Monkman–Grant Relation

In 1956 F. C. Monkman and N. J. Grant published, in the Proceedings of the ASTM, an observation of striking simplicity: multiply a creep specimen's minimum creep rate by its time to rupture and the product is roughly constant for a given alloy, no matter what combination of stress and temperature produced that creep rate. Write it as t_r·ε̇ₛ^m = C, with m close to 1, and it says that a metal creeping twice as fast lasts about half as long.

The physical reading, when m is exactly 1, is that C is the creep strain accumulated during the steady-state stage — a creep ductility. The alloy has a certain amount of creep deformation in it before it lets go, and it does not much matter how slowly it gets there. That is a strong statement, and the fact that it holds across a wide range of alloys and conditions is the reason the relation is still in use.

What makes it valuable in practice is that it needs no rupture test. The minimum creep rate appears in the secondary stage, which a few hundred hours of testing will reach, and from it the relation predicts a rupture life that would have taken years to measure. It is also directly useful as an acceptance criterion: name the life the component needs, invert the relation, and you have the maximum steady-state creep rate a specimen at service conditions is allowed to show. That is a measurable, checkable number, which a rupture life is not.

C is unit-bound, and its dimensions depend on m. Because m is not exactly 1, C carries units of time^(1−m), so its numerical value changes both with the exponent and with the time unit. This site works with rupture time in HOURS and creep rate in 1/HOUR, which is the convention nearly all the literature uses. A C fitted with the rate in reciprocal seconds differs by 3600^m — a factor of about three and a half thousand — and a C quoted without both its exponent and its time unit is not a number, it is a guess. Write all three down together.

Where the relation fails is instructive, because it fails in exactly one direction. It is blind to anything that changes the ductility rather than the rate. If a component's creep ductility is reduced by embrittlement — sigma phase, temper embrittlement, hydrogen, an aggressive environment attacking the surface, or the growth of grain-boundary cavities — then it will rupture at a strain well below C while its creep rate looks entirely normal. A component that fails at a fraction of the Monkman–Grant prediction has usually failed by a mechanism the creep rate never saw, and that is a genuinely common outcome in service, particularly in welds and heat-affected zones where the microstructure is not the parent metal's. The modified form due to Dobeš and Milička divides the constant by the rupture elongation, which improves the collapse when ductility varies between conditions, and it is worth using whenever the data allows.

Pair the relation with Norton's law and the pair does real work: Norton gives the creep rate from stress and temperature, Monkman–Grant turns that rate into a life, and Larson–Miller offers an independent check on the same life from a different direction. Where the two disagree, the difference is telling you something about which assumptions have broken.