Application of copper as a pulse shaper in SHPB tests on brittle materials- experimental study, constitutive parameters identification, and numerical simulations

Abstract

Generally, optimum dimensions of a pulse shaper (PS) in SHPB tests on brittle materials like rock are chosen by performing numerous experiments with different sizes of PS. The dimensions that give the best force equilibrium and constant strain rate loading in the specimen are selected. Experimental efforts can be saved if the constitutive behavior of the PS can be simulated numerically. In the current work, the behavior of pure copper is investigated at various strain rates (up to ∼4000 /s) and temperatures (till 250 °C) in as-received and annealed conditions. The mechanical behavior of copper is assessed in terms of strain hardening rate, strain rate sensitivity, and temperature sensitivity. It is found that the strain hardening rate in annealed samples is almost twice that of as-received ones. A strain rate increase strengthens copper while a temperature rise weakens it. Fractographs of quasi-static samples tested at various temperatures indicate that all samples undergo ductile failure. The experimental data is used to derive constitutive parameters of the Johnson-Cook (JC) model using a multi-objective optimization method. It is concluded that the modified JC model fits better than the original form, as substantiated by higher R2 and lower AARE (average absolute relative error) values. The derived parameters are successfully applied to model the dynamic behavior of the copper PS in SHPB tests on Kota sandstone samples. It is observed that the experimental and numerical incident pulses are qualitatively similar, and the Russell comprehensive error is well within 0.15 for all the cases. It is concluded that investigating copper behavior till ∼4000 /s yields sufficiently accurate results to predict PS behavior during SHPB tests, although the actual strain rates experienced by the pulse shapers are higher. A sensitivity and probabilistic analysis are carried out to understand the effect of parameters variations on the incident rise time.