On the longitudinal impact of two phase transforming bars. Elastic versus a rate-type approach. Part I: The elastic case

Longitudinal impact experiments of thin bars are proposed as an effective mean for understanding the kinetics of stress-induced phase transformations. We consider on one side the elastic model and on the other side an augmented theory, which includes the Maxwellian rate-type viscoelasticity with finite instantaneous response and as a limiting case the Kelvin–Voigt viscoelasticity with infinite instantaneous response. By using the chord criterion, we investigate the complete set of Goursat and Riemann problems which could arise as a result of dynamic interactions when we consider a piecewise linear elastic model corresponding to a three phase material. Subsequently we use our Riemann solvers to construct solutions for the longitudinal impact of two elastic phase transforming bars for a variety of impact conditions. We focus on the results which can be measured in laboratory experiments like the time of separation of the two bars after impact, the profile of the particle velocity at the rear end of the target and the stress history at the contact point. In Part II of this paper we continue with a theoretical and numerical comparative analysis on the wave structure predicted by our general rate-type approach for the same impact problem.