Dislocation locking and temperature

6.4.8 Dislocation locking and temperature

The binding of a solute atom to a dislocation is short range in nature, and is effective only over an atomic distance or so (Figure 6.28). Moreover, the dislocation line is flexible and this enables yielding to begin by throwing forward a small length of dislocation line, only a few atomic spacings

long, beyond the position marked x 2 . The applied stress then separates the rest of the dislocation line from its anchorage by pulling the sides of this loop outward along the dislocation line, i.e. by double kink movement. Such a breakaway process would lead to a yield stress which depends sensitively on temperature, as shown in Figure 6.29a. It is observed, however, that k y , the grain-size dependence parameter in the Hall–Petch equation, in most annealed bcc metals is almost independent of temperature down to the range (<100 K) where twinning occurs, and that practically all the large temperature dependence is due to σ i (see Figure 6.29b). To explain this observation it is argued that when locked dislocations exist initially in the material, yielding starts by unpinning them if they are weakly locked (this corresponds to the condition envisaged by Cottrell–Bilby), but if they are strongly locked it starts instead by the creation of new dislocations at points of stress concentration. This is an athermal process and thus k y is almost independent of temperature. Because of the rapid diffusion

Mechanical properties I 319

s max

Stress O

Displacement C

Dislocation line B

A Unstable position

Figure 6.28 Stress–displacement curve for the breakaway of a dislocation from its atmosphere (after Cottrell, 1957; courtesy of the Institution of Mechanical Engineers).

Low-carbon steel at 77 K

2 ) 350 2 ) ⫺ 700 ⫺ Niobium at 77 K

Low-carbon steel

Low-carbon steel at 195 K

Niobium Niobium at 195 K

Lower yield tensile stress (MN m

Lower yield tensile stress (MN m

Niobium at 293 K Low-carbon

Nickel steel at 293 K 0 100

0 10 20 30 40 Temperature (K)

Grain size d ⫺ 1/2 (cm ⫺ 1/2 )

(b) Figure 6.29 Variation of lower yield stress with temperature (a) and grain size (b), for low-carbon

(a)

steel and niobium; the curve for nickel is shown in (a) for comparison (after Adams, Roberts and Smallman, 1960; Hull and Mogford, 1958).

of interstitial elements the conventional annealing and normalizing treatments should commonly produce strong locking. In support of this theory, it is observed that k y is dependent on temperature in the very early stages of ageing following either straining or quenching, but on subsequent ageing k y becomes temperature independent. The interpretation of k y therefore depends on the degree of ageing.

320 Physical Metallurgy and Advanced Materials Direct observations of crystals that have yielded show that the majority of the strongly anchored

dislocations remain locked and do not participate in the yielding phenomenon. Thus, large numbers of dislocations are generated during yielding by some other mechanism than breaking away from Cottrell atmospheres, and the rapid dislocation multiplication, which can take place at the high stress levels, is now considered the most likely possibility. Prolonged ageing tends to produce coarse precipitates along the dislocation line and unpinning by bowing out between them should easily occur before grain boundary creation. This unpinning process would also give k y independent of temperature.