Monkman-grant analysis of creep fracture in dispersion-strengthened and particulate-reinforced aluminum
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INTRODUCTION
THE Monkman–Grant relationship[1] relates the failure time tf to the minimum (or secondary) creep rate εz min as tf z εz mmin 5 C
[1]
where m and C are constants. For the metals and alloys originally evaluated by Monkman and Grant, the exponent m had values between 0.8 and 0.95, while the constant C varied between 3 and 20 (with tf and εz min expressed in units of hours and pct z h21, respectively) depending on the material system. A better fit for many materials can be obtained by introducing the failure strain ε f into Eq. [1].[2] The modified Monkman–Grant relationship then takes the form m' tf z εz min 5 C' εf
[2]
where m' is close to unity and C' is a temperature-independent constant. The modified Monkman–Grant relationship with m' 5 1 reflects that the mean creep rate εf /tf is linearly related to the minimum creep rate εz min. Another correlation has been observed to exist for many materials between the applied stress s and the Larson–Miller parameter P:[3] P 5 T z (K 1 log tf )
[3]
where K is about 20 when the failure time tf and the temperature T are expressed in units of hours and Kelvin, respectively.[4] Similarly, the applied stress can be correlated with the Orr-Sherby-Dorn parameter u:[5]
u 5 Q/(2.303 z R z T) 2 log tf
[4]
where Q is the activation energy and R is the gas constant.
D.C. DUNAND, Associate Professor, formerly with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, is with the Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208. B.Q. HAN, Postdoctoral Fellow, is with the Department of Materials Science and Engineering, Northwestern University. A.M. JANSEN, formerly Graduate Research Assistant, Department of Materials Science and Engineering, Massachusetts Institute of Technology, is Manager, Arthur D. Little Inc., Acorn Park, Cambridge, MA 02140 Manuscript submitted July 15, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
If the minimum strain rate is related to the stress through an exponential law, the Larson–Miller parameter (Eq. [3]) can be derived from the Monkman–Grant relationship (Eq. [1]) with m 5 1. Conversely, if minimum strain rate and stress are related through a power law, the Orr–Sherby– Dorn parameter (Eq. [4]) can be derived from the Monkman–Grant relationship with m 5 1.[6] The technological significance of the Monkman–Grant relationship is that once the constants C and m have been determined from a limited number of creep tests on a given material, the relationship can be used (1) to estimate the time to rupture of a long-time test as soon as the minimum creep rate is reached and (2) to check the reliability of individual creep-rupture tests. Similarly, once the constant K or Q is known for the Larson–Miller or Orr–Sherby–Dorn parameters, the failure time can be predicted based on the testing temperature and stress. However, because plots of stress vs Larson–Miller or Orr–Sherby–Dorn parameter often exhibit a pronounced curvature, these relat
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