Page 313 - Materials Science and Engineering An Introduction

8.14 Data Extrapolation Methods • 285

terms drop out, which
If we subtract the second equation from the first, the ln K 1
yields the following:
ln(2.0 * 10 h ) - ln(3.65 h ) = (n)[ln(3 MPa) - ln(25 MPa)]
-1
-1
-4
And solving for n,
-1
-1
-4
ln(2.0 * 10 h ) - ln(3.65 h )
n = = 4.63
[ln(3 MPa) - ln(25 MPa)]
It is now possible to calculate K 1 by substitution of this value of n into either of the
preceding equations. Using the first one,
-4
-1
ln K 1 = ln(2.0 * 10 h ) - (4.63)ln(3 MPa)
= -13.60
Therefore,
K 1 = exp(- 13.60) = 1.24 * 10 -6

#
And, finally, we solve for P s at s 10 MPa by incorporation of these values of n and
K 1 into Equation 8.24:
# -6 4.63
n
P s = K 1 s = (1.24 * 10 )(10 MPa)
-2
= 5.3 * 10 h -1

Several theoretical mechanisms have been proposed to explain the creep behavior for
Tutorial Video: various materials; these mechanisms involve stress-induced vacancy diffusion, grain bound-
Creep Failure ary diffusion, dislocation motion, and grain boundary sliding. Each leads to a different value
How do I Interpret the of the stress exponent n in Equations 8.24 and 8.25. It has been possible to elucidate the
Creep Failure Graphs creep mechanism for a particular material by comparing its experimental n value with values
and Equations? predicted for the various mechanisms. In addition, correlations have been made between the
activation energy for creep (Q c ) and the activation energy for diffusion (Q d , Equation 5.8).
Creep data of this nature are represented pictorially for some well-studied systems
in the form of stress–temperature diagrams, which are termed deformation mechanism
maps. These maps indicate stress–temperature regimes (or areas) over which various
mechanisms operate. Constant-strain-rate contours are often also included. 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.

8.14 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 order of
years). One solution to this problem involves performing creep and/or creep rupture tests
at temperatures in excess of those required, for shorter time periods, and at a comparable
stress level, and then making a suitable extrapolation to the in-service condition. A com-
monly used extrapolation procedure employs the Larson–Miller parameter, m, defined as
The Larson–Miller
parameter—in terms m = T(C + log t r ) (8.27)
of temperature and
rupture lifetime