Dynamic viscosity and material relaxation time during shock loading

Abstract

The dynamic viscosity and characteristic relaxation time at various scale-structural levels of deformation of a shock-loaded medium are determined using concepts of multilevel solid-state mechanics. The notion of the quasi-time fractal dimension is introduced and used to calculate the indicated characteristics. Computational-experimental data for the viscosity and relaxation time are given for three materials: M2 copper, AMg6 aluminum base alloy and Armco iron.Introduction. In the rapid plastic deformation of metals under shock loading, an important factor is the dissipative energy loss due to the dynamic viscosity, which is generally the material response to the rate of the process.The viscous resistance of a material is characterized by the proportionality coefficient at the strain rate tensor in the equations for strain resistance or for the dissipative function, which is called the dynamic viscosity μ. Generally, this quantity is a fourth-rank tensor.A considerable body of data exists on the dynamic viscosity of many metals and alloys over a wide range of strain rate (ε = 10 3 -10 6 sec −1 ) (see [1] and the bibliography therein). However, first, these data differ by several orders of magnitude (even for the same materials and the same loading parameters), which is apparently due to the use of different methods to determine the dynamic viscosity and its dependence on the structural level scale at which it is obtained [1]. Second, the dynamic viscosity is determined, as a rule, in the same experiments in which it is used for modeling and prediction.The material characteristic which is inversely proportional to the dynamic viscosity is the shear stress relaxation time. It should be noted that methods for direct experimental determination of this characteristic under shock loading conditions are not currently available. It is therefore, reasonable to develop a theoretical model (at least, semi-empirical) to calculate the dynamic viscosity or characteristic relaxation time through fundamental structural microconstants of material and (or) the minimum number of experimental parameters at the lowest (highest) structural level. For other scale-structural levels of deformation (which will be considered below), it is reasonable to determine the viscosity and relaxation characteristics (these parameters play an important role in modeling multilevel plastic deformation) through the characteristic time or geometrical scale of the process.As is known, crystalline materials are fading-memory materials which can be described using a generalized Maxwell relaxation model [2]. Depending on the material parameters included in this generalized model, it is possible to obtain various particular governing equations describing the deformation resistance of elastoplastic, viscoplastic, and relaxing media [3].As noted above, the dynamic viscosity can be defined in terms of the characteristic relaxation time t r , which generally depends on the stress state of the medium and its temperature T [2]. For a generalized Maxwell medium, the...