Reflected 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 ... 

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. 

The more common type of spalling failure of concrete occurs when (and where) the transmitted compressive wave reflects from the free surface back face of the slab as a tensile wave, and the head of the reflected tensile wave and tail of the transmitted compressive wave combine to produce net tensile stress exceeding the dynamic tensile strength of the concrete. This process is shown schematically in Figure 21 for the simplified case of a plane, triangular compressive... 

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

The normal stress must be zero at the free surface, so a tension wave of a similar profile but opposite sign must start propagating in from the rear surfaces when the compressive front reaches this surface. The actual stress state shortly thereafter is shown in state 2 in Figure 21. When the tensile stress exceeds the tensile strength of the material, spall occurs on a plane parallel to the free surface. The normal stress then drops to zero again, and the process continues. In brittle materials weak in tension (such as concrete), it is possible for multiple spalls to occur before the reflected tensile waves decay enough to fall below the tensile strength. 

Detonation Wave, Plastic. These waves are complicated by the fact that there is no longer a linear relation between stress and strain. A plastic wave does not maintain its form as it progresses but rather the front of increasing stress tends to become longer and longer, at least in normal cases. The reflection at a discontinuity resembles generally the reflection of an elastic wave. Reflection of stress wave at a fixed end in an elastic member gives rise to stresses strains that ass exactly double those in the incident wave... 

The main focus of this of this work is to investigate the interaction between the transmitted wave and dislocation sources. However, when the stress wave hits the rigid base, it reflects back to the material block and interacts with the dislocations again. In order to minimize the effects of the reflected waves, the length of the cell (25 pm) is chosen such that once the wave front reaches the bottom surface, the value of the stresses in the position where the dislocations are located is small so that dislocation relaxation process can take place well before the wave hits the bottom of the RVE. A better solution to isolate the effect of the reflected wave would be by implementing a suitable non-reflective FE boundary condition. 

In order to guarantee a quasi-static state in the dynamic Brazilian test, pulse shaping technique is employed for all our dynamic tests. The dynamic force balance on the two loading ends of the sample is critically assessed. Figure 3 shows the forces on both ends of the specimen in a typical test. From Eq. 1 and 2, the dynamic force on one side of the specimen PI is proportional to the sum of the incident (In) and reflected (Re) stress waves, and the dynamic force on the other side P2 is proportional to the transmitted (Tr). It can be seen from Figure 3 that the dynamic forces on both sides of the specimens are almost identical during the whole dynamic loading period. The... 

Target size. In order to ensure that the flexure stress wave and shear stress wave be transmitted and reflected many times by the boundary, and to homogenize the stresses sufficiently, a smaller sized target tends to result in a quasi-static response. 

Numerical simulation of seismic wave propagation along a slender rods done by Tang Chun-an (Tang, 2009) displays that, the reflection wave at the slope surface will form the tensile stress wave, which will lead to tensional deformation at the part of slope, even projectile. It can be used for the... 

Low-intensity ultrasonic waves are used for nondestructive probing to locate flaws in materials for which complete reliability is mandatory, such as those used in spacecraft components and nuclear reactor vessels. When an ultrasonic transducer emits a pulse of energy into the test object, flaws reflect the wave and are detected. Because objects subjected to stress emit ultrasonic waves, these signals may be used to interpret the condition of the material as it is increasingly stressed. Another application is ultrasonic emission testing, which records the ultrasound emitted by porous rock when natural gas is pumped into cavities formed by the rock to determine the maximum pressure these natural holding tanks can withstand. 

The boundary conditions for the model are defined as the situation in which a given stress wave transmits from adherend 1 into the joint, as shown in O Fig. 29.4. If a strain gage is bonded on adherend 1 far from the joint end, the strain variation due to the stress wave propagation can be measured. In this case, the information of the progressive stress wave can be obtained, but have no information on the stress wave reflection occurring at the joint end. 

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