Behaviour and modelling of polymers for crash applications
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The present work concerns the characterisation and modelling of ductile polymeric materials for crash applications. The materials investigated are two particle-reinforced polypropylenes (PP) used in automotive industry. One is rubber-modified while the other is mineral-filled. It is common in automotive industry to add particles to thermoplastics. One reason is to increase their toughness. Such particles have an effect on the macroscopic behaviour of the materials. Both materials have been tested under different stress states from tension via shear to compression at quasi-static and dynamic strain rates. All mechanical tests have been instrumented with a camera for a subsequent use of the digital image correlation technique to acquire the strain field. Both materials exhibit a significant rate and pressure sensitivity, and they also turn out to be compressible during plastic deformation. Microstructural analyses have been performed on original specimens, but also on fractured ones to understand the main mechanisms leading to the observed mechanical response. It was observed that the particles have a significant influence on the macroscopic behaviour because they are the places where cavities are initiated in the materials. A constitutive model that accounts for the specificities observed during the experimental campaign is thereafter reviewed. It is a hyperelastic-viscoplastic constitutive law, with a pressure-dependent yield criterion. An entropic hyperelastic contribution is also included in the constitutive model to account for the large non-linear elastic strains often reported in thermoplastic materials. The model is simple enough to be calibrated analytically and used by e.g. the automotive industry. As components made of thermoplastics typically are thin-walled, a shell version has also been developed for industrial applications. Simulations have been run on specimens to show the abilities of the model to capture the experimental response. The results are found well in agreement in the case of the rubbermodified material. However, the mineral-filled PP can not be accurately described due to the significant damage induced by cavitation around the mineral particles. A numerical analysis of the effect of the particle into a polymeric matrix was conducted and enabled to develop a modified version of the model, accounting for macroscopic damage. A Gurson-like framework was adopted. Results are in better agreement with the experiment, and the model is in particular able to describe large softening or hardening effects. The counterpart is an increased complexity of calibration. Finally, validation simulations are run on more complex components to show the ability of the models to predict the macroscopic response. From the three-point bending tests, it is noticed that both models give the same macroscopic response, which is found well in agreement with the experiment. The analysis of the strain field in the sample shows, however, some differences between the original version of the model and the modified one as better prediction of the strain field distribution are obtained with the second. This is an important feature for future investigation concerning ductile fracture. As an industrial demonstrator, a crash-box is also investigated. This is a more complex thin-walled structure, and it was impacted by a 200 kg projectile at a speed of 10 m/s. Results on the mineral-filled PP can not be exploited as a fragmentation process is observed, which can not be captured with the present constitutive models. A fracture criterion is needed. However, concerning the rubber-modified PP, prediction of the absorbed energy during the simulations using the original constitutive model is in good agreement with the experimental results, in its brick or shell version. This demonstrates the ability of the model to capture the important features of ductile polymeric materials and thus, its industrial benefit.