Showing papers in "Polymer Engineering and Science in 1985"
TL;DR: In this paper, the tensile mechanical properties and fracture toughness of a Bisphenol-A type difunctional epoxy resin, cured with different amounts of metaphenylene diamine, using two cure cycles, were determined over a range of temperature.
Abstract: The tensile mechanical properties and fracture toughness of a Bisphenol-A type difunctional epoxy resin, cured with different amounts of metaphenylene diamine, using two cure cycles, were determined over a range of temperature. The tensile modulus in the glassy state was seen to be predominantly related to intermolecular packing, while in the rubbery state crosslink density was the important factor. Yielding appeared to be due to an increase in free volume as a result of dilatation during the tensile test and was related to a critical shear stress. The large strain properties like tensile strength, elongation-to-break, and toughness showed a more complex dependence on chemical structure, molecular architecture, intermolecular packing, and crosslink density. The roles played by the relaxation processes in determining mechanical properties are highlighted.
193 citations
TL;DR: In this article, the properties of two high performance engineering thermoplastics, amorphous polyethersulfone (PES) and semicrystalline polyetheretherketone, are discussed.
Abstract: Properties of two high performance engineering thermoplastics, amorphous polyethersulfone (PES) and semicrystalline polyetheretherketone (PEEK), are discussed. Both resins can be processed by conventional techniques, compounded with high performance fibers, and have high service temperature (up to 300°C). Due to the amorphous character PES can be dissolved and spray coated into metals.
128 citations
TL;DR: In this article, a unique polymer blend approach to impart solvent and gas barrier properties to a polyolefin material is presented, which involves incorporation of small amounts of a modified nylon barrier material, and processing under controlled conditions, in single step blowmolding or other extrusion processes.
Abstract: Melt fabricated plastic articles with improved solvent and vapor barrier properties are of great need in the packaging industry. Various techniques, such as coextrusion, surface treatments, and coatings, are being employed currently towards this objective. Present work has identified a unique polymer blend approach to impart solvent and gas barrier properties to a polyolefin material. This involves incorporation of small amounts of a modified nylon barrier material, and processing under controlled conditions, in single step blowmolding or other extrusion processes. The unusual barrier effects obtained at small concentrations of the barrier material are obtained by the controlled morphology of the dispersed phase and optimum formulation of the ingredients.
127 citations
TL;DR: In this paper, the deformation and break-up behavior of liquid droplets in simple shearing matrices were investigated for both Newtonian and non-Newtonian systems.
Abstract: In order to achieve a better understanding of polymer blending processes some experimental work has been carried out on the deformation and break-up behavior of liquid droplets in simple shearing matrices. For Newtonian systems good agreement was obtained with existing theories. For non-Newtonian systems trends were established regarding the influence of fluid elasticity on droplet deformation and break-up.
120 citations
TL;DR: In this paper, the tensile crazing and Charpy impact behavior of polypropylene modified with styrene-butadiene copolymer (SBR) and ethylene-propylene-diene monomer (EPDM) was studied.
Abstract: The tensile crazing and Charpy impact behavior of polypropylene modified with styrene-butadiene copolymer (SBR) and ethylene-propylene-diene monomer (EPDM) was studied. Various rubber particle size distributions were obtained by varying the relative viscosities between rubbery phase and PP matrix. Transmission electron microscopy and computer-aided image analysis were used to provide particle size information. In general, PP blends with smaller rubber particles are tougher and more ductile than those with larger particles, probably because the former represents a more efficient use of rubbery phase in promoting crazing and/or shear yielding. Samples with average particle diameter D ≥ 0.5 μm were found to exhibit pronounced crazing. Within a given sample, no crazes appeared to develop around individual rubber particles with D < 0.5 μm. The higher the D, the greater the propensity to form crazes. The behavior of samples with D ≪ 0.5 μm appeared to be dominated by shear yielding; very few crazes could be found. That there exists a critical rubber particle size is explained by the requirement that sufficient stress concentration be maintained to a finite radial distance to permit the initiation and growth of a craze, which requires a finite volume. Small particles, inducing smaller stress-enhanced zones, are therefore not effective in initiating crazes.
116 citations
TL;DR: In this paper, the requirements for the development of toughening in the ductile/brittle systems are discussed, and the miniature evaluation system gave the same results as those from the conventional methods.
Abstract: Studies on plastic alloys consisting of particles of brittle polymers dispersed in the matrices of ductile polymers were undertaken using the miniature polymer evaluation system (CSI Mini-Max System). For the polycarbonate/poly(acrylonitrileco-styrene) system, which had been found to show improved impact strength by Kurauchi, et al. using the conventional methods of molding and mechanical testing, it was verified that the miniature evaluation system gave the same results as those from the conventional methods. Ten other different combinations of ductile and brittle polymers were evaluated by using the miniature evaluation system. Among them the polycarbonate/poly(methyl methacrylate) system is found to be a toughened alloy. From these results, the requirements for the development of toughening in the ductile/brittle systems are discussed.
109 citations
TL;DR: In this article, a non-Fickian sorption is observed for an insufficiently cured resin and is caused by the resin undergoing further postcuring in the sorption process.
Abstract: Diffusion of water in a glassy epoxy resin has been studied by the sorption method. Film thickness scaling is used as a diagnostic tool for non-Fickian sorption processes. A sorptiondesorption cycle effectively increases the preexisting free volume in the resin and renders the subsequent sorption process different from the original. The effect is understood by considering the time scale for diffusion and that for molecular relaxation of the glassy polymer network. A non-Fickian sorption process is observed for an insufficiently cured resin and is caused by the resin undergoing further postcuring in the sorption process. It is shown that oxidation of the resin during sorption also gives rise to non-Fickian processes previously described in the literature as diffusion anomalies for epoxies. It is further shown that the difference between sorption and resorption curves is not caused by irreversible damage to the resin but due to reversible changes in network conformations.
103 citations
TL;DR: The morphology and mechanical properties of binary blends of nylon 6 (N6), as the major component, and ethylene-methacrylic acid copolymers (E/MAA) as the minor component, have been analyzed in this article.
Abstract: The morphology and mechanical properties of binary blends of nylon 6 (N6), as the major component, and ethylene-methacrylic acid copolymers (E/MAA), as the minor component, have been analyzed. It was found that the methacrylic acid content of the copolymer used as the second component has a profound effect upon the properties of the resulting blends. In particular, with increasing methacrylic acid content, the size of the domains of the E/MAA dispersed phase in the N6 matrix decreased in a regular fashion while the ultimate tensile properties increased regularly. This behavior has been attributed to a series of chemical and physico-chemical interactions taking place between the two components. The interactions are due to the presence of the acid functionality on the copolymer and do not occur when this functionality is absent. Chemical analysis of the blends was performed to confirm that chemical modification took place during the blending process.
87 citations
TL;DR: In this article, the thermal and tensile properties of some silane-grafted crosslinked polyethylene samples and peroxide-crosslinked materials are compared and analyzed in different environments at various temperatures.
Abstract: Silane-grafted polyethylene materials are processed in conventional thermoplastic fabrication machines. The shaped articles are then crosslinked in water by the formation of Si-O-Si crosslinks. This paper represents studies on the crosslinking progress in different environments at various temperatures. Molecular orientation is shown to become permanent and mostly irrecoverable even at 150°C, in the silane-grafted solid state crosslinked specimens (the crosslinking temperature in water is well below the polymer melting temperature). These frozen molecular orientations have a significant effect on the tensile properties of the crosslinked materials causing higher yield stresses and lower elongations at break. The thermal and tensile properties of some silane-grafted crosslinked polyethylene samples and peroxide-crosslinked materials are compared and analyzed.
84 citations
TL;DR: In this paper, Petrie's work on film-blowing is extended to cover viscoelastic non-isothermal flow for both the convected Maxwell and the Leonov models.
Abstract: This paper extends Petrie's work on film-blowing to cover viscoelastic non-isothermal flow for both the convected Maxwell and the Leonov models. Good agreement with experimental data is shown for the former. The calculations are highly unstable, however, and it is difficult to obtain convergence with arbitrary values of the film-blowing parameters. The general effect of viscoelasticity is to stiffen the film and restrain the increase in bubble diameter. There is some difference between bubble shapes generated using the Maxwell and Leonov constitutive models but the temperature variation of properties is seen as the dominant effect, The Leonov model tends not to be stiff enough in its response to the present flow, which is purely extensional and good agreement with experiment was not obtained. For the Maxwell model the relevant mean relaxation time must be used for good agreement between experiment and calculation.
79 citations
TL;DR: In this article, a review summarizes reports of polymer stress reactions published principally after 1980 and a survey is organized by polymer type and by analysis technique, organized by type and analysis technique.
Abstract: A singular class of polymer reactions can be caused by mechanical stress. Sufficient storage of mechanical energy to break chemical bonds in the main chain is generally possible only on deformation of polymers of high molecular weight. The corresponding appropriate conditions of high stress may occur in both polymer processing and use. This review summarizes reports of such polymer stress reactions published principally after 1980. The survey is organized by polymer type and by analysis technique.
TL;DR: In this paper, a model for the diffusion mechanism of water in glassy epoxy resins is proposed, where the polymer network is assumed to consist of two regions in which water molecules possess different mobilities.
Abstract: A model is proposed for the diffusion mechanism of water in glassy epoxy resins. The polymer network is assumed to consist of two regions in which water molecules possess different mobilities. By considering the distribution of water molecules among these regions it is possible to describe the concentration dependency of the diffusion coefficient in the sorption and resorption processes. The diffusion coefficient becomes constant when the sorption temperature is close to the effective glass transition temperature of the epoxy-water binary mixture. An explanation of this effect is also provided by the model.
TL;DR: In this article, the tensile behavior of polypropylene (PP) filled with calcium carbonate particles has been studied using a tensile test, in particular, the effect of strain rate, filler content, and filler size upon the elastic modulus, yield stress, and strain of surface-modified and unmodified particles-filled PP were investigated.
Abstract: The tensile behavior of polypropylene (PP) filled with calcium carbonate particles has been studied using a tensile test. In particular, the effect of strain rate, filler content, and filler size upon the elastic modulus, yield stress, and strain of surface-modified and unmodified particles-filled PP were investigated. The results indicated that the elastic modulus and yield stress of an unmodified system were increased with an increase of strain rate and filler content, and with a decrease of filler size. The yield strain was decreased with an increase of filler content, and with a decrease of filler size, but did not depend on the strain rate. Although the dependence of elastic modulus on the filler size was maintained even by the surface-modified fillers, that dependence on the strain rate and filler content was decreased by such fillers. This may be because the modifier is present at the interface of filler and polymer matrix.
TL;DR: In this article, a thermotropic liquid crystalline copolyester based on poly(ethylene terephthalate) (PET) and para hydroxybenzoate (PHB) copolyesters has been subjected to different types of flow histories.
Abstract: Morphological studies have been carried out on a thermotropic liquid crystalline copolyester based on poly(ethylene terephthalate) (PET) and para hydroxybenzoate (PHB) that has been subjected to different types of flow histories. Wide angle X-ray scattering investigations and chemical etching (n-propylamine is the etchant) in conjunction with electron microscopy studies conducted on end gated injection molded plaques of the 60 percent PHB and 80 percent PHB copolyesters indicate that a highly oriented skin region and a less oriented core region is present. Chemical etching studies performed on microtomed layers of end gated and center gated plaques show that the etching is less pronounced in the skin region and is more pronounced in the core. The microtomed layers of the end gated injection molded plaques when analyzed by ESCA indicate the presence of a “PHB rich” skin region and a “PET” rich core region. Biaxial orientation, as denoted by WAXS measurements, is observed when the 60 percent PHB copolyester is squeezed between lubricated parallel plates.
TL;DR: In this article, the effect of crosslinking on viscosity of thermoplastic polypropylenenenatural rubber blends has been evaluated with specific reference to the effects of blend ratio, extent of dynamic cross-linking of the rubber phase and temperature, on viscoverage, flow behavior index, and deformation of the extrudate.
Abstract: The melt flow behavior of thermoplastic polypropylenenatural rubber blends has been evaluated with specific reference to the effects of blend ratio, extent of dynamic crosslinking of the rubber phase and temperature, on viscosity, flow behavior index, and deformation of the extrudate. The proportion of rubber in the blend and the extent of dynamic crosslinking of the rubber phase were found to have profound influence on the viscosity of the blends at lower shear stresses. But at higher shear stresses, the effect of blend ratio on viscosity was comparatively less for the uncrosslinked blends than that for the crosslinked blends. At lower shear stress, the viscosity of the blend increased with increase in degree of crosslinking but at higher shear stress, the effect of crosslinking on viscosity was found to vary depending on the ratio of the plastic and rubber components in the blend. The deformation of the extrudates was also very much dependent on both blend ratio and degree of crosslinking.
TL;DR: In this article, it was shown that for n-paraffins and molten polymers η is a single parameter function: η = η (y) (P, T, and Ṽ, respectively), and that for polymers the correlation depends on molecular weight, molecular weight distribution, branching, and composition.
Abstract: Simha's equation of state provides the relation between reduced pressure, temperature, and volume (P, T, and Ṽ, respectively) and the occupied site fraction, y = y (P, T). The latter theoretical parameter combines the P and T effects on the occupied and unoccupied (“free volume”) part of the model liquid. It can be computed for each liquid once the thermodynamic reducing parameters are known. Empirical correlation between published zero shear viscosity data, η = η (P, T), and y indicates that for n-paraffins and molten polymers η is a single parameter function: η = η (y). The mathematical form of this dependence was explicitly given for n-paraffins. However, for polymers the correlation depends on molecular weight, molecular weight distribution, branching, composition, etc. In Practical terms, η = η (y) should be determined for each polymer by measuring the temperature dependence of η in as wide a range of T as possible. Then pressure effect on η can be determined from η = η(y) plot, knowing the y = y(P, T) relation.
TL;DR: In this paper, phase separation effects occurring in injection molding of glass-bead and glass-fiber-filled thermoplastics were studied and a qualitative interpretation of the origin of the observed separation phenomena is feasible.
Abstract: Dumb-bell specimens and rectangular boxes were used to study phase separation effects occurring in injection molding of glass-bead and glass-fiber-filled thermoplastics. The separation effects were more pronounced with beads than with fibers and they increase with increasing bead diameter. The filler distribution is further influenced by mold geometry, filler concentration, matrix material, and processing conditions. If the use of fillers, which promote inhomogeneity, is unavoidable it is possible to improve the distribution of the rigid phase by a favorable choice of injection speed and melt temperature. With the theories available at present a qualitative interpretation of the origin of the observed separation phenomena is feasible.
TL;DR: In this article, the shape of flow fronts studied by short-shots is affected predominantly by the thickness of the cavity with other parameters playing a less important role, and the orientation of fibers in the cavity is examined using a reflect-type microscope.
Abstract: Mold filling of a rectangular cavity of three different thick nesses fed from a reservoir is studied for unfilled and glass fiber-filled polypropylene and polystyrene. The shapes of flow fronts studied by short-shots are affected predominantly by the thickness of the cavity with other parameters playing a less important role. Pressure drop versus volumetric flow rate inside the thinnest cavity is studied experimentally and predictions are made from a computer simulation of mold filling. The orientation of fibers in the cavity is examined using a reflect-type microscope and the orientation is found to depend on cavity thickness, melt temperature, fiber content, and to a lesser extent, on volumetric flow rate. In the thinnest cavity, where the flow is quasi-unidirectional, the fibers remain in the plane of flow oriented either along the flow direction or perpendicular to it, except in the region near the flow front, where they follow a “fountain” flow behavior.
TL;DR: In this article, a deconvolution of dynamic melt viscoelastic properties in the terminal and plateau zones is used to determine the molecular weight and its distribution of polystyrenes.
Abstract: A method is developed by which polymer molecular weight and its distribution can be accurately determined by deconvolution of dynamic melt viscoelastic properties in the terminal and plateau zones. The method is illustrated with a series of monodisperse (narrow-distribution) and polydisperse (broaddistribution) polystyrenes. The Mn, Mw, and Mn/Mw values obtained are in excellent agreement with those determined by light scattering, osmometry and gel permeation chromatography with less than 5 to 10 percent error. The differential molecular-weight distribution curves obtained coincide wall with those obtained by gel permeation chromatography. The method is applicable to insoluble as well as soluble polymers.
TL;DR: A slit die viscometer (SDV) was built and evaluated extensively in this paper, where the authors compared viscosity data of the SDV to data from a capillary rheometer (CR) and a Rheometrics Mechanical Spectrometer (RMS).
Abstract: A slit die viscometer (SDV) was built and evaluated extensively. A major advantage of the SDV is the ability to measure in-line rheological data in a continuous fashion, using a setup that most closely approximates the conditions encountered in a real extrusion process. Comparisons will be presented of viscosity data of the SDV to data from a capillary rheometer (CR) and a Rheometrics Mechanical Spectrometer (RMS). Viscosity values as measured on the SDV tend to be lower than those measured on the CR and RMS. Possible reasons for this disagreement will be discussed. The effect of temperature on viscosity, the effect of pressure on viscosity, and the effect of compressibility will be analyzed in detail. It will be shown that these effects can be substantial, particularly with certain types of polymers. Finally, the feasibility of using the slit die viscometer to determine first normal stress differences will be explored.
TL;DR: In this paper, the use of various conductivity-enhancing fillers, such as graphite, metallized glass, or stainless steel fibers, is discussed, and properties of composites containing rapid-solidified aluminum flakes are of particular interest.
Abstract: Conductivity of plastics and polymeric composites is reviewed. The use of various conductivity-enhancing fillers, such as graphite, metallized glass, or stainless steel fibers are discussed. Properties of composites containing rapid-solidified aluminum flakes are of particular interest.
TL;DR: In this paper, the melting strength and breaking stretching ratio (BSR) of polyethylenes with different molecular structures (HDPE, low density (LDPE), and linear low density) are compared.
Abstract: Melt strength (MS) and breaking stretching ratio (BSR) data relative to polyethylenes with different molecular structure (high density (HDPE), low density (LDPE), and linear low density (LLDPE)) are shown. HDPE and LLDPE samples show high breaking stretching ratio and low melt strength values. The LDPE samples exhibit very large melt strength values but low breaking stretching ratio values. For the last mentioned samples, differences are shown in the non-isothermal elongational behavior between samples polymerized with tubular and vessel technology. For all the samples, MS decreases with increasing melt index while BSR increases with melt index.
TL;DR: In this article, a general-purpose finite-element program has been used to simulate the flow of Newtonian, power-law, and viscoelastic fluids in calendering.
Abstract: A general-purpose finite-element program has been used to simulate the flow of Newtonian, power-law, and viscoelastic fluids in calendering. The analysis is fully two-dimensional and does not make use of the lubrication approximation. Isothermal and nonisothermal calendering is studied and the results are compared with predictions from the lubrication approximation. The free surface is determined and circulatory flow patterns are predicted in the melt bank. Detailed calculations have been performed for a rigid poly(viny1 chloride) (PVC) resin that exhibits slip at the wall using rheological data for the melt and machine parameters. The results include determination of the shape and location of the free surface, vortex patterns, temperature and pressure distributions, and predictions of roll-separating force, torque, and power consumption. Comparisons are made with experimental data available in the literature.
TL;DR: In this paper, the dual phase continuity of the IPN system poly(n-butyl acrylate)/polystyrene has been investigated and decrosslinking and extraction studies on sequential IPN's have led to an improved understanding of the dual-phase continuity sometimes present in these materials.
Abstract: Recent research on IPN’s has emphasized thermoplastic IPN’s based on physical crosslinks, and the factors controlling the variation of domain sizes in sequential IPN’s. Most recently, decrosslinking and extraction studies on sequential IPN’s has led to an improved understanding of the dual phase continuity sometimes present in these materials. The sequential IPN system poly(n-butyl acrylate)/polystyrene is emphasized.
TL;DR: In this article, a maximum lifetime of three years was predicted for the best-behaving polycarbonate (PC) grades, mainly based on loss of ductility in tensile tests, as well as loss of optical clarity and chain scission.
Abstract: Polycarbonate (PC), one of the leading engineering plastics, suffers from deterioration under harsh environmental conditions. It is sensitive to the effects of light (UV) radiation, to thermal degradation, and to the attack of hot water, due to hydrolysis. By exposure of various commercial PC grades—at various molecular weights and stabilization—to either natural or accelerated conditions, a maximum lifetime of three years was predicted for the best-behaving grades. The criterion for failure was mainly based on loss of ductility in tensile tests, as well as loss of optical clarity and chain scission. Hot water has a significant effect on the performance of PC samples, and this is considered to be its greatest weakness. Degradation after exposure at various temperatures (without UV or humidity) leads to estimation of a temperature-endurance index, that may serve as a practical limiting criterion for polymer life expectancy.
TL;DR: In this paper, the structure formed in the coagulation stage of the spinning process of poly(p-phenylene benzobisthiazole) fiber is studied by electron microscopy.
Abstract: The structure formed in the coagulation stage of the spinning process of poly(p-phenylene benzobisthiazole) fiber is studied by electron microscopy. An oriented network of microfibrils with typical fibril diameters of about 80-100A is observed. We suggest that these microfibrils are the fundamental structural elements of the fiber. Thus, knowledge of the mechanism by which this initial structure is formed may allow for better control of final fiber properties. The relation of structure formation during coagulation to the phase diagram of a rigid polymer solution and to the kinetic mechanism of the phase transition is discussed.
TL;DR: In this article, a new model for the analysis of impact resistance of polymers was proposed, which takes into account the first stable stage and the point of instability in order to allow the determination of two fracture energies.
Abstract: The method proposed by C. E. Turner and J. G. Williams for characterizing the impact resistance of polymers was reanalyzed and a new method has been developed for the study of semi-ductile polymers. In these polymers, the fracture occurs by a set of stable and unstable crack propagation stages. The new model takes into account the first stable stage and the point of instability in order to allow the determination of two fracture energies Ḡst and Ginst. These fracture parameters characterize the material impact behavior. The model has been applied to polyamide 11 and 12. Molding condition and orientation effects on the impact fracture energies are presented.
TL;DR: In this article, the flow of molten polymers in the calender bank has been computed using a finite-element method with stream function and vorticity, and two nonsymmetrical recirculating regions have been obtained fully in agreement with the experimental observations on poly(vinyl chloride) melt banks.
Abstract: The flow of molten polymers in the calender bank has been computed using a finite-element method with stream function and vorticity. Two nonsymmetrical-recirculating regions have been obtained fully in agreement with the experimental observations on poly(vinyl chloride) melt banks. The pressure distribution along the flow axis is very close to the one obtained using the classical-lubrication approximation.
TL;DR: In this paper, the subject of crazing in polypropylene (PP) was reviewed and specific consideration given to CRAZY in crystalline polymers, and tensile tests conducted over a wide spectrum of temperatures and strain rates indicate that, for a given test temperature, there exists a critical strain rate above which crazing is the dominant deformation mode of PP, while low rates and high temperatures favor shear yielding.
Abstract: The subject of crazing in crystalline polymers is reviewed and specific consideration given to crazing in polypropylene (PP). Tensile tests conducted over a wide spectrum of temperatures and strain rates indicate that, for a given test temperature, there exists a critical strain rate above which crazing is the dominant deformation mode of PP. Similarly, for a given strain rate, there exists a critical temperature which demarcates crazing from shear yielding as the characteristic process of deformation. High deformation rates and low temperatures favor crazing, while low rates and high temperatures favor shear yielding. Crazes in crystalline PP were found to be morphologically similar to those in glassy polymers: high reflectivity, large area-to-thickness ratio, and planarity. They have a higher tendency to bifurcate than those in glassy polymers. Two types of craze fibrils could be identified: those parallel to σ11, and the randomly oriented interconnecting fibrils. It is demonstrated that microtome-trimming at low temperature followed by suitable chemical treatment is an effective technique of sample preparation for SEM examination of craze morphology in crystalline polymers. Further evidence has been provided that crazes in spherulitic polymers do not in general follow an interspherulitie path, but propagate through spherulites. The length of a craze in PP is not restricted to one spherulite diameter, nor does it grow radially.
TL;DR: In this paper, a numerical simulation of the density variation in quenched parts and their aging has been performed by using first-order rate theory for volumetric changes in conjunction with solving the transient one-dimensional heat-conduction equation with a convective heat transfer boundary condition at surface.
Abstract: Density and shrinkage measurements have been performed in quenched and molded slabs from polystyrene (PS) and poly (methylmethacrylate) (PMMA). Various processing conditions have been employed and their effect on density and shrinkage variation in the final parts, as well as volumetric aging vs. Elapsed time at room temperature, have been elucidated. A numerical simulation of the density variation in quenched parts and their aging has been performed by using first-order rate theory for volumetric changes in conjunction with solving the transient one-dimensional heat-conduction equation with a convective heat-transfer boundary condition at surface. A numerical simulation of the shrinkage in molded parts has been carried out by using the equation of state with a simultaneous solving of the governing equations for one-dimensional mold filling during the cavity filling stage followed by transient one-dimensional conduction during packing and cooling stages. Predicted results for density and shrinkage are compared with experimental data.