New experimental data on the dynamic strength of the lead-antimony (2.77%) alloy comprised of different structures formed after thermal treatment in various regimes are presented in this work. The optimal alloy thermal treatment regime (quenching from 250°C) providing the best strength characteristics under explosion or high-speed impact is revealed.

This paper presents the results of metallographic analysis of the melting of S1 lead under shock-wave loading and unloading. Lead samples in a titanium capsule were loaded by a plane shock wave using an aluminum impactor 6 mm thick, which was accelerated by detonation products of an explosive. The results of metallographic analysis of samples in the initial state, subjected to heat treatment under normal conditions, and recovered after shock-wave loading are given. Melting traces were found in lead after shock-wave loading by a pressure of 25.6 GPa and subsequent unloading.

This paper presents the results of numerical simulation of Zaretskii’s experiments on loading of natural uranium in the phase-transition region at temperatures of 27–862°C. Simulation of these experiments is of interest because of the observed features of spall fracture of uranium in the phase-transition region. Spall fracture and compaction was simulated using the DGC-L model of the dynamics of growth and compaction in a liquid medium, which takes into account the effect of strength properties, pressure, surface tension, viscosity, and inertial forces on the growth and collapse of pores. Calculations were carried out according to the UP program— a Lagrangian method for calculating deformation problems of continuum mechanics in a onedimensional approximation.

A model for the spall fracture and compaction of a damaged material based on a description of the motion of a single pore is proposed. The model takes into account the strength properties, the effect of pressure, surface tension, and viscosity of materials and inertial forces. Equations describing the dynamics of growth and collapse of pores are presented. The proposed model can be used to calculate the spall fracture and compaction of liquids and metals in both solid and liquid (molten) states.

We present a set of high explosive driven Rayleigh-Taylor strength experiments for beryllium to produce data to distinguish predictions by various strength models. Design simulations using existing strength model parameterizations from Steinberg-Lund and Preston-Tonks-Wallace (PTW) suggested an optimal design that would delineate between not just different strength models, but different parameters sets of the PTW model. Application of the models to the post-shot results, however, suggests growth consistent with little material strength. We focus mostly on efforts to simulate the data using published strength models as well as the more recent RING relaxation model developed at VNIIEF. The results of the strength experiments indicate weak influence of strength in mitigating the growth with the RING model coming closest to predicting the material behavior. Finally, we present shock and ramp-loading recovery experiments.

Рентгенографическим способом изучена плотность дислокаций в сохраненных образцах меди и тантала с различным размером зерна после высокоскоростного нагружения ударными и квазиизэнтропическими волнами амплитудой 20–100 ГПа. Скорость деформации составляла 106 109 с-1. Подтверждено, что высокоскоростное нагружение генерирует в меди бoльшую плотность дислокаций, чем квазистатическая деформация, а ударноволновое нагружение – чем квазиизэнтропическое. В образцах меди наблюдается максимум в области давления Р = 30–40 ГПа (что соответствует деформации 0.25–0.3), за которым следует падение. Такое падение объясняется отжигом дефектов при адиабатическом нагреве в результате сжатия. Отмечается увеличение в меди с уменьшением температуры образца. В тантале с увеличением давления в ударной волне зафиксирован монотонный рост плотности дислокаций. Влияния разогрева на отжиг дефектов в тантале даже при максимальном давлении не обнаружено. Как в меди, так и в тантале наблюдается рост с увеличением среднего размера зерна.

The dislocation density ρ in copper and tantalum specimens with various grain size that remained after high-strain-rate loading by shock and quasi-isentropic waves with amplitudes of 20–100 GPa has been studied using X-ray diffraction analysis. The deformation rate was 10 6 –10 9 s −1 . It has been confirmed that high-strain-rate loading generates a higher dislocation density in copper than does quasi-static deformation, as well as that the shock-wave loading generates a higher dislocation density than quasi-isentropic loading. In copper, a maximum of ρ has been found in the pressure range of P = 30–40 GPa, which corresponds to a degree of deformation of 0.25–0.3, followed by a drop. This drop in ρ is explained by the partial annealing of defects during adiabatic heating resulting from compression. An increase in ρ in copper with decreasing specimen temperature has been noted. In tantalum, an increase in the shock wave pressure leads to a monotonic increase in the dislocation density. No effect of heating on the annealing of defects in tantalum has been found, even under the maximum pressure. As the average grain size increases, ρ increases in both copper and tantalum.

About practicality of Hall-Petch law in metals O.N.Ignatova, V.V.Losev, A.N.Malyshev, D.M.Petrova, A.M.Podurets, V.A.Raevsky, M.I.Tkachenko, A.N.Tsibikov RFNC-VNIIEF, Sarov To construct wide-range constitutive equations of solid substances suitable for calculations of dynamic processes accompanied by great deformations, temperatures and pressures, consideration must be given to structural changes to be occurred in this case. Shear stress is dependent not only on state parameters at the present instant of time, but also on the history of straining, which determines a substance structure at the given point of time. At the same time the most advanced models take into account a growth of dislocation density, a change of microcrystals sizes (grain size), twinning, appearing at high-rate strain, annihilation of dislocations (or an decrease in dislocation density) at heating higher than the critical one [1], [2]. The effect of the average grain size on stress intensity is expressed in terms of the so-called Hall-Petch law, which at other constant parameters takes the form of [3], [4]: =0+К1D -1/2 , (1) where 0 is the flow stress in a single crystal, К1 is the constant of material, D is the average grain size. Hall justified this regularity in theory [3], and Petch confirmed it experimentally [4] (s.Fig.1). Similar relations exist for the flow stress at various degrees of strain and ultimate strength. It is agreed that relation (1) is performed in a wide interval of grain sizes down to nanosizes.

The VISAR free surface velocity histories have been measured for commercial grade coarse grain (CG, 50 - 60 mu m) and ultra fine grained (UFG, similar to 0.5 mu m grain size) after severe plastic deformation tantalum and for comparison tantalum single crystals, at peak stresses around 12-14 GPa and strain rates of 10(5)-10(6) s(-1). The decrease in the grain size, which resulted in similar to 25% increase of the hardness did not cause any significant influence on the HEL, the value of which is similar to 2 GPa, but increases slightly the spall strength of the UFG tantalum (7.4 GPa) in comparison with the CG samples (similar to 7 GPa). In both cases the spall strength does not noticeably vary with increase of the peak shock stress up to 70 GPa. The experiments using samples precompressed at 40 and 100 GPa peak pressure have confirmed weak influence of preceding shock compression on the tantalum spall strength. The tantalum single crystals display the highest spall strength equal to similar to 10 GPa. The influences of the grain size on static and dynamic yield stresses are discussed in terms of general strain rate effects.

The paper presents the results for construction of defining relations of beryllium. The phenomenological elastic-plastic relaxation model is utilized to calculate the deviatoric component of a shear stress. A spherical component of stress tensor is expressed through the equation of state in the form of Mie-Gruneisen. Melting temperature dependence on density is determined on the basis of the equation of Lindeman. The model takes account of strain and compression hardening, thermal softening, stress history, as well as relaxation of elastic stress.

This paper presents the results of measurements of the strength properties of technically pure tantalum under shock wave loading. It has been found that a decrease in the grain size under severe plastic deformation leads to an increase in the hardness of the material by approximately 25%, but the experimentally measured values of the dynamic yield stress for the fine-grained material prove to be less than those of the initial coarse-grained specimens. This effect has been explained by a higher rate of stress relaxation in the fine-grained material. The hardening of tantalum under shock wave loading at a pressure in the range 40–100 GPa leads to a further increase in the rate of stress relaxation, a decrease in the dynamic yield stress, and the disappearance of the difference between its values for the coarse-grained and fine-grained materials. The spall strength of tantalum increases by approximately 5% with a decrease in the grain size and remains unchanged after the shock wave loading. The maximum fracture stresses are observed in tantalum single crystals.

Beryllium strength has been investigated under dynamic loading conditions using platforms that span a limited range of pressure and strain-rate space. Multiple Be strength models that are ostensibly calibrated to these experiments persist, and yet they predict dierent outcomes for results beyond the limited phase space where data exist. We discuss experiments using high explosives (HE) to accelerate a solid rippled Be target quasi-isentropically. The interface between the low-density gaseous HE and the perturbed face of the solid target is Rayleigh-Taylor (RT) unstable. The amplitude of the ripples will grow with time, and the Be strength will mitigate the ripple growth. By measuring and modeling the amplitude growth, we can discriminate among various strength models for Be. Our RT designs extend the pressures up to 50 GPa and the strain-rates to 10 6 s 1 . As a part of the design process, we analyze existing plate impactor and Taylor anvil experiments using available models. We present the results of this analysis as well as the designs and preliminary experimental results from the RT experiments.

The paper presents experimental data on the mechanical behavior of coarse-grained (80 mu m) tantalum and cold-forged fine-grained (1-2 mu m) tantalum under static, dynamic and shock wave loading. The data includes sigma-epsilon compression diagrams for a strain rate of 10(-3)-10(3) s(-1), impact velocity dependences of the relative change in cylinder length in Taylor impact tests, and time dependences of the free surface velocity in the Ta specimens under shock wave loading. It is found that the 80-fold decrease in Ta grain size only slightly affects the strength properties of the material under static and dynamic loading. Measurements of the free surface velocity under shock wave loading at similar to 17 GPa point to a decrease in elastic precursor in the fine-grained tantalum by similar to 35 % and to an increase in its critical fracture stress by 15-20 A compared to those in the coarse-grained tantalum. A complex strain rate dependence of the tantalum strength properties was revealed. The microstructure of the coarse-grained Ta specimens loaded at a shock wave pressure of 20-130 GPa for different times was examined, and the dislocation density and the number of shear bands formed under shock wave loading were measured.

The effect of the initial microstructure and microstructure obtained after quasi-isentropic and shock compression on the elastic-plastic and strength characteristics of grade M1 copper upon static, quasistatic, and dynamic loading has been investigated. It has been revealed that the parameters of a shock wave play an important role in the formation of the substructure and related mechanical properties of the samples and that the values of the elastic-plastic and strength characteristics in coarse-crystalline samples of copper M1 vary substantially depending on the defect structure at the identical grain size. Measurements of the elastic limit and critical fracture stresses over a wide range of the loading durations have been performed by different methods, including a VISAR laser interferometer. Based on the experimental data obtained, models of the shear and spall strength of copper for different loading conditions have been developed. With the aid of a NAG two-stage kinetic model, a numerical simulation of the dynamic fracture of coarse-crystalline samples of copper M1 with different internal structure has been performed. An analysis of the experiments in combination with the numerical simulation made it possible to describe the deformation behavior of the samples in the entire range of loading rates.

The paper describes a new method of research on micro- and mesoscalc high-rate (similar to 10(5)-10(7) s(-1)) deformation of metals. The method consists in studying the collapse of cylindrical holes of initial diameter D(0) = 0.5-2 mm by shock waves of known intensity and duration. The method was tested on annealed coarse-grained MI copper.