Stress Waves

The common civil engineering seismic testing techniques work on the principles of ultrasonic through transmission (UPV), transient stress wave propagation and reflection (Impact Echo), Ultrasonic Pulse Echo (UPE) and Spectral Analysis of Surface Waves (SASW). 

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 ... 

The abrasion resistance of cobalt-base alloys generally depends on the hardness of the carbide phases and/or the metal matrix. For the complex mechanisms of soHd-particle and slurry erosion, however, generalizations cannot be made, although for the soHd-particle erosion, ductihty may be a factor. For hquid-droplet or cavitation erosion the performance of a material is largely dependent on abiUty to absorb the shock (stress) waves without microscopic fracture occurring. In cobalt-base wear alloys, it has been found that carbide volume fraction, hence, bulk hardness, has Httie effect on resistance to Hquid-droplet and cavitation erosion (32). Much more important are the properties of the matrix. 

Prompt instrumentation is usually intended to measure quantities while uniaxial strain conditions still prevail, i.e., before the arrival of any lateral edge effects. The quantities of interest are nearly always the shock velocity or stress wave velocity, the material (particle) velocity behind the shock or throughout the wave, and the pressure behind the shock or throughout the wave. Knowledge of any two of these quantities allows one to calculate the pressure-volume-energy path followed by the specimen material during the experimental event, i.e., it provides basic information about the material s equation of state (EOS). Time-resolved temperature measurements can further define the equation-of-state characteristics. 

The objective in these gauges is to measure the time-resolved material (particle) velocity in a specimen subjected to shock loading. In many cases, especially at lower impact pressures, the impact shock is unstable and breaks up into two or more shocks, or partially or wholly degrades into a longer risetime stress wave as opposed to a single shock wave. Time-resolved particle velocity gauges are one means by which the actual profile of the propagating wave front can be accurately measured. 

The gauge element in the form of a foil (50 ohms) is normally embedded in materials such that the active gauge element is normal to the stress-wave propagation direction. Manganin is the only in situ stress gauge available for... 

Figure 3.14. Manganin stress-wave profiles for Arkansas novaculite at 25 GPa (Grady et al., 1974).

Of all the piezoelectric crystals that are available for use as shock-wave transducers, the two that have received the most attention are x-cut quartz and lithium-niobate crystals (Graham and Reed, 1978). They are the most accurately characterized stress-wave transducers available for stresses up to 4 GPa and 1.8 GPa, respectively, and they are widely used within their stress ranges. They are relatively simple, accurate gauges which require a minimum of data analysis to arrive at the observed pressure history. They are used in a thick gauge mode, in which the shock wave coming through the specimen is... 

G.E. Duvall, Propagation of Plane Shock Waves in a Stress-Relaxing Medium, in Stress Waves in Anelastic Solids (edited by H. Kolsky and W. Prager), Springer-Verlag, Berlin, 1964, pp. 20-32. 

W. Herrmann, D.L. Hicks, and E.G. Young, Attenuation of Elastic-Plastic Stress Waves, in Shock Waves and the Mechanical Properties of Solids (edited by J.J. Burke and V. Weiss), Syracuse University Press, Syracuse, 1971, pp. 23-63. 

Spall is the process of internal failure or rupture of condensed media through a mechanism of cavitation due to stresses in excess of the tensile strength of the material. Usually, a dynamic failure is implied where transient states of tensile stress within the body are brought about by the interaction of stress waves. Free surfaces are assumed to be well removed from the material point of interest and play no role in the spall process. 

Up to this point we have addressed primarily the flaw structure and energy concepts in stress-wave loaded solids governing the creation of new fracture surface area (or the mean fragment size) in catastrophic fragmentation events. It remains to consider a concept which is frequently the end concern in impulsive fracture applications, namely, the distribution in sizes of the particles produced in the dynamic fragmentation event. 

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

Figure 8.36. Calculation of Taylor impact of a 1100-0 aluminum cylinder including stress wave evolution and damage formation. Symmetric impact at 0.15 km/s.

L.D. Bertholf et al.. Kinetic Energy Projectile Impact on Multi-Layered Targets Two-Dimensional Stress Wave Calculations, Prepared by Sandia National La-... 

Herrman, W., Nonlinear Stress Waves in Metals, in Wave Propagation in Solids (edited by Miklowitz, J.), American Society of Mechanical Engineers, New York, 1969, pp. 129-183. 

Gurtman, G.A., Review of Techniques Used to Analyze Stress Wave Propagation in Composites, Systems, Science and Software Report No. 3SR-154, Part II, La Jolla, CA, 40 pp., December 1969. 

Seaman, L., SRIPUFF 3 Computer Code for Stress Wave Propagation, Air Force Weapons Laboratory Technical Report No. AFWL-TR-70-51, Kirtland AFB, NM, 370 pp., September 1970. 

In many cases, less intense pressure or stress waves are encountered in which times to achieve peak pressure may be hundreds of nanoseconds or more. The study of solids under these conditions can be the source of mechanical, physical, and chemical properties of solid materials at large strain, high pressure, and high strain rates. 

The linear piezoeleetrie model can be used to demonstrate that the magnitude of the electric field encountered for a given polarization function is a sensitive function of the thickness of the sample. This behavior can be demonstrated by noting that the electric displacement at a given time is inversely proportional to the thickness. Thus, the thickness of the sample is an important variable for investigating effects such as conductivity that depend upon the magnitude of the electric field. Conversely, various input stress wave shapes can be used to cause various field distributions at fixed thicknesses. 

From the mechanical viewpoint, ferroelectrics exhibit unsteady, evolving waves at low stresses. Waves typical of well defined mechanical yielding are not observed. Such behavior is sensitive to the electrical boundary conditions, indicating that electromechanical coupling has a strong influence. Without representative mechanical behavior, it is not possible to quantitatively define the stress and volume compression states exciting a particular electrical response. 

Fig. 6.4. At relatively low pressures the shock speeds observed for stress waves in low density powder compacts are dominated by the crush-up of the powder toward solid density. The figure shows measured wavespeeds for a range of densities and fits to the data based on Herrmann s P-a model on Fe. Note the unusually low wavespeeds compared to solid density (after Herrmann [69H02]).

The technique utilises arrays of transducers attached to the external surfaces of the equipment, which detect small-amplitude elastic stress waves emitted when defects propagate . Using sophisticated computational techniques, events can be characterised in terms of their severity and location. 

On the loaded side of a slab subjected to an intense reflected blast wave, a region of the slab will fail if the intensity of the compressive wave transmitted into the slab exceeds the dynamic compressive strength of the material. For an intense wave striking a thin concrete slab, the failure region can extend through the slab, and a sizeable area turned to rubble which can fall or be ejected from the slab. For a thicker slab or localized loaded area, spherical divergence of the stress wave can cause it to decay in amplitude within the slab so that only part of the loaded face side is crushed by direct compression. 

Figure 21. Stress Wave Reflection at a Free Surface in a Solid.

Davids, N. (ed.), International Symposium on Stress Wave Propagation in Materials, Interscience Publishers, New York,... 

Kolsky, H., Stress Waves in Solids, Dover Publications, Inc., New York, NY, 1963. 

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