Subsequently, flow curves were simulated using the just described procedure. Figure 4.10b displays the comparison between an experimental flow curve of alloy 800H deformed at 1100◦C with a strain rate of 10−2 (gray curve) and a corresponding simulated curve (black curve) that only contained the extensions of section 4.2.1, i.e. the reduction of the fraction of cell walls, and the reduction of the dislocation densities after the onset of mobility. The simulated flow curve shows good conformity to the experimental curve up to the peak stress. The corresponding curves of the fraction of cell walls and different dislocation densities are given in figure 4.11. Figure 4.11a shows that the incorporation of equation 4.24 results in a linear decrease of the fraction of cell walls (dotdashed curve). From figure 4.11b - d it is evident that the incorporation of the mobility only leads to a noticeable decrease of the dislocation density in the cell interior which is causative for the decrease of the flow curve beyond the peak.
The integration of equation 4.29 in the model which introduces the adjustment of the grain size to the steady-state value gives rise to the damped decrease of the flow curve to the steady- state flow stress as displayed in figure 4.12a. The effect of equation 4.29 is also noticeable in the change of the fraction of cell walls and the dislocation densities in figure 4.11 (solid curves). The cell wall fraction decreases asymptotically to an almost steady-state value and the dislocation densities exhibit a maximum approximately at the same strain value as the maximum of the flow curve and a subsequent steady-state.
Figure 4.10.: a) Representation of the simulated flow curve (black curve) after the fitting process in com- parison to the experimental curve of alloy 800H deformed at 1100◦C with a strain rate of 10−2 (gray curve); b) Illustration of the incorporation of the decrease of the cell wall fraction and of mobile subboundaries
Furthermore, the point of inflection in the curve of the hardening rate, which describes the onset of dynamic recrystallization by Poliak and Jonas [9], was calculated for the simulated flow curve and compared to the experimental curve, illustrated in figure 4.12b. The critical flow stresses at the inflection points of both curves are indicated. The value of the simulated curve is about 5 MPa lower than the experimental which fits to the slightly lower flow curve in the simulation in figure 4.12a. Additionally, the hardening curve and corresponding saturation stress of the initial
Figure 4.11.: Illustration of the impact of the changes within the model on a) the fraction of cell walls fw(θ), b) the dislocation density of the mobile dislocations ρm, c) the dislocation density
in the cell interior ρi , and d) the dislocation density in the cell walls ρw; the dashed line
represents the simulation using the inital model, the dotdashed line the simulation after incorporating the reduction of the cell wall fraction and dislocation densities, and the solid line the simulation using the model with all extensions
work hardening curve (see figure 4.10a) are displayed as the dashed line. It can be seen that the extension of the model leads to the steep decrease in stage V that is characteristic for the onset of dynamic recrystallization.
Figure 4.12a showed only the results of one fitted flow curve. However, the extended model should also be able to simulate flow curves under different conditions simultaneously. This is illustrated in figure 4.13 for concurrent simulations for different strain rates and temperatures. The deviation between experimental and simulated flow curves increased compared to the single curve fitting. Nonetheless, the characteristic shapes of the flow curves with single peak behavior are well captured.
The discussion on the quality of the model extensions and the usability of the new model is given in the following chapter.
CHAPTER 4. SIMULATION OF DYNAMIC RECRYSTALLIZATION
Figure 4.12.: a) Representation of the experimental (gray) and simulated (black) flow curve after the incorporation of the extensions explained in section 4.2.2; b) Comparison of critical flow stresses in the derived dependencies of the hardening rate with stress for the simulated (black) and experimental (gray) flow curve determined by the Poliak-Jonas criterion [9] together with the corresponding saturation stress of the initial work hardening curve
Figure 4.13.: Results of the simulations under different parameter: a) modeling of flow curves with dif- ferent strain rates at the same temperature b) modeling of flow curves with the same strain rate at different temperatures; full lines represent the simulated curves, dashed lines the experimental curves
The process of dynamic recrystallization can be divided in three characteristic stages as men- tioned in chapter 2.2.2: onset, transient and steady-state regime, illustrated in figure 5.1. The onset is defined as the stage from the deformation start to the initiation of dynamic recrystal- lization including all occurring substructure changes. The transient stage describes the process of consumption of the initial grains and comprises the single or multiple peak area of the flow curve until the beginning of the steady-state which is characterized by the constant flow stress and grain size.
Figure 5.1.: Stages of the process of dynamic recrystallization which are discussed in the following sections
The evaluations of the conducted experiments and simulations are arranged to the respective stages of the process which are presented in different sections below. Finally, a coherent model to describe dynamic recrystallization will be drawn from the evaluated results in chapter 6. However, the first section is concerned with the reliability of the results.