Abstract
Ninety-two sets of observed dislocation densities for crept specimens of 21 types of ferritic/martensitic and austenitic steels, Al, W, Mo, and Mg alloys, Cu, and Ti including germanium single crystals were collected to verify an equation for evaluating the dislocation density during steady-state creep proposed by Tamura and Abe (2015). The activation energy, Qex, activation volume, Vex, and Larson–Miller constant, Cex, were calculated from the creep data. Using these parameter constants, the strain rate, and the temperature dependence of the shear modulus, a correction term, Gamma, was back-calculated from the observed dislocation density for each material. Gamma is defined in the present paper as a function of the temperature dependences of both the shear modulus and pre-exponential factor of the strain rate. The values of Gamma range from −394 to 233 and average 2.1 KJmol-1, which is a value considerably lower than the average value of Qex (410.4 KJmol-1), and values of Gamma are mainly within the range from 0 to 50 KJmol-1. The change in Gibbs free energy, Delta G, for creep deformation is obtained using the calculated value of , and the empirical relation Delta G~Delta GD is found, where Delta GD is the change in Gibbs free energy for self-diffusion of the main componential element of each material. Experimental data confirm the validity of the evaluation equation for the dislocation density.
Highlights
The measurement of dislocation density has been recognized as a major step in clarifying deformation mechanisms (Dorn & Mote, 1964; Kassner, Ziaai-Moayyed, & Miller, 1985), because the dislocation density during deformation is closely related to deformation resistance (Taylor, 1934; Orowan, 1940)
We analyze the steady-state creep rates or the minimum creep rate (MCR) tested under uniaxial tensile creep stresses, but flow stresses due to tension or torsion under a constant strain rate are analyzed, if the flow rates are judged to be in a steady state
The instantaneous strain is generally small at sufficiently high temperatures, rather high stresses are applied at mid-range or low temperatures to detect observable MCRs, and as a result, many dislocations are introduced immediately after loading, which may affect the observed dislocation densities even in steady-state creep
Summary
The measurement of dislocation density has been recognized as a major step in clarifying deformation mechanisms (Dorn & Mote, 1964; Kassner, Ziaai-Moayyed, & Miller, 1985), because the dislocation density during deformation is closely related to deformation resistance (Taylor, 1934; Orowan, 1940). It is not unusual that the differences among the dislocation densities of the same specimen measured employing the different methods are more than an order of magnitude (Hayakawa et al, 2007a; Umezaki, Murata, Nomura, & Kubushiro, 2014; Roodposhti, Sarkar, Murty, & Scattergood, 2015). This suggests the importance of selecting an appropriate method for a given specimen and of considering the physical meanings of the observed values (Yoshinaga, Horita, & Kurishita, 1981; Pesicka, Kuzel, Dronhofer, & Eggeler, 2003). It is reasonable that 1.5E12 m is close to the observed dislocation densities of the crept ferrous materials in a steady state, as is seen in Figure 2 and Figures A6, A7, A8, and A10
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