Common structure, compatibility and complementarity of mathematical models of injection molding

The hierarchy of mathematical models of injection molding is reviewed. Compatibility of the models of the hierarchy, usefulness of simultaneous applications of models formulated on several different levels of the hierarchy and compatability between physical approximations leading to the formulation of a model, and mathematical approximations used to solve numerically the governing equations of the model are discussed. This review is intended to facilitate the search for a model that is best suited to a given need and to indicate future research.

[1]  George L. Hand,et al.  A theory of anisotropic fluids , 1962, Journal of Fluid Mechanics.

[2]  Costas G. Gogos,et al.  A numerical simulation of the cavity filling process with PVC in injection molding , 1973 .

[3]  M. W. Darlington,et al.  Shear anisotropy of short glass fibre reinforced thermoplastics injection mouldings , 1979 .

[5]  A. Tobolsky,et al.  A New Approach to the Theory of Relaxing Polymeric Media , 1946 .

[6]  J. J. Van Deemter Basics of process modeling , 1982 .

[7]  R. S. Spencer,et al.  Some flow phenomena in the injection molding of polystyrene , 1951 .

[8]  Mustafa Kamal,et al.  The injection molding of thermoplastics part I: Theoretical model , 1972 .

[9]  Misazō Yamamoto The Visco-elastic Properties of Network Structure I. General Formalism , 1956 .

[10]  P. M. Naghdi,et al.  On thermal effects in a special class of viscoelastic fluids , 1973 .

[11]  H. A. Lord,et al.  Mold‐filling studies for the injection molding of thermoplastic materials. Part I: The flow of plastic materials in hot‐ and cold‐walled circular channels , 1975 .

[12]  L. G. Leal,et al.  Strong flow criteria based on microstructure deformation , 1982 .

[13]  E. J. Hinch,et al.  Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations , 1976, Journal of Fluid Mechanics.

[14]  C. Petrie Mathematical modelling and the systems approach in plastics processing: The blown film process , 1975 .

[15]  R. G. Parrott,et al.  Numerical simulation of injection mold filling , 1970 .

[16]  M. Kamal,et al.  The fluid mechanics and heat transfer of injection mold filling of thermoplastic materials , 1976 .

[17]  M. Kamal,et al.  The injection molding behavior of thermoplastics in thin rectangular cavities , 1975 .

[18]  J. Pearson,et al.  Mechanical Principles Of Polymer Melt Processing , 1966 .

[19]  C. A. Hieber,et al.  Toward a viscoelastic modelling of the injection molding of polymers , 1980 .

[20]  L. McIntire,et al.  Non-isothermal rheology of polymers and its significance in polymer processing , 1979 .

[21]  Mesoscopic kinetic theory , 1983 .

[22]  H. A. Lord,et al.  Mold‐filling studies for the injection molding of thermoplastic materials. Part II: The transient flow of plastic materials in the cavities of injection‐molding dies , 1975 .

[23]  M. E. Ryan,et al.  Conformal mapping analysis of infection mold filling , 1980 .

[24]  R. Bird Use of simple molecular models in the study of the mechanical behavior of solutions of flexible macromolecules , 1979 .

[25]  Misazō Yamamoto The Visco-elastic Properties of Network Structure III. Normal Stress Effect (Weissenberg Effect) , 1958 .

[26]  G. C. Sarti,et al.  Testing of a constitutive equation for entangled networks by elongational and shear data of polymer melts , 1973 .

[27]  A. I. Leonov Nonequilibrium thermodynamics and rheology of viscoelastic polymer media , 1976 .

[28]  L. C. Woods On the local form of the second law of thermodynamics in continuum mechanics , 1981 .

[29]  I. H. Hillier,et al.  Mechanism of secondary crystallization of polymethylene , 1965 .

[30]  A. S. Lodge A network theory of flow birefringence and stress in concentrated polymer solutions , 1956 .

[31]  Bernard P. Zeigler,et al.  Theory of modeling and simulation , 1976 .

[32]  Norio Takeuchi,et al.  Mixed finite element method for analysis of viscoelastic fluid flow , 1977 .

[33]  D. Soong,et al.  Time‐dependent rheological properties and transient structural states of entangled polymeric liquids—A kinetic network model , 1981 .

[34]  W. E. Langlois A Recursive Approach to the Theory of Slow, Steady‐State Viscoelastic Flow , 1963 .

[35]  A. B. Metzner,et al.  Modeling of Nonisothermal Polymer Processes , 1982 .

[36]  Paul C. Martin,et al.  Unified Hydrodynamic Theory for Crystals, Liquid Crystals, and Normal Fluids , 1972 .

[37]  D. Soong,et al.  Kinetic Network Model for Nonlinear Viscoelastic Properties of Entangled Monodisperse Polymers. I. Steady‐State Flow , 1981 .

[38]  Marcel Crochet,et al.  Numerical Methods in Non-Newtonian Fluid Mechanics , 1983 .

[39]  J. Oldroyd On the formulation of rheological equations of state , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[40]  J. Z. Zhu,et al.  The finite element method , 1977 .

[41]  Costas G. Gogos,et al.  Simulation of the mold filling process , 1974 .

[42]  Z. Tadmor,et al.  Principles of Polymer Processing , 1979 .

[43]  J. Pearson The Lubrication Approximation Applied to Non-Newtonian Flow Problems: A Perturbation Approach , 1967 .

[44]  P. Carreau,et al.  Generalized hydrodynamical equations obeying the entropy principle , 1982 .

[45]  S. F. Shen,et al.  A finite-element/finite-difference simulation of the injection-molding filling process , 1980 .

[46]  S. Richardson,et al.  Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel , 1972, Journal of Fluid Mechanics.

[47]  James L. White,et al.  Fluid mechanical analysis of injection mold filling , 1975 .

[48]  M. Booy A network flow analysis of extrusion dies and other flow systems , 1982 .

[49]  E. J. Hinch,et al.  Constitutive equations in suspension mechanics. Part 1. General formulation , 1975, Journal of Fluid Mechanics.

[50]  Robert C. Armstrong,et al.  Approximation error in finite element calculation of viscoelastic fluid flows , 1982 .

[51]  B. Finlayson The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[52]  Misazō Yamamoto The Visco-elastic Properties of Network Structure II. Structural Viscosity , 1957 .

[53]  B. D. Coleman,et al.  An approximation theorem for functionals, with applications in continuum mechanics , 1960 .

[54]  J. F. Stevenson,et al.  Injection molding in disk-shaped cavities , 1977 .

[55]  J. Lumley,et al.  Mechanics of non-Newtonian fluids , 1978 .

[56]  L. Goettler Mechanical property enhancement in short-fiber composites through the control of fiber orientation during fabrication , 1984 .

[57]  M. Kamal,et al.  The effect of glass fibers on the rheological behavior of polypropylene melts between rotating parallel plates , 1984 .

[58]  L. Utracki,et al.  Rheology of mica-reinforced polyethylene melts† , 1984 .

[59]  W. Rose Fluid–Fluid Interfaces in Steady Motion , 1961, Nature.

[60]  G. Titomanlio Estimation of injection pressure during mold filling , 1982 .

[61]  Z. Tadmor Molecular orientation in injection molding , 1974 .

[62]  S. Middleman,et al.  Fundamentals of polymer processing , 1977 .

[63]  J. F. Stevenson A simplified method for analyzing mold filling dynamics† Part I: Theory , 1978 .