FINITE ELEMENT ANALYSIS OF HIGH STRAIN RATE MATERIAL DEFORMATION

Abstract

Mechanical properties of metals in general are strain rate dependent i.e. they respond differently at quasi-static condition and at higher strain rate loading condition. Under dynamic loading the yield stress of material changes with rate of loading, also change is observed in other properties such as fracture toughness/mechanism, percentage elongation etc. To describe the behavior of material at high strain rate of loading, material models are required. Johnson-Cook material model is one such phenomenological material model that represents the high strain rate material response of many metals and alloys fairly accurately. G. R .Johnson and W. H. Cook proposed this model in 1983. The model contains five parameter constants, which need to be determined experimentally. Both quasi-static as well as high strain rate testing is required to determine the constant parameters. In the present work J-C material model of copper has been developed for further analysis using FE method. For this purpose quasi-static compressive test of cylindrical specimen of copper has been done performed using UTM. Also a split Hopkinson pressure bar set-up has been fabricated for high strain rate testing. SHPB works on the principle of one dimensional wave propagation. The set up consists of two long cylindrical bars, a gas gun and data acquisition system. Strain gauges are glued to the center of incident and transmission bar to read the magnitude of pulse in the bar. The specimen to be tested is sandwiched between the bars. Gas gun is used to fire the striker bar, which on striking the incident bar generates the compressive stress pulse in the bar. The pulse generated in the incident and transmission bar helps to generate stress-strain curve at high strain rate for given material specimen with the help of standard formula already established for the technique. MATLAB programs have been made to post process the SHPB data and to obtain stress-strain curve at high strain rate. The strain rate parameter in J-C model is evaluated by using the SHPB data. Once the material model parameters are known those are used in FE analysis. FE simulation of non-linear transient dynamics problem need `high strain rate' material model to be implemented. Numerical simulation of transient structural dynamic problem such as 11 impact penetration, crash, shock loading etc is carried out using explicit finite element procedure. PAM-CRASH software is used for FE analysis. Before using the calculated JC parameter for FE simulation the PAM-CRASH software is benchmarked by simulating existing experimental result. The calculated J-C parameter for copper is then used to simulate the vertical drop of a copper cylindrical specimen, of same size as used in benchmarking problem, from a fixed height with a known velocity. The J-C results are then compared with result obtained using different material models namely power law and bilinear relation. iii