[1]
Where σm is the maximum stress of the 1st curve and σ0 and σr the yield strength of the 1st and 2nd curves, respectively. Fractional softening data can be fitted to an Avrami type curve, whose main parameters are the t0.5srx (time for 50% fractional softening) and n (Avrami exponent). Fig. 4. Stress-Strain curves corresponding to control test heating conditions and estimated fractional softening. The softening curves obtained after the different heating cycles are shown in Fig. 5. From these curves, the recrystallization time and the Avrami exponent were determined and the resulting values are indicated in Table 2. It can be observed that for e=0.25 the softening kinetics is quite fast and it is difficult to calibrate the differences from the curves. Therefore, in the most critical cases, the tests were repeated for a lower deformation level of e=0.15. It can be observed that at these conditions the fastest softening kinetics is determined for the cold charging condition at 1000ºC, which is expected since in this condition the initial grain size is the smallest, and the amount of precipitates the largest (less Nb in solid solution). However, the low Avrami exponent determined from this curve (see table) suggests that some interaction between the softening and the small precipitates observed in the replicas could be taking place. In the rest of the cases, the differences are not so apparent. Fig. 5. Softening curves obtained after different heating conditions. Dissolution calculations As mentioned before, Nb in solid solution can delay the static recrystallization kinetics of austenite during hot working. Based on that, the degree of dissolution of Nb can be indirectly estimated from its effect on the static recrystallization time (t0.5srx). The following expression quantifies the relationship between the amount of Nb in solid solution and the time t0.5srx [4]:.
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[2]
where Do is the initial austenite grain size, e is the strain, is the strain rate, T the deformation temperature and [Nb] the amount of Nb in solid solution (wt%). Table 2. Recrystallization times and Avrami exponent values determined from the fractional softening curves of Fig. 5. Condition D0 (mm) e t0.5srx (s) n Control Test 182±13 0.25 4.2 1.2 Hot charging 825ºC-1000ºC 232±14 0.25 2.7 2.1 Hot charging 825ºC-1100ºC 259±30 0.25 5.2 1.8 0.15 10.7 1 Hot charging 1000ºC-1100ºC 240±18 0.25 7.2 1.6 Cold charging 1000ºC 22±1 0.25 0.6 0.5 Cold charging 1100ºC 73±5 0.25 4.6 1.3 0.15 12.4 1 The amount of Nb in solution can be modified during the prior reheating cycle and the recrystallization time in each case can be experimentally quantified. Fig. 6 illustrates schematically the proposed procedure. As a first step, a reheating condition (T1) is selected to assure that all the niobium is in solid solution (Control test in the present case), that is Nb1 = Nb content of the steel and the corresponding t0.5srx time determined (t1). Then, another reheating temperature is considered, T2, that will lead to another t0.5srx value (t2). Taking Eq. 2, the amount of Nb in solid solution at this condition, Nb2, can be determined as follows:.
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[3]
Fig. 6. Scheme of Avrami curves corresponding to different amount of Nb in solution. From the experimental recrystallization times shown in Table 2 and, applying Eq. 3, the amount of Nb present in solution after the different heating cycles has been calculated. The results have been represented as a function of heating temperature in Fig. 7, where the dissolution curve predicted by Irvine's solubility product equation for Nb (C,N) (Log[Nb][C+12/14N]=2.26-6770/T) [[] K.J. Irvine, F.B. Pickering and T. Gladman, ISIJ (1967), 161. ] for this steel is also drawn (dashed line). Additionally, some experimental data obtained after cold charging laboratory simulations performed with another steel of similar composition (0.24C – 1.25Mn – 0.03Nb – 56 ppm N) have been included in the figure for comparison (black squares)[[] Internal report ]. It should be noted the good agreement between experimental values of dissolved Nb and Irvine's solubility curve. Regarding the present results, for Hot charging 1000ºC-1100ºC, all the Nb is predicted to be in solid solution, in good agreement with the replica analysis results where nearly no particles were found. On the other hand, for hot charging at lower temperature (825ºC), partial dissolution was estimated at both 1000 and 1100ºC heating temperatures. For cold charging 1000ºC, no Nb in solid solution is calculated. This agrees with the large amount of precipitates detected in the replicas. However, the low Avrami exponent of the curve at these conditions suggests that the precipitates could be also exerting some retardation on the softening. This would lead to an underestimation of the amount of Nb in solid solution calculated using this method. For cold charging 1100ºC, the values calculated using either deformation values seem unreliable. At this condition, partial dissolution would be expected, in line with that observed for the steel of Ref. 9 with similar composition. It should be noted that at this condition the highest austenite microstructure heterogeneity was observed, with some areas where the grain size was significantly coarser than the measured mean value of 73 mm. This heterogeneity can be related with an heterogeneous dissolution of Nb(C, N) particles in the matrix. In areas where particles dissolve, grain growth can take place easier. It is expected that in these special situations the calculations may be more complicated. The results clearly indicate that in hot charging situation more Nb can remain in solution than that corresponding to cold charging at similar heating conditions. Fig. 7. Calculated amount of Nb in solid solution plotted against the heating temperature. Conclusions In this work, the dissolution behavior of Nb under different heating cycles applied before deformation has been investigated. Cold and hot charging conditions, using different heating temperatures have been analyzed. It has been observed that for a given heating temperature, in hot charging, there is more Nb in solution at the entry of the rolling mill than that corresponding to cold charging. The amount of Nb in solution depends on both charging temperature and reheating condition, but the results denoted that it can be higher than that predicted by equilibrium calculations. Acknowledgments Part of the results present in this work have been obtained under the frame of a Project funded by CBMM. References.
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