Riñas de Gallos

Cyclic plastic deformation is the decisive factor in the progress of cumulative damage taking place during cyclic loading. Cyclic deformation throughout the volume of the loaded metal may also cause changes in the mechanical response i.e. hardening/softening. After a number of cycles, the intensity of variation in the hardening and softening decreases and a saturation stage is reached when a hardening or softening process stabilizes as represented by hysterises loops in Figure 2.10 (a and b). For example22_{, when polycrystalline copper was cycled}

at different total strain amplitudes, the stress amplitude increased quickly and then reached a more or less constant saturated value in a fraction of the total number of cycles to failure. The fatigue hardening and softening of materials stems from the movement, generation and interaction of structural defects such as dislocations. During the initial rapid hardening stage, a large number of dislocations is produced, the pile up of which hinders the slip process23_{. With}

continued cycling, the dislocation density increases and the spacing among the bundles of dislocations and the dislocation free area decreases. At high strain amplitudes, a three dimensional dislocation cell structure is produced. During the saturation stage, slip bands of inhomogeneous plastic deformation are produced provided the cyclic strain amplitude was sufficient24_{. These slip bands have a different dislocation structure from the matrix and are}

softer25 _{than the matrix. This phenomenon gives rise to the creation of persistent slip bands. The}

term persistent slip bands (PSBs) arose from the fact that these slip bands were reformed in the same locations even after electropolishing the fatigued specimen26_{. Figure 2.11 shows a}

micrograph of polycrystalline Cu showing these PSBs. For homogeneous microstructures with a smooth polished surface (i.e. in the absence of local stress concentration features) the nucleation of a crack starts along the PSBs.

The process of nucleation of a crack under cyclic load is not simple to understand as it commences within the atomic structure of the crystal from the first few cycles of stress and will continue growing over thousands or millions of subsequent cycles until the eventual failure.

It was postulated by Gough27 _{that fatigue crack initiation is a consequence of}

exceeding the limit of local strain hardening. Further to that, Orowan28 _{concluded that the local}

exhaustion of ductility leads to the localized increase of stress and ultimately to cracking. Fundamental knowledge of crack initiation was refined during the 1950s when dislocation theory was further developed. Stroh29 _{postulated that piling up of dislocations around}

microstructural obstacles increases the local stress field, which then becomes sufficiently high to cause local cleavage. Various researchers carried out further investigations30 . For example, dislocation models were proposed by Cottrell and Hull31_{, which were based upon the}

intersecting slip systems generating a microcrack. Further models proposed by Mott32 _were

based upon generation of vacancies.

In the case of homogeneous materials, the microcracks usually originate at the free surface. This is also true for those non-homogeneous materials in which maximum stress (i.e. bending and torsion loading conditions) occurs at the surface. This is because, at the free surface, the restraint on cyclic slip is lower than inside the material. In addition, microcracks start more easily at slip bands with slip displacements normal to the material surface33_.

The idealized behaviour of slip systems during cyclic deformation has been depicted34

in Figure 2.12. This figure shows the creation of extrusions and intrusions during cyclic slip, with extrusions and intrusions along slip bands. These extrusions and intrusions for polycrystalline Cu fatigued at -183oC are shown in Figure 2.13. According to Wood35 _{, repeated}

cyclic straining of the material leads to different amounts of net slip on different glide planes. The shear displacements produced are irreversible. The reason for this irreversibility is the cyclic strain hardening that stops all the dislocations from coming back to their original positions36_{. Another important reason may be environmental factors, during slip when a fresh}

surface is exposed to the non-inert environment; it is covered with a very thin oxide layer or some chemo-absorption of foreign atoms. These phenomena may be effective together or alone depending upon the inherent characteristics of the material such as resistance to oxidation and mechanisms of slip i.e. planar or wavy.

In the early work by Forsyth30 and Plumbridge37on the fatigue initiation of soft and hard metals, it was found that the crack usually initiated at slip bands and that the number of cycles required to produce a detectable crack was a small proportion of the total life. Early work reported by Tryon et al38 showed that in a continuous material, microcracks have been

observed to initiate from slip bands formed in the early stage of damage accumulation and stretch across one grain

The initial crack developed along the slip plane (stage I) eventually propagates across other grains along appropriately oriented slip planes. The crack may only grow in stage I in a polycrystalline metal for a few grain diameters before it changes its direction to be perpendicular to the direction of the maximum applied tensile stress. During this stage (II), a well-defined crack propagates at a relatively rapid rate. Fatigue striations may be created as the crack advances across the cross section of the specimen. In stage III, the local crack tip stress states are reaching static failure levels while the remaining uncracked material is insufficient to support the applied load giving rise to rapidly increasing crack growth rates until final rupture.