Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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2nd Revised Pages

9.17 Data Extrapolation Methods • 329

30

20

10

8 6 4 3 2 1

Stress (10

3 psi)

200

100

20

10

8

Stress (MPa)

Steady-state creep rate (h–1)

10 –7 10 –6 10 –5

427 °C (800°F)

538 °C (1000°F)

649 °C (1200°F)

80

60

40

30

Figure 9.38 Stress (logarithmic scale) versus steady-state creep rate (logarithmic scale) for

a low carbon–nickel alloy at three temperatures. [FromMetals Handbook: Properties and

Selection: Stainless Steels, Tool Materials and Special-Purpose Metals,Vol. 3, 9th edition,

D. Benjamin (Senior Editor), American Society for Metals, 1980, p. 131.]

whereK 1 andnare material constants. A plot of the logarithm of ̇sversus the

logarithm ofσyields a straight line with slope ofn; this is shown in Figure 9.38 for a

nickel alloy at three temperatures. Clearly, a straight line segment is drawn at each

temperature.

Now, when the influence of temperature is included,

 ̇s=K 2 σnexp

(

−

Qc

RT

)

(9.21)

Dependence of creep

strain rate on stress

and temperature

(in K)

whereK 2 andQcare constants;Qcis termed the activation energy for creep.

Several theoretical mechanisms have been proposed to explain the creep behav-

ior for various materials; these mechanisms involve stress-induced vacancy diffusion,

grain boundary diffusion, dislocation motion, and grain boundary sliding. Each leads

to a different value of the stress exponentnin Equation 9.20. It has been possible

to elucidate the creep mechanism for a particular material by comparing its ex-

perimentalnvalue with values predicted for the various mechanisms. In addition,

correlations have been made between the activation energy for creep (Qc) and the

activation energy for diffusion (Qd, Equation 6.8).

Creep data of this nature are represented pictorially for some well studied sys-

tems in the form of stress–temperature diagrams, which are termeddeformation

mechanism maps. These maps indicate stress–temperature regimes (or areas) over

which various mechanisms operate. Constant strain rate contours are often also in-

cluded. Thus, for some creep situation, given the appropriate deformation mechanism

map and any two of the three parameters—temperature, stress level, and creep strain

rate—the third parameter may be determined.

9.17 DATA EXTRAPOLATION METHODS

The need often arises for engineering creep data that are impractical to collect from

normal laboratory tests. This is especially true for prolonged exposures (on the or-

der of years). One solution to this problem involves performing creep and/or creep