Inhomogeneous stress field

This chapter is concerned with the influence of mechanical stress upon the chemical processes in solids. The most important properties to consider are elasticity and plasticity. We wish, for example, to understand how reaction kinetics and transport in crystalline systems respond to homogeneous or inhomogeneous elastic and plastic deformations [A.P. Chupakhin, et al. (1987)]. An example of such a process influenced by stress is the photoisomerization of a [Co(NH3)5N02]C12 crystal set under a (uniaxial) chemical load [E.V. Boldyreva, A. A. Sidelnikov (1987)]. The kinetics of the isomerization of the N02 group is noticeably different when the crystal is not stressed. An example of the influence of an inhomogeneous stress field on transport is the redistribution of solute atoms or point defects around dislocations created by plastic deformation. 

Craze growth at the crack tip has been qualitatively interpreted as a cooperative effect between the inhomogeneous stress field at the crack tip and the viscoelastic material behavior of PMMA, the latter leading to a decrease of creep modulus and yield stress with loading time. If a constant stress on the whole craze is assumed then time dependent material parameters can be derived by the aid of the Dugdale model. An averaged curve of the creep modulus E(t) is shown in Fig. 13 as a function of time, whilst the craze stress is shown in Fig. 24. 

In contrast to other methods of measuring elastic stress, the X-ray method is not subject to distortion of the results by plastic deformation. Furthermore, highly inhomogeneous stress fields can be measured, because the irradiated surface can be as small as l-10mm . The technique has the disadvantage that X rays penetrate only some 10" cm into steels, so that only stresses at the surface can be determined. 

Additionally, in some cases, the degree of roughness of the probe may lead to trapped air and inhomogeneous stress fields which are also bound to vary with the time of contact [15]. Experimentally, in the regime where relaxation times of the... 

The deformation of a material is governed not oidy by a constitutive relation between deformation and stress, like the neo-Hookean equation discussed above, it also must obey the principles of conservation of mass and conservation of momentum. We have already used die mass conservation principle (conservation of volume for an incompressible material) in solving the uniaxial extension example, eq. 1.4.1. We have not yet needed the momentum balance because the balance was satisfied automatically for the simple deformations we chose that is, they involved no gravity, no flow, nor any inhomogeneous stress fields. However, these balances are needed to solve more complex deformations. They are presented for a flowing system because we will use these results in the following chapters. Here we see how they simplify for a solid. Detailed derivations of these equations are available in nearly every text on fluid or solid mechanics. 

Most of the time, the three-point bending test (Fig. 12.2c) induces fracture without exhibiting yielding. The stress calculated here is a maximum stress due to the inhomogeneity of the stress field along the thickness ... 

The best approach, however, consists of controlling the defect size and geometry and taking into account the corresponding stress-field inhomogeneity. This is realized in the frame of linear elastic fracture mechanics (LEFM), which was first applied to metals and ceramics and then adapted with success to polymers (Williams, 1984). 

It should be stressed that this is a purely hypothetical concept which involves splitting the nucleus of the atom into two nuclei [2]. As for the true case of separated atoms, these two hypothetical new nuclei produce an inhomogeneous electric field in the direction of the internuclear axis. L and S... 

In externally imposed inhomogeneous magnetic fields (TO 0) the rotational forces may generate sufficiently strong vortices in the solid/liquid interface sublayers to destroy the layer structure on account of large MHD-stresses appearing on the capillary walls (also on the surface of microscopic particles and entrapped gas bubbles in the flow, if impurities are present). The critical flow velocity for structure destruction is [125]... 

Weibull Distribution for Arbitrarily Oriented Cracks in an Inhomogeneous Uniaxial Stress Field... 

Inhomogeneous stresses produced by localized defects may induce local phase transitions above the normal phase transition temperature Tc, causing the material to have mixed low and high symmetry phases in certain temperature regions. Such a two-phase mixture is usually very sensitive to external fields or stresses since the phase change among the mixture becomes barrierless even for a first order phase transition [10]. 

We also studied in-situ crack propagation in an AFM by inducing cracks electrically, see Fig. 9. Poled PIC 151 PZT samples were loaded electrically with dc voltage of —900 V between the electrodes. Because the upper electrode was smaller than the ground electrode, an inhomogeneous electric field developed which was large enough to induce cracks due to the piezoelectric stresses. 

In most real situations, the stress field is inhomogeneous (i.e. finite with respect to the length of the crack) and the characteristic length is then to be identified with a characteristic length xo associated with the stress field, e.g. the size of a plastic zone or the length of a craze. We then have... 

A more realistic view may be that the presence of a surface roughness creates an inhomogeneous strain field around the surface and creates therefore pockets of residual tensile stress which will become preferential nucleation sites for cavities. More systematic experiments [69] have shown that the amplitude of the surface roughness had a direct effect on the level of stress at which the cavities appeared, as shown in Fig. 23. 

---