Best Material Model for Polycarbonate at High and Low Strain Rates

Journal of Eng. Materials and Tech., 2006, Vol 128, 543.


Polycarbonate (PC) is commonly used amorphous thermoplastic with excellent mechanical properties, with both high modulus and toughness. One common challenge for Finite Element engineers designing parts from PC is the significant drop in true stress after macroscopic yielding. Simply designing PC parts based on the yield stress is often too conservative due to the significant ductility of the material. This also causes problems with sustainability, weight, and cost due to the conservative design.

In this article I will focus on 2 topics:

  • I will examine the accuracy of different material models when if comes to predicting the large-strain, strain-rate dependent response of PC.
  • I will also discuss what factors control how the yields stress depend on the applied strain rate. PC is a thermoplastic where the yield stress has a different dependence on the strain rate at low and high strain rates.

Also see our post on: “Predicting Creep of Polycarbonate“.


I this study I extracted the stress-strain response from Fig. 7 in the Mulliken-Boyce paper [J. Eng. Mat. Tech, 2006, Vol 128, 543]. I used a new data extraction feature in MCalibration to quickly convert a screenshot of that figure into MCalibration load cases. I then used the results from my previous studies on Hytrel and thermoplastic elastomers to select the following candidate material models:

All material models were then calibrated using the MCalibration software. In all calibrations I added one Poisson’s Ratio load case in order to be able to find an appropriate bulk modulus for each model.

Ansys Bergstrom-Boyce Model

The Bergstrom-Boyce (BB) model is a model that I developed for predicting the large-strain viscoelastic response of elastomers. It was not meant to capture the response of thermoplastics, so it is no surprise that it cannot capture the softening in the stress-strain response that occurs in PC after yielding. 

The average error in the BB model predictions is 7.0%, which is not too bad, but it is not able qualitatively capture the nature of the stress-strain curves.

Abaqus Johnson-Cook

The Johnson-Cook plasticity model is an isotropic hardening plasticity model with built-in strain rate dependence. The average predicted error in this case is 6.5%, but as is shown in the figure, the predicted strain-rate dependence is not right, and the model cannot predict stress softening after yielding.

Abaqus Parallel Rheological Framework (PRF) Model

The figure shows the best stress-strain predictions from a 3 network Abaqus PRF model with Yeoh hyperelastic networks with power law flow. One of the weaknesses of the PRF model is that it cannot predict stress softening after yielding.

The average error in the model predictions is 7.4%.

PolyUMod Three Network (TN) Model

The PolyUMod TN model can accurately predict the response of the PC. The model captures both the strain-rate dependence and the softening after yielding. The average error in the model predictions is 3.2%.

The model predictions in this case are looking quantitatively correct.

PolyUMod TNV Model

The most accurate material model for polycarbonate (PC) is the PolyUMod TNV model. The model captures the strain-rate dependence of the Young’s modulus, the strain-rate dependence of the yield stress, and the softening after yielding. 

The average error in the model predictions is 2.8%. 


The following figure plots the average error in the model predictions from the different material models examined in this study. The Abaqus PRF model has an error that is 160% larger than the error from the PolyUMod TNV model. 

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