Abstract
We present a general internal state variable (ISV) elastic-viscoplastic constitutive model that was initially applied to amorphous polymers (Bouvard et al J Eng Mater Technol 131(4), 041206, 2013) but has been extended to apply to semi-crystalline polymers along with a fracture criterion. In this work, we experimentally calibrated and validated the mechanical behavior of two semi-crystalline polymers (a polypropylene (PP) and a copolymer polypropylene (co-PP)) under different stress states, temperatures, and nominal strain rates. The experiments included compression, tension, impact, and three point bending tests with the notion of capturing the time, temperature, stress state dependence, and failure mechanisms under large strains. The ISV model was integrated into a finite element (FE) code and the FE simulations agreed very well with the PP and co-PP mechanical behavior under compression, impact, and three point bending thus exercising the model under different nominal strain rates, temperatures, and stress states. Two failure criteria were determined from the numerical simulations to build failure criteria maps that distinguished brittle and ductile failure as validated by the experimental observations. This study illustrates the generality of the Bouvard et al. (J Eng Mater Technol 131(4), 041206, 2013), which was previously employed to analyze an amorphous polycarbonate polymer.
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Acknowledgments
We would like to thank Mr. Jim Kolb, senior director of Automotive for the American Chemistry Council for funding this effort under Grant No. 011104-001 as well as Dr. Mike Wyzgoski, consultant for American Chemistry Council, for his guidance in this project. The authors would also like to thank ExxonMobil Chemical Company for providing the different thermoplastics investigated in this project and the Center for Advanced Vehicular Systems (CAVS) at Mississippi State University for its support. CAVS acknowledges the collaboration provided through the SIMULIA Research & Development program under which licenses of ABAQUS were provided.
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Appendices
Appendix A: Ductile failure strain
Figure 21 displays the determination of the equivalent plastic strain-to-failure for the impact tests. Applying the ductile failure criterion to the impact tests, the displacement at the point of maximum loading, Udisp, is determined first. The peak load is chosen as the point of failure since the time when cracks or tears begin to appear is unknown. The equivalent plastic strain at this displacement is then found using results from the simulation. The failure strain as a function of strain rate can then be plotted.
Appendix B. Brittle failure criteria
The values for maximum principal stress were calculated from ABAQUS simulations. For each geometry, the maximum principal stress is plotted as a function of displacement as shown in Fig. 22. The maximum principal stress curves display a plateau which has been marked by a dashed line. After the plateau, several of the curves begin to increase again. This increase is the result of a lack of damage in the model and element distortion as the simulation progresses. The stress ratio used by [50] is achieved by normalizing the maximum principal stress obtained from the simulation of the three point bending tests (and estimated from the plateau of the curve) to the yield stress determined from the compression test results. If the stress ratio of a future test is below the stress ratio required for craze initiation, then brittle failure is not a concern.
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Bouvard, J.L., Denton, B., Freire, L. et al. Modeling the mechanical behavior and impact properties of polypropylene and copolymer polypropylene. J Polym Res 23, 70 (2016). https://doi.org/10.1007/s10965-016-0947-z
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DOI: https://doi.org/10.1007/s10965-016-0947-z