Semi-analytical modeling of steady weak shock wave front for solid metals following the Swegle-Grady relation

In this article, the stress-time or speed-time relations for steady weak shock wave fronts and their effective parameters were studied for solid metals (except alkaline metals). The purpose was to determine the effective parameters for steady shock wave fronts and find the relations for prediction of the shape of these profiles in pure metals. First, the range of the steady weak shock wave was determined. Then, based on an empirical relationship for the maximum strain rate in the weak shock wave regime, a relation was assumed for the whole weak shock wave front. Then by utilizing simplified assumptions, such as elastic-perfectly plastic material model, a stress change equation and by integration, two implicit equations were obtained for describing the weak shock wave front profile that one of them was used in the calculations. Subsequently, the strain-hardening material model was used. The strain-hardening material model was further simplified as piecewise linear functions. The same procedure was followed in the strain-hardening model. The results show that the proposed weak shock wave model is adequate for an elastic-perfectly plastic material or a material in which its yield stress has slight change during wave rise. The results of solving the equations simulated the profile of the steady weak shock wave fronts and the strain-hardening model has a better solution than the elastic-perfectly plastic model.