Relief wave

Expansion waves are the mechanism by which a material returns to ambient pressure. In the same spirit as Fig. 2.2, a rarefaction is depicted for intuitive appeal in Fig. 2.7. In this case, the bull has a finite mass, and is free to be accelerated by the collision, leading to a free surface. Any finite body containing material at high pressure also has free surfaces, or zero-stress boundaries, which through wave motion must eventually come into equilibrium with the interior. Expansion waves are also known as rarefaction waves, unloading waves, decompression waves, relief waves, and release waves. Material flow is in the same direction as the pressure gradient, which is opposite to the direction of wave propagation. 

In Seetion 2.8, we noted that most expansion waves are isentropie. It was shown in Seetion 2.4 that the differenee between the Hugoniot and isentrope is small for hydrodynamie materials at small strains. Thus we ean also represent relief waves in the P-u plane with the same eurve used to represent shoek waves, if the strains are not too large. 

The complexity of the stress waves generated by explosive charges or projectile impact, and the appearance of relief waves that emanate from free sur-... 

The isentrope, the path function that describes a continuity and not a jump, is different from the Hugoniot. Remember that a relief wave is a continuous... 

Now remember that we said that a relief wave unloads along the path of the isentrope, which we earlier said could be closely approximated by the Hugoniot. If we took this material, which we have just shocked to Pi,U, and allow a relief wave to bring it back to Po,Uo, then, by the same arguments, the change in specific internal energy for the relief wave is the total area under the Hugoniot... 

In the next chapter we will examine the properties and behavior of rarefaction, or relief, waves. We will solve problems, on the P-u plane, involving rarefactions and interactions of rarefactions. We will see how these interactions lead to material failure as in the cases of spall and scabbing (multiple spall). 

It takes (5)/7.65 = 0.65 fjs to traverse the flyer. The total time from impact until a relief wave reaches the interface is 0.95 (shock) + 0.65 (rarefaction). 

There are several theories of how fragments are formed and hence how large or small they would be one of the earliest is from N. F. Mott (Refs. 11, 12). Mott explained the sizes of fragments as a function of the rate of cylinder expansion as compared to rate of a tensile relief wave around the cylinder s periphery. See Figure 27.12. 

It is assumed that the cylinder is placed in greater and greater hoop stress (tensile) as it expands. A fracture eventually will occur at some point. The fracture presents a free surface, and a relief wave can now travel away from it. 

Fracture can no longer occur in the relieved regions (shown in Figure 27.12 as shaded), but tensile stress and plastic flow are still growing in the unrelieved region where a new fracture is free to form. The size of the fragments then are determined by the balance between the rate of increasing strain and the rate of the relief wave. 

Figure 27.12. Stress-relief waves leaving a fracture.

Figure 4. Damage distribution and mean stress contour plot at 2.0 ms in computer simulation of Experiment 79S. The contour level and plot dimensions are the same as in Figure 1. At this time, a layer of spall damage can be seen near the free surface. It developed as the tensile relief wave propagated downward following the interaction of the explosively generated shock with the free surface. This figure shows the final computed damage distribution.

Extensive testing and numerical analyses of past tests have shown that pressure measurements In tests with no confinement (weak-walled vessels) can greatly underpredict peak pressures due to interactions with relief waves in the foregoing test, we believe that the actual pressures were much higher. Pressures of as much as 100 MPa have been directly measured on some previous steam explosion tests, and this is probably more representative of the actual pressures. Impulse measurements, however, tend to be more accurate because they are not strongly influenced by high-pressure, short-duration pulses.]... 

Rarefaction wave A wave that reduces the normal stress (or pressure) inside a material as it propagates the mechanism by which a material returns to ambient pressure after being shocked (the state behind the wave is at lower stress than the state in front of it). Also known as unloading, expansion, release, relief, or decompression waves. 

The motion of disloeations under eonditions of shoek-wave eompression takes plaee at sueh high veloeities (approaehing the elastie sound speed) that many vaeaneies and interstitials are left behind. However, these point defeets ean anneal out at room temperature and are thus diflieult to study by shoek-reeovery teehniques. The presenee of point defeets has little effeet on the material eompressibility and other properties related to equation of state. While they also have little direet influenee on the relief of shear stresses, point defeets do influenee the mobility and multiplieation of disloeations. This, in turn, affeets most of what happens under shoek-wave loading eonditions. 

The maximum pressure from an explosion of a hydrocarbon and air is 7 x initial pressure, unless it occurs in a long pipe where a standing wave can be set up. It may be cheaper to design some small vessels to withstand an explosion than to provide a safety relief system. It is typical to specify %" as minimum plate thickness (for carbon steel only). 

Ninety minutes after the fire started, the sphere burst. Ten out of 12 firemen within 50 m were killed. Men 140 m away were badly burned by a wave of propane that came over the eompound wall. Altogether, 15-18 men were killed (reports differ), and about 80 were injured. The area was abandoned. Flying debris broke tbe legs of an adjacent sphere, w hich fell over. Its relief valve discharged liquid, which added to the fire, and 45 minutes later this sphere burst. Altogether, five spheres and two other pressure vessels burst, and three were damaged. The fire spread to gasoline and fuel oil tanks. 

Deflagrative combustion of an extended, flat vapor cloud is very ineffective in producing damaging blast waves because combustion products have a high rate of side relief accompanied by vortex formation. 

ITie Henry and Fauske model employs curves similar to Fig. 16. Immediately upon initial contact, they assume that there is rapid pressurization at the interface. Nucleation in this vicinity is then prevented [Po in Eq. (7) is large and so is Dq] until the pressure is acoustically relieved by the wave moving to a free surface and returning. During this period, the thermal boundary layer in the cold liquid continues to develop. At relief, there still may be no intersection of the t-Do curve (in Fig. 16), so until such a time... 

Under the title Shear Fracture, Cook (Ref 4, p 346) noted that under conditions in which the tensile forces cannot develop or are restricted, a type of fracturing that can be associated with trajectories of maximum shear stress may develop. Rinehart 8t Pearson (Ref 1) detonated a 1/8 inch layer of expl on the cylindrical surface of a 2)4 inch OD aluminum (24S-T) cylindrical block with a 3/4 inch cylindrical relief hole drilled thru the longitudinal axis. The shock wave moving in toward the relief hole developed at each point of the block two mutually orthogonal trajectories of maximum shear stress. The trajectories, where the shear stress was maximal, spread out in 8 to 12 curved continuous lines from points on the surface of the relief hole. The shear fraction patterns observed along trajectories of maximum shear resembled the "Luder s... 

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