Stress at interface

The finite element method (FEM) has been used to evaluate thermal residual stresses at interface of Diaraond/TiB2/Si composites. Axisymetric cylindrical specimens were used, allowing two dimensional models to be employed. A model system composed three layers. Diamond, Diamond/(TiB2/Si) and TiB2/Si. 

Compared with the thermal stress sharp change at the bonding interface of ceramic-metal two-layered composite plate, the thermal stress of the Zr02/FGM/Ti-6A1-4V three-layered composite plate is very gentle, and the largest tensile stress reduces by 51.8%. With the increase of the convective heat transfer coefficients, the variations of thermal stress curves become big, and the maximum tensile stress at interface between FGM layer and ceramic layer increases 3.75 times. 

Figure 19.5 Variation of tensile stress in fibre and shear stress at interface occurring along the fibre length. If the fibre aspect ratio is lower than its critical value, l, the fibres are not loaded to their maximum stress value.

Both approaches are useful. The energy approach relates interfadal tension to thermodynamics and thus allows useful results to be derived (e.g., the Kelvin equation of Example 1.1, which gives the effect of drop size on vapor pressure). The force approach is needed to justify using interfacial tension in boimdary conditions involving forces and stresses at interfaces. Such boundary conditions are employed in solving the governing equations of fluid mechanics when fluid interfaces are present. 

Structural consolidation depends on placing the consoUdant where strengthening is required. Distribution of the solid consolidant in the object should be as uniform as possible to reduce stresses at interfaces. However, uniformity of distribution is not easily achieved and seems possible only if the consolidant can be immobilized where it is needed. This can be achieved using consolidants, which react by cross-linking with themselves or the object, for example silane consolidation of fossils but not the matrix (Davidson and Alderson, 2009). The consolidant can be immobilized by freezing it in situ, as in the poly(ethylene glycol) consolidation of waterlogged wood (Jensen and Jensen, 2006). The penetration of the consolidant into the smaller pores or molecular structure is... 

Fig. 3.9 Tensile and compressive stresses at interfaces in a monolithic polycrystal and a particulate composite (schematic). After application of tensile load, the distribution of stresses should bring about crack bridging in the case of a, branching in the case of a > Ug—, respectively...

Asmatulu, R., Claus, R. O. and Tuzcu, I. Adhesion Failures of Thin Film Coatings by Internal and External Stresses at Interfaces, Proceedings of 5th International Congress on Thermal Stresses and Related Topics, TS2003, 8-11 June, 2003, MA-6-3-1. 

Shear strength and defomiability Durabihty Vertical effective stress and shear stress at interface... 

The electric stress at the interface between the insulation and the insulation shield is less than at the conductor shield—insulation interface. 

The major load-bearing member of cord—mbber composites is the cord, which provides strength and many other critical properties essential for tire performance. Cords in pHes form the stmctural backbone of the tire. The mbber plays the important but secondary role of transmitting load to the cords via shearing stresses at the cord—mbber interface. Other expected performance characteristics of the tire are due to design and manufacturing processes. Table 5 (96) identifies several tire performance characteristics and how they are dependent on tire cord properties. 

The higher solubility of carbon in y-iron than in a-iroii is because the face-ceiiued lattice can accommodate carbon atoms in slightly expanded octahedral holes, but the body-centred lattice can only accommodate a much smaller carbon concentration in specially located, distorted tetrahedral holes. It follows that the formation of fenite together with cementite by eutectoid composition of austenite, leads to an increase in volume of the metal with accompanying compressive stresses at die interface between these two phases. 

The stored strain energy can also be determined for the general case of multiaxial stresses [1] and lattices of varying crystal structure and anisotropy. The latter could be important at interfaces where mode mixing can occur, or for fracture of rubber, where f/ is a function of the three stretch rations 1], A2 and A3, for example, via the Mooney-Rivlin equation, or suitable finite deformation strain energy functional. 

Figure 4-53 Stresses at the Interface (After Pipes and Pagano [4-12j)...

At this stage of the technique, it is necessary for the analyst to make a general assessment of any error-inducing conditions due to poor PIFs in the situation under consideration, to determine if these are likely to give rise to any of the errors that will be considered at the next stage of the analysis. Typical error-inducing conditions such as poor procedures, time stress, inadequate interface design, have already been considered in Chapter 3. 

In this method [89], a single fiber is taken and partially embedded in a drop of uncured resin placed on a holder. The resin is then cured with the fiber held upright. The holder, with resin and fiber, is held in a grip attached to the crosshead and then pulled out from the resin. The force pulling the fiber out of the resin is balanced by shear stress at the resin-fiber interface holding the fiber in place. The maximum shear stress occurs as the embedded length tends to zero and is given by ... 

There are two well-accepted models for stress transfer. In the Cox model [94] the composite is considered as a pair of concentric cylinders (Fig. 19). The central cylinder represents the fiber and the outer region as the matrix. The ratio of diameters r/R) is adjusted to the required Vf. Both fiber and matrix are assumed to be elastic and the cylindrical bond between them is considered to be perfect. It is also assumed that there is no stress transfer across the ends of the fiber. If the fiber is much stiffer than the matrix, an axial load applied to the system will tend to induce more strain in the matrix than in the fiber and leads to the development of shear stresses along the cylindrical interface. Cox used the following expression for the tensile stress in the fiber (cT/ ) and shear stress at the interface (t) ... 

For values of Ild less than l/d)c, the tensile stress in the fiber is always less than that in the matrix. The transfer of load from the matrix to the fiber is poor and the mechanical properties of the fiber are not fully utilized. If lid > l/d)c, the tensile stress at the interface remains at a maximum over a greater proportion of fiber length. Here, the transfer of stress from the matrix to the fiber is very efficient, but the average tensile stress in the fiber is always less than that in the matrix because of reduced tensile stress at the end of the fiber. 

When a fiber breaks, the normal stress at each of its broken ends become zero. Over a distance of 1 /2 from each end, stress builds back up to the average value by shear stress transfer at the fiber-matrix interface. Also, the stress state in a region close to the broken ends contain the following ... 

Studying the steady motion of a single medium-size bubble rising in a liquid medium under the influence of gravity, Levich (L3, L4) solved the continuity equation simultaneously with the equations of motion by introducing the concept of a boundary layer for the case of a bubble. This boundary layer accounts for the zero, or extremely low, shear stress at the interface. Despite some errors in deriving the equations, his result was later confirmed with minor improvements (A4, M3, M10). 

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