Wave speeds

Ultrasonic wave speed, Impact Echo and Spectral Analysis of Surface Waves... 

Ultrasonic wave speed, SASW and Impact Echo... 

Ultrasonic wave speed and Impact Echo High-Energy Radiography... 

In the example shown a covermeter is used to detennine the distance to a known single bar, and this information is in turn used to establish a reference for the radar measurements. A wave speed of 110 m/ps is calculated for this concrete. 

A problem obviously exists in trying to characterise anomalies in concrete due to the limitations of the individual techniques. Even a simple problem such as measurement of concrete thickness can result in misleading data if complementary measurements are not made In Fig. 7 and 8 the results of Impact Echo and SASW on concrete slabs are shown. The lE-result indicates a reflecting boundary at a depth corresponding to a frequency of transient stress wave reflection of 5.2 KHz. This is equivalent to a depth of 530 mm for a compression wave speed (Cp) of 3000 m/s, or 706 mm if Cp = 4000 m/s. Does the reflection come from a crack, void or back-side of a wall, and what is the true Cp ... 

SASW-result (dispersion curve) showing Rayleigh Wave speed as a function of wavelength (depth)... 

Erequendy, a single ultrasonic transducer serves both as the sender of the ultrasonic pulse and as a receiver for the sound waves reflected from surfaces and interior discontinuities. The receiver transforms the stress pulse back into electrical oscillations. AH of the signals are displayed on an oscilloscope screen for interpretation. Eor a material of length E having a wave speed C, the anomaly shown in Eigure 4 would reflect a signal back to the... 

Gas entrained in the fluid and the flexibiflty of the pipe wall both result in lowering of the wave speed. For deaerated water, the wave speed is about 1250 m/s. Detailed methods of analysis and evaluation of hydraulic transients may be found in the flterature (25). 

Example 10 Response to Instantaneous Valve Closing Compute the wave speed and maximum pressure rise for instantaneous valve closing, with an initial velocity of 2,0 m/s, in a 4-in Schedule 40 steel pipe with elastic modulus 207 X 10 Pa, Repeat for a plastic pipe of the same dimensions, with E = 1.4 X 10 Pa. The liquid is water with P = 2.2 X 10 Pa and p = 1,000 kg/m. For the steel pipe, D = 102,3 mm, b = 6,02 mm, and the wave speed is... 

It may be noted that an elastic material for which potentials of this sort exist is called a hyperelastic material. Hyperelasticity ensures the existence and uniqueness of solutions to intial/boundary value problems for an elastic material undergoing small deformations, and also implies that all acoustic wave speeds in the material are real and positive. 

When we translate these observations into Lagrangian wave speed, the data would look like that shown in the lower diagram of Fig. 7.11. The points e and q represent volume strains at whieh elastie-perfeetly-plastie release (e) and quasi-elastie release (q) would undergo transition to large-seale, reverse plastie flow (reverse yield point). The question is the following What is responsible for quasi-elastie release from the shoeked state, and what do release-wave data tell us about the mieromeehanieal response in the shoeked state ... 

Figure 7.13. Lagrangian wave speed in release from shoek-eompressed state of 20.7 GPa in 6061-T6 Al data (solid line) ealeulation (dashed line).

If we accept the assumption that the elastic wave can be treated to good aproximation as a mathematical discontinuity, then the stress decay at the elastic wave front is given by (A. 15) and (A. 16) in terms of the material-dependent and amplitude-dependent wave speeds c, (the isentropic longitudinal elastic sound speed), U (the finite-amplitude elastic shock velocity), and Cfi [(A.9)]. In general, all three wave velocities are different. We know, for example, that... 

Figure 8.7. Propagation of wave profile in an elastic-plastic material from the spall plane to the monitoring interface. The wave front propagates at a plastic wave speed whereas the wave release propagates at an elastic wave speed and complicates the analysis of the material spall strength.

Attenuation occurs because the tensile release, which is traveling at an elastic longitudinal wave speed, Q, overtakes the tensile front traveling at a plastic wave speed Cp < Q. Assuming a pulse as shown in Fig. 8.10 with a stress rate in the tensile front and tensile release of a and b, respectively, an approximate analysis shows that the peak will decay by an amount... 

The data shown in Fig. 8.11 are for an 80 ml/kg grade oil shale obtained from a mine near central Colorado. Oil shale grades from this region vary from 40-320 ml/kg. Properties such as fracture toughness and elastic constants are found to depend on oil shale grade. For the oil shale studied in Fig. 8.11, a fracture toughness of x 0.9 MN/m, a density of p = 2000 kg/m and an elastic wave speed of c = 3000 m/s are representative. 

For simple centered waves, each level of stress propagates at a discrete speed c. In this case, the wave speed corresponds to a given increment of stress or particle velocity and is a function of stress alone. Accordingly,... 

Melting, a major physical event, has small, subtle effects on shock-compression wave profiles. The relatively small volume changes and limited mixed-phase regions result in modest, localized changes in loading wave speed. Consequently, shock-induced melting and freezing remains an area with little data and virtually no information on the influence of solid properties and defects on its kinetics. 

Because of the subtle effects on the loading wave profile, many of the melting studies have utilized physical property measurements such as resistivity or optical opacity. Perhaps more direct are the release-wave speed... 

In lower pressure environments, the wave profiles are dominated by the consequences of deformation of the samples to fill the voids. This irreversible crush-up process strongly controls the wave speeds, which have anomalously low values at low initial sample densities. Modeling of this problem is... 

Table 6.2 summarizes the low pressure intercept of observed shock-velocity versus particle-velocity relations for a number of powder samples as a function of initial relative density. The characteristic response of an unusually low wavespeed is universally observed, and is in agreement with considerations of Herrmann s P-a model [69H02] for compression of porous solids. Fits to data of porous iron are shown in Fig. 6.4. The first order features of wave-speed are controlled by density, not material. This material-independent, density-dependent behavior is an extremely important feature of highly porous materials. 

Lu, Vyn, Sandus and Slagg (Ref 17) conducted ignition delay time and initiation studies on solid fuel powder-air mixts in an attempt to determine the feasibility of solid-air detonations. The materials investigated included Al, Mg, Mg-Al alloy, C and PETN. Ignition delay time was used as a method of screening the candidate fuels for further work in initiation studies which determined detonation wave speed, detonation pressure, detonation limits, initiation requirements, and the effect of particle size and confinement. The testing showed the importance of large surface area per unit mass, since the most... 

For very rough tubes, the flame acceleration is much more rapid as shown in the previous section. Transition to detonation is also clearly marked by a local explosion and abrupt change in the wave speed. The wall roughness controls the propagation of the wave by providing [5] ... 

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