Stress resolved

Figliola has made steady flow velocity and shear stress measurements downstream from a 25 mm spherical disc aortic valve (47,89). At a flow rate of 25 1/min he measured a maximum wall shear stress of 722 dynes/cm and an occluder wall shear stress (resolved on the upper side of occluder) of 440 dynes/cm. He also monitored a maximum turbulent shear stress of 545 dynes/ cm2, a 25 mm downstream from the valve. His velocity measurements also showed a large region of stagnation across the outflow face of the disc. Tillman has measured the "wall" (i.e. surface) shear stresses along the orifice ring in the major and minor outflow regions of an aortic valve under pulsatile flow... 

How are problems with worker fatigue and/or stress resolved ... 

In summary, CRSS is the necessary component of shear stress, resolved in the direction of slip, which initiates slip in the crystal. It is a constant for a given crystal. 

Therefore, the shearing stress resolved on the slip plane and in the slip... 

Many normally brittle solids can undergo considerable plastic deformation when, in addition to an axial stress, they are subjected to a hydrostatic pressure. If the brittle strength of the material is Og and the specimen has a hydrostatic pressure p applied to it, the tensile stress needed to produce brittle fracture is Og + p. This tensile stress gives rise to a shear stress resolved in the slip direction in the slip plane and if this resolved shear stress reaches a value corresponding to the axial yield stress Oy before it reaches Og 4- p the material will deform plastically without brittle fracture taking place. 

The creation terms embody the changes in momentum arising from external forces in accordance with Newton s second law (F = ma). The body forces arise from gravitational, electrostatic, and magnetic fields. The surface forces are the shear and normal forces acting on the fluid diffusion of momentum, as manifested in viscosity, is included in these terms. In practice the vector equation is usually resolved into its Cartesian components and the normal stresses are set equal to the pressures over those surfaces through which fluid is flowing. 

This behavior is usually analy2ed by setting up what are known as complex variables to represent stress and strain. These variables, complex stress and complex strain, ie, T and y, respectively, are vectors in complex planes. They can be resolved into real (in phase) and imaginary (90° out of phase) components similar to those for complex modulus shown in Figure 18. 

The stress—relaxation process is governed by a number of different molecular motions. To resolve them, the thermally stimulated creep (TSCr) method was developed, which consists of the following steps. (/) The specimen is subjected to a given stress at a temperature T for a time /, both chosen to allow complete orientation of the mobile units that one wishes to consider. (2) The temperature is then lowered to Tq T, where any molecular motion is completely hindered then the stress is removed. (3) The specimen is subsequendy heated at a controlled rate. The mobile units reorient according to the available relaxation modes. The strain, its time derivative, and the temperature are recorded versus time. By mnning a series of experiments at different orientation temperatures and plotting the time derivative of the strain rate observed on heating versus the temperature, various relaxational processes are revealed as peaks (243). 

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. 

If the maximum resolved shear stress r and the plastic shear strain rate y are defined according to (it is assumed that the Xj and Xj directions are equivalent)... 

Appleton and Waddington [40] present experimental evidence that pulse duration also affects residual strength in OFHC copper. Samples shock loaded to 5 GPa for 1.2 ps pulse duration exhibit poorly developed dislocation cell structure with easily resolvable individual dislocations. When the pulse duration is increased to 2.2 ps (still at 5 GPa peak stress) recovered samples show an increase in Vickers hardness [41] and postshock electron micrographs show a well-developed cell structure more like samples shock loaded to 10 GPa (1.2 ps). In the following paragraphs we give several additional examples of how pulse duration affects material hardness. 

These techniques have very important applications to some of the micro-structural effects discussed previously in this chapter. For example, time-resolved measurements of the actual lattice strain at the impact surface will give direct information on rate of departure from ideal elastic impact conditions. Recall that the stress tensor depends on the elastic (lattice) strains (7.4). Measurements of the type described above give stress relaxation directly, without all of the interpretational assumptions required of elastic-precursor-decay studies. 

Figure 8,4. The planar impact configuration is illustrated showing the spall plane in the sample and the interface at which time-resolved stress or particle velocities are measured.

Figure 8.5. Representative time-resolved stress or particle velocity profiles illustrating features critical to the spall analysis.

Suppose now that the force acted not normal to the face but at an angle to it, as shown in Fig. 3.1(b). We can resolve the force into two components, one, F(, normal to the face and the other, F, parallel to it. The normal component creates a tensile stress in the block. Its magnitude, as before, is F, /A. 

But we want the tensile yield strength, A tensile stress a creates a shear stress in the material that has a maximum value of t = a/2. (We show this in Chapter 11 where we resolve the tensile stress onto planes within the material.) To calculate cr from t,, we combine the Taylor factor with the resolution factor to give... 

A tensile stress applied to a piece of material will create a shear stress at an angle to the tensile stress. Let us examine the stresses in more detail. Resolving forces in Fig. 11.1 gives the shearing force as... 

The failure determining stresses are also often loeated in loeal regions of the eomponent and are not easily represented by standard stress analysis methods (Sehatz et al., 1974). Loads in two or more axes generally provide the greatest stresses, and should be resolved into prineipal stresses (Ireson et al., 1996). In statie failure theory, the error ean be represented by a eoeffieient of variation, and has been proposed as C =0.02. This margin of error inereases with dynamie models and for statie finite element analysis, the eoeffieient of variation is eited as Q = 0.05 (Smith, 1995 Ullman, 1992). 

To determine the stress at any point on the seetion requires that the load be resolved into eomponents parallel to the prineipal axes. Eaeh eomponent will eause bending in the plane of a prineipal axis and the total stress at a given point is the sum of the stress due to the load eomponents eonsidered separately. However, first we must eonsider the nature of the loading distribution and how it is resolved about the prineipal axes. 

Analysis of stress distributions in epitaxial layers In-situ characterization of dislocation motion in semiconductors Depth-resolved studies of defects in ion-implanted samples and of interface states in heterojunctions. 

Figure 4,2, Medal struck in Austria to commemorate the 50th anniversary of the discovery of the critical shear stress law by Erich Schmid. The image represents a stereographic triangle with "isobars showing crystal orientations of constant resolved shear stress (courtesy H.P. Stiiwe).

Mark, Polanyi and Schmid, of the constant resolved shear-stress law, which specifies that a crystal begins to deform plastically when the shear stress on the most favoured potential slip plane reaches a critical value. 

The first step in the analysis of this situation is the transformation of the applied stresses on to the fibre axis. Referring to Fig. 3.10 it may be seen that Ox and Oy may be resolved into the x, y axes as follows (the reader may wish to refer to any standard Strength of Materials text such as Benham, Crawford and Armstrong for more details of this stress transformation) ... 

As loading stresses approach or exceed the shear strength of a solid, inelastic effects are to be expected, and details of the behavior have been readily observed with modern, time-resolving measurement techniques. There are many observations of these behaviors. 

Fig. 2.17. Fused quartz is known to have an anomalous softening with stress or pressure in both static and shock loading. The time-resolved wave profile measured with a VISAR system shows the typical low pressure ramp followed by a shock at higher pressure. The release to zero pressure is with a shock, in agreement with the shape of the pressure-volume curve (after Setchell [88S01]).

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