Stress interface

When an adhesive solidifies and the joint is loaded through such an interface, stress is transferred from the substrate to the adhesive through these attachment points, and the adhesive resin adjacent to these attachment points is loaded. The strain energy in this system is expressed by the following equation [53] ... 

Tsai, H.C., Arocho, A.M. and Cause, L.W. (1990). Prediction of fiber-matrix interphase properties and their influence on interface stress, displacement and fracture toughness of composite materials. Mater. Sci. Eng. A126, 295-304. 

Impedance, Acoustic and Shock is the product of density and sound velocity, namely pc. Analogously shock impedance is pQU where U is the shock- velocity in a medium whose density (ahead of the shock)is p0. Both acoustic shock impedances are used to estimate the interface stress, a, and interface particle velocity, u, for planar shocks moving from one medium into another medium. A simple method of doing this, based on the so-called acoustic approximation, is illustrated below... 

Or = 2ai (see diagram Eq (3)). This means that the interface stress on a rigid wall (consequently u2 = 0), in contact with a condensed medium shocked to the state a 1, u, is 2ai That ufs — 2u, is also obtained from the exact solution (analytical or graphical) of the consevation equations for shocks in condensed media (Refs 1, 2 3). The exact solutions, however, show that ar > 2ai, but usually not much greater. In fact, for a rigid wall OflOi = 2.4... 

Jiang Q., Zhao D. S. and Zhao M., Size-dependent interface energy and related interface stress, Acta Mater. 49 (2001) pp. 3143-3147. 

The craze interface stress required for craze with the optimum microstructure to grow at the velocity v can be shown to be... 

Beyerlein, 1., Amer, M.S., Schadler, L.S., and Phoenix, S.L., New methodology for determining in situ fiber, matrix and interface stresses in damaged multifiber composites, Sci. Eng. Composite Mater., 7, 151, 1998. 

The concept of surface and interface stress has been widely used for several years to generate thin layers of specific magnetic, electronic [15],. .. properties. It starts now to be also used as a tool for tuning the chemical reactivity of surfaces. For example, stressed Pd deposited on Mo(llO), Ta(llO) or Nb(llO)... 

The determination of the interface stress When the temperature varies, the TiC ceramic sphere and NisAl spherical shell are deformed simultaneously. The displacement of the interface between TiC sphere and NisAl spherical shell are equal, namely, it must satisfy the condition of compatibility of the interface displacement, and the radial stress is equal and opposite in the interface.It can be written as R1 r2 (14)... 

If two polymorphs are strongly bonded at a planar interface and subjected to a constriction stress field about the interface s normal as the constriction axis, for the strain to be uniform the compressive stress profile must be exponential. Within a few nanometers of the interface, stress gradients and diffusion of material become noticeable. Equation (12.6) applies and Figure 13.3 illustrates the results. 

However, there is no solution of this equation that satisfies the conditions (6 142) atx = 0 andx = 1, as well as the constant-volume constraint (6-143). This tells us that the gravitational contribution to the interface stress balance is insufficient, by itself, to enforce the condition that the interface is pinned at the ends of the thin gap. In fact, the solution of (6-158) is linear inx and thus can only satisfy the constant-volume constraint, (6 143), by falling below the mean height for x < (1/2) (i.e., h < 0) and rising above it for x > (1/2) (i.e., h >0). This makes sense only if the end walls exceed // = <7 in height so that the fluid at x = 1 remains within the container, and then only if the interface is not required to satisfy the conditions (6-142) or any other condition at the end walls. Typically, however, if the interface is not pinned at the corner as required by (6-142), it is required to satisfy a condition that fixes the contact angle between the interface and the end walls, and this condition also cannot be satisfied by the solution of (6-158). 

The initial surfactant concentration is denoted as Teq and the corresponding surface tension is Yo- We further assume that the surfactant concentration is low enough that we can approximate the relationship between T and y as linear, hence yielding the interface-stress balance in the form of Eq. (2-171) ... 

Duan, H. L. Wang, J. Huang, Z. P Kaiihaloo, B. L. Size-dependenteffective elastic constants of solids containing nano-inhomogeneities with interface stress . J. Mech. Phys. Solids. 2005, 53(7), 1574-1596. 

For DBE-5, the earthquake design spectrtam load for the core lateral restraint structures was estimated as approximately 0.5 g. The value is based on a very stiff core barrel and key support design yielding a natural frequency of about 25 Hz. The lateral restraints must also accomodate the loads caused by lateral impact of the core against the core barrel. Overall, the design shows barrel/key interface stresses well below the material strength. Consequently, the core barrel will prevent excessive core deflections and will ensure that control rod reserve shutdown materials are capable of being inserted into the core when required. 

As alluded to earlier, knowledge of the interface stress distribution between the residual limb and the prosthetic socket enables objective evaluation of prosthetic fit. It is this desire for quantitative description of the prosthetic interface stress distributitHi that has motivated many experimental and numerical investigations of prosthetic interface stress. 

Several groups have used computer models of the residual limb to investigate the residual limb-prosthetic socket interface. Many investigators have also used finite-element modeling of the residual limb and the prosthetic socket of lower extremity amputees to investigate residual limb-prosthetic socket biomechanics and to estimate the interface stress distribution (for review, see refs. 38, 46, and 47). 

Two primary limitations of these modeling efforts involve the representation of tissue properties across the entire limb and the interface condition between the residual limb and prosthesis. The ability of current finite-element models to estimate prosthetic interface stresses, while performing reasonably well in some cases, has not been highly accurate. Nevertheless, the methodology has potential. Advances in finite-element software enabling nonlinear elastomeric formulations of bulk soft tissue, contact analysis, and dynamic analysis may help address some of the current model limitations. Corresponding advances in pressure-transducer technology will help validate the computer models and facilitate interpretation of the analyses. 

Finally, finite-element models have potential sqiplicability in CAD of prosthetic sockets. Current prosthetic CAD systems emulate the hand-rectification process, whereby the socket geometry is manipulated to control the force distribution on the residual limb. Incorporation of the finite-element technique into future CAD would enable prescription of the desired interface stress distribution (i.e., based on tissue tolerance). The CAD would then compute the shape of the new socket that would theoretically yield this optimal load distribution. In this manner, prosthetic design would be directly based on the residual limb-prosthetic socket interface stresses. 

When bonding elastic material, forces on the elastomer during cure should be carefully controlled, as too much pressure will cause residual stresses at the bond interface. Stress concentrations may also be minimized in rubber-to-metal joints by elimination of sharp comers and by the use of metal adherends sufficiently thick to prevent peel stresses that may arise with thinner-gauge metals. As with all joint designs, polymeric joints should avoid peel stresses. Figure 7.16 illustrates methods of bonding flexible substrates so that the adhesive will be stressed in its strongest direction. ... 

Since a substantial amount of material is contained in the interlamellar region, the properties of the latter give significant contributions to the overall material behavior. The properties of the interlamellar material he between those of the unconstrained amorphous melt and those of the crystalline phase [9-11], and the influence of the crystalline constraints can be addressed experimentally [12-14]. Furthermore, the properties of the crystal-melt interface have various ramifications that can be observed experimentally [15], e.g., interface stresses lead to distortion of the crystal lattice spacing [16-18], and they are possibly responsible for lamella twisting [19]. In addition, the surface tension enters in theoretical models for crystallization rates [20,21]. 

Fig. 14.10. Interface stresses, plotted versus temperature at atmospheric bulk stresses in the adjoining crystal and melt phases ( ), Ttyy ( ), and Ttxy (A).

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