A theoretical and experimental analysis of high-strain-rate tensile tests using Malvern's theory

Abstract

The theoretical behaviour of a cylindrical specimen of finite length during a high-strain-rate tensile test has been studied with the help of a strain-rate dependent theory. The behaviour is compared with experimental observations of tests on a specimen partially fixed at one extremity and submitted to a constant velocity impact at the other end. The chosen plasticity function is that introduced by Malvern which predicts a linear relationship between the stress and plastic strain rate. The calculations and experiments have been done in two cases: (i) ideal elastic-plastic material and (ii) highly work-hardened material.The main results are as follows: two stages can be distinguished, a `transient' state at the beginning of the test, where the values of state variables are heterogeneous, and a `steady' state where stress and strain rate are uniform in the whole specimen. The strain distribution in the steady state depends markedly upon the `quasi-static' stress-strain relation σ=h(ϵ) and the parameter of the plasticity function. Malvern's theory is a good approximation of the experimental results in the `steady' state, but it cannot predict those of the `transient' state; in particular the theory gives too low values of the peak stress at the extremity of the specimen opposite to the impact section. The use of a more complex plasticity function is briefly investigated.