Analysis of the Thermal Coupling of the Molten Mass, Structure, and Tool to Precisely Predict Schrinkage and Warpage in Injection Moulding Processes

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Christian Hopmann

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Both plastics and metal processing have in common with regard to the primary moulding processes that a melt is first conveyed into the cavity of the mould to be moulded and solidifies there. Temperature equalisation processes between the melt, the microstructures that form and the mould shape determine the resulting states of order at the molecular and atomic level, which have a decisive influence on both the formation of the morphology and the development of residual stresses. Residual stress and morphology-related inhomogeneities of the mechanical properties lead to shrinkage and warpage in plastic components. This leads to serious problems during the manufacturing process of high-precision components that require a low tolerance with regard to the final contour. However, the underlying mechanisms have not yet been considered in the research on plastics processing as a whole. The reasons for this are both the lack of models for the temperature equalisation processes between melt, microstructure and tool and the lack of thermal and mechanical material data in relation to the morphology and the complex determination of heat transfer coefficients of the material pairings metal/plastic. In sub-project B04, the temperature equalisation processes and the resulting local mechanical properties are to be investigated with the aim of improving the prediction accuracy of the warpage of plastic components and modelled in the subsequent production periods as well as taken into account in the injection moulding simulation. Previous integrative simulation approaches neglect the formation of microstructures during the process and use material models that are calibrated at non-process-relevant cooling rates. This leads to significant differences between simulation and reality, making cost-intensive and subsequent adjustments to the injection mould necessary.

In order to improve the simulation, a multi-scale simulation chain is being developed in collaboration with B07 (cf. Figure 1).

  Figure 1: Schematic of the multi-scale simulation chain consisting of the filling simulation, the microstructure simulation, the homogenisation and the warpage prediction. Copyright: © SFB 1120 Figure 1: Schematic of the multi-scale simulation chain consisting of the filling simulation, the microstructure simulation, the homogenisation and the warpage prediction.
 
 

Multi-scale simulation chain). The multi-scale simulation chain is initiated by a filling and solidification simulation on the macro scale (~cm) in COMSOL, Comsol Multiphysics GmbH, Göttingen. The calculated temperature and velocity fields from the filling simulation are used in the second step to calculate local microstructures using the specially developed software SphäroSim. Based on the microstructure, thermal and mechanical properties of the local microstructure distribution are calculated using HOMAT (B07). The local mechanical properties are combined with the calculated shrinkage from the filling simulation in ABAQUS, ABAQUS Inc. Palo Alto, California, USA, and the resulting total warpage is calculated.

The multi-scale simulation chain was extended in the second funding period of the project to include the calculation of the heat of crystallisation during solidification in the microstructure simulation. This allows the heat development at the solidification front during the growth of the individual microstructures to be taken into account. However, the consideration of the heat of crystallisation requires a thermal coupling of the microstructure simulation with the filling simulation, since the exact solidification behaviour has a special influence on the process steps "filling" and "holding pressure" in the injection moulding process. For this reason, an iteration loop was developed between the microstructure simulation and the filling simulation in order to align the solidification and temperature behaviour between the simulations.

In addition, a pvT material model, which describes the relationship between pressure, the specific volume and the temperature of a material, was developed in the second funding period for process-relevant cooling rates for the isotactic polypropylene under consideration.

 
  Prediction of the CTD model in the diagram with the measurement data of the pvT measurement cell, the DSC and the flash DSC (left). Schematic of the measurement ranges covered by the different measurement techniques (right). Copyright: © SFB 1120 Figure 2: Prediction of the CTD model in the diagram with the measurement data of the pvT measurement cell, the DSC and the flash DSC (left). Schematic of the measurement ranges covered by the different measurement techniques (right).
 
 

Using a pvT measuring cell (low cooling rates under various pressures), Differential Scanning Calorimetry (DSC) (low and medium cooling rates under ambient pressure) and Flash DSC (high cooling rates under ambient pressure), the Continuous Two-Domain pvT model (CTD model) was calibrated for the isotactic polypropylene (cf. Figure 2). However, the model could not yet be validated at simultaneously high pressures and high cooling rates, as is the case in the injection moulding process. Nevertheless, the model shows high agreement with a coefficient of determination of R² = 0.993 with the measurement data of all three measurement systems (cf. Figure 2). The measurements of the flash DSC were also used to determine the crystallisation behaviour at high cooling rates for the microstructure simulation. A coefficient of determination of R² = 0.957 was achieved with a non-isothermal model for the formation and growth of the microstructures.

In the final funding period, the new material models and techniques will be used to provide a precise and reliable warpage prediction. Based on this, a compensation strategy will be developed to minimise the final component warpage based on the resulting microstructure. Particular emphasis is placed on the thermal conditions in the component during the injection moulding process, as these are decisive for the formation and growth of the microstructures.