Variation of yield stress with temperature and strain rate

6.4.2 Variation of yield stress with temperature and strain rate

The high Peierls–Nabarro stress, which is associated with materials with narrow dislocations, gives rise to a short-range barrier to dislocation motion. Such barriers are effective only over an atomic spacing or so, hence thermal activation is able to aid the applied stress in overcoming them. Thermal activation helps a portion of the dislocation to cross the barrier after which glide then proceeds by the

Mechanical properties I 305

10 7 Velocity of (110) [110] shear

10 6 waves ⫽ 3.6 ⫻ 10 5 cm s ⫺ 1

Edge 10 components

Screw components

elocity (cm s

Dislocation v 10 ⫺ 2

10 ⫺ 5 10 ⫺ 6 Yield stress

C.R.S.S. 10 ⫺ 7 0.1 0.5 1.0

Applied shear stress (kg mm ⫺ 2 )

Figure 6.15 Stress dependence of the velocity of edge and screw dislocations in lithium fluoride (from Johnston and Gilman, 1959; courtesy of the American Physical Society).

sideways movement of kinks. (This process is shown in Figure 6.28, Section 6.4.8.) Materials with narrow dislocations therefore exhibit a significant temperature sensitivity; intrinsically hard materials rapidly lose their strength with increasing temperature, as shown schematically in Figure 6.17a. In this diagram the (yield stress/modulus) ratio is plotted against T /T m to remove the effect of modulus which decreases with temperature. Figure 6.17b shows that materials which exhibit a strong temperature- dependent yield stress also exhibit a high strain-rate sensitivity, i.e. the higher the imposed strain rate, the higher the yield stress. This arises because thermal activation is less effective at the faster rate of deformation.

In bcc metals a high lattice friction to the movement of a dislocation may arise from the dissociation of a dislocation on several planes. As discussed in Chapter 3, when a screw dislocation with Burgers vector a/2[1 1 1] lies along a symmetry direction it can dissociate on three crystallographically equivalent planes. If such a dissociation occurs, it will be necessary to constrict the dislocation before it can glide in any one of the slip planes. This constriction will be more difficult to make as the temperature is lowered so that the large temperature dependence of the yield stress in bcc metals, shown in Figure 6.17a and also Figure 6.29, may be due partly to this effect. In fcc metals the dislocations lie on {1 1 1} planes, and although a dislocation will dissociate in any given (1 1 1) plane, there is no direction in the slip plane along which the dislocation could also dissociate on other planes; the temperature dependence of the yield stress is small, as shown in Figure 6.17a. In cph metals the dissociated dislocations moving in the basal plane will also have a small Peierls force

306 Physical Metallurgy and Advanced Materials

1 3 Velocity (cm s

Iron–silicon

(units of 10 ⫺ 9 d cm ⫺ 2 ) 6 10

Lithium fluoride

(units of 10 8 d cm ⴚ2 )

Tension

velocity of 10 nm s

Bending

Shear stress for dislocation

0 1 2 3 4 5 0.5 1 2 3 4 5 Macroscopic shear yield stress

[10 8 Nm ⫺ 2 ] Stress

(b) Figure 6.16 (a) Correlation between stress to cause dislocation motion and the macro-yield

(a)

stresses of crystals. (b) Edge dislocation motions in Fe–3% Si crystals (after Stein and Low, 1960; courtesy of the American Physical Society).

and be glissile with low temperature dependence. However, screw dislocations moving on non-basal planes (i.e. prismatic and pyramidal planes) may have a high Peierls force because they are able to extend in the basal plane, as shown in Figure 6.18. Hence, constrictions will once again have to be made before the screw dislocations can advance on non-basal planes. This effect contributes to the high critical shear stress and strong temperature dependence of non-basal glide observed in this crystal system, as mentioned in Chapter 3.