A Viscoelastic-Viscoplastic Time-Temperature Equivalence for Thermoplastics

For automotive suppliers, it is essential to model the behavior of thermoplastics under crash loading and for a large range of temperature typically from -30° until 85°c. Thermoplastics are very sensitive to both strain rate and temperature with an inverse relation: hardening with strain rate and softening with temperature. Generally, a large experimental campaign has to be carried out to identify different behavior laws of the material, each of them for a specific range of strain rate and temperature. Then, according to the characteristics of the loading case, e.g. impact, corresponding behavior laws are chosen in the database to run the numerical simulations. This results in an important experimental cost and a large database to manage. It is then interesting to explore the time-temperature equivalence of thermoplastics to act on both aspects. Relations between strain rate and temperature sensitivities are identified through dynamic mechanical analysis (DMA) in the viscoelastic domain and described through the Williams, Landel and Ferry model or the Arrhenius model for example. For that, a shift factor is experimentally determined and introduced to modify the time step in the behavior model for the finite element simulation, thus simulating an adapted strain rate. As a novelty, the time-temperature equivalence is here extended to the viscoplastic domain by keeping the same shift factor. It therefore becomes possible to cover all the scope of temperature and strain rate of automotive applications from only DMA and tensile tests at room temperature and different strain rates. This approach is implemented in association with viscoelastic, viscoplastic with non-associative plasticity constitutive laws and non-local damage model [1][2][3] and applied to the case of a polypropylene. The time temperature equivalence is validated for the viscoelastic as well as for the viscoplastic parts of the behavior with good experimental/numerical correlation. As a result, the number of material cards required in Ls Dyna is reduced to only one to cover all the simulations. This approach is also under investigation to be applied to the failure model.