scholarly journals On Thresholds for Dynamic Strength in Solids

2021 ◽  
Author(s):  
N. K. Bourne
Keyword(s):  
Strong Shock ◽  
Dynamic Strength ◽  
Weak Shock ◽  
Theoretical Strength ◽  
Elastic Behaviour ◽  
Fourth Power ◽  
Homogeneous State ◽  
Ultimate Shear Strength ◽  
Shear Component ◽  
Shock Behaviour

AbstractThe limits of elastic behaviour change with the nature of the impulse applied to a target and the size of volume interrogated by a measurement, since it is the pre-existing defects sampled within its rise that determine the response observed. This review considers a range of solids of different material classes and tracks the development of the strength of the material during shock loading, from yield at the Hugoniot elastic limit, across the weak shock regime, to its transition to strong shock behaviour. It is shown that at this stress, the weak shock limit (WSL), the shear component of the applied stress exceeds the theoretical strength of the material. Beyond this threshold, there are a number of new responses that confirm a transition from an inhomogeneous to a homogeneous state. Further, whilst strength rises across the weak shock regime, it saturates at the WSL. For instance, failure in shocked glasses transitions from localised fracture initiated at target boundaries to a global failure at this threshold at the theoretical strength. Sapphire′s strength asymptotes to the theoretical strength of the strongest direction in its lattice. Finally, the fourth-power dependence of strain rate upon stress appears to be a consequence of the homogeneous flow in the strong shock regime. This review suggests that µ/2π is a good approximation for the unrelaxed theoretical strength of solids at increasing stresses beyond the WSL. The methodology unfolded here represents a new means to experimentally determine the ultimate shear strength of solids.

The determination of arc temperatures from shock velocities

1957 ◽  
Vol 240 (1220) ◽  
pp. 54-66 ◽  
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Wave Theory ◽  
New Method ◽  
Shock Propagation ◽  
Plane Shock ◽  
Gas Temperature ◽  
Specific Heats ◽  
Arc Discharges

The measurement of the high gas temperatures associated with arc discharges requires special techniques. One such method, developed by Suits (1935), depends on the measure­ment of the velocity of a sound wave passing through an arc column, although in fact Suits measured the velocity of a very weak shock wave. The new method described in the present paper is one in which temperatures are determined from the measurement of the velocity of a relatively strong shock wave propagated through an arc. The new method has the merit of consistently producing accurately measurable records and of increasing the accuracy of the temperature determination. The shock velocities are measured by means of a rotating mirror camera. Within the arc, the shock propagation is observable by virtue of the increased arc brightness produced by the shock. In the non-luminous regions surrounding the arc, the shock propagation is displayed by means of a Schlieren system. The interpretation of the measurements depends upon a one-dimensional analysis given in this paper which is similar to that of Chisnell (1955) and which describes the interaction of a plane shock with a con­tinuously varying temperature distribution. In our analysis account is taken also of the continuous variation in specific heats and molecular weight which are of importance under high gas temperature conditions. In practice plane wave theory cannot adequately describe the shock propagation, since attenuation occurs both in the free gas and in the arc column. The effects of this attenuation on the temperature determinations may be accounted for by the use of an experimentally determined attenuation relationship given in the paper. The finally developed method yields temperature values to an accuracy of ± 2%. Experiments are described for carbon and tungsten arcs in air and nitrogen for currents up to 55 amperes and pressures up to 3 atmospheres. The values obtained range from 6200 to 7700° K and are in good agreement with values determined by other techniques.

Experiments on the diffraction of weak blast waves: the von Neumann paradox

1980 ◽  
Vol 369 (1739) ◽  
pp. 537-555 ◽  
Keyword(s):  
Strong Shock ◽  
Weak Shock ◽  
Blast Waves ◽  
Shock Diffraction ◽  
Self Similarity ◽  
Von Neumann ◽  
Shock System ◽  
Series Of Experiments ◽  
Mach Reflexion ◽  
Good Agreement

This paper presents the results of our experiments with weak incident shocks diffracting over concave corners. For Mach reflexion, the experiments reveal a fundamental difference between weak and strong shock diffraction, namely that for weak shock diffraction the corner signal can always catch up with the three-shock confluence, but this does not happen for strong shock diffraction except for comparatively small corner angles. We show that by taking into account the attenuating effect of the corner signal it is possible in principle to modify the well-known von Neumann theory and that this is then in good agreement with the experimental data. Evidence is presented which shows that another effect of the corner signal is to cause a partial loss of the self-similarity property of the three-shock system. Indeed, for one series of experiments the oncoming flow relative to the Mach stem behaved as though it were parallel to the sloping wall of the corner and therefore did not have the familiar radial distribution centred on the corner. The modified theory can be extended to include the persisted regular reflexion phenomenon suggesting that this is an unresolved Mach reflexion. In that event there is some experi­mental evidence that transition to Mach reflexion would then be consistent with the normal shock point as Henderson and Lozzi found for strong shock diffraction.

A model for the atmospheric shock wave produced by a strong volcanic explosion

2020 ◽  
Vol 222 (2) ◽  
pp. 735-742
Author(s):  
Michele Dragoni ◽  
Dalila Santoro
Keyword(s):  
Shock Wave ◽  
Shock Front ◽  
Sound Pressure ◽  
Strong Shock ◽  
Weak Shock ◽  
Volcanic Eruptions ◽  
Density Inhomogeneity ◽  
Acoustic Effect ◽  
Explosive Volcanic Eruptions ◽  
Spherical Shock

SUMMARY Atmospheric shock waves are a common phenomenon in explosive volcanic eruptions. We consider the motion of a spherical shock wave generated by a point source in the strong shock approximation. The shock front corresponds to discontinuities in the gas velocity, density, pressure and temperature, which are calculated as functions of the energy of the explosion. The problem is solved analytically for the distributions of velocity, density, pressure and temperature in the atmosphere as functions of the distance from the source. The motion of the shock wave being supersonic, the solution is valid for a few seconds after the explosion, corresponding to a distance of few kilometres. The acoustic effect of the shock wave, expressed by the peak sound pressure level, is calculated and may reach hundreds of decibels. The pressure waveform that could be recorded in the vicinity of the volcano is calculated and compared with typical waveforms in weak shock conditions. The change in the refractive index of air due to density inhomogeneity is calculated and the conditions under which a condensation cloud is formed behind the shock front are investigated.

scholarly journals Hydrogen Abundances and Shock Waves

2021 ◽  
pp. 187-219
Author(s):  
Donald V. Reames
Keyword(s):  
Shock Waves ◽  
Power Law ◽  
Strong Shock ◽  
Weak Shock ◽  
Shock Acceleration ◽  
Seed Particle ◽  
Abundance Patterns ◽  
Seed Population ◽  
Suprathermal Ions ◽  
Strong Shock Waves

AbstractHow well do protons fit into the abundance patterns of the other elements? Protons have Q = 1 and A/Q = 1 at all temperatures of interest. When does their relative abundance fit on the power law in A/Q defined by the elements with A/Q > 2? For small “pure” impulsive events, protons fit well, but for larger CME-associated impulsive events, where shock waves boost the intensities, protons are enhanced a factor of order ten by addition of seed protons from the ambient plasma. During most large gradual SEP events with strong shock waves, protons again fit the power law, but with weaker or quasi-perpendicular shock waves, dominated by residual impulsive seed particle abundances at high Z, again protons are enhanced. Proton enhancements occur when moderately weak shock waves happen to sample a two-component seed population with dominant protons from the ambient coronal plasma and impulsive suprathermal ions at high Z; thus proton-enhanced events are a surprising new signature of shock acceleration in jets. A/Q measures the rigidity dependence of both acceleration and transport but does not help us distinguish the two. Energy-spectral indices and abundances are correlated for most gradual events but not when impulsive ions are present; thus we end with powerful new correlations that probe both acceleration and transport.

scholarly journals The focusing of weak shock waves

1976 ◽  
Vol 73 (4) ◽  
pp. 651-671 ◽  
Author(s):  
B. Sturtevant ◽  
V. A. Kulkarny
Keyword(s):  
Shock Waves ◽  
Wave Field ◽  
Amplification Factor ◽  
Strong Shock ◽  
Weak Shock ◽  
Expansion Waves ◽  
Initial Wave ◽  
Geometrical Acoustics ◽  
Complex Wave ◽  
Maximum Amplification

This paper reports an experimental investigation, using shadowgraphs and pressure measurements, of the detailed behaviour of converging weak shock waves near three different kinds of focus. Shocks are brought to a focus by reflecting initially plane fronts from concave end walls in a large shock tube. The reflectors are shaped to generate perfect foci, arêtes and caustics. It is found that, near the focus of a shock discontinuity, a complex wave field develops, which always has the same basic character, and which is always essentially nonlinear. A diffracted wave field forms behind the non-uniform converging shock; its compressive portions steepen to form diffraction shocks, while diffracted expansion waves overtake and weaken the diffraction shocks. The diffraction shocks participate in a Mach reflexion process near the focus, whose development is determined by competition between the convergence of the sides of the focusing front and acceleration of its central portion. In fact, depending on the aperture of the convergence and the strength of the initial wave, the three-shock intersections of the Mach reflexions either cross on a surface of symmetry or remain uncrossed. In the former case, which is observed if the shock wave is relatively weak, the wavefronts emerge from focus crossed and folded, in accordance with the predictions of geometrical acoustics theory. In the latter, the strong-shock case, the fronts beyond focus are uncrossed, as predicted by the theory of shock dynamics. It is emphasized that in both cases the behaviour at the focus is nonlinear. The overtaking of the diffraction shocks by the diffracted expansions limits the amplitude of the converging wave near focus, and is the mechanism by which the maximum amplification factor observed at focus is determined. In all cases, maximum pressures are limited to rather low values.

Stability of a supersonic flow over a wedge containing a weak shock wave satisfying the Lopatinski condition

2014 ◽  
Vol 11 (02) ◽  
pp. 215-248 ◽  
Author(s):  
A. M. Blokhin ◽  
D. L. Tkachev
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Wave Solution ◽  
Strong Shock ◽  
Weak Shock ◽  
Weak Sense ◽  
Strong Shock Wave ◽  
Weak Shock Wave ◽  
Heat Conducting ◽  
Shock Wave Solution

We study the stability problem for a stationary supersonic flow of inviscid non-heat-conducting gas in thermodynamical equilibrium moving onto a planar infinite wedge. As it is known, this problem has two solutions: a solution with a strong shock wave (when the velocity behind the front of the shock wave is subsonic) and a solution with a weak shock wave (when the velocity behind the front of the shock wave is supersonic). We consider the case of a weak shock wave and we prove that if the Lopatinski condition for the shock wave holds (in a weak sense), then the corresponding linearized initial boundary-value problem is well-posed. We thus find a classical solution to this problem. Unlike the case when the uniform Lopatinski condition holds, additional plane waves appear. For compactly supported initial data we show that the solution of the linearized problem converges to the zero solution as time tends to infinity. Therefore, for the case of a weak shock wave and when the Lopatinski condition holds in a weak sense, these results complete the proof of the well-known Courant–Friedrichs' conjecture that the strong shock wave solution is unstable whereas the weak shock wave solution is stable.

scholarly journals Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone

2010 ◽  
Vol 199 ◽  
pp. 151-181 ◽  
Author(s):  
Gang Xu ◽  
Huicheng Yin
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Vertex Angle ◽  
Transonic Shock ◽  
Euler Flow ◽  
Flow Past ◽  
Curve Method ◽  
Sharp Cone ◽  
Supersonic Shock

AbstractIn this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the book Supersonic Flow and Shock Waves by Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.

scholarly journals Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone

2010 ◽  
Vol 199 ◽  
pp. 151-181 ◽  
Author(s):  
Gang Xu ◽  
Huicheng Yin
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Vertex Angle ◽  
Transonic Shock ◽  
Euler Flow ◽  
Flow Past ◽  
Curve Method ◽  
Sharp Cone ◽  
Supersonic Shock

AbstractIn this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the bookSupersonic Flow and Shock Wavesby Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.

scholarly journals On the Strength of the Galactic Shock Wave and the Degree of Development of Spiral Structure

1974 ◽  
Vol 58 ◽  
pp. 439-441 ◽  
Author(s):  
William W. Roberts ◽  
Morton S. Roberts ◽  
Frank H. Shu
Keyword(s):  
Shock Waves ◽  
Spiral Structure ◽  
Density Wave ◽  
Spiral Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Wave Crest ◽  
Wave Models ◽  
The One ◽  
Spiral Arm

The luminosity of a spiral arm is believed to originate primarily in the very young, newly forming stars; and the spiral arm itself to be a spiral wave which is capable of triggering the formation of the young stars selectively along the wave crest. A semi-empirical study of the density wave patterns predicted in the density wave models of twenty-five external galaxies has been made and one result of this study is presented here. It is found that those galaxies of the sample whose models predict the possibility of strong shock waves are also the galaxies which exhibit long, well-developed spiral arms; and those galaxies whose models predict weak shock waves are also the galaxies which exhibit less-developed spiral structure. This trend is seen through a correlation between w⊥0, the velocity component of basic rotation normal to a spiral arm, which is an important parameter in determining the shock strength on the one hand, and luminosity class, which is a measure of the degree of development of spiral structure on the other.

Two Failures to Prevent Avoidance Decrement

1966 ◽  
Vol 19 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Norman H. Anderson ◽  
Howard A. Rollins
Keyword(s):  
Avoidance Response ◽  
Strong Shock ◽  
Weak Shock ◽  
Acquisition Training ◽  
Distributed Practice

Two experiments were performed in attempts to prevent avoidance decrement (disappearance of an initially learned avoidance response with continued acquisition training). In Exp. 1, widely distributed practice appeared to lower initial performance but did not otherwise prevent the decrement. In Exp. 2, the decrement was found with weak shock, strong shock, and with pulsed strong shock.

Sign in / Sign up

Export Citation Format

Share Document