We present a model of metallic plastic flow suitable for numerical simulations of explosive loading and high velocity impacts. The dependence of the plastic strain rate on applied stress at low strain rates is of the Arrhenius form but with an activation energy that is singular at zero stress so that the deformation rate vanishes in that limit. Work hardening is modeled as a generalized Voce law. At strain rates exceeding 109 s−1, work hardening is neglected, and the rate dependence of the flow stress is calculated using Wallace’s theory of overdriven shocks in metals [D.C. Wallace, Phys. Rev. B 24, 5597 (1981); 24, 5607 (1981)]. The thermal-activation regime is continuously merged into the strong shock limit, yielding a model applicable over the 15 decades in strain rate from 10−3 to 1012 s−1. The model represents all aspects of constitutive behavior seen in Hopkinson bar and low-rate data, including a rapid increase in the constant-strain rate sensitivity, with 10% accuracy. High-pressure behavior is co...

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Model of plastic deformation for extreme loading conditions

Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part I: Experiments

T he split Hopkinson pressure bar is widely used to measure the dynamic properties of solid materials. This paper presents the results of the first comprehensive two-dimensional numerical analysis of the technique, and quantitatively describes the effects of realistic friction and of variations in both the specimen geometry and the imposed strain-rate on the validity of the assumptions used in analyzing experimental data. A two-dimensional axisymmetric numerical analysis is used to compute all components of the stress, strain and strain-rate tensors at each mesh point within the specimen and the elastic bars. The calculated response of the pressure bars is used to reconstruct the stress-strain behavior of the specimen and this is compared to both the input stress-strain curve and the actual calculated stress-strain states in the specimen. Thus, the validity of the assumptions and the corrections used in the analysis of the data is determined. Inertia and friction between the specimen and the elastic bars affect the response of the specimen differently for different length-to-diameter ratios. Inertia effects produce stress waves propagating radially and axially in the specimen and may result in an oscillating reconstructed stress-strain curve. If the ends of the specimen are well lubricated and care is taken to minimize the effects of inertia, the reconstructed stress-strain curve agrees with the input. However, serious stress and strain nonuniformity exists when the ends are not lubricated and this results in a reconstructed stress-strain curve where, for any given strain, the stress magnitude is larger than the correct value. A comparison of the calculations with experiment shows excellent agreement for various interface conditions. Finally, the inertia correction of E.D.H. Davies and S.C. Hunter (1963) is found to be reasonable.

Two-dimensional analysis of the split hopkinson pressure bar system☆

Upper limits of power law creep of rocks

The strain rate sensitivity of two commercial aluminium alloys AA6082 and AA7108 in peak temper T6 and overaged T79 condition is analysed. These alloys are precipitation hardenable and as such, are expected to have a relatively low strain rate sensitivity. Their response to rapid loading has been tested over a wide range of strain rates, from 0.1 to 3000 s −1 at room temperature, 375 and 515°C for AA6082 and room temperature, 280 and 340°C for AA7108. Specimens were cut from planar extruded sections and tested in uniaxial compression with the deformation axis parallel to the extrusion direction. Intermediate strain rate testing was carried out using a computer controlled servo-hydraulic testing machine and high strain rate testing above 500 s −1 on a Split Hopkinson Pressure Bar (SHPB). Owing to inaccuracies of the conventional Kolsky solution of the SHPB, a numerical simulation was performed. The flow stress at a plastic strain of 5% was plotted as a function of strain rate and temperature. Up to 2000 s −1 , there is very little change of the activation volume with increasing temperature for both alloys, indicating that barriers to thermal activation are large and approximately the same. However, at higher strain rates, the rate controlling mechanism appears to change and at lower temperatures, a trend towards negative strain rate sensitivity was observed. Metallographic examination of AA7108 revealed strain localisation, seen as parallel deformation bands. The strain localisation could be the cause of the negative strain rate sensitivity.

High strain rate properties of selected aluminium alloys

T he mechanical behaviour of two annealed face-centred cubic metals, aluminium and copper, at elevated temperatures has been investigated experimentally to determine their rate sensitivity. The results indicate that hot compression is a thermally-activated process. The experimental value of the activation energy for aluminium obtained from the present work is almost similar to that for creep and self-diffusion. This indicates that hot dynamic compression may be a diffusion-controlled thermally-activated process. However, the experimental activation energy of 74 kcal/mole obtained from the present work for copper is higher than that observed both for creep and self-diffusion. Experimental evidence (D. Hardwick and W.J. McG. Tegart in 1961) suggests that recrystallization is the rate-controlling process in dynamic deformation, while in creep it is usually recovery in the form of sub-grain formation. For aluminium specimens the dislocation density decreases with increasing temperature; for increasing strain rate the dislocation density remains almost constant, while the size of dislocation cells diminishes. If the dislocation density did not change substantially, one should conclude (as did L. Taborský in 1969) that the rise in flow stress caused by high strain rate is due to the reduction of the size of dislocation cell structure and by the increased rate of movement of the moving individual dislocations.

S.K. Samanta

Papers

Dynamic deformation of aluminium and copper at elevated temperatures