The Freiburg glassy polymer model

This work presents a simple material model suitable for dynamic simulations of glassy polymers, considering the effects of strain rate and temperature. Glassy polymers typically exhibit strong strain rate effects and are strongly influenced by the changes in temperature. Currently, they are the greatest choice for light weight body armours due to its capability to withstand high deformations even under impact. To accurately model such a material at impact rates of strain and varying temperatures, a trustworthy material model is required that is suitable for implementation into explicit continuum mechanics solvers and can capture the characteristics with good accuracy. To the author's knowledge, currently no model which is both simple and accurate exists to date. This situation is in stark contrast with metals, where the rather simple Johnson-Cook plasticity model has been used with great success for the last three decades. Despite being a purely phenomenological model, the Johnson-Cook plasticity model has been very successful because of its simplicity and a well-defi ned parameter space. A similar practical Ansatz for glassy polymers such as polycarbonate is introduced in this work. The stress-strain behaviour of a glassy polymer exhibits detailed structure with characteristic features including upper and lower yield points, strain hardening, and a well-de fined ultimate failure point. This work begins by introducing piecewise analytical functions, that are uniquely determined by the characteristic points. These analytical functions model the elastic regime, the onset of yield at the upper yield point, the smooth decay to the lower yield point, and the subsequent strain hardening up to the failure point. To this end, a power-law dependency of the characteristic points on strain rate is assumed and the time-temperature superposition principle is invoked via the WLF (Williams, Landel and Ferry) equation thus leading to the development of a purely empirical fitting approach. As the analytical functions depend parametrically only on the characteristic points, the material model is obtained as a simple closed set of equations, valid over an entire range of strain rates and temperatures. The combined use of parametrized analytical functions, a power law dependence on strain rate, and the time temperature superposition principle facilitated to reduce the hyper-surface of yield strength values to a tractable problem. The calibration data required for the empirical fitting approach is obtained by performing tension experiments at various strain rates and temperatures. Identifying the lack of failure strain information at elevated rates of strain and temperature, an elevated-temperature testing methodology on the Split-Hopkinson Tension bar (SHTB) is designed. This led to the development of a heat chamber suitable for glassy polymers and makes a good t to the existing SHTB setup. The resulting material model is implemented as a user-subroutine in the commercial finite element code LS-Dyna, suitable for explicit simulations. An efficient J2 plasticity algorithm based on the radial return method is employed, augmented by a strain rate and temperature dependent yield surface. The implementation is verif ed by reproducing the experimental input data. To further validate the model, the simulation predictions are compared to a gas gun impact experiment wherein a polycarbonate plate is impacted by a steel sphere at various velocities and temperatures. The model yields a good quantitative agreement where the maximum out-of-plane deformation of the plate is fairly well captured.