Calculation of residual stresses in amorphous wires

The residual internal stresses in a cylindrical wire produced in the rotating-water melt spinning process and a coated wire obtained by drawing from a melt have been calculated within the thermal viscoelasticity and structural relaxation theories. The coated wire consists of the core and the sheath with different thermal properties. The problem is considered with allowance made for the generation and the relaxation of stresses in the core and the sheath in the temperature range from initial (corresponding to the liquid state of a two-layer wire) to room temperature. The distributions of the residual stresses have been calculated for the free amorphous metallic wire and the amorphous wire with the sheath having a different elastic modulus and thermal expansion coefficient. The influence of preparation conditions and thermal properties of materials on the calculated parameters is analyzed.     

Residual stresses in injection-molded amorphous polymers

Nonisothermal flow of a polymer melt into a cold cavity and its rapid cooling give rise to the buildup of flow and thermal stresses in the molded article. In the present investigation the resultant residual stresses (RS) induced by these two sources were studied in two stages. First, the flow-induced stresses were relaxed by proper heat treatment followed by quenching, resulting in only thermal stresses. The experimentally determined RS profiles in polysulfone and amorphous polyamide showed a parabolic shape and were correlated with the initial and final quenching temperatures, the glass transition temperature, and Biot Number. In the second stage, the combined effect of thermal- and flow-induced stresses was studied using injection-molded specimens prepared under a wide speptrum of molding conditions including melt and mold temperatures and injection rate and pressure. Results here indicated that the basic thermal-induced parabolic RS profiles are altered by the flow-induced stresses resulting in complicated profiles including local maxima and unbalanced RS. Finally, the tensile mechanical properties obatained for plaques molded under the various injection-molding conditions were studied and correlated in part with the previously determined RS profiles. Results have shown that a property gradient exists as a function of distance from both the gate and surface of the molded plaque.     

PBT/PET conjugated fibers: Melt spinning,fiber properties,and thermal bonding

This work examines the PBT/PET sheath/core conjugated fiber, with reference to melt spinning, fiber properties and thermal bonding. Regarding the rheological behaviors in the conjugated spinning, PET and PBT show the smallest difference between their melt‐viscosity at temperatures of 290°C and 260°C respectively, which has been thought to represent optimal spinning conditions. The effect of processing parameters on the crystallinity of core material‐PET was observed and listed. In order of importance, these factors are the draw ratio, the heat‐set temperature, and the drawing temperature. The crystallinity of sheath material‐PBT, however, can be considered to be constant, independent of any processing parameters. The bulk orientation, rather than the crystallinity of PET core, dominates the tenacity of PBT/PET sheath/core fiber. Moreover, heat‐set treatment after drawing is recommended to yield a highly oriented conjugated fiber. With respect to thermal bonding, PBT/PET conjugated fibers processed via high draw ratio but low‐temperature heat setting can form optimal thermal bonds at a constant bonding temperature of 10°C above the T_m of PBT.     

Residual thermal stresses in injection moldings of thermoplastics: A theoretical and experimental study

Internal stresses in injection molded components, a principal cause of shrinkage and warpage, are predicted using a three‐dimensional numerical simulation of the residual stress development in moldings of polystyrene and high‐density polyethylene. These residual stresses are mainly frozen‐in thermal stresses due to inhomogeneous cooling, when surface layers stiffen sooner than the core region as in free quenching. Additional factors in injection molding are the effects of melt pressure history and mechanical restraints of the mold. Transient temperature and pressure fields from simulation of the injection molding cycle are used for calculating the developing normal stress distributions. Theoretical predictions are compared with measurements performed on injection molded flat plates using the layer removal method on rectangular specimens. The thermal stress development in the thinwalled moldings is analyzed using models that assume linear thermo‐elastic and linear thermo‐viscoelastic compressible behavior of the polymeric materials. Polymer crystallization effects on stresses are examined. Stresses are obtained implicitly using displacement formulations, and the governing equations are solved numerically using a finite element method. Results show that residual stress behavior can be represented reasonably well for both the amorphous and the semicrystalline polymer. Similarities in behavior between theory and experiment indicate that both material models provide satisfactory results, but the best predictions of large stresses developed at the wall surface are obtained with the thermo‐viscoelastic analysis.     

Reducing residual stresses in molded parts

Means of reducing the flow-induced residual stresses in injection molded parts through optimization of the thermal history of the process are presented. An approach through the use of a passive insulation layer with low thermal inertia on the cavity surface was investigated. The passive insulation layer prevents the polymer melt from freezing during mold filling and allows the flow-induced stresses to relax after the filling. The criteria for the optimal thermal properties and the required thickness of the layer are presented. A numerical simulation model of non-isothermal filling and cooling of viscoelastic materials was also used to understand the molding process and to evaluate this approach. This model predicts the stress development and relaxation in the molding cycle. Both simulation and experimental results show that the final stresses in the molded parts can be reduced significantly with the use of an insulation layer. This technique can also be applied to other molding or forming processes in order to decouple the material flow and cooling process for minimum residual stresses in the molded parts.     

Theoretical and experimental studies of anisotropic shrinkage in injection moldings of various polyesters

A novel approach to predict anisotropic shrinkage of slow crystallizing polymers in injection moldings was proposed, using the flow‐induced crystallization, frozen‐in molecular orientation, elastic recovery, and PVT equation of state. In the present study, three different polyesters, polyethylene terephthalate, polybutylene terephthalate, and polyethylene‐2,6‐naphthalate (PEN), are used. The anisotropic thermal expansion and compressibility affected by the frozen‐in orientation function and the elastic recovery that was not frozen during moldings were introduced to obtain the in‐plane anisotropic shrinkages. The frozen‐in orientation function was calculated from the amorphous contribution based on the frozen‐in and intrinsic amorphous birefringence and crystalline contribution based on the crystalline orientation function determined from the elastic recovery and intrinsic crystalline birefringence. To model the elastic recovery and frozen‐in stresses related to birefringence during molding process, a nonlinear viscoelastic constitutive equation was used with the temperature‐dependent viscosity and relaxation time. Occurrence of the flow‐induced crystallization was introduced through the elevation of melting temperature affected by entropy production during flow of the viscoelastic melt. Kinetics of the crystallization was modeled using Nakamura and Hoffman‐Lauritzen equations with the rate constant affected by the elevated melting temperature. Numerous injection molding runs were carried out by varying the packing time, packing pressure, flow rate, melt and mold temperature, and anisotropic shrinkage of moldings were measured. The experimental results were compared with the simulated data and found in a fair agreement. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3526–3544, 2006     

Residual thermal stresses in injection molded products

Nonisothermal flow of a polymer melt in a cold mold cavity introduces stresses that are partly frozen-in during solidification. Flow-induced stresses cause anisotropy of mechanical, thermal, and optical properties, while the residual thermal stresses induce warpage and stress-cracking. In this study, the influence of the holding stage on the residual thermal stress distribution is investigated. Calculations with a linear viscoelastic constitutive law are compared with experimental results obtained with the layer removal method for specimens of polystyrene (PS) and acrylonitrile butadiene-styrene (ABS). In contrast to slabs cooled at ambient pressures, which show the well-known tensile stresses in the core and compressive stresses at the surfaces, during the holding stage in injection molding, when extra molten polymer is added to the mold to compensate for the shrinkage, tensile stresses may develop at the surface, induced by the pressure during solidification.     

Prediction of process-induced warpage in injection molded thermoplastics

The main cause of warpage in injection moldings is the imbalance of the thermal residual stresses that are caused by a non-uniform temperature distribution through the thickness of the moldings resulting from variation in cross sections, part geometries, and temperature difference between the mold surfaces. As the hot plastic melt is injected into the relatively cooler mold, a temperature gradient develops between the core of the molding and its surfaces, determining the magnitude of the residual stresses and warpage deflection. The relationship between the temperature difference of the two halves of the mold and warpage for a flat plate was measured and predicted by use of a finite element software package. The development of warpage in a 3D component (L-shaped bracket) was also measured, and the results were compared with computer predictions.     

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.     

Optimization of Residual Stresses in the Surface Regions of Injection Moldings

The present study focused on the optimization of the injection molding process parameters to minimize thermal residual stresses in the surface regions of the polystyrene and high density polyethylene parts. Process parameters such as melt temperature, mold temperature and cooling time were considered as variables and their effects on residual stresses in surface regions of the parts were investigated by utilizing design of experiment (DOE), Taguchi and analysis of variance (ANOVA) methods. As a result, the most important parameters for residual stresses in surface regions of the PS and HDPE parts were found melt temperature and mold temperature, respectively.     

Incorporation of density relaxation in the analysis of residual stresses in molded parts

Thermo-rheologically/piezo-rheologically simple viscoelastic constitutive equations are adopted for the material behavior of a generic polystyrene, in both the deviatoric and dilatational domains, in order to investigate the effect of density relaxation on the development of the thermal residual stresses in a thin injectionmolded strip. A preliminary study is undertaken to assess the ability of the proposed dilatational viscoelastic constitutive equations to capture some of the density-relaxation behavior such as the isobaric volume relaxation following a sudden quench from above the glass-transition temperature and upon constant rates of cooling at different temperatures and pressures. In this preliminary study, different combinations of relaxation functions and shift factors are investigated. An appropriate combination is selected and used for the residual-stress analysis. The numerical simulation of the development of the stresses in a one-dimensional cavity qualitatively predicts the correct stress profile across the thickness of the molded part, as well as the dependency of this profile on some of the material properties and molding conditions. In general, the investigation presented in this paper suggests that density relaxation plays an important role in the development of residual stresses in molded parts.     

Delayed curvature and residual stresses in porcelain tiles

Most industrial porcelain tiles suffer changes in their curvature after firing: such process is known as delayed curvature. One of the hypotheses used to explain this phenomenon is based on the relaxation of residual stresses by creep. In this study two types of industrial glazed porcelain tiles have been studied. One of them displayed delayed curvature after firing, whereas the other one presented a stable curvature. The main objective was to determine if the delayed curvatures were caused by the residual stresses generated during rapid industrial cooling. Both types of existing residual stresses (thermal stresses, caused by thermal gradients inside the tile during cooling, and body–glaze fit stresses, due to the thermal expansion mismatch between body and glaze) were measured, as well as related samples properties (elastic modulus, creep behaviour, thermal expansion). The results demonstrated that the residual stresses are not the main cause of the delayed curvature phenomenon.     

A simple procedure of accounting for physical aging in the prediction of the modulus of glassy plastic materials

The basic relationships are presented for predicting the creep and stress relaxation as a function of physical aging, loading time, and temperature of amorphous polymers processed under such conditions that their thermal treatment amounts to a quench from the melt to the glassy state. A nomogram construction, based on these relations, is proposed and developed for a particular polymer, namely an extrusion type acrylonitrile-butadiene-styrene (ABS), RONFALIN EST. The applicability of the procedure is restricted to the isothermal viscoelastic behavior at low stresses and strains of unplasticised amorphous plastic materials quenched from the melt to the glassy state.     

Hot Pressing of Annular Alumina–Zirconia Composites

An analysis is performed to predict the densification during and the state of residual stress after hot pressing of annular alumina/zirconia (3Y-TZP) composites. The objective of the analysis was to study the residual stresses resulting from stress gradients during pressing and those from thermal expansion mismatch during the cooling of the compact from the pressing temperature to room temperature. It is predicted that the residual stresses are affected by the respective densification rates of the core and the annulus, their elastic modulus, and thermal expansion coefficient. For the system analyzed in this study, it is predicted that hot pressing reduces the residual stresses that result from the mismatch in thermal expansion coefficients. This is due in part to the high densification rate and in part to the high elastic modulus of the alumina annulus compared to the zirconia core. For surface compression strengthening, a system where the annulus would have similar elastic modulus but lower densification rate and lower thermal expansion coefficient than the core would be more beneficial.     

Effect of oxidation and residual stress on mechanical properties of SiC seal coated C/SiC composite

The effect of oxidation and thermal residual stress on mechanical properties of SiC seal coated C/SiC composite at ambient temperature and high temperature were studied. The oxidation of SiC seal coated C/SiC composite at 1300 and 1500 °C resulted in carbon fibres burn area near through thickness micro cracks in the SiC seal coating. With the increase in exposure time, the formation of SiO₂ layer in SiC matrix near carbon fibres burns area was found. Residual mechanical properties of SiC seal coated C/SiC composite after exposure in air show significant degradation. First time, a continuous measurement of Young's modulus with temperature of C/SiC composite was carried out using an impulse excitation technique. The effect of relaxation of thermal residual stress on mechanical properties was observed with the help of continuous measurement of Young's modulus as a function of temperature in an inert atmosphere.     

Finite element analysis of wire coating

A general-purpose finite element program has been used to simulate the flow of polymers through wire-coating dies. The analysis includes Newtonian and power-law fluids. The effect of normal stresses was examined through a simple viscoelastic constitutive equation, Nonisothermal wire coating was studied to obtain the temperature field within the melt. The effect of a slip condition at the solid boundaries was also examined. The determination of the coating melt free surface was carried out through an iterative procedure. The finite element solution provides details about the existence and extent of recirculation regions, about hot spots due to viscous dissipation, and also captures the stress singularities present at the impact of the melt with the wire and at the exit from the die. Pressure distribution, maximum temperature rise, haul-off wire tension, maximum wire tension, and stresses at the wire surface and die wall are also presented.     

Residual Stresses in Meta/Ceramic Bonded Strips

Residual stresses that develop during cooling of a metal/ ceramic strip are calculated analytically. It is shown that the metal may behave elastically or plastically (with full or partial plasticity) depending on the mechanical properties, the thickness of the two constituents, and the mismatch in thermal expansion. Residual stresses are also calculated for a sequence consisting of constrained undercooling, removal of the constraint, and reheating. It is demonstrated that reheating, which results in elastic stress relaxation, may be used to eliminate the residual stress. The optimum undercooling and reheating conditions needed to produce a stress-free strip, at the operational temperature, are calculated, and specific results are presented for the system Cu/A₂, O₂.     

Theoretical and experimental studies of anisotropic shrinkage in injection moldings of semicrystalline polymers

A novel approach to predict anisotropic shrinkage of semicrystalline polymers in injection moldings was proposed using flow‐induced crystallization, frozen‐in molecular orientation, elastic recovery, and PVT equation of state. The anisotropic thermal expansion and compressibility affected by the frozen‐in orientation function and the elastic recovery that was not frozen during moldings were introduced to obtain the in‐plane anisotropic shrinkages. The frozen‐in orientation function was calculated from amorphous and crystalline contributions. The amorphous contribution was based on the frozen‐in and intrinsic amorphous birefringence, whereas the crystalline contribution was based on the crystalline orientation function, which was determined from the elastic recovery and intrinsic crystalline birefringence. To model the elastic recovery and frozen‐in stresses related to birefringence during molding process, a nonlinear viscoelastic constitutive equation was used with temperature‐ and crystallinity‐dependent viscosity and relaxation time. Occurrence of the flow‐induced crystallization was introduced through the elevation of melting temperature affected by entropy production during flow of the viscoelastic melt. Kinetics of the crystallization was modeled using Nakamura and Hoffman‐Lauritzen equations with the rate constant affected by the elevated melting temperature. Numerous injection molding runs on polypropylene of various molecular weights were carried out by varying the packing time, flow rate, melt temperature, and mold temperature. The anisotropic shrinkage of the moldings was measured. Comparison of the experimental and simulated results indicated a good predictive capability of the proposed approach. POLYM. ENG. SCI., 46:712–728, 2006. © 2006 Society of Plastics Engineers     

Effects of the lamination temperature on the properties of poly(ethylene terephthalate-co-isophthalate) in polyester-laminated tin-free steel can — I. Characterization of poly(ethylene terephthalate-co-isophthalate)

The effects of lamination temperature on the properties of poly(ethylene terephthalate-coisophthalate) (co-PET), such as thermal, mechanical, and barrier properties, have been investigated in co-PET laminated steel. The variation of the degree of crystallinity and the orientation of the co-PET film during the lamination process was examined using DSC, X-ray diffraction, and birefringence, and water vapor permeability was also measured with varying lamination temperature. Both the degree of crystallinity and the orientation of the co-PET film decreased and water vapor permeability increased with increasing lamination temperature. The stress-strain curves of the co-PET films were different, depending on the lamination temperature. The stress in the co-PET film laminated at higher temperature was lower at a given strain, due to the increase of the amorphous region. The effects of annealing temperature and the extent of drawing on the residual stress in co-PET/tin-free steel (TFS) joints were investigated by examining the stress relaxation behavior of co-PET. It was necessary to heat co-PET/TFS joints at more than 150°C in order to eliminate the residual stress.     

Numerical prediction of residual stresses and birefringence in injection/compression molded center‐gated disk. Part I: Basic modeling and results for injection molding

The present study attempted to numerically predict both the flow‐induced and thermally‐induced residual stresses and birefringence in injection or injection/compression molded center‐gated disks. A numerical analysis system has been developed to simulate the entire process based on a physical modeling including a nonlinear viscoelastic fluid model, stress‐optical law, a linear viscoelastic solid model, free volume theory for density relaxation phenomena and a photoviscoelasticity and so on. Part I presents physical modeling and typical numerical analysis results of residual stresses and birefringence in the injection molded center‐gated disk. Typical distribution of thermal residual stresses indicates a tensile stress in the core and a compressive stress near the surface. However, depending on the processing condition and material properties, the residual stress sometimes becomes tensile on the surface, especially when fast cooling takes place near the mold surface, preventing the shrinkage from occurring. The birefringence distribution shows a double‐hump profile across the thickness with nonzero value at the center: the nonzero birefringence is found to be thermally induced, the outer peak due to the shear flow and subsequent stress relaxation during the filling stage and the inner peak due to the additional shear flow and stress relaxation during the packing stage. The combination of the flow‐induced and thermally‐induced birefringence makes the shape of predicted birefringence distribution quite similar to the experimental one.