Critical Stresses in Spalling and Dynamic Rupture of Metals

Abstract

Results of dynamic rupture tests of a series of metals obtained using a composite Hopkinson bar and shock-wave loading of plane specimens are described. It is shown that the actual rupture strength at a strain rate of 5 · 10 3 sec −1 is very close to the spall strength at higher strain rates. Results of testing the same metals using a composite Hopkinson bar within a temperature range of 20-350 • C are given.Despite numerous papers that have been published on the strength of materials under shock-wave loading and certain progress in general understanding of the physical processes that occur therein, the problems of correct determination of the spall strength and comparability of data obtained with results of other types of dynamic and quasi-static tests are still unsolved.The main results, which are believed to be most reliable, on determining the spall strength are obtained by methods based on continuous recording of the free-surface velocity of a specimen (target) under uniaxial strain conditions. In the acoustic approach, the spall strength of an ideal material (amplitude of tensile stresses σ tens acting in the spall section inside the specimen) is [1]where ρ 0 is the initial density of the material, c 0 is the volume velocity of sound, V 0 is the maximum free-surface velocity, V m is the free-surface velocity at the first minimum of the dependence V (t), and t is the time.In the case of materials with explicit manifestation of elastoplastic properties in both incident and reflected waves, a correction factor associated with the determination of the difference in velocities ∆V = V 0 −V m is introduced into formula (1) to take into account that the unloading part of the incident compressive pulse with a velocity ≈ c 0 catches up with the leading part of the spalling pulse that propagates with a velocity of the longitudinal elastic wave c lead : σ 0 = 0.5ρ 0 c 0 (∆V + δV ).(2)Various types of relations for δV can be found in [1][2][3]. The existing models for spall fracture are based on the stage nature of the spalling process. Most authors consider two to four stages: "explosion-like" formation of numerous single micro-and mesocracks, combination of them into groups (finite clusters), growth and merging of clusters into one macrocrack (infinite cluster) extending over the entire specimen, and, finally, total failure of the specimen into fragments (so-called formation of a spalling "plate"). All the stages are considered in the zone of the extension-wave action; nevertheless, even in the case of a low-intensity shock wave, there is a possibility of formation of micro-and mesodefects with dimensions l 1,2 10 −6 m, which can be parallel or perpendicular to the shock-wave front (l 1 and l 2 are the lengths of the perpendicular and parallel defects, respectively). The reason is that, as was shown in a number of papers (see, e.g., [4] and the literature cited therein), the motion of micro-and mesoflows of particles of the material under shock-wave loading possesses Krasnoznamenets Research-and-Production Enterprise,...

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