Fracture stress intensity factor

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. 

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 ... 

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 ... 

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. 

Fracture mechanics analysis requires the determination of the mode I stress intensity factor for a surface crack having a circular section profile. Here the circular section flaw will be approximated by a semi-elliptical flaw. 

Step 2. After a contact time t, the material is fractured or fatigued and the mechanical properties determined. The measured properties will be a function of the test configuration, rate of testing, temperature, etc., and include the critical strain energy release rate Gic, the critical stress intensity factor K[c, the critical... 

The critical stress intensity factor is sometimes referred to as the fracture... 

The stress-intensity factors are quite different from stress concentration factors. For the same circular hole, the stress concentration factor is 3 under uniaxial tension, 2 under biaxiai tension, and 4 under pure shear. Thus, the stress concentration factor, which is a single scalar parameter, cannot characterize the stress state, a second-order tensor. However, the stress-intensity factor exists in all stress components, so is a useful concept in stress-type fracture processes. For example. 

Composite materials have many distinctive characteristics reiative to isotropic materials that render application of linear elastic fracture mechanics difficult. The anisotropy and heterogeneity, both from the standpoint of the fibers versus the matrix, and from the standpoint of multiple laminae of different orientations, are the principal problems. The extension to homogeneous anisotropic materials should be straightfor-wrard because none of the basic principles used in fracture mechanics is then changed. Thus, the approximation of composite materials by homogeneous anisotropic materials is often made. Then, stress-intensity factors for anisotropic materials are calculated by use of complex variable mapping techniques. 

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). 

Fracture Mechanics Tests One problem of both sustained load and slow strain-rate tests is that they do not provide a means of predicting the behaviour of components containing defects (other than the inherent defect associated with the notch in a sustained load test). Fracture mechanics provides a basis for such tests (Section 8.9), and measurements of crack velocity as a function of stress intensity factor, K, are widely used. A typical graph of crack velocity as a function of K is shown in Fig. 8.48. Several regions may be seen on this curve. At low stress intensity factors no crack growth is... 

Stress Intensity Factor K,5cc a fracture toughness parameter used for evaluating susceptibility to stress-corrosion cracking (the subscript I signifies a tensile mode of stressing). 

J.P. Bentham and W.T. Koiter, Mechanics of Fracture, ed. by G.C. Sih, Noordhoff International Publishing, Leiden, 1972, pp. 131-178 referred to in Stress Intensity Factors Handbook by Y. Murakami, Pergamon Press, New York, 1987, pp. 6-9. 

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. 

Monta, N., Whitfill, D.L., and Wahl, H.A. "Stress Intensity Factor and Fracture Cross Sectional Shape Precictions From a 3 0 Model for Hydraulically Induced Fractures," SPE paper 14262, 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, September 22 25. 

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