Propagation intensity factor

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. 

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. 

In metals, inelastic deformation occurs at the crack tip, yielding a plastic zone. Smith [34] has argued that the elastic stress intensity factor is adequate to describe the crack tip field condition if the inelastic zone is limited in size compared with the near crack tip field, which is then assumed to dominate the crack tip inelastic response. He suggested that the inelastic zone be 1/5 of the size of the near crack tip elastic field (a/10). This restriction is in accordance with the generally accepted limitation on the maximum size of the plastic zone allowed in a valid fracture toughness test [35,36]. For the case of crack propagation, the minimum crack size for which continuum considerations hold should be at least 50 x (r ,J. 

This is the probability that failure will occur due to the propagation of one tip of the initial defect c under stress o, where is the critical stress intensity factor of the filler particle and a is the filler particle size. 

The stress corrosion resistance of maraging steel has been evaluated both by the use of smooth specimens loaded to some fraction of the yield strength and taking the time to failure as an indication of resistance, and by the fracture mechanics approach which involves the use of specimens with a pre-existing crack. Using the latter approach it is possible to obtain crack propagation rates at known stress intensity factors (K) and to determine critical stress intensity factors (A iscc) below which a crack will not propagate (see Section 8.9). 

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... 

Critical stress intensity factor Klc and critical strain energy release rate G1C quantify the stability of a polymer against the initiation and propagation of cracks. Stress intensity factor and energy release rate G, are not independent but they are related [76] by means of the appropriate modulus E. ... 

Fracture toughness is the resistance to propagation of cracks through a material and is usually quantified by the stress intensity factor, K, defined as... 

This result indicates that the stress necessary to cause brittle fracture is lower, the longer the existing crack and the smaller the energy, P, expended in plastic deformation. The quantity Of represents the smallest tensile stress that would be able to propagate the crack of length 2 L. The term Of (tt L)°5 is generally denoted by the symbol K and is known as the stress-intensity factor (for a sharp elastic crack in an infinitely wide plate). Fracture occurs when the product of the nominal applied stress and the stress concentration factor of a flaw attains a value equal to that of the cohesive stress. 

In a first testing series, the fracture behavior of the neat, fully crosslinked epoxy network was studied. A fully unstable crack propagation behavior was observed and the critical stress intensity factor, Kj (0.82 MPaxm ), and the critical energy release rate, Gj (0.28 kj/m ), were determined [87]. These are typical values for highly crosslinked epoxy networks prepared with DGEBPA and aromatic or cycloaliphatic diamines. 

The fracture behaviour of polymers, usually under conditions of mode I opening, considered the severest test of a material s resistance to crack initiation and propagation, is widely characterised using linear elastic fracture mechanics (LEFM) parameters, such as the plane strain critical stress intensity factor, Kic, or the critical strain energy release rate, Gic, for crack initiation (determined using standard geometries such as those in Fig. 1). LEFM... 

Evans (1975), Evans and Charles (1977), and Emery (1980) performed more refined fracture mechanics studies regarding the onset and arrest conditions Bahr et al. (1988) and Pompe (1993) extended this work and considered the propagation of multiple cracks while Swain (1990) found that materials showing non-linear deformation and A-curve behaviour have a better resistance to thermal shock. More specifically, the behaviour of a crack in the thermal shock-induced stress field was deduced from the dependence of the crack length on the stress intensity factor. Unstable propagation of a flaw in a brittle material under conditions of thermal shock was assumed to occur when the following criteria were satisfied ... 

Exposure to seawater results in decrease in critical stress intensity factor and the susceptibility to SCC68 0.2% Fe improves the resistance to SCC presence of >5 wt percent of A1 increases the velocity of cracking Sn in the alloy decreases SCC resistance chloride bromide and iodide induce or accelerate SCC69 Occurs by trangranular cleavage of a-phase in which a-phase controls the crack propagation rate Intergranular corrosion due to formation of titanium methoxide... 

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