Deformation stress field

Fig. 4. Model of local plastic deformation of lamellae beneath the stress field of the indenter. The mosaic block structure introduces a weakness element allowing faster slip at block boundaries leading to fracture (right)...

From the morphology of the fibrous structure of the deformed polymer one concludes that the dominant deformation modes of the drawn polymer under the stress field of the indenter involve ... 

When the probe makes contact with the film, it generates a radial stress field around the point of contact. If the film is isotropic, it deforms in a uniform ring around the probe, as shown in Fig. 8.11 a). If the film is oriented, it deforms in a non-uniform manner. When the film is mildly oriented, the deformation area becomes ellipsoidal, as we see in Fig. 8.11 b), with its long axis... 

Sandorf, 1980 Whitney, 1985 Whitney and Browning, 1985). According to the classical beam theory, the shear stress distribution along the thickness of the specimen is a parabolic function that is symmetrical about the neutral axis where it is at its maximum and decreases toward zero at the compressive and tensile faces. In reality, however, the stress field is dominated by the stress concentration near the loading nose, which completely destroys the parabolic shear distribution used to calculate the apparent ILSS, as illustrated in Fig 3.18. The stress concentration is even more pronounced with a smaller radius of the loading nose (Cui and Wisnom, 1992) and for non-linear materials displaying substantial plastic deformation, such as Kevlar fiber-epoxy matrix composites (Davidovitz et al., 1984 Fisher et al., 1986), which require an elasto-plastic analysis (Fisher and Marom, 1984) to interpret the experimental results properly. 

The explanation of the effect of secondary inclusions on the delocalization of shear banding is based on the concept of modification of the local stress fields and achieving favorable distribution of stress concentrations in the matrix due to presence of inclusions. This leads to a reduction in the external load needed to initiate plastic deformation over a large volume of the polymer. As a result, plastically deformed matter is formed at the crack tip effectively reducing the crack driving force. Above approximately 20 vol% of the elastomer inclusions. 

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. 

Let us return to the reduction of shear stress at the crack tip due to the emission of dislocations. Figure 14-9 illustrates a possible stress reduction mechanism. It can be seen that the tip of a crack is no longer atomically sharp after a dislocation has been emitted. It is the interaction of the external stress field with that of the newly formed dislocations which creates the local stress responsible for further crack growth. Thus, the plastic deformation normally impedes embrittlement because the dislocations screen the crack from the external stress. Theoretical calculations are difficult because the lattice distortions of both tension and shear near the crack tip are large so that nonlinear behavior is expected. In addition, surface effects have to be included. 

When the experimentalist set an ambitious objective to evaluate micromechanical properties quantitatively, he will predictably encounter a few fundamental problems. At first, the continuum description which is usually used in contact mechanics might be not applicable for contact areas as small as 1 -10 nm [116,117]. Secondly, since most of the polymers demonstrate a combination of elastic and viscous behaviour, an appropriate model is required to derive the contact area and the stress field upon indentation a viscoelastic and adhesive sample [116,120]. In this case, the duration of the contact and the scanning rate are not unimportant parameters. Moreover, bending of the cantilever results in a complicated motion of the tip including compression, shear and friction effects [131,132]. Third, plastic or inelastic deformation has to be taken into account in data interpretation. Concerning experimental conditions, the most important is to perform a set of calibrations procedures which includes the (x,y,z) calibration of the piezoelectric transducers, the determination of the spring constants of the cantilever, and the evaluation of the tip shape. The experimentalist has to eliminate surface contamination s and be certain about the chemical composition of the tip and the sample. 

Evans (1975), Evans and Charles (1977), and Emery (1980) performed more refined fracture mechanics studies regarding the onset and arrest conditions Bahr et al. (1988) and Pompe (1993) extended this work and considered the propagation of multiple cracks while Swain (1990) found that materials showing non-linear deformation and A-curve behaviour have a better resistance to thermal shock. More specifically, the behaviour of a crack in the thermal shock-induced stress field was deduced from the dependence of the crack length on the stress intensity factor. Unstable propagation of a flaw in a brittle material under conditions of thermal shock was assumed to occur when the following criteria were satisfied ... 

The surface forces that act on the control volume are due to the stress field in the deforming fluid defined by the stress tensor ji. We discuss the nature of the stress tensor further in the next section at this point, it will suffice to state that ji is a symmetric second-order tensor, which has nine components. It is convenient to divide the stress tensor into two parts ... 

In the previous section we discussed the nature and some properties of the stress tensor t and the rate of strain tensor y. They are related to each other via a constitutive equation, namely, a generally empirical relationship between the two entities, which depends on the nature and constitution of the fluid being deformed. Clearly, imposing a given stress field on a body of water, on the one hand, and a body of molasses, on the other hand, will yield different rates of strain. The simplest form that these equations assume, as pointed out earlier, is a linear relationship representing a very important class of fluids called Newtonian fluids. 

It was Wollaston (30) who in 1829 recognized the great pressures needed for compaction of dry powders—an observation that led to his famous toggle press. Since that time, compaction and deformation of powders and particulate systems have been extensively studied (31-35). There are many difficulties in analyzing the compaction process. Troublesome in particular are the facts that the properties of particulate solids vary greatly with consolidation, and that stress fields can be obtained, in principle, only in... 

In the solid state deformation, the nonlinear viscoelastic effect is most clearly shown in the yield behavior. The activation volume tensor is a key parameter. In addition to the well known dependence of yield stress on temperature and strain rate, the functional relationships between yield, stress field, and physical aging are presented. 

K. Ohji, K. Ogura, and S. Kubo, Stress Field and Modified 7 Integral near a Crack Tip under Condition of Confined Creep Deformation, J. Soc. Mater. Sci. Jpn., 29, 465-471 (1980). 

For many applications, the toughness of sPS is insufficient, which has thus led to many attempts in the past to increase its toughness significantly compared with HIPS by blending with rubbers. In the stress field of softer or harder particles than the sPS matrix, typical deformation processes inherent to the matrix are initiated. For rubber modification it is important that the application or test temperature is above the glass transition temperature of the rubber, otherwise the stiffnesses of the two components hardly differ from each other and local stress fields around the rubber particles are not formed. The formation of numerous deformation zones round the rubber particles is generally the basis of impact modification [10]. 

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