Viscoplastic Effects Occurring in Impacts of Aluminum and Steel Bodies and Their Influence on the Coefficient of Restitution

Abstract

Generally speaking, impacts are events of very short duration and a common problem in machine dynamics. During impact, kinetic energy is lost due to plastic deformation near the contact area and excitation of waves. Macromechanically, these kinetic energy losses are often summarized and expressed by a coefficient of restitution, which is then used for impact treatment in the analysis of the overall motion of machines. Traditionally, the coefficient of restitution has to be roughly estimated or measured by experiments. However, more recently finite element (FE) simulations have been used for its evaluation. Thereby, the micromechanical plastic effects and wave propagation effects must be understood in detail and included in the simulations. The plastic flow, and thus the yield stress of a material, might be independent or dependent of the strain-rate. The first material type is called elastic-plastic and the second type is called elastic-viscoplastic. In this paper, the influence of viscoplasticity of aluminum and steel on the impact process and the consequences for the coefficient of restitution is analyzed. Therefore, longitudinal impacts of an elastic, hardened steel sphere on aluminum AL6060 rods and steel S235 rods are investigated numerically and experimentally. The dynamic material behavior of the specimens is evaluated by split Hopkinson pressure bar tests and a Perzyna-like material model is identified. Then, FE impact simulations and impact experiments with laser-doppler-vibrometers are performed. From these investigations it is shown that strain-rate effects of the yield stress are extremely small for impacts on aluminum but are significant in impacts on steel. In addition, it is demonstrated that it is possible to evaluate for both impact systems the coefficient of restitution numerically, whereas for the aluminum body a simple elastic-plastic material model is sufficient. However, for the steel body an elastic-viscoplastic material model must be included.

Effect of strain rate on the forming behaviour of sheet metals

“…For DC04 a remarkable increase of strength is observed as the strain rate increases, however with a decreasing ductility (Schael and Bleck, 2001). S235 also displays a significant positive strain rate effect on the yield stress as is shown by Seifried et al (2010). Whether the influence of the strain rate on the FLD is positive or not, is dependent on the materials' strain rate response.…”

On the mechanics of edge chipping from spherical indentation

“…Consequently, the peak load transmitted to the target during impact, and hence coefficient e, would be greatly reduced. Other factors which may reduce e are plastic deformation in the target (Weir and Tallon 2005;Constantinides et al 2009;Seifried et al 2010) and loss of energy from multiple reflections. Again, quantitative elucidation of these effects appears prohibitive, which points to the difficulties involved in predicting chipping under dynamic loading.…”

On the Effect of Isotropic Hardening on the Coefficient of Restitution for Single or Repeated Impacts Using a Semi-Analytical Method

“…These equations are defined for specified ranges of yield strain y = σ y /E and Poisson's ratio ν that correspond to the values used in this article. [18]. Using the residual interference after impact as defined by Etsion,et al (52), Jackson et al (14) predicted the evolution of the coefficient of restitution as defined in Eq.…”