Constitutive equation for describing high strain rates of Al and Mg in a shock wave

Glushak, B. L.; Novikov, S. A.; Bat'kov, Yu. V.

doi:10.1007/bf00754973

Cited by 5 publications

(2 citation statements)

References 8 publications

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“…The curve of dynamic yield strength, Y d , along the Hugoniot is of a peculiar "bell-like" shape with a peak at σ 1 ≈ 0.4 − 0.5σ 1melt (σ 1melt is the principal stress at T = T melt ) [36]. In the ascending branch of the Y d (σ 1 ) curve, the dominant factor is isothermal hardening, in the descending branch the dominant factor is thermal softening.…”

Section: Aluminum and Its Alloysmentioning

confidence: 99%

Dynamic Strength of Materials

Glushak¹,

Tyupanova²,

Bat'kov³

2006

Material Properties Under Intensive Dynamic Loading

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The methods used in practice for the acquisition and interpretation of experimental data pertaining to the resistance of materials to plastic-strain (shearstrength) are based on the concepts of the nature of motion of a material possessing strength and the features of high-rate deformation discussed in Chap. 1. These methods are briefly described below. Additional information on this topic is available to the reader in monographs [1-3], review [4], and the original papers cited in [1-4]. Comparison between the Shock Hugoniot and the Hydrostatic Compression IsothermGiven two assumptions: (1) material strength is isotropic, and (2) the difference between isothermal hydrostatic compression and the mean stress σ ii /3 is small, the dynamic yield strength is calculated to be the difference between the stress σ 1 on the elastic-plastic shock Hugoniot and the pressure P on the hydrostatic compression isotherm (given in terms of specific volume V (or strain ε)) as Y d = 3(σ 1 − P )/2. This approach to the estimation of Y d is limited to cases wherein the stresses σ 1 are relatively low, and the temperature rise during shock compression is modest (resulting in a thermal component of pressure that is low in comparison to the total pressure).For the aluminum alloy Al-2024, [5] recommends that for shock pressures in the 2.7 GPa ≤ σ 1 ≤ 9.4 GPa range, one should use the following relations for σ 1 (ε) (the normal stress component in a plane wave shock) and P (ε) (the hydrostatic compression) in calculations of the dynamic yield strength: σ 1 = 0.18 + 72.06ε − 347.1ε 2 (GPa); P = 75.9ε + 201ε 2 (GPa). This method for the evaluation of Y d , among other things, requires a highly accurate determination of the curves σ 1 (ε) and P (ε) since minor changes in ε can lead to significant changes in σ 1 and P .

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Section: Aluminum and Its Alloysmentioning

confidence: 99%

Dynamic Strength of Materials

Glushak¹,

Tyupanova²,

Bat'kov³

2006

Material Properties Under Intensive Dynamic Loading

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“…In this case, however, at strain ratesε = 10 5 -10 6 sec −1 , the viscous component of the strain resistance σ g ≈ με for any metals and alloys is equal to 2G (or G, according to Frenkel), which is not observed in experiments. (Dynamic yield points exceed static values by a factor of 3-4, and in some cases by a factor of 6 (for example, for aluminum) and a factor of 9 (for magnesium) [9], but this is an exception rather than a rule, because a paper [9] also gives data on a decrease in the yield point under shock loading. A similar tendency toward a sharp decrease in the yield point was noted in [10]).…”

mentioning

confidence: 91%

Dynamic viscosity and material relaxation time during shock loading

Savenkov¹

2010

J Appl Mech Tech Phy

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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...

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