMA molded disks obtained by CIM. The interface distribution and residual birefringence in the molded disks were measured. The measured interface distributions and the gapwise birefringence distributions in CIM disks were found to be in a fair agreement with the predicted interface distributions and the total residual birefringence obtained by the summation of the predicted frozen‐in flow and thermal birefringence. POLYM. ENG. SCI., 55:88–106, 2015. © 2014 Society of Plastics Engineers     

Gapwise density distributions in injection-molded poly(methylmethacrylate)

Residual density distributions are determined in injection-molded poly(methyl-methacrylate) (PMMA) with the aid of a quantitative Schlieren optical technique. The gapwise distributions typically show a maximum beneath the surface. The height of the maximum as well as the level in the core vary with distance from the gate of the mold. The density distributions and the influence of the molding parameters are explained by the pressure course measured in the cavity and the process of vitrification of the sample during molding. The magnitudes of the variations of the gapwise distributions agree with the average density variations measured in a density gradient column. Residual stresses do not contribute significantly to the determined distributions. The density maximum is found closer to the surface than the maximum in birefringence that is induced by the shear flow during filling. The magnitude of the density variations is less than predicted by the pseudocompressibility, as determined in samples vitrified under constant pressure.     

Studies of converging flows of viscoelastic polymeric melts. III. Stress and velocity distributions in the entrance region of a tapered slit die

An experimental and theoretical study has been carried out, as a continuation of our previous investigation, to better understand the problems associated with converging flows of viscoelastic polymeric melts. In the present study, measurements were taken of both stresses and velocities in the converging velocity field of polymeric melts flowing into a tapered slit die, stresses by means of the flow birefringence technique and velocities by means of streak photography. The material used was polystyrene. A theoretical analysis was also made of converging flow, using a modified second-order fluid model which assumes that all three material functions depend on the second invariant of the rate of deformation. Numerical solutions were obtained of the equations of motion, which give predicted velocity profiles in reasonable agreement with the measured velocity profiles. A comparison was also made of the experimentally determined stress distributions with the theoretically predicted ones.     

Effect of winding tension and cure schedule on residual stresses in radially-thick fiber composite rings

In filament winding, both the tension applied to the fiber strands and the subsequent cure schedule are important manufacturing variables that produce residual stresses and strains. A “radial cut method” was used to determine the circumferential and radial residual stress profiles in S2-glass fiber/epoxy and E/XA-A carbon fiber/epoxy circumferentially-wound composite rings. Of particular interest in this study were radially-thick composite rings in which the effect of cure schedules as well as constant and variable winding tension profiles on the radial residual stress profiles were evaluated. Several design-oriented relationships for estimating the maximum radial residual stress were developed.     

Calculated internal stress distributions in melt-spun fibers

Although melt spinning is a basic process in the synthetic fiber industry, theoretical understanding of heat transfer and stress development in a melt-spun fiber is limited. In this work, the finite-element method is first applied to the melt-spinning process to determine radial and axial temperature distributions in a solidfying fiber. A thermal stress analysis is then made, again by the finite-element method. Calculated stresses are found to reach maximum values shortly after the fiber solidifies. Because material properties are reduced at these elevated temperatures, this is a location of potential mechanical failure. Anisotropy due to drawing may add to this problem. Analysis of the effects of spinning parameters shows that ambient air temperature is the most critical variable in controlling the internal stresses. Mass flow rate and take-up speed have smaller effects.     

Residual Stress Distributions in Ceramics

Residual stress distributions in ceramics can be calculated for a coordinate system fixed by the specimen geometry as well as for the crystal system. Computations were performed using alumina as a model system with the residual stresses caused by thermal expansion anisotropy. Mean values and standard deviations of the stress distributions are calculated for a plane stress as well as a plane strain scenario in a laboratory coordinate system and compared to distributions of stresses occuring along the a -axis and c -axis of alumina. In addition, stress fluctuations in the whole assembly of grains are compared with stress fluctuations within and between individual grains.     

Model of steady-state melt spinning at intermediate take-up speeds

A model of melt spinning has been developed for speeds above which the effects of gravity, inertia, and aerodynamic drag become significant. The model has as an upper bound the speed at which stress crystallization begins to occur on the spin line. For poly(ethylene terephthalate), these velocities are approximately 750 and 3500 meters/minute. The calculated temperature and velocity profiles are shown to agree with measured values. The stress at the freeze point is calculated and found to correlate well with the spun yarn birefringence which, in turn, is shown to predict uniquely the spun yarn physical properties on a “simple” spin line. The stress-optical coefficient derived from the calculated stress at the freeze point and measured birefringence agrees well with the literature.     

Viscoelastic behavior of amorphous polymers in the glass-rubber transition region: Birefringence studies

Viscoelastic processes associated with the glass-rubber transition of an amorphous polymer are considered to involve hindered rotations around main-chain bonds, which give rise to a decrease in molecular distortion in the stressed material and to an orientation or disorientation of chain segments. The local distortional changes are associated with variations in energy-elastic stress. The orientational rearrangements yield changes in conformational entropy and energy and may be described in the long-time region by the normal mode motions of Gaussian submolecules. Assuming that the net time-dependent stress and birefringence may each be expressed as the sum of distortional and orientational contributions, methods are proposed on the basis of stress-optical data for resolving the distortional and orientational stresses or moduli during stress-relaxation, creep, and dynamic mechanical tests. An analysis of dynamic birefringence data for different amorphous polymers indicates that the orientational processes become important in the long relaxation-time region and are consistent with predictions of the submolecular theory. The distortional changes dominate the shorter relaxation-time behavior and are characterized by somewhat narrower distributions of relaxation times than are apparent from the unresolved data.     

Approximate calculation and measurement of the pressure distribution in radial flow of molten polymers between parallel discs

The known generalized Newtonian fluid “power law” solution of the radial flow between parallel discus has been used to estimate the normal stress, the magnitude of inertia, and the temperature changes due to viscous dissipation. The flow near the wall has been found to be “nearly steady shear flow;” thus the three viscometric functions can be expected to describe the stress at the wall. Further away from the walls, however, the flow is very different from “steady shear flow.” The temperature field in the radial flow section depends on the dimensionless parameters Nahme number, Graetz number, and ratio of inner to outer radius, as well as on the thermal initial and boundary conditions. Experimentally the radial pressure profiles for flow of three different polyethylenes and of one polystyrene have been studied. The measured pressure profiles are about 20 percent lower than the calculated ones from the “power law” solution. This discrepancy cannot yet be explained; the effects of normal stresses, of inertia, or of viscous heating in these experiments are too small to give a measurable effect.     

Residual stresses in epoxy systems by 3-D photoelastic method

The new 3-D photoelastic method was applied to the studies of residual stresses around spherical inclusion in polymeric matrices. Full stress tensor for several model samples was measured. The extent of significant stresses is not greater than three radii of an inclusion. It was found that the stress follows the 1/R³ rule at distances far from the inclusion, while in the narrow zone at the interface a plateau is observed. The level of stress ranges from few MPa up to the plastic yield of the polymeric matrix. The radial stress component is usually twice as large as the tangential stress component. Radial negative stress and tangential positive stresses are found in configuration with a hard inclusion, while radial positive stress and tangential negative stresses are in the systems with soft inclusion. The pressure in the matrix at points around inclusions calculated from the stress tensor is always near zero MPa, which indicates the action of purely deviatoric stresses in the matrix.     

Improvement of optical quality and vibration characteristics of injection molded disk with processing condition control

Increased application of optical disks has required a rotating disk with more dynamic stability and better optical quality. A new concept of controlling the processing condition of injection molded disks is developed to improve their optical quality and vibration characteristics. To assess the effect of process conditions on residual stresses, birefringence, and critical speed, an orthogonal array for design of experiments is used. Melt temperature, filling speed, and packing pressure were effective parameters, but mold temperature and interactions among process conditions were not. The birefringence and critical speed were affected by the residual stress distribution, which varied according to the distance from the gate and processing condition. Considering the effect of the processing conditions and distance from the gate, we calculated the weight factors on residual stresses along the radial direction. Choosing weighted stress to be the target value for optimization of residual stresses, processing conditions control was accomplished. Under the newly proposed conditions, optical quality and stability of injection molded disk were simultaneously improved. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 3275–3285, 2006     

Some relationships between injection molding conditions and the characteristics of vitrified molded parts

The various mold filling phenomena influencing the characteristics of fabricated parts are surveyed. The phenomena leading to jetting in injection mold filling are considered. These are associated with the magnitude of swell by the melt as it exits the gate into the mold. Special attention is given to the influence of non-isothermal runner flow. A theory of extrudate swell of polymer melts with temperature profiles is developed using Tanner's unconstrained recovery theory. In the. absence of jetting, mold filling by a simple advancing front takes place. The hydrodynamics of the advancing front and the stress fields in the flowing melt are determined. Analysis and modeling are presented based on the use of hydrodynamic lubrication theory involving a solid layer along the mold wall and a hot isothermal melt core. This theory is compared with experimental measurements of pressure losses in mold filling. The development of birefringence in injection molding processes is analyzed. Birefringence distributions are due to frozen-in flow birefringence. A new experimental study is presented and its results compared with theoretical predictions. The problem of thermal stresses in injection molded parts is considered.     

Determination of radial structural properties and spectral dispersion curves of poly(aryl ether ether ketone) fibre

Poly(aryl ether ether ketone) (PEEK) fibre was studied using a variable wavelength interferometric technique (VAWI). This technique was used in conjunction with a Pluta polarizing interference microscope to determine the spectral dispersion curves of fibre refractive indices and birefringence fibre. The results were used to calculate the dispersion properties of the fibre, ie dispersion and oscillation energies, Cauchy's constants of dispersion relation and the natural wavelength of the fibre. The radial refractive index and birefringence profiles were also determined, taking into consideration the refraction of light beam by the fibre, and some radial structural profiles were then calculated using a ring‐zonal model. The measurements of these radial profiles are required for optimizing the spinning and processing of manufactured textile fibres. The Fraunhofer diffraction pattern of a He–Ne laser beam was used to determine the average thickness of the fibre. Microinterferograms are presented for illustration. Copyright © 2003 Society of Chemical Industry     

Control the strain-induced crystallization of polyethylene terephthalate by temporally varying deformation rates: A mechano-optical study

The mechano-optical behavior of PET is, for the first time, investigated under temporally varying rates to influence the basic mechanisms of structural organization leading to strain-induced crystallization. For this purpose, four rate profiles, Linear, Sigmoidal, Logarithmic and Exponential, were chosen and films were stretched in Uniaxial Constrained Width mode using newly developed biaxial stretching machine. This machine allows real time direct measure of true stresses, strains, in-plane and out-of-plane birefringences during the deformation. Substantial differences in the mechano-optical behavior and resulting structural mechanism were observed in all of the chosen rate profiles. Linear profile, taken as a standard, yields three stress-optical regimes (SOR) during deformation. At early stages of deformation the birefringence remains linear with stress and material remains amorphous. This is designated as Regime I representing classical stress-optical behavior observed in large number of non-crystallizable polymers. In Regime II, a fast increase of birefringence accompanies formation of crystalline structure with establishment of long-range connected network. In the final Regime III birefringence levels off as the chains approach their finite extensibilities.All three regimes observed in Linear profile are also observed in Logarithmic and Exponential cases. However, Sigmoidal deformation shows only the first two regimes even though the film was stretched to the same total engineering strain as applied to all profiles. Logarithmic profile was found to induce early strain crystallization leading to early development of strain hardening. Exponential profile on the other hand retards the formation of “potentially constraining” long-range physical networks. This allowed the development of higher birefringence and crystallinity levels using this mode. A logarithmic birefringence-work relationship with two distinct stages was found to apply to all temporally varying profiles.     

Analysis of molecular orientation and internal stresses in extruded plastic sheets

The development of molecular orientation and internal stresses in extruded sheet made of polypropylene was analyzed, and their correlations to operating conditions such as draw ratio, cooling rate, die temperature, melt temperature, and die gap opening were studied. Measurements of attenuated-total-reflectance infrared dichroic ratio for the surface molecular orientation, birefringence for the orientation stress distribution in the thickness direction, and free shrinkage ratio for the overall frozen-in stresses were carried out to determine the amount of orientation stresses in the extruded samples. As expected, the overall orientation stress depends strongly on draw ratio, while higher melt temperature reduces the overall orientation. It was found that faster cooling rates and lower die temperatures cause surface orientation stresses to increase as the core orientation stresses remain almost unchanged.     

On-line measurement of orientation development in the high-speed melt spinning process

On-line measurement of birefringence was performed in the high-speed melt spinning process of poly(ethylene terephthalate) using an apparatus that incorporates a rotating polarizer for the measurement of the optical retardation of running filament. Particular attention was paid to the detailed measurements in the vicinity of neck-like deformation. Through the measurement at the take-up velocity of 5 km/min, development of birefringence under the strain rate up to about 1 ms^?1 was investigated. To analyze the relation between applied stress and birefringence, tension and temperature profiles of the spin-line were calculated based on the experimentally obtained diameter profiles. Even though the strain rate is extremely high, a linear relationship between birefringence and a parameter calculated by dividing stress by temperature was confirmed to hold up to birefringence and stress/temperature values of about 0.017 and 10 kPa/K, respectively.