Abstract
An equation for dislocation density during creep was introduced for martensitic heat-resistant steel using Orowan’s equation and a thermal activation equation of Kauzmann type based on several assumptions. The dislocation density discussed here corresponds to the number of dislocations swept out of an imaginary deformable domain in an activated state and is not the so-called mobile dislocation density. The one adjustable parameter, the actual deformable domain size, was adopted in the equation as a size intermediate of the lath martensite and packet. The activation energy and volume, and , were calculated using creep curves for 9Cr-1W tempered martensitic steel as a function of creep strain. The changes in the dislocation density during creep were estimated nondestructively to be roughly to using the values of and . The obtained densities were approximately comparable to the values of total dislocation density reported for directly observed ferritic/martensitic steels. It was found that the dislocation density of 9Cr-1W steel initially increased and then decreased in a transition creep range, which relate to hardening and recovery, respectively. This point of inversion from hardening to recovery can be confirmed easily and nondestructively far before the time to minimum creep rate and as a matter of course the time to rupture. It is suggested that monitoring of the dislocation density can predict the unexpected decrease in long-term rupture strength in advance.
Highlights
It is well known that continuous recovery occurs during the creep of high-strength martensitic steel (Abe, Nakazawa, Araki & Noda, 1992; Sawada, Maruyama, Komine, & Nagae, 1997), except in cases of work hardening immediately after high-stress loading (Cottrell, 1997; Kimura, Sawada, Kubo, & Kushima, 2004) or precipitation hardening within specified conditions (Abe, 2005)
The minimum creep rate (MCR) approach is not so realistic for two reasons: first, it requires both advanced instrumentation and facilities, because the MCRs are very low, below 10−5 h−1 for a creep test at stress levels near the 105-h rupture strength, and second, it still requires a long time before the MCR can be determined, because the time to the MCR for martensitic steel is approximately 25% of the time to rupture of 105 h, at least. (Abe, 2003; Abe, 2011)
1) An equation for the dislocation density is introduced by making several assumptions and using one variable, as an adjustable parameter
Summary
It is well known that continuous recovery occurs during the creep of high-strength martensitic steel (Abe, Nakazawa, Araki & Noda, 1992; Sawada, Maruyama, Komine, & Nagae, 1997), except in cases of work hardening immediately after high-stress loading (Cottrell, 1997; Kimura, Sawada, Kubo, & Kushima, 2004) or precipitation hardening within specified conditions (Abe, 2005). More than 10 years passed following the development of high-strength steels before it was clarified that the longterm rupture strengths of some of the steels tended to lower unexpectedly (Kushima, Kimura, & Abe, 1999; Tamura, 2015). It requires a very long time and much effort to investigate metallurgically the recovery behavior during the creep of these steels. It is proposed to study how to predict within a short time the decrease in long-term rupture strength by analyzing creep curves at stress levels near the 105-h rupture strength. Zener (1952) expressed the rate, , at which an atom moves to an adjacent lattice point as
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