Comparison between Linear and Nonlinear Modelling of Viscoelastic Material Behaviour on the Example of Polymer Encapsulation for Advanced Electronic Virtual Design

Electronic components and electronic packages consist majorly of polymer-based materials. Polymers are applied for various purposes such as environmental protection, stabilization, weight reduction, performance increases or cost minimization. Several functional polymer materials are combined by potting compounds, adhesives and underfills and result in material mixtures. These combinations generate complex thermal-mechanical behaviour. Today’s electronic designs require numerical evaluation tools to support the product design process an fulfil the time to market demands. The finite element method (FEM) fills this role. Often material behaviour needs to be predicted while considering temperature and time dependencies. For polymers in particular, viscoelastic material models are widely used, but they are only valid for small strains and are therefore limited to the linear deformation range. For large deformations and strains, other more sophisticated material models are needed to calculate the nonlinear, temperature-dependent, and time-dependent effects.Based on previous efforts from the authors, this paper extends the overview for the Three-Network-Model (TN), which can describe nonlinear viscoelastic behaviour of thermoset materials (NLVE). The focus of this work is to compare the nonlinear viscoelastic characterisation with the currently established linear viscoelastic characterisation from dynamic mechanical analysis (DMA). The goal is to help to understand whether the increased effort for more complex nonlinear modelling is justified. To determine the needed model parameters for the NLVE-modelling, mechanical measurements with variable force-deformation-time regimes were performed at multiple temperatures on the example of encapsulation compounds. A digital representation of the experiment, based on finite-element-analysis, was created. Subsequently the FE- model was used to determine the required NLVE model parameters. The mechanical experiments were performed within deformation rates between 1e-4 mm/s to 1e-2 mm/s. The mechanical response has further been measured under multiple temperature levels. In the second step, the model parameters have been determined and calibrated. This is achieved with an inverse method by using the FEM response calculations of the digital experiment and optimization towards the root-mean-square error of the comparison with the real measurement curves. Additionally, the linear viscoelastic behaviour of the material has been measured using Dynamic-Mechanical-Analysis (DMA). Here the parametrisation towards a Prony-series based master curve and corresponding shift function has been utilized to bring the material response into the FEM environment.The comparison of both modelling approaches within a virtual comparison based on tensile, bending and temperature cycle load has been done. The results show that the increase in accuracy generally depends on the material and varies depending on the application. The methodology shows that careful evaluation towards complex modelling is required and characterisation should include all strain ranges which occur later. Overall, the proposed nonlinear viscoelastic model, data acquisition and coefficient fit methods have shown to be efficient to bring small and large strain viscoelastic material behaviour into electronic design support simulations. More accurate simulation results for polymer strains, will increase the overall acceptance of virtual prototyping. However, efficiency in terms of characterisation effort still should be considered. Our current approach can handle both while offering an overview of the possible accuracy gain.