Weaker stress concentration

Comparing the Eqs. (5.9) and (5.10) one can see, that the value reflects stress concentration by the crack, moreover, the higher the weaker stress concentration (the smaller KJ. 

In the wet state, the inter-fibrillar bonding is weaker still, and an untreated fibre acts as a bundle of separate fibrils, which break independently. This is the fibrillar form of fracture shown in fig. 6 of the 3rd paper in this volume. The progressive increase of water absorption leads to a continuous increase of tenacity from dry to wet cotton. This is an interesting example of where a reduction of intermolecular cohesion leads to greater strength, as a result of relieving stress concentrations and allowing other modes of deformation. 

Czamocki and Piekarski s) used a nonlinear elastic stress-strain law for three-dimensional failure analysis of a symmetric lap joint. Taking into account the variation of Poisson s ratio with strain within the adhesive, the authors concluded that the failure of the adhesive layer originates in the central plane of a joint (at the front edge). It was also observed that the joint width did not have any effect on the stress peaks in the central plane and that the application of a weaker but more flexible adhesive resulted in higher load-carrying capacity and lower stress concentrations in the adherends. 

A flaw such as a simple spherical pore concentrates the stress on the bonds in the vicinity of the pore by a factor of two over the appHed stress (6) however, most ceramics contain imperfections that enhance the stress to a much greater degree, leading to severe strength reductions. A typical ceramic such as alumina is as much as one hundred times weaker than the theoretical strength. 

The effect of these small cracks is to concentrate the stress at localised points within the specimen. Figure 7.4 illustrates how this happens, using lines to indicate the stress distribution in the sample. For the unnotched specimen, (a), the stress is uniformly distributed throughout the material. However, for the notched specimen, (b), the lines of stress can be seen to converge at the notch tip, this giving a local stress greater than the apparent applied stress. When this happens, the breaking stress, will occur in the material at an actual stress somewhat less than this. As a result, the material as a whole is weaker than predicted on the basis of is chemical composition. 

Long term rearrangement, i.e., after gel formation, can occur under some conditions. In first instance, it leads to straightening of strands of particles in the gel, which causes an increase in modulus, a weaker dependence of the modulus on particle concentration, and a decrease in fracture strain the fracture stress and the permeability are hardly affected. Stronger rearrangement does lead to an increase in permeability, and syneresis can readily occur. All these changes depend on gel type, formation temperature, storage temperature, pH, etc. 

Higher temperature may result in a weaker Rehbinder effect as well. This occurs due to the facilitation of a plastic flow at elevated temperatures. Thermal fluctuations result in the relaxation of deformational microheterogeneities. As a result, at elevated temperatures local concentrations of stresses are too low to initiate the formation of primary microcracks. An increase in temperature thus often leads to a transition from brittle fracture in the presence of adsorption-active medium to plastic deformation. The decrease in the rate of deformation of a solid has an analogous effect slow deformation also results in an increased probability of the thermally activated relaxation of locally concentrated deformations and stresses. 

As mentioned in the introduction to this paper, scientific study has concentrated on the tensile mode. Except for two forms of break in cotton, all the tensile failures discussed in this paper consist of breaks that run transversely aeross the fibre. However, the fibres arc fairly highly oriented, so that the bonding across the fibre is much weaker than along the fibre. Transversely, there are weak intermolecular bonds plus a small component of the covalent bonding. In use, failure is rarely due to a direct tensile overload, unless this is on fibres weakened by chemical degradation. The common forms of wear in use are due to weakness in the transverse direction, related either to shear stresses or to axial compression. There is no detailed structural prediction of the response to shear stresses or axial compression at a molecular or fine-structure level. All that one can say is that at a certain level of shear stress cracks will form and that at a certain level of axial compressive stress the structure will buckle internally. What can be described is how these stresses occur. 

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