Generalized smooth and weak-discontinuous unsteady waves

Journal of Applied Physics

2009

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To decide whether many dislocations are generated in lithium fluoride ͑LiF III b ͒ and to examine whether the precursor decay anomaly exists, an equation that predicts the dislocation densities on the precursor decay curve without using any modeled dislocation generation rate has been derived. The value of the density of at most about 2.0ϫ 10 12 m −2 evaluated on the decay curve in the material III b for a projectile velocity of 340 m / s indicates that extremely many dislocations are not generated in the material. This value is not significantly larger than the value of about 10 10 m −2 measured at a projectile velocity of 186 m / s. It is inferred from the evaluated value of 2.0ϫ 10 12 m −2 that the measured value of 10 10 m −2 is not unreasonable and therefore that the precursor decay anomaly does not exist. In addition, it has been revealed that dislocation densities largely increase on the decay curve.

Section: A Strain Particle Velocity and Stress Wavesmentioning

confidence: 99%

Evaluation of the precursor decay anomaly in single crystal lithium fluoride

Journal of Applied Physics

2009

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“…Recently, Sano [8][9][10] has theoretically studied the precursor decay in LiF ͑III b ͒. 6 Sano 8 inferred that a precursor in a weak-discontinuity plane wave front 11 was decayed by an evolving follower overtaking the precursor from behind, which appeared in sequence during the decay process as a contraction ͑compression͒ wave C, degenerate contraction waves I and II, a subrarefaction wave RЈ, and a rarefaction wave R b . In addition, he 8 found from the stress-time ͑-t͒ profiles measured by Asay et al 6 that the amplitude of the stress wave ͓the stress at the rear ͑impacted surface͒ of the -x profile͔ reached a maximum at T Х 0.05 s after impact and then the stress wave separated from the impacted surface.…”

Section: Introductionmentioning

confidence: 99%

“…A part of the work [8][9][10][11] described above includes contents useful for the development of the study on dynamic yielding. Some of the contents are necessary to advance this study, so that they are widely applied to this study.…”

Section: Introductionmentioning

confidence: 99%

Dynamic yielding in lithium fluoride and aluminum

Journal of Applied Physics

2010

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At a time immediately after shock loading, a kink ͑a weak discontinuity or a discontinuity in slope͒ occurs at a position in an unsteady portion in a smooth plane wave front in a lithium fluoride single crystal ͑material III b ͒ or in 1060-0 aluminum due to the instability of the wave front. After the occurrence of the kink, a zone is produced and broadened with time between a near steady precursor ahead of the kink and a plastic wave behind it in a weak-discontinuity plane wave by the difference in the propagation velocity between them. Stress relaxes in the zone, which is called a follower, and the precursor decay takes place due to the stress relaxation. During the decay process, the large increase in plastic flow occurs in the vicinity of the leading edge of the follower, causes yielding at the leading edge, and stabilizes the weak-discontinuity wave. The stress-strain ͑-͒ history caused by the follower rotates clockwise with time around the yield point. The rotation yields differenthistories behind the point and therefore different types of the dynamicrelation. Dynamic yield phenomena are illustrated by showing the schematic diagrams of three different types of the dynamicrelation, which are caused by weak-discontinuity plane waves composed of a precursor C, a follower ͑i͒ C, ͑ii͒ I or II, or ͑iii͒ RЈ or R b , and a plastic wave C behind the follower. Here C is the contraction ͑compression͒ wave, I and II are the degenerate contraction waves I and II, RЈ is the subrarefaction wave, and R b is the rarefaction wave.

Jumps Across an Outgoing Spherical Shock Wave Front

Journal of Applied Mechanics

2008

The shock jump conditions have been used since Rankine published in 1870 and Hugoniot in 1889. However, these conditions, in which the geometrical effect is never included, may not be correctly applied to material responses caused by a spherical wave front. Here, a geometrical effect on jumps in radial particle velocity and radial stress across an outgoing spherical wave front is examined. Two types of jump equations are derived from the conservation laws of mass and momentum. The first equations of Rankine–Hugoniot (RH) type show that the geometrical effect may be neglected at distances of movement of the rear of the wave front that are more than ten times as long as the effective wave front thickness. Furthermore, using four conditions required to satisfy the RH jump conditions, which are contained in the RH type equations, a method is developed to judge the applicability of the RH jump conditions to the jumps. The second type equations for spherical wave fronts of general form are obtained by expressing a volumetric strain wave ε in the wave front by more general wave forms. In the neighborhood of the center of the wave front, for ε<0.09, radial particle velocity in the jump in any materials is inversely proportional to the square of a dimensionless distance from the center to the rear, and for ε<0.04, radial stress in the jump in some viscous fluids and solids is inversely proportional to the distance. In conclusion, an outgoing spherical wave front attenuates greatly near the center due to the geometrical effect as well as rarefaction waves overtaking from behind, while the geometrical effect is negligible at the specified positions that are distant from the center.