Session H3: ID-4: Strength of Metals

Variation of Shear Strength in Shock Loaded Niobium

Previous work on the shock response of body centred cubic (bcc) metals, notably tantalum and tungsten has shown that whilst the shear strength increases with applied shock stress, it decreases with duration behind the shock front. In tantalum, post shock microstructural examination has shown only a minor increase in dislocation density occurs, in keeping with the high Peierl's stress in these materials that restrict dislocation generation. We now extend this work to another bcc metal, niobium. Shear strengths are monitored through the use of manganin stress gauges mounted such that they are sensitive to the lateral component of stress, in combination with knowledge of the shock induced impact stress. British Crown Copyright MOD/2009   

Yield Response of Tantalum for Quasi-Isentropic Loading and Unloading

Magnetic loading was used to study initial yield strength of pure annealed and cold-worked polycrystalline and single crystal Ta samples for ramp loading at strain rates of $\sim $10$^{6}$/s and the flow strength after peak compression to $\sim $17 GPa at about 5x10$^{4}$/s. For sample thicknesses of 0.5--6 mm, it was found that for annealed pure polycrystalline Ta, the quasi-isentrope elastic limit (IEL) was essentially constant at $\sim $3.2 GPa with propagation distance. There was no apparent effect of sample purity on precursor amplitude to within experimental uncertainty, although cold-working resulted in loss of the elastic peak and a reduced IEL of $\sim $1.7 GPa. The flow strength at peak loading stress was estimated from the quasi-elastic unloading and found to increase with peak stress. These results will be discussed in terms of constitutive models for Ta. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.   

Modeling of the elastic-plastic behavior of annealed tantalum under low amplitude ramp wave loading

Ramp wave experiments were conducted to determine elastic-plastic response of annealed Ta to peak loading stresses of about 17 GPa. These results revealed a strong elastic overshoot, followed by substantial stress relaxation behind the elastic precursor. Similar effects are observed in shock loading. However, unlike shock loading, the peak of the elastic precursor exhibited very little decay with propagation distance. Several commonly used viscoplasticity type material models for high rate deformation were used to evaluate this effect, but were unable to describe the measured elastic overshoot and stress relaxation. However, a dislocation multiplication model used to describe the yield point phenomenon was able to capture the essential features of the experimental observations. The dislocation multiplication model is based on dislocation-dislocation self interactions and dislocation-solid matrix interactions. Work is in progress to refine the model for better quantitative agreement with the experimental data.   

Determining Material Strength in Ramp Loading Experiments

A material's deviatoric (strength) behavior is typically more important under ramp loading than shock loading. Measuring strength remains a challenge, but the method of Fowles [1961] is particularly attractive because of its simplicity. It involves comparison of a measured longitudinal stress under shock or ramp loading with the expected hydrostatic pressure for the same density and temperature. The difference between the pressure and longitudinal stress is then proportional to the strength. The temperature along an isentrope can be calculated using thermodynamic relationships, but additional heating is created by the plastic work that occurs during compression of a material with strength. This heating must be accounted for in order to make a valid calculation of the strength, with the correct strength being lower than might otherwise be expected. Since the plastic heating is cumulative, it can lead to temperatures significantly hotter than the isentrope and large errors in the strength calculated for high compression levels.   

Shock-wave response of Ti-Ni shape memory alloys in the transformation temperature range

The behavior of Ti$_{51.1}$Ni$_{48.9}$ and Ti$_{49.4}$Ni$_{50.6 }$alloys under shock wave loading was investigated to observe their martensitic transformations. Tested samples had the grain sizes $\sim $30 $\mu $m and 0.05 to 0.3 $\mu $m. Reduction of the grain size was done by means of severe plastic deformation methods. In the experiments, the VISAR velocity histories were recorded over the test temperatures range from 193 K to 415 K which involves the temperatures of thermoelastic martensitic transformations of the alloys. Waveforms demonstrate temperature dependences of the Hugoniot elastic limits which is controlled by the critical stress for inducing martensitic transformation, phase transformation without expected so called plateau, and in some cases signatures of pseudo-elastic behavior. The reduction of the material grain size has led to rise in both the HEL values and transformation rates and decrease of the spall strength over whole temperature range.   

Shock Attenuation in Distended Solids

There are many applications in which attenuation of the intensity of a shock wave with propagation distance is of concern. Classic solutions include the Sedov-Taylor similarity solution for air blast shocks, and the analytic solutions of Kompaneets for shock attenuation in solid compacting media. When the governing physics of shock compression does not introduce a characteristic length scale the dependence of field variables are necessarily power-law dependent on distance. Even when length scales emerge from the physics, domains of asymptotic power-law dependence can emerge. The present paper describes an analytic solution of shock attenuation in distended media that illustrates asymptotic power-law attenuation bounded by physical length scales that emerge from the material constitutive description.