Interaction of Two Slip Planes on Extrusion Growth in Fatigue Band

Micromechanic theory of fatigue crack initiation by Lin and his associates is reviewed. Intrusions and extrusions have been observed in fatigue specimens. An initial stress field favorable for the growth of extrusion or intrusion can be produced by arrays of dislocation dipoles as shown by Lin (1969). These dipoles cause an initial tensile strain giving an elongation which is called the static extrusion. It has been suggested tiiat after extrusion reaches the height of static extrusion, extrusion growth terminates. Along the direction of an extrusion, tensile strain and tensile stress occurs. This tensile stress causes the resolved shear stiess to reach critical and slide in a secondary slip system. The slip causes plastic tensile strain which increases significantiy the extrusion growth. Similarly tiie same mechanism exists for the growth of intrusions. This explains why extrusion grows much more tiian the static extrusion. Introduction McCommon & Rosenberg [1] and MacCrone et al. [2] show that metal are subject to fatigue at temperature as low as l.l°k. This seems to indicate that although surface corrosion, gas adsorption, gas diffusion into the metal or vacancy diffusion to form voids can have important effect on but are not necessary to the fatigue crack initiation. Local plastic deformation resulting from the displacement of dislocation generally proceeds this initiation. Forsyth and Stubbington 1954 [3] reported the detection of extrusion in slip bands during fatigue of some aluminum alloys. Thompson, Wadsworth and Louat [4] and Hull [5] detected the extrusion process in both copper and aluminum. This initiation of extrusion process was also observed by Meke and Blochwitz [6] and Mughrabi [7] in their studies of persistent slip bands. Following the clue, which the observation on extrusions and intrusions in slip bands have provided, a number of theories of fatigue crack initiation have been proposed by different distinguished investigators. For example, Mott [8] proposed that a screw dislocation repeats its path through cross slip. He considered a column of metal containing a single screw dislocation intersecting a free surface. When this dislocation travels a complete circuit, the volume contained in the circuit is translated parallel to the dislocation. This causes the metal to extrude. This mechanism does not explain why the dislocation under cyclic stressing, does not oscillate back and forth along the same path rather than traversing a closed circuit. Clearly some form of gating mechanism is required to convert the back and forth oscillations of screw dislocations into unidirectional circuits. Cottrell and Hull [9] proposed that Frank Read sources exist on two intersecting slip planes and a complete cycle of forward and reversed loading results in an extrusion and intrusion. Such a model would predict the extrusion and intrusion to form in neighboring slip bands and to be inclined to each other, but they have been found to occur in the same slip band and to be parallel to each other. Thompson [10] proposed an edge-screw interaction model for the initiation of extrusion. This model assumes a change of spacing of a pair of parallel screw dislocations after being cut an edge dislocation. This cut causes jogs in both edge and the screw dislocations and this cut will inhibit the change of the spacing of the pair of screw dislocations [11]. It is also hard to see how intrusions are formed by such a model. McEvily and Machlin [12] proposed a model, in which two screw dislocations terminate in a surface and intersect a node where three dislocations meet. Under an alternating shear stress, the two screw dislocations are assumed to shift around a circuit causing an intrusion and an extrusion formed in the same slip band. However, this model as pointed out by Kennedy does not explain why these two dislocations travel around a circuit instead of back and forth. Wood [13] proposed a simple model of a single operative slip system. An undirectional stressing causes layers of metal to sUde in the same direction; but forward and reverse stressing causes different amounts of net slip on different planes and results in peaks and valleys. However, this model and other models of random slip do not explain why, under an alternate loading, the slip continues to monotonically deepen the valley and raise the peaks as observed in experiments. Drawbacks of other theories have also been discussed by Kennedy [11]. For a dislocation to glide, it (1) must glide along a certain direction on a crystal plane (2) must subject to a resolved shear stress equal or greater than the critical shear stress. The above mentioned theories show the possible paths of dislocation movement to satisfy condition (1) but the resolved shear stress field caused by the dislocation movement that has significant effect on (2) was not considered. In the micromechanic theory developed by Lin and his associates, [14-16], this important effect of this stress field in causing the initiation of extrusion and intrusion is considered. Dependency of slip on resolved shear stress Single crystal tests [17] have shown that under stress, slip occurs along certain directions on certain crystal planes. These directions and planes are generally those of maximum atomic density. Slip has been found to depend on the resolved shear stress and not on the normal stress on the sliding plane. This dependency of slip on the resolved shear stress under monotonic loadings has also been found to hold under cyclic loadings [18]. Hence to find the slip in a slip band or fatigue band, we need to determine the resolved shear stress distribution in the metal. To determine this stress field, the following analogy between plastic strain and applied force is used. Analogy between plastic strain and applied force The resolved shear stress to cause sliding is called the critical shear stress. When this critical shear stress is reached in some region in a body, slip occurs and causes plastic strain. If the load is removed, plastic strain remains and cause a residual stress field. To find this stress field, the analogy between plastic sti^in and applied force developed by Lin [19,20] is used. This analogy is briefly reviewed as follows: Referring to a set of rectangular coordinates, the strain component is composed of the elastic part denoted by single prime and the inelastic part denoted by double prime