Equivalent elastic stress Subject

The value of alternating stress taken from the fatigue curve is subject to other factors given hy the ASME Code. The ultimate allowable stress for a given number of cycles should be adjusted for these factors as follows (for elastic stress analysis and equivalent stresses ... 

The equivalent elastic modulus, Gip, for the mechanically interlocked interphase is calculated by assuming an isostress condition for the interphase, illustrated in Pig. 23.13. In other words, the adhesive and the adherend surface (projections) are subjected to the same level of shear stress, tjp, at the interphase, while the composite interfacial shear strain, yjp, is a volumetric weighted average of the adhesive and adherend strains, that is,... 

In this constant-load-amplitude method, crack length is measured visually or by an equivalent method as a fimction of elapsed cycles, and these data are subjected to numerical analysis to establish die rate of crack growth. Crack growth rates are ttien expessed as a function of crack tip stress intensity range AAT, which is calculated from expressions basal on linear-elastic stress analysis. 

The assemblage of chains is constructed to represent the affine network model of rubber elasticity in which all network junction positions are subject to the same affine transformation that characterizes the macroscopic deformation. In the affine network model, junction fluctuations are not permitted so the model is simply equivalent to a set of chains whose end-to-end vectors are subject to the same affine transformation. All atoms are subject to nonbonded interactions in the absence of these interactions, the stress response of this model is the same as that of the ideal affine network. 

In mathematical terms, the implementation of the eigenstrain concept is carried out by representing the geometrical state of interest by some distribution of stress-free strains which can be mapped onto an equivalent set of body forces, the solution for which can be obtained using the relevant Green function. To illustrate the problem with a concrete example, we follow Eshelby in thinking of an elastic inclusion. The key point is that this inclusion is subject to some internal strain e, such as arises from a structural transformation, and for which there is no associated stress. 

As has already been stated, the elastic modulus has the units of pressure. Pa, or N/m, which is also equivalent to J/m. The latter means that, in agreanent with Equation 3.1, it is possible to formally view the elasticity modulus as twice the elastic energy stored by the unit volume subjected to the unit strain. At a given shear stress, in agreement with Eqnation 3.1, the smaller the modnlns G, the higher the elastic energy density stored by the body. 

When fee stress-strain measurement shown in Fig. 1.26 is reversed at a point after fee yield stress, Op but before failure, fee stress-strain relationship will initially follow a line wife a slope equivalent to fee elastic modulus E. This is illustrated by segment A-B in Fig. 1.28. If fee process were stopped at point B, fee length of fee specimen does not fully recover to its initial value. However, in this particular example fee specimen is then subjected to a compressive load to <7 to point C in Fig. 1.28. 

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