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The objective of this section is first to give a brief description of slip and differentiate slip from twinning. Then, the significant effect of slip on elongation at the early stage of plastic flow and also the role of strain transfer in the activation of deformation twinning in grain boundaries are discussed. Finally, an example will be given to show stress concentration as a result of slip bands formation.

It is known that plasticity in crystalline materials, especially metals with HCP unit cell structure, greatly depends on the preferred crystallographic orientation of individual grains, known as texture. Texture mostly develops during thermo-mechanical processing and becomes more pronounced during forming processes. Therefore, the nature of plastic deformation is closely referred to understanding the mechanical state of stress and strain in individual crystals, which can be quantified to within a good approximation by Schmid’s law. It should be noted that Schmid’s law neglects crystal interaction (crystal compatibilities). Schmid’s Law states that for yield in crystals: a single crystal yields on any particular slip system (plane and direction comprise what is known as a deformation/slip system) if the shear stress resolved on that slip plane and slip direction reaches a critical value, the “yield strength” on that slip system (details are given in section 2.3.3) [27]. Of special interest regarding slip is the establishment of a

criterion for predicting the onset of plasticity. According to Schmid’s law [28], if a polycrystal is stressed, initial yield stress varies from crystal to crystal as a function of the relative positions of the crystal lattices with respect to the loading axes. Accordingly, slip begins when the shear stress on a slip system reaches a CRSS. The prevalence of deformation modes greatly depends on the (CRSS) of each deformation mode, which is significantly influenced by crystal orientation with respect to the loading direction. Consequently, both CRSS values and texture define the sequential deformation modes by introducing slip, twinning and their interactions [29-31].

Table 2 Slip direction and planes[32]

Structure Slip direction Slip planes

FCC 110

 ₁₁₁

BCC 111

     _{110 , 112 , 123}

HCP ₁₁₂₀





Slip regularly arises as a consequence of dislocation glide. It is an experimental fact that in metallic crystals, slip occurs on planes of high-atomic density [33]. Nevertheless, this statement does not mean that slip cannot occur in planes other than the mostly close packed plane [34]. The slip planes and direction for the most common crystalline structures are tabulated in Table 2. There are number of ways that dislocations may be created as a result of an exerted load. If dislocations are not generated by dislocation sources such as the Frank-Read source, then they must be created by a nucleation process. Complete descriptions of dislocation sources can be found in references [33] and [34]. In a slip mechanism, external loading causes plastic deformation to occur in well-defined slip planes. The planes on which slip occurs are called slip

planes and the directions of the shear are the slip directions. These are crystallographic planes

Figure 5 (a) Microstructure study of commercial purity titanium sample after ~1.5 % tensile strain, showing distinct slip bands and twinning. (c)Examples of surface topography measured by atomic force microscopy in grain 2 (left) and grain 3 (right) after deformation. Line section profiles reveal that much larger and more homogeneous surface steps result from twins (left) than from slip lines (right). The dashed line is interpreted as the undistorted surface inclination and serves as the basis for evaluating the overall height change along the section. surface steps form because that slip is an inhomogeneous phenomenon on an atomic scale [32].

and directions that are characteristic of the crystal structure. The magnitude of the shear displacement is an integral number of interatomic distances, so that the lattice is left unchanged. When plastic deformation takes place by slipping, visual examination of the surface of a deformed crystal will usually reveal slip lines. Figure 5a clearly shows slip bands and deformation twinning on the surface grain of commercially pure titanium alloy as a result of 1.5% tensile straining [35]. It is evident that the density and directions of the slip traces and twins vary strongly from one grain to another. For instance, grains 3, 6, and 9 display the most obvious slip traces, while less pronounced slip bands are found in grains 8 and 10. This observation can be attributed to the fact that the grains 3, 6, and 9 are more favorable to slip (Schmid’s law). The thick lenticular crystallographycal feature appearing in grain 2 was

confirmed to be deformation twinning using Electron Backscatter Diffraction (EBSD) (Figure 5b). Atomic force microscopy scans of grains 2 and 3 shown in Figure 5c are being used here to quantify slip and twin traces on the surface. As it can be observed in Figure 5c, surface step occurs as a consequence of slip and twinning. However, the line scan provided in the same image indicates that the twinning effect is more pronounced on the surface morphology. Deformation twinning will be discussed with more detail in the following section.

Displacements of thousands of atomic diameters must occur on discrete or closely spaced planes to create visible steps on the surface. A slip band is a group of closely spaced slip lines that appear at low magnification. Hence, if a single crystal of a metal is stressed in tension or compression beyond its elastic limit, elongation/compression is usually accompanied by step appearance on the surface. This is accepted to be possibly given through the intersection of dislocations with surface dislocations [34]. If the step lies on the slip plane of a dislocation, the generated step is commonly referred to as a kink. If the step is normal to the slip plane of dislocation, the step is referred to as a jog. Close inspection of Figure 6 shows that slip bands tend to appear in an irregular wavy pattern. This can be attributed to the fact that the dislocations that produce the bands are not restricted to motion in a single plane. Shifting of dislocations from one slip plane to another usually results from cross-slipping of screw dislocations[34].

Besides the importance of slip bands for plasticity, direct evidence also indicates that slip bands have an effect on fatigue crack development. In this regard, one of the most visible features of cyclic saturation is the localization of slip along certain bands. For example, observation of structural details underlying the fatigue surface revealed that slip bands in fatigued copper mono- and polycrystals were persistent [36]. They are termed persistent because if one polishes the sample, the slip bands would reappear at their former sites whenever fatigue resumes.

Conventionally, fatigue slip bands are referred to as Persistent Slip Bands (PSB). It thus became gradually evident that fatigue damage in the form of irreversible microscopic changes at the surface resulted from the accumulation of very small irreversible plastic cyclic micro-strains and that metal fatigue was actually a problem of micro-plasticity [37]. It is crucial to note that although the surface slip steps form in proportion to the average plastic amplitude, the displacement between the bands is not fully reversible [38]. This leads to formation of slip offset and a rough topography within the bands (shown also earlier in Figure 5c) which appears to be a precursor to crack nucleation [39]. Figure 6a demonstrates crack propagation along PSB in the fatigued sample. PSBs consist of extrusions and intrusions on surface, which can potentially become incipient fatigue crack sites. Figure 6b&c clearly demonstrate that the extrusions and intrusions are closely related to the specific dislocation structure of the PSBs, and that this dislocation structure is present even in the extruded region of the material. Close attention to Figure 6c shows that very short incipient cracks start from intrusions adjacent to extrusions and initially grow parallel to the PSB [40].

Figure 6 (a) Crack propagating along PSB in tungsten monofilament-reinforced multi-crystalline copper composites [41]. Scanning Transmission Electron Microscopy (STEM) overview (b) and TEM detail (c) of initiated fatigue cracks imaged in a foil covered by Pt coating. Foil taken from fatigued 316L steel [40].