Stress propagation

Fig. 6. Stress propagation across the wood cell walls, cell walls microbuckling and wood densification leading to the characteristic plastic deformation which wood undergoes during panel manufacture and hot-pressing.

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,... 

Inner slip, between the solid wall and an adsorbed film, will also influence the surface-liquid boundary conditions and have important effects on stress propagation from the liquid to the solid substrate. Linked to this concept, especially on a biomolecular level, is the concept of stochastic coupling. At the molecular level, small fluctuations about the ensemble average could affect the interfacial dynamics and lead to large shifts in the detectable boundary condition. One of our main interests in this area is to study the relaxation time of interfacial bonds using slip models. Stochastic boundary conditions could also prove to be all but necessary in modeling the behavior and interactions of biomolecules at surfaces, especially with the proliferation of microfluidic chemical devices and the importance of studying small scales. 

This is the equation for the displacement propagation wave. It should be noted that a similar equation could be obtained for the stress propagation wave. 

When a load is applied to the surface of a large mass of uniform soil, the induced stresses propagate in all directions and attenuate with distance from the point of load application. Except for directly beneath the load, where stress can be calculated by dividing the load by the application area, the actual value of stress cannot be found by simple arithmetic. This is because the size of the stressed area is not known, and the stress intensity over the stressed area varies. 

The variation of the amplitude of the stress propagated through the lead azide is shown in Figure 25. No evidence of reaction in lead azide was noted below 6 kbar in the thicknesses examined, nor for 1-mm-thick specimens at any stress below 8.9 kbar. 

To this point the discussion has focused primarily on so-called proper or ideal adhesive joints, assuming intimate contact between components and the absence of flaws and contaminants. In the real world, such conditions are difficult to attain, so that the question of practical joint failure may not be concerned so much with intermolecular forces and entanglement, but with the mechanics of stress propagation in the system. That subject, like so many related to practical applications of surface chemistry, is very extensive and beyond the scope of this book. However, the basic principles involved are such that a few words may serve a useful purpose. 

Due to the affineness assumption, the stress propagator reduces to an isotropic form... 

The characteristics which determine the properties filler that will impart to a composite are particle shape, particle size, surface area, and particle-matrix compatibility (Fig. 1). Particle-matrix compatibility relates to the ability of the polymer to coat and adhere to the filler. The shape of most mineral filler particles can be a sphere, cube, block, plate, needle, or fiber whereas some filler also contain a mixture of shapes. Mineral particles resembling plates, needles, and fibers are further characterized by their aspect ratio (http //www.rtvanderbilt.com/ fillersintroweb.pdf). In rubber/polymer composites, applied stress is transferred from the rubber/polymer matrix to the strong and stiff mineral. It seems reasonable that this stress transfer will be better affected if the mineral particles are smaller, because greater surface is thereby exposed for a given mineral concentration. Moreover, if these particles have a high aspect ratio (are needle-like, fibrous or platy in shape), they will better intercept the stress propagation through the matrix (Fig. 2) (http //www.rtvanderbilt.com/fillersintroweb.pdf). 

Evans A.G., Tappin G. Effects of microstructnre on the stress propagate inherent flaws. Proc. Br. 

Mechanisms of SCC. Over the years, a variety of mechanisms or models have been proposed to explain SCC phenomena in titanium alloys (Ref 80). In general, SCC is the anodic dissolution in highly localized areas that, aided by an applied tensile stress, propagates cracks into the metal. Crack advance occurs by discontinuous rupture of the oxide film at the crack tip. 

R. C. Hidalgo, I. Zuriguel, D. Maza, and I. Pagonabarraga. Role of particle shape on the stress propagation in granular packings. Physical Review Letters, 103(11) 118001, September 2009. 

A. V. Tkachenko and T. A. Witten. Stress propagation through frictionless granular material. Physics Review E, 60 687, 1999. 

---