Internal stress redistribution

As is known, a highly elastic deformation is accompanied by redistribution of internal stresses and is always associated with viscous deformation. Because of this, for full deformation of a viscous polymer we will have a rheological model (Figure 2.42c), which is governed by the equation ... 

The fundamental difference between mechanical stresses and tliermal stresses lies in the nature of the loading. Thermal stresses as previously stated are a result of restraint or temperature distribution. The fibers at high temperature are compressed and those at lower temperatures are stretched. The stress pattern must only satisfy the requirements for equilibrium of the internal forces. The result being that yielding will relax the thermal stress. If a part is loaded mechanically beyond its yield strength, the part will continue to yield until it breaks, unless the deflection is limited by strain hardening or stress redistribution. The external load remains constant, thus the internal stresses cannot relax. 

All polymer materials used in reinforced plastics display some viscoelastic or time-dependent properties. The origins of creep in composites stem from the behaviour of polymers under load together with local stress redistributions between fibre and matrix as a function of time. There is little creep at normal temperatures in the reinforcing fibres. The origin of the creep mechanisms is related to the nature and levels of internal bonding forces between the chains of the polymer, which are influenced by temperature and moisture. 

For straight metal pipe under internal pressure the formula for minimum reqiiired w thickness is applicable for D /t ratios greater than 6. Tme more conservative Barlow and Lame equations may also be used. Equation (10-92) includes a factor Y varying with material and temperature to account for the redistribution of circumferential stress which occurs under steady-state creep at high temperature and permits slightly lesser thickness at this range. 

As contrasted with stress from sustained loads such as internal pressure or weight, displacement stresses may be permitted to cause hm-ited overstrain in various portions of a piping system. When the system is operated initially at its greatest displacement condition, any yielding reduces stress. When the system is returned to its origin condition, there occurs a redistribution of stresses which is referred to as self-springing. It is similar to cold springing in its effects. 

Fig. 2.8. Factors controlling the production of free radicals in cells and tissues (Rice-Gvans, 1990a). Free radicals may be generated in cells and tissues through increased radical input mediated by the disruption of internal processes or by external influences, or as a consequence of decreased protective capacity. Increased radical input may arise through excessive leukocyte activation, disrupted mitochondrial electron transport or altered arachidonic acid metabolism. Delocalization or redistribution of transition metal ion complexes may also induce oxidative stress, for example, microbleeding in the brain, in the eye, in the rheumatoid joint. In addition, reduced activities or levels of protectant enzymes, destruction or suppressed production of nucleotide coenzymes, reduced levels of antioxidants, abnormal glutathione metabolism, or leakage of antioxidants through damaged membranes, can all contribute to oxidative stress.

When residual stresses are considered, the stress distributions flatten considerably and become almost uniform at in situ length and pressure. Figure 57.10 shows the radial stress distributions computed for a vessel with /3 = 1 and /3 = 1.11. Takamizawa and Hayashi have even considered the case where the strain distribution is uniform in situ [9]. The physiologic imphcations are that vascular tissue is in a constant state of flux. New tissue is synthesized in a state of stress that allows it to redistribute the internal loads more uniformly. There probably is no stress-free reference state [7,8,17]. Continuous dissection of the tissue into smaller and smaller pieces would continue to relieve residual stresses and strains [ 10). 

The almost horizontal portions of the hysteresis loop represent saturated states in which the crystal is a single domain during a cycle. Defects and internal strains within the crystallites impede the movement of domain walls. Domain wall mobility has been found to decrease with time (even without an applied mechanical or electrical stress or thermal changes). This is due to internal fields associated with charged defects, redistribution of lattice strains, and accumulation of defects at domain walls. 

The present work mainly focuses on the influence of D on the redistribution stresses and radial displacements around an axisymmetrical cavern. The D-value is taken to be gradually decreased from the elastic-plastic interface to the excavation surface but it is fixed to be 0 within the elastic zone. Under the condition without any internal pressure, the D-vslIuq is 1 near excavation and 0 at the elastic-plastic interface. 

Even with a carefully controlled manufacturing environment there will be regions within the composite of differing compliance and stress variations which will lead to some redistribution of the internal forces. 

Failure ean take place by inclined principal tensile eraeks produced by inclined prineipal tensile stresses in zones of larger shear. These cracks can spread rapidly through the section across the compression zone. Unless conventional steel reinforeements are present in such zones, an internal redistribution of forees is not possible. 

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