THE DISLOCATION

The discrepancy between the theoretical and actual strength of metals was not understood until 1934. Three scientists (Orowan, Polanyi, and Taylor) independently suggested that real metals do not have a perfect lattice structure as assumed in Fig. 8.7, but contain a special form of defect called. dislocation (Fig. 8.8). 

The dislocation is a crystal imperfection in which there is one more atom in the upper row than in the lower row. When shear stresses are applied, there are as many atoms resisting displacement on one side of the dislocation center as there are tending to promote it on the other. Hence, it takes much less energy to cause a dislocation to move across a crystal, than to move one layer of a perfect array of atoms over another. Dislocations are present as defects occurring during solidification, or are generated at cracks or other points of stress concentration when a metal is stressed. 

A useful analogy to the role a dislocation plays in reducing the force required for shear deformation in a crystal is shown in Fig. 8.9. Producing a hump (ruck) in the rug and moving it to the other side requires much less force than when the flat rug is moved across the floor all at the same time. 

When a dislocation is caused to move across a crystal, one layer will have been displaced relative to its neighbor by one atom spacing. Very large shear displacements are possible when a defect (grain boundary, crack, impurity, etc.) is present. This defect is capable of generating many dislocations one after the other when shear stress is applied. 

Dislocations may be demonstrated by means of a soap bubble analogy. This consists of a raft of small bubbles, all the same size, generated on the surface of a soap solution. The bubbles represent atoms and are subjected to two forces just as the atoms in a metal are. Surface tension causes the bubbles to attract each other and form a dense array, while pressure within the bubbles prevents them from approaching each other closer than a characteristic distance. When a raft of bubbles is formed on a fluid surface, grain boundaries are evident as well as dislocations (Fig. 8.10). When such a raft of bubbles is sheared, deformation is seen to occur as dislocations move across the crystal. While the forces at work are not identical to those associated with atoms, the soap bubble model is a useful analogy. A film has been produced by Sir Lawrence Bragg who devised the soap bubble analogy, and this film lends considerable credibility to the relatively sophisticated dislocation concept. 

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Fig. VII-7. Motion of an edge dislocation in a crystal undeigoing slip deformation (a) the undeformed crystal (b, c) successive stages in the motion of the dislocation from right to left (d) the undeformed crystal. (From Ref. 113 with permission.)...

One type of dislocation is the edge dislocation, illustrated in Fig. VII-7. We imagine that the upper half of the crystal is pushed relative to the lower half, and the sequence shown is that of successive positions of the dislocation. An extra plane, marked as full circles, moves through the crystal until it emerges at the left. The process is much like moving a rug by pushing a crease in it. 

Acetic acid has a place in organic processes comparable to sulfuric acid in the mineral chemical industries and its movements mirror the industry. Growth of synthetic acetic acid production in the United States was gready affected by the dislocations in fuel resources of the 1970s. The growth rate for 1988 was 1.5%. 

An analogy to sHp dislocation is the movement of a caterpillar where a hump started at one end moves toward the other end until the entire caterpillar moves forward. Another analogy is the displacement of a mg by forming a hump at one end and moving it toward the other end. Strain hardening occurs because the dislocation density increases from about 10 dislocations/cm to as high as 10 /cm. This makes dislocation motion more difficult because dislocations interact with each other and become entangled. SHp tends to occur on more closely packed planes in close-packed directions. 

Dislocations are characterized by the Burgers vector, which is the exua distance covered in traversing a closed loop around die core of the dislocation, compared with the conesponding distance traversed in a normal lattice, and is equal to about one lattice spacing. This circuit is made at right angles to the dislocation core of an edge dislocation, but parallel to the core of a screw dislocation. 

An example of research in the micromechanics of shock compression of solids is the study of rate-dependent plasticity and its relationship to crystal structure, crystal orientation, and the fundamental unit of plasticity, the dislocation. The majority of data on high-rate plastic flow in shock-compressed solids is in the form of ... 

Kumar and Clifton [31] have shock loaded <100)-oriented LiF single crystals of high purity. The peak longitudinal stress is approximately 0.3 GPa. Estimates of dislocation velocity are in agreement with those of Flinn et al. [30] when extrapolated to the appropriate shear stress. From measurement of precursor decay, inferred dislocation densities are found to be two to three times larger than the dislocation densities in the recovered samples. 

To answer questions regarding dislocation multiplication in Mg-doped LiF single crystals, Vorthman and Duvall [19] describe soft-recovery experiments on <100)-oriented crystals shock loaded above the critical shear stress necessary for rapid precursor decay. Postshock analysis of the samples indicate that the dislocation density in recovered samples is not significantly greater than the preshock value. The predicted dislocation density (using precursor-decay analysis) is not observed. It is found, however, that the critical shear stress, above which the precursor amplitude decays rapidly, corresponds to the shear stress required to disturb grown-in dislocations which make up subgrain boundaries. 

Meir and Clifton [12] study shocked <100) LiF (high purity) with peak longitudinal stress amplitudes 0.5 GPa. A series of experiments is reported in which surface damage is gradually eliminated. They find that, while at low-impact velocities the dislocations in subgrain boundaries are immobile and do not affect the dislocation concentration in their vicinity, at high-impact velocities ( 0.1 km/s) dislocations emitted from subgrain boundaries appear to account for most of the mobile dislocations. 

Since the dislocation drag coefficient B represents the transfer of momentum per unit area, we assume that B/m remains constant as the velocity increases and hence... 

For very strong pinning points at T = 0 K, dislocations can mechanically break away only when the dislocation segment is bowed enough to meet another segment on the other side of the pinning point (shown as the burst in Fig. 7.6). This will occur when... 

The variation of r and f through 3.0 GPa and 5.4 GPa shock waves is shown in Fig. 7.7 [38]. This figure shows clearly that the shock-wave path is in the dislocation drag regime (r > f). The mechanical threshold stress f increases from 10 MPa to 80 MPa in the 5.4 GPa shock thus from (7.37)... 

The dislocation multiplication law N = (l/L)N i is path-independent i.e., N depends only on y and not on the rate at which the deformation occurs. Show that the multiplication law given by... 

The response is extremely fast on the time scale of a shock-wave experiment. The dislocation loop adjusts very quickly to the applied stress t. 

But crystals (like everything in this world) are not perfect they have defects in them. Just as the strength of a chain is determined by the strength of the weakest link, so the strength of a crystal - and thus of our material - is usually limited by the defects that are present in it. The dislocation is a particular type of defect that has the effect of allowing materials to deform plastically (that is, they yield) at stress levels that are much less than [Pg.95]

Fig. 9.3. An edge dislocation, (a) viewed from a continuum standpoint (i.e. ignoring the atoms) and (b) showing the positions of the atoms near the dislocation.

Dislocation motion produces plastic strain. Figure 9.4 shows how the atoms rearrange as the dislocation moves through the crystal, and that, when one dislocation moves entirely through a crystal, the lower part is displaced under the upper by the distance b (called the Burgers vector). The same process is drawn, without the atoms, and using the symbol 1 for the position of the dislocation line, in Fig. 9.5. The way in... 

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