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Composites and Coatings Group

Department of Materials Science & Metallurgy

Johnson-Cook, High strain rate, Ballistic impact, Inverse FEM

It is well established that the relationship of material flow stress to equivalent plastic strain is dependent on the strain rate and temperature [1], as in figure 1. This can be demonstrated by the split Hopkinson bar test. It is generally seen that the yield and tensile strengths increase with strain rate, with the former generally being more sensitive. A dramatic increase in sensitivity has also been reported at high strain rates in testing of 316L steels [2]. Being able to effectively capture this behaviour has implications for a variety of applications where strain rates and temperatures are high; notably aerospace engineering, ballistics and crash mechanics in the automotive industry [3].


Figure 1 - True stress vs true strain curves for AZ31B magnesium alloy at varying strain rates [4].

As a result, an algorithm for extracting rate-dependent plasticity parameters using dynamic indentation and an inverse finite element method is being developed. The impact of tungsten-carbide spheres fired at high speed (from a gas gun) at static zinc targets is recorded using high speed photography (~100,000 frames per second) in order to measure their displacement-time histories. The impact events are then simulated using the finite element software package, ABAQUS, and the strain rate dependent plasticity model of Johnson & Cook. The simulations are run repeatedly, with each model run incorporating a different value for the strain rate sensitivity parameter in the Johnson & Cook plasticity model. The predicted displacement-time history from each model run is then compared with the measured displacement-time history, while the level of agreement between the two was characterised using a “goodness-of-fit parameter”. The rate-sensitivity parameter generating the best “goodness-of-fit” is chosen as the “correct” one and validated subsequently with impact tests at different velocities.


1.         Klepaczko, J.R., PHYSICAL-STATE VARIABLES - THE KEY TO CONSTITUTIVE MODELING IN DYNAMIC PLASTICITY. Nuclear Engineering and Design, 1991. 127(1): p. 103-115.

2.         Lee, W.S., C.F. Lin, and T.J. Liu, Impact and Fracture Response of Sintered 316L Stainless Steel Subjected to High Strain Rate Loading. Materials Characterization, 2007. 58: p. 363-370.

3.         Peroni, L., M. Scapin, and M. Peroni, Identification of strain-rate and thermal sensitive material model with an inverse method, in Icem 14: 14th International Conference on Experimental Mechanics, Vol 6, F. Bremand, Editor. 2010, E D P Sciences: Cedex A.

4.         Nguyen, N.-T., et al., Mechanical behavior of AZ31B Mg alloy sheets under monotonic and cyclic loadings at room and moderately elevated temperatures. Materials, 2014. 7(2): p. 1271-1295.


 Max  Burley
PhD Student - University of Cambridge