Injection moulding simulation using a CEL approach: sensitivity analysis for the equation of state and mass scaling

Overmoulding of three-dimensional continuous-fibre skeletons is an advanced manufacturing technique for producing high-performance structural components with exceptional mechanical properties and design flexibility. This process allows components to be tailored to specific load conditions while providing opportunities for novel geometries and lightweight constructions. Despite significant advancements in the development and optimization of process technologies [1], there remains a gap in understanding the material behaviour and interactions during overmoulding. To close this gap, numerical process simulation supports process understanding and is the basis for virtual process design and reliable prediction of component properties. Due to the interaction between the melt flow and the deformation of the fibre skeletons, a Coupled Eulerian-Lagrangian (CEL) approach is used in the simulation software Abaqus/Explicit to model the fluid phase. In CEL, for each time step, the considered phase is deformed in a Lagrangian step and projected back to an Eulerian mesh afterwards, taking into account the transport equations [2]. Therefore, the method is well suited to model both large deformations and fluid movement, as in the case of fluid-structure interaction. ... mehrFor example, it has been successfully used for fibre bundle simulation of compression moulding processes [3]. An equation of state (EOS) is required to describe the thermodynamic material behaviour for the fluid phase. To improve numerical stability, mass scaling may be necessary, which of course influences the material behaviour and may create unrealistic results. Therefore, in the present work, a sensitivity analysis is carried out to investigate the influence of the equation of state and the mass scaling on the mould filling behaviour. A form of the Mie-Grüneisen equation of state is used, where the pressure is a function of density and the specific energy. In the investigated example case, a plate is filled with a constant volume flow rate and all velocity components at the cavity walls are set to zero. The change in density over time is monitored as an output to achieve a nearly incompressible material behaviour for the fluid phase. When using mass scaling the kinetic energy should remain small compared to the total strain energy in the system. The result of the sensitivity analysis is the basis for the correct prediction of contact forces between the fluid and fibre strands during the overmoulding process.

References
[1] B. Beck, H. Tawfik, J. Haas, Y.-B. Park, and F. Henning, “Automated 3D Skeleton Winding Process for Continuous-Fiber-Reinforcements in Structural Thermoplastic Components,” in Advances in Polymer Processing 2020, C. Hopmann and R. Dahlmann, Eds., Berlin, Heidelberg: Springer Berlin Heidelberg, 2020, pp. 150–161. doi: 10.1007/978-3-662-60809-8_13.
[2] D. J. Benson, “Computational methods in Lagrangian and Eulerian hydrocodes,” Computer Methods in Applied Mechanics and Engineering, vol. 99, no. 2–3, pp. 235–394, Sep. 1992, doi: 10.1016/0045-7825(92)90042-I.
[3] N. Meyer, S. Ilinzeer, A. N. Hrymak, F. Henning, and L. Kärger, “Non-isothermal direct bundle simulation of SMC compression molding with a non-Newtonian compressible matrix,” Journal of Non-Newtonian Fluid Mechanics, vol. 310, no. 104940, Dec. 2022, doi: 10.1016/j.jnnfm.2022.104940.