STRESS CONCENTRATION Subject

Figure 27.1 summarises the methodology for designing a component which must carry load. At the start there are two parallel streams materials selection and component design. A tentative material is chosen and data for it are assembled from data sheets like the ones given in this book or from data books (referred to at the end of this chapter). At the same time, a tentative component design is drawn up, able to fill the function (which must be carefully defined at the start) and an approximate stress analysis is carried out to assess the stresses, moments, and stress concentrations to which it will be subjected. 

All the above modes of fracture are affected by the environment around the crack tip. This behaviour is typified by the phenomenon of stress-corrosion cracking where a crack, which is subjected to a subcritical stress concentration, will grow in a corrosive environment when /f, the critical stress concentration for stress-corrosion cracking). Therefore, to predict accurately the occurrence of cracking and crack growth rate, not only the materials properties are required but also information on the immediate environmental conditions. 

A metal s resistance to fatigue is markedly reduced in a corrosive environment. Many welded structures are subjected to fluctuating stresses which, with the superimposed tensile residual stress of the joint, can be dangerous. In addition to this a welded joint is a discontinuity in an engineering structure containing many possible sites of stress concentration, e.g. toe or root of the joint, weld ripple. 

Likewise, dead sharp corners or notches subjected to tensile loads during impact may decrease the impact resistance of a product by acting as stress concentrators, whereas generous radii in these areas may distribute the tensile load and enhance the impact resistance. This point is particularly important for products comprised of materials whose intrinsic impact resistance is a strong function of a notch radius. Such notch sensitive materials are characterized by an impact resistance that decreases drastically with notch... 

Uniform microstractuie is cracial to the superior performance of advanced ceramics. In a cerantic material, atoms are held in place by strong chentical bonds that ate impervious to attack by corrosive materials or heat. At the same time, these bonds are not capable of much "give." When a ceramic material is subjected to mechanical stresses, these stresses concentrate at minute imperfections in the microstmcture, initiating a crack. The stresses at the top of the crack exceed the threshold for breaking the adjacent atomic bonds, and the crack propagates throughout the material causing a catastrophic brittle failure of the ceramic body. The rehability of a ceramic component is directly related to the number and type of imperfections in its microstmcture. 

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

The microductile/compliant layer concept stems from the early work on composite models containing spherical particles and oriented fibers (Broutman and Agarwal, 1974) in that the stress around the inclusions are functions of the shear modulus and Poisson ratio of the interlayer. A photoelastic study (Marom and Arridge, 1976) has proven that the stress concentration in the radial and transverse directions when subjected to transverse loading was substantially reduced when there was a soft interlayer introduced at the fiber-matrix interface. The soft/ductile interlayer allowed the fiber to distribute the local stresses acting on the fibers more evenly, which, in turn, enhanced the energy absorption capability of the composite (Shelton and Marks, 1988). 

Mono- and polycrystalline natural and synthetic materials are not subject to plastic strain and have no independent slip system. Stress concentration occurs in them at.crack tips and at flaws in the material, affecting the maximum strength which originates from the chemical or physical cohesion forces present. Non-plastic materials (crystals, rocks, ceramics, glass) show brittle cracks—forming at very low plastic strain—usually originating from surface flaws. 

Abstract When subjected to a mechanical loading, the solid phase of a saturated porous medium undergoes a dissolution due to strain-stress concentration effects along the fluid-solid interface. Through a micromechanical analysis, the mechanical affinity is shown to be the driving force of the local dissolution. For cracked porous media, the elastic free energy is a dominant component of this driving force. This allows to predict dissolution-induced creep in such materials. 

A material that is subjected to cyclic application of stresses may fail after a large number of load cycles without nearly reaching the maximum failure stress of direct loading. The effect of such cyclic stresses is to initiate microscopic cracks at centres of stress concentration within the material or on the surface, and subsequently to enable these cracks to propagate, leading to eventual failure. For high stress amplitudes less cycles are needed for failure than for low stress amplitudes. For high frequencies less cycles are needed for... 

Determination of residual stress of a failed component is one of the most important steps in failure analysis. The determination of residual stress is useful when failed components experience stress concentration, overload, distortion or the formation of cracks in the absence of applied loads, subjected to corrosive environments as in stress corrosion, mechanical or thermal fatigue due to cyclic loading, or when faults in processing such as shot peening, grinding, milling and improper heat treatment such as stress relief, induction hardening, thermal strains, exposure temperature are involved. 

In this section the maximum stress concentration developed by an elliptic hole at arbitrary orientation in an infinite elastic sheet subjected to general biaxial stress loading is considered. In Figure 1, consider an elliptic hole of major axis a, minor axis b, and orientation angle fl with respect to an axis of applied uniaxial tension Si. If the sheet is isotropic, elastic, and infinite, then the major principal stress ([Pg.42]

Stress Bate at Particles. The stress component, avv, acting parallel to the boundary between rubber particles and matrix is important for the initiation of crazes. It reaches a maximum value (which can be about twice the outer stress, a0) at the equatorial regions of the particles. Besides depending on the shape of the particles and Poisson s ratio, the elastic-stress concentration at the rubber particles depends mainly on the ratio x = Gp/GM, where GP and GM are the Youngs modulus of the particles and the matrix, respectively. This ratio has been calculated by Michler (14) on the basis of the solution obtained by Goodier for an isolated particle embedded in a matrix and subjected to uniaxial tension (15) (see Figure 9). 

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