Stress concentration analysis

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. 

The code provides no guidance for analysis but requires that external and internal attachments be designed to avoid flattening of the pipe, excessive locahzed bending stresses, or harmful therm gradients, with further emphasis on minimizing stress concentrations in cyclic service. 

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. 

The second special case is an orthotropic lamina loaded at angle a to the fiber direction. Such a situation is effectively an anisotropic lamina under load. Stress concentration factors for boron-epoxy were obtained by Greszczuk [6-11] in Figure 6-7. There, the circumferential stress around the edge of the circular hole is plotted versus angular position around the hole. The circumferential stress is normalized by a , the applied stress. The results for a = 0° are, of course, identical to those in Figure 6-6. As a approaches 90°, the peak stress concentration factor decreases and shifts location around the hole. However, as shown, the combined stress state at failure, upon application of a failure criterion, always occurs near 0 = 90°. Thus, the analysis of failure due to stress concentrations around holes in a lamina is quite involved. 

Pre-cracked specimens are sometimes useful for other reasons than the analysis that they afiford in relation to stress-intensity factors. Such applications may be associated with the simulation of service situations, the relative ease with which stress-corrosion cracks can be initiated at pre-cracks or the advantages that sometimes accrue from the propagation of a single crack. The claim that has sometimes been made of pre-cracked specimen tests-that they circumvent the initiation stage of cracking in plain specimens, erroneously assumed invariably to be related to the creation of a corrosion pit that provides a measure of stress concentration approaching that... 

Sophisticated design engineers unfamiliar with plastics behavior will be able to apply the information contained in this and other chapters to applicable sophisticated equations that involve such analysis as multiple and complex stress concentrations. The various machine-design texts and mechanical engineering handbooks listed in the Appendix A PLASTICS TOOLBOX and REF-... 

ERENCES section at the end of this book provide detailed analysis of these stress-concentration factors and other load-bearing parameters. 

Sandorf, 1980 Whitney, 1985 Whitney and Browning, 1985). According to the classical beam theory, the shear stress distribution along the thickness of the specimen is a parabolic function that is symmetrical about the neutral axis where it is at its maximum and decreases toward zero at the compressive and tensile faces. In reality, however, the stress field is dominated by the stress concentration near the loading nose, which completely destroys the parabolic shear distribution used to calculate the apparent ILSS, as illustrated in Fig 3.18. The stress concentration is even more pronounced with a smaller radius of the loading nose (Cui and Wisnom, 1992) and for non-linear materials displaying substantial plastic deformation, such as Kevlar fiber-epoxy matrix composites (Davidovitz et al., 1984 Fisher et al., 1986), which require an elasto-plastic analysis (Fisher and Marom, 1984) to interpret the experimental results properly. 

One of the major differences between the results obtained from the micromechanics and FE analyses is the relative magnitude of the stress concentrations. In particular, the maximum IFSS values at the loaded and embedded fiber ends tend to be higher for the micromechanics analysis than for the FEA for a large Vf. This gives a slightly lower critical Vf required for the transition of debond initiation in the micromechanics model than in the FE model of single fiber composites. All these... 

Consider the same unidirectional lamina with the stresses now applied perpendicular to the fiber axis as shown in Fig. 12. The local stress at the fiber matrix interface can be calculated and compared to the nominally applied stress on the whole lamina to give K, the stress concentration factor. The plot of the results of this analysis shows that the interfacial stresses at the point of maximum principal stress can range up to 2.6 times the applied stress depending on the moduli of the constituents and the volume fraction of the reinforcement. For a typical graphite-epoxy composite, with a modulus ratio of 70 and a volume fraction of 70 % the stress concentration factor at the interface is about 2.4. That is, the local stresses at the interface are a factor of 2.4 times greater than the applied stress. 

Fig. 12. A unidirectional lamina under transverse tension. The points of stress concentration are at the dots. The micromechanical analysis shows that the stress concentration factor increases with volume fraction of fiber and fiber to matrix modulus ratio. From Adams et al.70)...

Imposing a shear stress parallel to the fiber axis of a unidirectional composite creates an interfacial shear stress. Because of the disparity in material properties between fiber and matrix, a stress concentration factor can develop at the fiber-matrix interface. Linder longitudinal shear stress as shown by the diagram in Fig. 13, the stress concentration factor is interfacial. The analysis shows that the stress concentration factor can be increased with the constituent shear modulus ratio and volume fraction of fibers in the composite. Under shear loading conditions at the interface, the stress concentration factor can range up to 11. This is a value that is much greater than any of the other loadings have produced at the fiber-matrix interface. 

Many variables used and phenomena described by fracture mechanics concepts depend on the history of loading (its rate, form and/or duration) and on the (physical and chemical) environment. Especially time-sensitive are the level of stored and dissipated energy, also in the region away from the crack tip (far held), the stress distribution in a cracked visco-elastic body, the development of a sub-critical defect into a stress-concentrating crack and the assessment of the effective size of it, especially in the presence of microyield. The role of time in the execution and analysis of impact and fatigue experiments as well as in dynamic fracture is rather evident. To take care of the specihcities of time-dependent, non-linearly deforming materials and of the evident effects of sample plasticity different criteria for crack instability and/or toughness characterization have been developed and appropriate corrections introduced into Eq. 3, which will be discussed in most contributions of this special Double Volume (Vol. 187 and 188). 

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. 

In any structure the entire structure responds to mechanical or thermal loads. It is also necessary to bear in mind that any structure will also experience localized stress concentrations at points of contact or separation in the structure. These points of contact or separation are sites susceptible to damage, cracking or failure initiation. Stress analysis using the finite element method in structures which are bolted, mating surfaces, vessels... 

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. 

Finite element modeling is also useful in failure analysis. The method has been successfully applied in failure analysis. An example involving the stressed condition with maximum stress concentration in cloverleaf radius is shown in Figure 2.29. Another example of finite element modeling applied to distorted transformer housing due to internal overpressurization has been cited in Figure 2.17. 

The deformation of the polymer within a thin active zone was originally represented by a non-Newtonian fluid [31 ] from which a craze thickening rate is thought to be governed by the pressure gradient between the fibrils and the bulk [31,32], A preliminary finite element analysis of the fibrillation process, which uses a more realistic material constitutive law [36], is not fully consistent with this analysis. In particular, chain scission is more likely to occur at the top of the fibrils where the stress concentrates rather than at the top of the craze void as suggested in [32], A mechanism of local cavitation can also be invoked for cross-tie generation [37]. 

The population of flaws can be characterized by a flaw spectrum which is defined by (a) the distribution of flaws in terms of their characteristic dimensions (for example, their lengths and radii of curvature) (b) the distribution in terms of mean spacing or distance between flaws and (c) the distribution in terms of anisotropy or directional preference with respect to some sample reference axis (e.g., an axis of orientation or draw direction). The interactive and collective probabilities which describe distributions (a), (b), and (c) comprise the flaw spectrum and through suitable analysis serve to determine, in principle, the distribution of stress concentration factors (SCF) in a given material. 

Usually the radius of curvature p at the sharp notch of the crack is determined by the atomic sizes and is very small. It is immediately evident that the stress concentration at the sharp notches of the microcracks can become extremely large due to the above stress intensity factor, and the fracture should start propagating from there. Although this analysis indicates clearly where the instabilities should occur, it is not sufficient to tell us when the instability does occur and the fracture propagation starts. This requires a detailed energy balance consideration. 

In a three-dimensional solid containing a single elliptic disk-shaped planar crack perpendicular to the applied tensile stress direction, a straightforward extension of the above analysis suggests that the maximum stress concentration would occur at the two tips (at the two ends of the major axis) of the ellipse. The Griffith stress for the brittle fracture of the solid would therefore be determined by the same formula (3.3), with the crack length 21 replaced by the length of the major axis of the elliptic planar crack. 

The stress distribution analysis shows that maximum stress concentration develops in the radial direction at the pole of the particle, and shear yielding is initiated at around 45° on the surface of rigid particles. Debonding occurs at the pole of the particle, and extends to a critical angle [27]. In case of total adhesion, debonding does not occur and there is cavitation in the matrix, at some distance from the particle pole (not at the interface). 

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