Shock Propagation in a Strain-Hardening Material

1969 ◽  
Vol 36 (2) ◽  
pp. 181-188 ◽  
Author(s):  
P. J. Rausch
Keyword(s):  
Shock Front ◽  
Stress Component ◽  
Weak Shock ◽  
Simple Wave ◽  
Entropy Change ◽  
Momentum Conservation ◽  
Shock Propagation ◽  
Wave Form ◽  
Hardening Material ◽  
Material State

Weak shock theory is used to analyze the propagation of the stress waves which are induced by nonuniform, instantaneous, internal heating of a nonlinearly elastic, semi-infinite solid. The material nonlinearity considered is caused by the increase in bulk modulus which occurs as the hydrodynamic stress component increases. Heating is assumed to occur instantaneously. Since the shock is assumed to be weak, the entropy change across it is negligible, and therefore the wave form both behind and in front of the shock is found by using a coordinate perturbation method to solve the nonlinear equations for constant entropy. This solution predicts a multivalued material state in the vicinity of the shock front without locating the front itself. The location of the shock front is found separately by using the principle of momentum conservation. If the front is then inserted at this location, a wave form is obtained for which the material state is everywhere single-valued. The results and conclusions which are presented are based on a comparison of the perturbation solution found in this paper, and a simple wave solution and on an assessment of shock strength.

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.

scholarly journals Thermal Elastic-Plastic Stress Analysis of an Aluminium Composite Disc under Linearly Decreasing Thermal Loading

2008 ◽  
Vol 17 (3) ◽  
pp. 096369350801700 ◽  
Author(s):  
Muzaffer Topcu ◽  
Gurkan Altan ◽  
Hasan Callioglu ◽  
Burcin Deda Altan
Keyword(s):  
Thermal Stress ◽  
Stress Analysis ◽  
Tangential Stress ◽  
Outer Surface ◽  
Thermal Stresses ◽  
Stress Component ◽  
Aluminium Composite ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Inner Surface

In this study, an elastic-plastic thermal stress analysis of an orthotropic aluminium metal matrix composite disc with a hole has been investigated analytically for non-linear hardening material behaviour. The aluminium composite disc reinforced curvilinearly by steel fibres is produced under hydraulic press. The mechanical properties of the composite disc are obtained by tests. A computer program is developed to calculate the thermal stresses under a linearly decreasing temperature from inner surface to outer surface. Elastic, elastic-plastic and residual thermal stress distributions are obtained analytically from inner surface to outer surface and they are presented in tables and Fig. s. The elastic-plastic solution is performed for the plastic region expanding around the inner surface. The magnitude of the tangential stress component has been found out in this study to be higher than the magnitude of the radial stress component. Besides, the tangential stress component is compressive at the inner surface and tensile at the outer surface. The magnitude of the tangential residual stress component is the highest at the inner surface of the composite disc.

scholarly journals Non-linear weak shock diffraction

1968 ◽  
Vol 8 (4) ◽  
pp. 737-754 ◽  
Author(s):  
N. J. De Mestre
Keyword(s):  
Shock Wave ◽  
Shock Front ◽  
Weak Shock ◽  
Weak Shock Wave ◽  
Shadow Region ◽  
Ray Theory ◽  
Perturbation Expansions ◽  
Shock Diffraction ◽  
Non Linear ◽  
Flow Variables

AbstractPerturbation expansions are sought for the flow variables associated with the diffraction of a plane weak shock wave around convex-angled corners in a polytropic, inviscid, thermally-nonconducting gas. Lighthill's method of strained co-ordinates [4] produces a uniformly valid expansion for most of the diffracted front, while the remainder of this front is treated by a modification of the shock-ray theory of Whitham [6]. The solutions from these approaches are patched just inside the ‘shadow’ region yielding a plausible description of the entire diffracted shock front.

scholarly journals Shock propagation into inhomogeneous media

1970 ◽  
Vol 43 (3) ◽  
pp. 487-495 ◽  
Author(s):  
J. D. Strachan ◽  
J. P. Huni ◽  
B. Ahlborn
Keyword(s):  
Shock Wave ◽  
Shock Front ◽  
Rarefaction Wave ◽  
Particle Velocity ◽  
Homogeneous Medium ◽  
Inhomogeneous Media ◽  
Front Velocity ◽  
Shock Propagation ◽  
Analytic Relation

An analytic relation is derived for the shock front velocity as a function of the initial parameters (pressure, density, and particle velocity) in a continuous, in-homogeneous medium. This relation was verified experimentally by using it to predict the propagation of a shock wave through a known rarefaction wave.

Effect of Finite Diaphragm Rupture Process on Microshock Tube Flows

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Arun K. R ◽  
H. D. Kim ◽  
T. Setoguchi
Keyword(s):  
Supersonic Flow ◽  
Flow Field ◽  
Shock Front ◽  
Supersonic Nozzle ◽  
Propagation Speed ◽  
Propagation Distance ◽  
Rupture Process ◽  
Shock Propagation ◽  
Diaphragm Rupture ◽  
Contact Distance

The study of flow physics in microshock tubes is of growing importance with the recent development of microscale technology. The flow characteristics in a microshock tube is considerably different from that of the conventional macroshock tube due to the boundary layer effects and high Knudsen number effects. In the present study an axisymmetric computational fluid dynamics (CFD) method was employed to simulate the microshock tube flow field with Maxwell's slip velocity and temperature jump boundary conditions, to accommodate the rarefaction effects. The effects of finite diaphragm rupture process and partial diaphragm rupture on the flow field and the wave propagations were investigated, in detail. The results show that the shock propagation distance attenuates rapidly for a microshock tube compared to a macroshock tube. For microshock tubes, the contact surface comes closer to the shock front compared to the analytical macroshock tube case. Due to the finite diaphragm rupture process the moving shock front will be generated after a certain distance ahead of the diaphragm and get attenuated rapidly as it propagates compared to the sudden rupture case. The shock-contact distance reduces considerably for the finite diaphragm rupture case compared to the sudden diaphragm rupture process. A partially burst diaphragm within a microshock tube initiates a supersonic flow in the vicinity of the diaphragm similar to that of a supersonic nozzle flow. The supersonic flow expansion leads to the formation of oblique shock cells ahead of the diaphragm and significantly attenuates the moving shock propagation speed.

On the near-equilibrium and near-frozen regions in an expansion wave in a relaxing gas

1964 ◽  
Vol 19 (1) ◽  
pp. 81-102 ◽  
Author(s):  
J. G. Jones
Keyword(s):  
Asymptotic Solution ◽  
Simple Wave ◽  
Expansion Wave ◽  
Wave Form ◽  
Time Interval ◽  
Finite Time Interval ◽  
Acoustic Equation ◽  
Equilibrium Region ◽  
Relaxing Gas ◽  
Asymptotic Equilibrium

A weak expansion wave propagating in a relaxing gas is discussed with particular reference to the ‘near-equilibrium’ and ‘near-frozen’ regions. The concept of bulk viscosity is used in conjunction with Burger's equation in the near-equilibrium region. The asymptotic equilibrium simple wave is modified by diffusive regions in the neighbourhood of the first and last rays. It is shown that in the case of a weak expansion wave, Chu's asymptotic solution of the acoustic equation describes the wave-form for a finite time interval before convection effects become noticeable. In the near-frozen region a characteristic perturbation method is used to describe the flow near the wave-front.

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.

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