Stress intensity

The computational process of analysis is hidden from the user, and visually the analysis is conducted in terms of M-02-91 or R6 [6] assessment procedure On the basis of data of stress state and defect configuration the necessary assessment parameters (limit load, stress intensity factor variation along the crack-like defect edge) are determined. Special attention is devoted to realization of sensitivity analysis. Effect of variations in calculated stress distribution and defect configuration are estimated by built-in way. 

Therefore, the magnitude of the stress at small distances from the crack tip is a function of the crack length, a, and the remotely appHed stress. O. Close to the crack tip (r ft) the stress can be scaled usiag a parameter called the stress intensity factor, K (9—11) ... 

D. P. Rooke and D. J. Cartwright, Compendium of Stress Intensity factors. Her Majesty s Stationery Office, London, 1974. 

Y. Murakami, ed.. Stress Intensity factors Handbook, Pergamon Press, Oxford, U.K., 1987. 

Lack of accepted stress intensity factors for internally pressurized components has, until recently, limited this appHcation. The factors are a function of the size and shape of both cracks and high pressure components as well as modes of loading (91). Stress intensity factors can be derived analytically for some simple geometries, but most require the appHcation of advanced numerical methods (105—107). Alternatively they may be deterrnined experimentally (108). 

Another important appHcation of LEFM is the rate of growth of a fatigue crack under cycHc loading. This is also controlled by the stress intensity factor through an equation of the following form (110) ... 

One aspect of pressure vessel design which has received considerable attention in recent years is the design of threaded closures where, due to the high stress concentration at the root of the first active thread, a fatigue crack may quickly initiate and propagate in the radial—circumferential plane. Stress intensity factors for this type of crack are difficult to compute (112,113), and more geometries need to be examined before the factors can be used with confidence. 

A more practical approach for quantifyiag the conditions required for fracture uses a stress intensity criterion instead of an energy criterion. Using linear elastic theory, it has been shown that under an appHed stress, when the stress intensity K,... 

Fracture Toughness. The fracture criterion was defined by a critical value of the crack tip stress intensity, known as the fracture toughness. Ceramics often fail ia pure tension, designated mode I, and Kj replaces ia equation 6. Thus die appHed tensile stress at which fracture... 

Under some citcumstances the crack tip stress intensity is different than far-field stresses would indicate because of microstmctural effects behind the crack tip, such as fibers, whiskers, and bridging grains. Often far-field values indicate the crack is propagating at a stress intensity value higher than Kj and this apparent value usually increases as crack length increases. In spite of indications to the contrary, bonds continue to break at the same value of the stress intensity however, the crack tip is being shielded from some of the appHed stress intensity. To minimize confusion about Kj it has been suggested that the farfield value of the stress intensity be called When there are no microstmctural features that effectively reduce the crack tip stress intensity,... 

Fig. 7. Crack velocity as a function of the applied stress intensity, Kj. Water and other corrosive species reduce the Kj required to propagate a crack at a given velocity. Increasing concentrations of reactant species shifts curve upward. Regions I, II, and III are discussed in text.

For a single-value toughness material, dT/dc = 0. Accordingly, if the applied stress intensity factor is always increasing with crack length, equation 4 is always satisfied. Thus, the condition for fracture is equation 5, where is given by the applied loading conditions. 

Figure 7 shows these results schematically for both twist and tilt crack deflections. Thus, for the stress intensity factor required to drive a crack at a tilt or twist angle, the appHed driving force must be increased over and above that required to propagate the crack under pure mode 1 loading conditions. Twist deflection out of plane is a more effective toughening mechanism than a simple tilt deflection out of plane. 

Toughening for whisker-reinforced composites has been shown to arise from two separate mechanisms frictional bridging of intact whiskers, and pullout of fractured whiskers, both of which are crack-wake phenomena. These bridging processes are shown schematically in Figure 13. The mechanics of whisker bridging have been addressed (52). The appHed stress intensity factor is given by ... 

Part AM This part lists permitted individual constnic tion materials, apphcable specifications, special requirements, design stress-intensity vafues, and other property information. Of particular importance are the ultrasonic-test and tou ness requirements. Among the properties for which data are included are thermal conduc tivity and diffusivity, coefficient of theiTnal expansion, modulus of elasticity, and yield strength. The design stress-intensity values include a safety factor of 3 on ultimate strength at temperature or 1.5 on yield strength at temperature. 

Appendixes Appendix 1 defines the basis used for defining stress-intensity values. Appendix 2 contains external-pressure charts, and Appendix 3 has the rules for bolted-flange connec tions these two are exact duplicates of the eqiiivalent appendixes in Division 1. 

Appendix 4 gives definitions and rules for stress analysis for shells, flat and formed heads, and tube sheets, layered vessels, and nozzles including discontinuity stresses. Of particular importance are Table 4-120.1, Classification of Stresses for Some Typical Cases, and Fig. 4-130.1, Stress Categories and Limits of Stress Intensity. These are veiy useful in that they clarify a number of paragraphs and simphfy stress analysis. 

Fracture Mechanics Methods These have proved very usebd for defining the minimum stress intensity K[scc. t which stress corrosion cracking of high-strength, low-ductihty alloys occurs. They have so far been less successful when apphed to high-ductility alloys, which are extensively used in the chemicm-process industries. 

The term a Tra crops up so frequently in discussing fast fracture that it is usually abbreviated to a single symbol, K, having units MN m " it is called, somewhat unclearly, the stress intensity factor. Fast fracture therefore occurs when... 

K,- = lG,. = fracture toughness (sometimes critical stress intensity factor). Usual units MN m ... 

H. Tada, P. Paris and G. Irwin, The Stress Analysis of Cracks Handbook, Del Research Corporation, St Louis, 1973 (for Tabulation of Stress Intensities). 

The cyclic stress intensity AK increases with time (at constant load) because the crack grows in tension. It is found that the crack growth per cycle, da/dN, increases with AK in the way shown in Fig. 15.8. 

First, the pressure vessel must be safe from plastic collapse that is, the stresses must everywhere be below general yield. Second, it must not fail by fast fracture if the largest cracks it could contain have length 2a (Fig. 16.4), then the stress intensity K CTV must everywhere be less than K. Finally, it must not fail by fatigue the slow growth of a crack to the critical size at which it runs. 

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