Solucionario Calculo Tom Apostol Vol 1 Y 2l

The example of FIB section (Fig. 12a) illustrates that the fatigue crack forms as a consequence of the local plastic deformation at or slightly below the external epitaxial martensite/austenite interface. The crack is initiated at the interface and spreads towards the surface due to the anisotropic elastic properties of the microstructure. Above the fracture threshold, in the crack tip region with the circumferential stress component, large grains of anisotropic elasticity are transformed into smaller grains with the radial stress component. In some cases where distortion above the MPa level persists shortly after the MPa (tensile chip) or shortly after the MPa/PSB (compressive chip) threshold, the coupling of local plastic and elastic distortion near the surface may give rise to plastic crack growth. This effect is analogous to the transient stresses generated at the interface between two nonmetallic materials [62]. The crack grows by removing material from the GB region, so that the formation of a brittle-tough transition zone just beneath the surface is observed (figure 12b). Local microstructure and compositional variations may lead to the formation of nonhomogeneous transition zones (figure 12c) or to the formation of strain softening zones where strain is dissipated at GBs [63]. Because of the peculiarities of the processes that occur in each particular fatigue damage zone, it is unsuitable to conduct in situ fatigue testing for such materials because it is not possible to determine experimentally the true fracture properties and the coupling of elastic and plastic fields of variation near the crack tip. In such cases, the safest way is to simulate crack initiation and growth in computer programs by means of an FEM model. This is possible if an adequate description of the crack paths is given in the FEM model. For example Bhattacharya et al. [64] used a 3D FEM model to simulate fatigue crack growth in high-temperature austenitic stainless steels. Figure 11 shows a typical crack along a GB as a smooth path that presents almost constant stress, whereas small distortions occur above the critical stress (Fig. 11a). Figure 11b shows the crack growth paths for different fatigue cycles (i.e. real crack length = K2λ, where K2 is the equivalent stress amplitude, λ is the cycle length or F. d2c66b5586