13th International Conference on Fracture June 16–21, 2013, Beijing, China -8considered to be related with the precipitation which occurs via the pipe diffusion of substitutional solute atoms. In this case it is considered that the segregation of the solute atoms at dislocations precedes the precipitation at the initial stage of aging. It is well known that the misfit parameters of solute atoms in atomic size and modulus determine the magnitude of the elastic interaction of the solute atoms with dislocations. The analysis of the hardness data of ferrous alloys measured by Stephans and Witzke [16] indicate that Mo atoms have the second largest interaction with dislocations, which is comparable to that of Ti atoms [15]. From the thermodynamical viewpoint, the degree of supersaturation of solute atoms is another significant factor which enhances the segregation at dislocations. According to the phase diagrams of Fe-Mo alloy [17] and Fe-Ti alloy [18], the solubility of Ti and Mo decreases rapidly as the temperature is lowered below 773 K. It is expected that more excess Mo atoms are present during the second-step-aging or the fatigue tests at 473 K and 673 K than Ti atoms, since the content of Mo is much larger than that of Ti in the maraging steels used here. Thus such excess Mo atoms play a predominant role in interacting with dislocations at these temperatures. One can see from Fig. 3 that under-aging state accelerates the increase in hardness due to the following second-step-aging. Since the degree of supersaturation of solute atoms is expected to be larger in the under-aging state, the driving force for the segregation increases. According to Nitta et al. [19] the coefficient of lattice diffusion of Mo in Fe is given by DMo = 0.0148exp(−282.6 kJ/mol/RT) m2/s. The diffusion coefficient at 473 K is too small to explain the static and dynamic agings observed at this temperature. The present results rather indicate that the pipe diffusion of solute atoms is attributable to the static aging, as mentioned in section 3.2. It is considered that Mo atoms very close to dislocations migrate to the dislocations with the assistance of their elastic interaction and then diffuse along the dislocations. The stress-induced migration followed by pipe diffusion may serve effectively at 473 K. Thus the evaluated values of Qd are considered to involve the contribution of stress-induced diffusion of solute atoms close to dislocations. Recently Christien et al. [20] have shown by using neutron diffraction that the dislocation density of 4 x 1015 /m2 are generated during martensitic transformation of 17-4PH steel and it is kept nearly constant with increasing aging temperature up to 773 K. The dislocation density measured by them agrees well with 7 x 1015 /m2 in Fe-18mass%Ni evaluated by Nakashima et al [3]. Nakashima et al. also reported that the dislocation density was lowered to 4 x 1015 /m2 by plastic deformation. Assuming that these results are applicable to the maraging steels investigated here, the mean spacing of dislocations becomes about 16 nm and the stress level between dislocations is 1 GPa. It is therefore considered that such high dislocation density enables the stress-induced and pipe diffusions of solute atoms to operate effectively at low temperatures. The present results clearly show that hardness is a good measure to get insight into the microstructural change with aging time or testing temperature. Viswanathan et al. [21] measured the Rockwell hardness (HRC) of 350G maraging steel aged at temperatures from 673 K to 823 K for various time. In order to compare their result with the present Vickers hardness data, the Rockwell hardness measured by Viswanathan et al. is converted into the Vickers hardness in GPa by using the hardness conversion table for steels given in ASTM E140-7. Fig. 10 shows the aging time-temperature-hardness (TTH) diagram deduced from the converted Vickers hardness data. The TTH curves have a nose-shape which is oriented toward higher temperature at shorter time. This indicates the general tendency of aging in which the nucleation and growth of precipitates proceed from the supersaturation of solute atoms to the peak aging and then decomposition and coarsening take place. It should be noted that the hardness increases to its maximum value at 673 K and 1000 ks, as the temperature is lowered. Tewari et al. [22] proposed a time-temperature-transformation (TTT) diagram for 350G maraging steel which is shown by broken curves in Fig. 11. The TTT curves proposed by them are conceptual ones and do not present exact profiles. The overlapping of the TTT curves on the TTH contours, however, provides a general trend pertinent to the dependence of hardness on microstructure at temperatures of 673 K ~ 823 K over a wide range of aging time.
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