Self stress

The back stress (or self-stress) ji acting on a pinned dislocation loop is given by... 

Ability to form and maintain strong bond with propellant, resist any delamination, cracking or interface separation due to self-stressing. The ability to bond itself with the propellant directly on application by casting technique without any barrier coat is considered an added attribute. 

In one dimensional diffusion experiments (e.g., starting with a thin film source of A on a B crystal surface) one often finds an exponential decrease in the A concentration at the far tail of the concentration profile. This behavior has been attributed to pipe diffusion along dislocation lines running perpendicular to the surface. Models have been introduced which assume a (constant) pipe radius, rp, inside which Dl = p-D, b and p denoting here bulk and dislocation respectively. P values of 103 have been obtained in this way. It is difficult to assess the validity of these observations. The model considerably simplifies the real situation. During diffusion annealing, the structure of the dislocation networks is likely to change because of self-stress (see Chapter 14) and chemical interactions. 

Figure 3-4. Dislocation decoration in an AgBr-NaCl interdiffusion zone. Dislocations formed by self-stress due to lattice parameter changes. The decoration density indicates the dislocation density [after H. Haefke, H. Stenzel (1989)].

In many cases of transport in solids, the atoms (ions) of one sublattice of the crystal are (almost) immobile. Here, we can identify the crystal lattice with the external (laboratory) frame and define the fluxes relative, to this immobile sublattice (to = 0). v° is bk-Xk (Eqn. (4.51)) where Xk is the sum of all local forces which can be applied externally (eg., an electric field), or which may stem from fields induced by the, (Fickian) diffusion process itself (eg., self-stresses). An example of such a diffusion process that leads to internal forces is the chemical interdiffusion of A-B. If the lattice parameter of the solid solution changes noticeably with concentration, an elastic stress field builds up and acts upon the diffusing particles, it depends not only on the concentration distribution, but on the geometry of the bounding crystal surfaces as well. 

So far, we have tacitly assumed that the stresses were applied externally. However, stresses which are induced by local changes in component concentrations and the corresponding changes in the lattice parameters during transport and reaction are equally important. These self-stresses can strongly influence the course of a solid state reaction. Similarly, coherent, semicoherent, and even incoherent interfaces during heterogeneous solid state reactions are sources of (local and nonlocal) stress. The... 

Let us first ask to what extent homogeneous stresses influence the mobilities of structure elements. We know that the temperature dependence of mobilities is adequately described by an Arrhenius equation, which reflects the applicability of the Boltzmann distribution for atoms in their activated states (Section 5.1.2). Let us therefore reformulate the question and ask in which way the activated states of mobile SE s are influenced by externally applied stresses and self-stresses. If we take into account the periodicity of the crystal and assume its SE s to reside in harmonic... 

An easy way of visualizing the structure of fullerenes is to make a physical model, for example, to assemble equal angle planar trivalent connectors and equal length plastic tubes. Mechanically, the polyhedron-like structure so obtained can be considered as a space frame with equal rigid nodes and equal elastic bars such that three bars meet and form angles of 120° at each node. The closed net shape arises by deformation of the bars in a state of self-stress. The edges of the polyhedron obtained... 

A simple way to appreciate the shape of fullerene is to construct a physical model in which rigid planar trivalent nodal connectors represent the atoms and flexible plastic bars (tubes) of circular cross-section represent the bonds. From a mechanical point of view the model may be considered as a polyhedron-like space frame whose equilibrium shape is due to self-stress caused by deformation of bars. We suppose that the bars are equal and straight in the rest position and that they are inclined relative to each other at every node with angle of 120°. The material of the bars is assumed to be perfectly elastic and that Hooke s law is valid. All the external loads and influences are neglected and only self-stress is taken into account. Then we pose the question What is the shape of the model subject to these conditions To answer this question we apply the idea used for coated vesicles by Tarnai Gaspar (1989). 

Similarly, in mechanics, the extended Maxwell condition for rigidity of bar and joint assemblies can be used to generate a relation between the permutation representations of the bars and joints and those of the states of self-stress and mechanisms of the assembled framework [17a,b]. 

The dislocation method of stress analysis is also useful for determining craze stress fields in anisotropic (e.g., oriented) polymers . All one needs here is the stress field of a single dislocation in a single crystal with the same symmetry as the oriented polymer (the text by Hirth and Lothe provides a number of simple cases plus copious references to more complete treatments in the literature) the craze stress field can be generated by superposition of the stress fields of an array of these dislocations of density a(x). Dislocations may also be used to represent the self-stress fields of curvilinear crazes (produced by craze growth in a non-homogeneous stress field for example). Such a method has been developed by Mills... 

As this mle is obeyed separately under every symmetry operation, rather than just under the identity as in the pure counting version, it can reveal extra information about the mechanisms and states of self stress, giving a count m - s for every irreducible representation of the group. Results such as the fact that the vibrations of a fully triangulated polyhedron... 

P.W. Fowler and S.D. Guest, Int. J. Solids and Structures, 39 (2002) 4385 393 Symmetry and states of self stress in triangulated toroidal frames. 

V. Violante, Effects of self-stress on hydrogen diffusion in Pd membranes in the coexistence of alpha and beta phases,/. AUoys Compd. 2004, 368, 287-297. 

Y. B. Fu, Numerical simulation of diffu-sivity of hydrogen in thin tubular metallic membranes affected by self-stresses, Int.J. Hydrogen Energy 2004, 29, 1165-1172. 

P. Zoltowski, Concentration transfer function of hydrogen diffusion in self-stressed metals,/. Electroanal. Chem. 2001, 532, 64-73. 

The purpose of surface preparation is to remove contamination and weak surface layers, to change the substrate surface geometry, and/or introduce new chemical groups to provide, at least in the case of metals, an oxide layer more receptive to the adhesive. An appreciation of the effects of pretreatments may be gained from surface analytical or mechanical test techniques. Experimental assessments of the effects of surface pretreatment, even when using appropriate mechanical tests, are of limited value unless environmental exposure is included. Self-stressed fracture mechanical cleavage specimens, as discussed in Chapter 4 and in the texts edited by Kinloch(2,5) for example, are therefore referred to wherever possible. 

The resulting expansion increases with increasing gypsum content and— up to about 40° C— also with increasing temperature. The self-stress value of the binder increases with increasing CA/CA ratio. 

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