Modeling of morphology evolution in the injection molding process of thermoplastic polymers

Fiber orientation in simple injection moldings. Part 1. Theory and numerical methods

Part 1 The Current State of Simulation: Introduction, Stress and Strain in Fluid Mechanics, Material Properties of Polymers, Governing Equations, Approximations for Injection Molding, Numerical Methods for Solution Part 2 Improving Molding Simulation: Improved Fiber Orientation Modeling, Improved Mechanical Property Modeling, Long Fiber-Filled Materials, Crystallization, Effects of Crystallizations on Rheology and Thermal Properties, Colorant Effects, Prediction of Post-Molding Shrinkage and Warpage, Additional Issues of Injection-Molding Simulation, Epilogue Appendices: History of Injection-Molding Simulation, Tensor Notation, Derivation of Fiber Evolution Equations, Dimensional Analysis of Governing Equations, The Finite Difference Method, The Finite Element Method, Numerical Methods for the 2.5D Approximation, Three-Dimensional FEM for Mold Filling Analysis, Level Set Method, Full Form of Mori-Tanaka Model.

https://bilder.buecher.de/zusatz/35/35650/35650163_inha_1.pdf

Flow Analysis of Injection Molds

This paper sets out the theory and numerical methods used to simulate filling and fiber orientation is simple injection moldings (a film-gated strip and a center-gated disk). Our simulation applies to these simple geometry problems for the flow of a generalized Newtonian fluid where the velocities can be solved independently of fiber orientation. This simplification is valid when the orientation is so flat that the fibers do not contribute to the gapwise shear stresses. A finite difference solution calculates the temperature and velocity fields along the flow direction and through the thickness of the part, and fiber orientation is then integrated numerically along pathlines. Fiber orientation is three-dimensional, using a second-rank tensor representation of the orientation distribution function. The assumptions used to develop the simulation are not valid near the flow front, where the recirculating fountain flow complicates the problem. We present a numerrical scheme that includes the effect of the fountain flow on temperature and fiber orientation near the flow front. The simulation predicts that the orientation will vary through the thickness of the part, causing the molding to appear layered. The outer “skin” layer is predicted only if the effects of the fountain flow and heat transfer are included in the simulation.

Fiber orientation in simple injection moldings. Part I: Theory and numerical methods

In this paper we present a detailed thermoviscoelastic formulation for the simulation of thermally and pressure induced residual stresses in injection moulded short-fibre-reinforced thermoplastics. The computed residual stresses enable us to predict shrinkage and warpage in the finished products. We also apply an anisotropic version of a rotary diffusion equation to calculate the flow-induced fibre orientation distribution. The predicted fibre orientation state, together with micromechanical theories, allows the incorporation of anisotropy in material properties into the thermoviscoelastic model. Finally we report three numerical examples to indicate the success of the present model.

/pdf/thermoviscoelastic-simulation-of-thermally-and-pressure-2dmqnvej1c.pdf

Thermoviscoelastic simulation of thermally and pressure-induced stresses in injection moulding for the prediction of shrinkage and warpage for fibre-reinforced thermoplastics

Moldability criteria and process optimization for both reactive and thermoplastic injection molding hinge on the mold-filling step. The fluid mechanics of the filling step is typically described in terms of a one-dimensional main flow and a complex two-dimensional flow near the advancing front, often termed the “fountain flow.” A unique apparatus which permits direct observation of the fountain flow in a rectangular cavity is described. The motion of tracer lines as well as the pathlines have been photographed for both Newtonian and shear-thinning liquids. The data show clearly the main flow, the transition to the front flow, and the deceleration and acceleration zones in the fountain flow, which lead to a “mushrooming” of the tracer line.

In addition, Galerkin finite-element analysis is used to predict the isothermal free-surface flow of a Newtonian liquid near the advancing front between parallel plates. The most interesting visualization of the calculated flow is obtained by tracking lines of material, thus producing numerical tracer experiments. The calculations show the widely varying residence times and the complex shear and extensional deformation histories of fluid elements as they move through the fountain flow region. The calculations are in agreement with the experiments and clarify previous results, both theoretical and experimental, that did not capture the details of the entire flow field.

The kinematics of fountain flow in mold‐filling

The residence time of a fluid particle in mold filling is total time spent in the mold. Displaying curves of constant residence time in the mold gives the space-time distribution during the filling process. A simple method to calculate space-time distributions is presented. Applications to mold filling in reaction injection molding (RIM) are illustrated.

Space-time distribution in filling a mold

Adiabatic reactive rheometry involves the simultaneous measurement of viscosity and temperature changes during adiabatic polymerization. Using the adiabatic reactor method to relate temperature to fractional conversion results in a useful rheokinetic tool ideally suited for fastreacting reaction injection molding (RIM) systems for which the mold-filling step is nearly adiabatic. In this work, a small laboratory RIM machine is used to mix the reactants and deliver them to a constant stress rheometer retrofitted with a wide-gap Couette geometry and two thermocouples. Measurements on two polyurethane systems are reported. A simple cross-linking system is used to verify the adiabatic rheokinetic method through comparison to a known gel conversion. Subsequent measurements on a phase-separating RIM system show that increases in catalyst level, hard segment content, and initial reactant temperature result in a decreased gel time and an increased gel conversion. The viscosity rise profiles aid our understanding of the onset and development of phase separation. They are also essential for mold-filling models and establishing moldability criteria for these RIM systems.

J. W. Blake

Papers

The kinematics of fountain flow in mold‐filling

Space-time distribution in filling a mold

Adiabatic reactive viscometry for polyurethane reaction injection molding