Approximation of Nonlinear Unloading Effects in the Strain Rate Dependent Deformation Analysis of Polymer Matrix Materials Utilizing a State Variable Approach

An experimental and analytical program is carried out to explore key behaviors in the loading and unloading behavior of polymers. Specifically, the effects of strain rate and hydrostatic stresses on the nonlinear portions of the deformation response are examined. Tension, compression, and shear load only and load/unload tests are conducted on a representative polymer across a range of strain rates, and key features of the experimental results are identified. To conduct a preliminary exploration of how the key features of the deformation response could be simulated analytically, a previously developed set of constitutive equations, which were developed to analyze the strain rate dependent, nonlinear deformation of polymers including the effects of hydrostatic stresses, were modified in order to approximate key features of the nonlinear unloading behavior observed in the polymer. The constitutive relations are based on state variable constitutive equations originally developed for metals. The nonlinear unloading observed in the experiments is approximated by reducing the unloading modulus of the material as the effective inelastic strain is increased. The effects of the hydrostatic stress state on the unloading modulus are also simulated analytically. To examine the revised formulation, the loading and load/unload responses of the representative polymer in tension, compression, and shear are examined at several strain rates. Results computed using the developed constitutive equations were found to correlate reasonably well with the experimental data.     

Numerical Implementation of Polymer Viscoplastic Equations for High Strain-Rate Composite Models

For polymer matrix composites subjected to large strain rates, it is important to correctly characterize the nonlinear and strain-rate dependent response of polymers. Viscoplastic constitutive material models have been developed to account for the effects of hydrostatic effects and inelastic strains in polymer materials. The effective implementation of such viscoplastic models is important for development of composite models geared toward practical applications. Goldberg’s polymer model numerical implementation into a commercial finite-element code constitutes the main objective of this paper. Special attention is given to the use of effective algorithms for solving the model nonlinear rate dependent viscoplastic equations. Existent experimental data are used to verify the accuracy and robustness of the computational polymer model. A phenomenological fiber model and a simplified iso-strain mixture theory used to obtain the resultant stresses in the composite by averaging the stresses of the individual constituents are also defined. The validation of the simplified mixture theory for the composite model will be presented later on.     

Effects of High Strain Rate on Properties and Microstructure Evolution of TWIP Steel Subjected to Impact Loading

 The mechanical properties of the TWIP steel subjected to impact loading at various strain rates were analyzed by the Split Pressure Hopkinson Bar. Meanwhile the microstructure of the TWIP steel fore-and-after the dynamic deformation were characterized and analyzed by optical microscopy (OM), X-ray diffraction (XRD), and transmission electron microscope (TEM). The result shows that when the TWIP steel was deformed under dynamic station, the stress, microshardness and work hardening rate increase with the increment of strain and strain rate; there exist stress fluctuation and decline of work hardening rate for adiabatic temperature rising softening. There exist many pin-like deformation twins in the microstructure of the TWIP steel subjected to impact loading, the grain size after deformation is bigger than that before; the interaction of twins with dislocation and twins with twins, especial emergence of high order deformation twins are the main strengthening mechanisms of the TWIP steel. The nucleation mechanism of deformation twins will be “rebound mechanism”; the incomplete deformation twins can be observed when the strain rate is low; when strain rate raises, deformation twins unite together; furthermore, deformation twins become denser because the nucleation rating enhancing with strain rate increasing.