Critical dislocation slip

In nearly all metal-forming operations, slip is the dominant method of deformation, although twinning can be significant in some materials. Slip occurs when the shear stress is high enough to cause layers of atoms to move relative to one another. The critical resolved shear stress is lowered when the crystalline lattice is not perfect but contains linear defects called dislocations. Slip-induced plasticity was covered in Chapter 9 of the companion to this text (Lalena and Cleary, 2005) and is reviewed here only briefly. The interested reader is advised to consult Lalena and Cleary (2005), Honeycombe (1984), or Dieter (1976). 

Figure 21. Model of dislocation string detachment from point defect. Pinning in A and B points supposed rigid /i, /j are lengths of vibrating dislocation segments. Arrow shows direction of dislocation slipping and outer stress (p is critical detachment angle.

Some materials have a small lattice mismatch with the substrate, less then 1%, and can adopt the same lattice constants at the interface. This, however, still results in some strain, which builds until released, forming slip dislocations etc.. The thickness at which defects occur is of considerable interest and referred to as the critical thickness [14, 15]. Strain can be minimized by adjusting the lattice constants of the... 

Beside dislocation density, dislocation orientation is the primary factor in determining the critical shear stress required for plastic deformation. Dislocations do not move with the same degree of ease in all crystallographic directions or in all crystallographic planes. There is usually a preferred direction for slip dislocation movement. The combination of slip direction and slip plane is called the slip system, and it depends on the crystal structure of the metal. The slip plane is usually that plane having the most dense atomic packing (cf. Section 1.1.1.2). In face-centered cubic structures, this plane is the (111) plane, and the slip direction is the [110] direction. Each slip plane may contain more than one possible slip direction, so several slip systems may exist for a particular crystal structure. Eor FCC, there are a total of 12 possible slip systems four different (111) planes and three independent [110] directions for each plane. The... 

An explanation of the tendency for crystalline solids to deform plastically at stresses that are so much smaller than the calculated critical resolved shear stress was first given in 1934 independently by Taylor, Oro-wan, and Polanyi. They introduced the concept of the dislocation into physics and showed that the motion of dislocations is responsible for the deformation of metals and other crystalline solids. At low temperatures, where atomic diffusion is low, dislocations move almost exclusively by slip. 

This equation says that the critical stress on the slip system can change as a result of the accumulation of plastic strain on the slip system. The accumulation of plastic strain on the slip system is measured in terms of the shear strain yp. The matrix hap is the so-called hardening matrix and is the backbone of a hardening law for single crystal plasticity. One of the dominant tasks facing those who aim to build viable models of plasticity on the basis of insights at the dislocation level is to probe the veracity of expressions like that given above. 

For screw-dislocation dipoles with dipole height just above the critical dipole height for annihilation by spontaneous cross slip the activation energy is so low that the annihilation process can be modeled by molecular dynamics (Vegge et al. [20]). This allowed us to determine the preexponential for cross slip P (with dimension m s 1) in the equation... 

The octahedral shear stress criterion has some appeal for materials that deform by dislocation motion In which the slip planes are randomly oriented. Dislocation motion Is dependent on the resolved shear stress In the plane of the dislocation and In Its direction of motion ( ). The stress required to initiate this motion is called the critical resolved shear stress. The octahedral shear stress might be viewed as the "root mean square" shear stress and hence an "average" of the shear stresses on these randomly oriented planes. It seems reasonable, therefore, to assume that slip would initiate when this stress reaches a critical value at least for polycrystal1ine metals. The role of dislocations on plastic deformation in polymers (even semicrystalline ones) has not been established. Nevertheless, slip is known to occur during polymer yielding and suggests the use of either the maximum shear stress or the octahedral shear stress criterion. The predictions of these two criteria are very close and never differ by more than 15%. The maximum shear stress criterion is always the more conservative of the two. 

Kink nucleation on partial dislocations has also been considered [27] because of the experimental observation that the critical resolved shear stress for 110 (111) slip in molybdenum disilicide decreases when substitutional alloying elements are added that decrease the stacking fault energy, and increases when substitutional elements are added that increase the stacking fault energy. This modification may apply not only to other intermetallics but also to ceramics such as spinel, where increasing... 

The inevitable conclusion is that real crystals must contain defects, such as dislocations suggested by Taylor, Orowan and Polanyi, which reduce their mechanical strength or, more specifically, their resistance to slip when the applied stress reaches a critical value. The 1934 postulate showed that shear is possible at much lower stresses than in a perfect crystal. 

At the critical shear stress of the applied stress, yielding occurs (=Ty) and dislocations are nucleated at the head of the pile-up for slip into a neighboring grain (across the grain boundary). At this stage, Eq. (4.19) may be written as ... 

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