Stress concentration effect

Any material which contains a geometrical discontinuity will experience an increase in stress in the vicinity of the discontinuity. This stress concentration effect is caused by the re-distribution of the lines of force transmission through the material when they encounter the discontinuity. Causes of stress concentration include holes, notches, keyways, comers, etc as illustrated in Fig. 2.62. 

Three modes are clearly defined for crack propagation from a very thin (radius of the order of 10 gm) notch-machined in the specimen (Fig. 12.3). This notch induces a stress concentration effect, higher than those produced by all the other defects already present in the specimen, which governs the fracture initiation. For isotropic materials, mode I (the most severe) is generally used and gives the lowest value of toughness. In the case of adhesives and laminates, modes II and III are also performed. 

At the crack tip, there is a stress concentration effect but, in LEFM, stress is limited to plastic zone. The dimensions of this plastic zone can be calculated using Irwin s theory and is ... 

The role of morphology in inhomogeneous networks is also not very clear. Is the mechanical behavior under the influence of molecular/macro-molecular parameters or is it controlled by stress concentration effects at the boundaries of dispersed domains ... 

For a single rubber particle in an infinite uniaxial tensile stress field, it was demonstrated that there is a stress concentration effect with a factor around 2, at the particle equator (Fig. 13.1). 

Increasing the concentration of particles (roughly for a volume fraction approaching 10%), the stress concentration effects of neighboring particles can overlap (Fig. 13.2). Therefore, a large volume fraction of the matrix supports an average load higher than the applied load and can yield. This stress concentration effect increases when the volume fraction of dispersed particles increases or the interparticle distance decreases. 

Figure 13.9 Sequence of events in a croid formation, (a) Initial state at the crack tip. (b) Cavitation ofthe rubber particles dueto loading head of the crack tip. (c) Cavitation of rubber particles near the already cavitated particles due to stress-concentration effect. The croid is forming, (d) Croids are propagating ahead ofthe crack and inside the craze-like damaged zone many shear bands develop between cavitated rubber particles. (Sue, 1992 with kind permission from Kluwer Academic Publisher.)...

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. 

Electrode potential and pH at an active crack tip may be significantly different from those on boldly exposed surfaces of a material. Low-pH conditions can lead to local dissolution of metal and crack-tip blunting, which reduces stress concentration effects. In contrast, low-pH conditions favor hydrogen generation and, consequently increased risk of HEC. Reduction in local ductility associated with HEC is more likely to produce sharp crack tips, which, in turn, can exacerbate stress concentration effects for any synergistic SCC or CF. (Phull)5... 

At the same stress amplitude, rubber modified polymers fail sooner in fatigue than do the unmodified polymers even though they have superior resistance to fatigue crack propagation. This is a result of much earlier initiation of crazing, localized plastic deformation, and subsequent crack development due to the stress concentrating effect of the dispersed second phase particles. 

Under tensile loading, the stress concentrating effect of an unbonded spherical particle is dmilar to that of a void. Nicolais and co-workers have studied the tensile stress-strain behaviour of composites based on SAN, ABS, PPO, and epojgr resins " 4-36) jjj jj g g polymers, unbonded glass beads cause yielding... 

The microphase structure and mechanical properties of the blends containing neat acrylonitrile-butadiene-styrene copolymer (ABS), styrene-acrylonitrile copolymer (SAN) and sodium sulfonated SAN ionomer have been investigated as a function of ion content of the ionomer in the blend by Park et a/.51 The interfacial adhesion was quantified by H NMR solid echo experiments. The amount of interphase for the blend containing the SAN ionomer with low ion content (3.1 mol%) was nearly the same as that of ABS, but it decreases with the ion content of the ionomer for the blend with an ion content greater than 3.1 mol%. Changing the ionomer content in the blends shows a positive deviation from the rule of mixtures in tensile properties of the blends containing the SAN ionomer with low ion content. This seems to result from the enhanced tensile properties of the SAN ionomer, interfacial adhesion between the rubber and matrix, and the stress concentration effect of the secondary particles. 

This procedure assumes that the pin diameter is no less than in. less than the hole diameter. If the pin diameter is greater than Xe in. smaller than the hole diameter, then the bearing stresses in the lug at the contact point are increased dramatically due to the stress concentration effect. 

The case of an infinite plate with an elliptical hole was solved by Lekhnitskii [20]. Using anisotropic elasticity and treating the plate as homogeneous, he determined the stresses anywhere in an infinite composite plate with a hole. Due to the stress concentration effect created by the hole, the highest stresses are on the hole boundary. It is important to note that, unlike metals, where the critical location is at 0 = 90° (see Figure 6.8) the critical location for a composite plate is a function of the stacking sequence. It can be shown that Lekhnitskii s solution on the hole edge becomes ... 

The strength of two-phase syntactic foam composites will decrease with decreasing content of hollow microspheres. This is due to two factors a decreased load bearing cross-sectional area and a stress concentration effect of the microporosity. One can combine these effects in the following form (19) ... 

The measured shear stresses in the matrix at the ends of fibers are in fact much larger than those given by equation 22 because of stress concentration effects. Therefore, the maximum shear stress will be the smaller of the following two stresses the shear yield stress of the matrix, or the shear strength of the fiber-matrix interface. Whichever of these two stresses is attained first will control the load transfer phenomenon. 

Another approach to improve the accnracy of the formnlae for El nd Gj2 was snggested by Spencer [17]. The proposed model was also based on a sqnare array bnt inclnded the stress concentration effects at the points where the hbres were closer. The formnlae are given as... 

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