Tensile stress concentration

Figure 4. Same model as in Fig. 3, except that the hydrofracture tip has been allowed to propagate to the bottom of the stiff surface layer A. The sharp and narrow tip gives rise to relatively high tensile stress concentration in layer A, and the tip may continue its propagation through this layer.

Socrate et al. (2000) considered an axially symmetric problem, with a rubber sphere in the centre of a short cylinder of matrix the spheres are in a row, aligned with the tensile stress axis. The potential positions of crazes were predetermined, initially running radially from the material interface, then becoming normal to the tensile stress along the cylinder. The initial stress concentration is greatest in the polymer near the equator of the sphere (Fig. 4.11a). The model, for a 20% volume fraction of rubber, predicts a yield point in the tensile stress-strain curve at an average strain of 1%, and 24 MPa stress, when the first craze propagates across the section. However, this relieves the stress in the polystyrene, and a tensile stress concentration... 

According to electron spin resonance data, free radicals are produced at chain ends even before a macroscopic break occurs. The free radical concentration depends only on the extension, and not on the tensile stress. Concentrations of lO -lO free radicals/cm are generally observed. Since free radical concentrations of only about 10 free radicals/cm occur on the surface, free radicals must form in the test sample interior, that is, from the breaking of polymer chains. In addition, chemical decomposition products are produced by a ductile break, but not by a brittle fracture. 

In the simulation models, it is easy to see that the main differences are direction, size and zone of stress and yield area that all offset centralized. Figure 2c and d, show that the difference of tensile stress in distribution. The two models both have the asymmetries of tensile stress concentration around the goaf The area of tensile stress is larger in model b and extends to a higher position in the overburden rock mass, while the tensile stress is limited in the area of the overburden rock mass in model a and forms a narrow stretching zone on the uphill side above the working face. These differences reveal that alters of symmetry comes from coal seam inclination and the stretching band on the uphill caused by the inclination of the unconformity. 

Gordon (1964). In these mechanisms, the interface fails ahead of the crack tip due to the tensile stress concentration, which is shown schematically in Figure 7.13a. The following sequence of events is then supposed, as shown in Figure 7.13b ... 

Division 2. With the advent of higher design pressures the ASME recognized the need for alternative rules permitting thinner walls with adequate safety factors. Division 2 provides for these alternative rules it is more restrictive in both materials and methods of analysis, but it makes use of higher allowable stresses than does Division 1. The maximum allowable stresses were increased from one-fourth to one-third of the ultimate tensile stress or two-thkds of the yield stress, whichever is least for materials at any temperature. Division 2 requkes an analysis of combined stress, stress concentration factors, fatigue stresses, and thermal stress. The same type of materials are covered as in Division 1. 

Zirconium resists attack by nitric acid at concentrations up to 70 wt % and up to 250°C. Above concentrations of 70 wt %, zirconium is susceptible to stress-corrosion cracking in welds and points of high sustained tensile stress (29). Otherwise, zirconium is resistant to nitric acid concentrations of 70—98 wt % up to the boiling point. 

Sufficient tensile stress. Sufficiency here is difficult to define since it depends on a number of factors such as alloy composition, concentration of corrodent, and temperature. In some cases, stresses near the jdeld strength of the metal are necessary. In other cases, the stresses can be much lower. However, for each combination of environment and alloy system, there appears to be a threshold stress below which SCC will not occur. Threshold stresses can vary from 10 to 70% of yield strength depending on the alloy and environment combination and temperature (Fig. 9.6). 

No one steel exceeds the tensile modulus of mild steel. Therefore, in applications in which rigidity is a limiting factor for design (e.g., for storage tanks and distillation columns), high-strength steels have no advantage over mild steel. Stress concentrations in mild steel structures are relieved by plastic flow and are not as critical in other, less-ductile steels. 

There are two well-accepted models for stress transfer. In the Cox model [94] the composite is considered as a pair of concentric cylinders (Fig. 19). The central cylinder represents the fiber and the outer region as the matrix. The ratio of diameters r/R) is adjusted to the required Vf. Both fiber and matrix are assumed to be elastic and the cylindrical bond between them is considered to be perfect. It is also assumed that there is no stress transfer across the ends of the fiber. If the fiber is much stiffer than the matrix, an axial load applied to the system will tend to induce more strain in the matrix than in the fiber and leads to the development of shear stresses along the cylindrical interface. Cox used the following expression for the tensile stress in the fiber (cT/ ) and shear stress at the interface (t) ... 

The implication of the foregoing equations, that stress-corrosion cracking will occur if a mechanism exists for concentrating the electrochemical energy release rate at the crack tip or if the environment in some way serves to embrittle the metal, is a convenient introduction to a consideration of the mechanistic models of stress corrosion. In so far as the occurrence of stress corrosion in a susceptible material requires the conjoint action of a tensile stress and a dissolution process, it follows that the boundary conditions within which stress corrosion occurs will be those defined by failure... 

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. 

Internal stress of copper deposits may vary between —3.4MN/m (compressive) and -1- l(X)MN/m (tensile). In general, tensile stress is considerably lower in deposits from the sulphate bath than in those from cyanide solutions " , while pyrophosphate copper deposits give intermediate values. In cyanide solutions, tensile stress increases with metal concentration and temperature decreases if the free cyanide concentration is raised. P.r. current significantly lowers tensile stress. With some exceptions, inorganic impurities tend to increase tensile stress . Thiocyanate may produce compressive stress in cyanide baths . 

The fatigue strength of most TPs is about 20 to 30% of the ultimate tensile strength determined in the short-term test but higher for RPs. It decreases with increases in temperature and stress-cycle frequency and with the presence of stress concentration peaks, as in notched components. 

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... 

Higher extent of silica generation with high TEOS concentration improves the mechanical properties severalfolds as illustrated by the tensile stress-strain plots on ACM-sdica hybrid nanocomposites on increasing TEOS concentrations in Figure 3.6. 

FIGURE 3.6 Tensile stress-strain plots of acrylic mbber (ACM)-silica hybrid nanocomposites using different tetraethoxysilane (TEOS) concentrations. The number in the legends indicates wt% TEOS concentrations. (From Bandyopadhyay, A., Bhowmick, A.K., and De Sarkar, M., J. Appl. Polym. Sci., 93, 2579, 2004. Courtesy of Wiley InterScience.)... 

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