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Copper material modelling using Johnson Cook model in LS DYNA


I am performing high strain rate testing/dynamic testing in split Hopkinson pressure bar (SHPB). As part of validating my experimental results, I have created a numerical model in LS DYNA. The model consists of striker bar, pulse shaper made of copper and incident bar (Fig 1 and Fig 2 in the attached pdf). Copper pulse shaper typically filters out high frequency oscillations of the incident pulse and also increases its rise time. The size of pulse shaper is 2.5 mm thick *12 mm diameter. It is circular in shape. The output I am looking is z-stress on an incident bar element (typically its center of the bar where strain gage is installed). The incident stress vs time obtained numerically and experimentally must match each other. However, I am not able to achieve it. Refer to Fig 3. 

From my quasi-static tests on copper specimen, I obtained A, B and n parameter. I had a sheet 1 ft by 1 ft by 2.5 mm thick from which 4 tensile test specimens were created (2 in one direction and 2 in direction perpendicular to it). My SHPB is suitable for testing rocks and not metallic specimens. Hence I was not able to do dynamic tests to obtain parameter C. Now since I am not able to match my experimental and numerical incident stress vs time curves, I have the following question. Please help me. I am stuck at this point from past many weeks.

1. The rise of incident pulse numerically is very slow more than double that of experimentally obtained pulse (Fig 3). This is most probably because the rate at which copper pulse shaper is deforming is also very slow. This I checked by obtained z stress vs time (Fig 4) and effective plastic strain vs time (Fig 5) curves for a element in pulse shaper. Now I am not able to find solution as to what parameter shall I change to get a good match. I have played with C parameter from 0.009 to 0.2 but the rate of loading in pulse shaper does not change and same holds for rate of loading of incident pulse. Are my A, B and n parameters incorrect? Please refer to engineering stress vs engineering strain curve of the copper (Fig 7) I have got from tensile tests. It might give you some idea if my parameters are right or wrong? If A, B and n are correct, I can at least be sure that I have to change C.

I have already done validations to check my contact and I think it is working fine. So all my attention is on material model parameters. I am using log linear Johnson Cook parameter C for strain rate sensitivity.



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