There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A review of dynamic recrystallization phenomena in metallic materials

The Avrami kinetics of dynamic recrystallization

Thermomechanical processing of advanced high strength steels

In order to improve the understanding of the dynamic and post-dynamic recrystallization behaviours of AISI 304 austenitic stainless steel, a series of hot torsion test have been performed under a range of deformation conditions. The mechanical and microstructural features of dynamic recrystallization (DRX) were characterized to compare and contrast them with those of the post-dynamic recrystallization. A necklace type of dynamically recrystallized microstructure was observed during hot deformation at 900 °C and at a strain rate of 0.01 s−1. Following deformation, the dependency of time for 50% recrystallization, t50, changed from “strain dependent” to “strain independent” at a transition strain (ɛ*), which is significantly beyond the peak. This transition strain was clearly linked to the strain for 50% dynamic recrystallization during deformation. The interrelations between the fraction of dynamically recrystallized microstructure, the evolution of post-dynamically recrystallized microstructure and the final grain size have been established. The results also showed an important role of grain growth on softening of deformed austenite.

Recrystallization in AISI 304 austenitic stainless steel during and after hot deformation

The dynamic recrystallization (DRX) behavior of Nb and Nb–Ti microalloyed steels has been investigated. It has been observed that the initial austenite grain size, the amount of microalloying elements in solid solution, and the deformation conditions (temperature and strain rate), affect dynamic recrystallization kinetics. To characterize the dynamic recrystallization behavior of the microalloyed austenite, continuous torsion tests were carried out after reheating the specimens at different temperatures between 1000 and 1420 °C, leading to a wide range of initial grain sizes, from 16 to 805 μm. It has been observed that decreasing the values of the Zener–Hollomon parameter and the initial grain size, promotes dynamic recrystallization. Microalloying elements in solid solution produce a retardation of dynamic recrystallization, resulting in higher values of the characteristic critical, e c , and peak, e p , strains. A corrective factor has been applied to quantify the retardation produced by the increase in the amount of Nb and Ti dissolved as the reheating temperature increases. In this manner, it has been possible to propose a unique relationship to predict the e p peak strain for both steels.

Dynamic recrystallization behavior covering a wide austenite grain size range in Nb and Nb–Ti microalloyed steels

Deformation dilatometry has been used to simulate controlled hot rolling followed by cooling of a Nb–V low carbon steel, looking for conditions corresponding to wide austenite grain size distributions prior to transformation. Recrystallization and non-recrystallization deformation schedules were applied, followed by controlled cooling at rates from 0.1 °C/s to about 200 °C/s, and the corresponding continuous cooling transformation (CCT) diagrams were constructed. The resultant microstructures ranged from polygonal ferrite (PF) and pearlite (P) at slow cooling rates to bainitic ferrite (BF) accompanied by martensite (M) for fast cooling rates. Plastic deformation of the parent austenite accelerated both ferrite and bainite transformations, displacing the CCT curve to higher temperatures and shorter times. However, it was found that the accelerating effect of strain on bainite transformation weakened as the cooling rate diminished and the polygonal ferrite formation was enhanced. Moreover, it was found that plastic deformation had different effects on the refinement of the microstructure, depending on the cooling rate. An analysis of the microstructural heterogeneities that can impair toughness behavior has been done.

Effect of austenite microstructure and cooling rate on transformation characteristics in a low carbon Nb–V microalloyed steel

The recrystallization behaviour of a Nb microalloyed steel, under deformation conditions corresponding to the initial stands of a thin slab hot rolling process which is characterized by coarse initial austenite grain sizes and large strains per pass, has been investigated. A range of strain levels were studied ranging from below the critical strain for the onset of dynamic recrystallization, e c , well into the steady state for dynamic recrystallization, e > e ss . There is a transition strain, e c e T e ss , separating the post-dynamic softening strain-dependent range from that which is strain-independent. At strains above e T , the kinetics of recrystallization is independent of strain but strongly dependent on strain rate. Under these conditions, metadynamic recrystallization operates as the prime softening mechanism and the kinetics have been derived. At strains between e c and e T , both metadynamic and classical static recrystallization are involved in post-dynamic softening. A model is derived to predict the evolution of softening as a function of the holding time for different strain ranges, based on the contributions of the individual components to the overall softening.

Transition between static and metadynamic recrystallization kinetics in coarse Nb microalloyed austenite

The static recrystallization kinetics of four steels microalloyed with Nb, Ti and Nb-Ti have been investigated, covering conventional and hot direct rolling conditions. The influence of the grain size on the recrystallization time has been studied for a wide range of grain sizes (20-1000 μm). For the same deformation conditions it has been observed that the quadratic dependence on grain size works well in the range of finer grain sizes (< 160 μm). In contrast, the recrystallization times measured at coarse grain sizes are significantly lower than those predicted by this dependence. However, when the whole grain size range analysed is considered, a linear dependence on grain size gives the best fit to experimental data. The effect of strain on the recrystallization kinetics has been also analysed for different initial grain sizes. It has been observed that the time to reach a 50% recrystallized fraction (t 0.5 ) shows a dependence on strain of the type t 0.5 e -p . the exponent being influenced by the initial grain size. A unique equation has been proposed to describe the static recrystallization kinetics of Nb, Ti and Nb-Ti microalloyed steels. The predictions of the equations have been compared to previously published data on similar steels.

Static recrystallization behaviour of a wide range of austenite grain sizes in microalloyed steels

A mathematical model has been developed to predict the austenite microstructure evolution of Nb microalloyed steels during “Thin slab casting” and “Hot direct rolling” (TSDR) processing. The model is based on empirical equations specifically derived for the microstructural and processing features typical in these new technologies. Its main novelty is that it works with austenite grain size distributions instead of the typical mean values as used in conventional models to represent the microstructure. This fact is particularly important in working with as-cast austenite due to the wide range of grain sizes present in this microstructure. In the model the different softening and hardening mechanisms that can operate during hot working in austenite are considered: static, dynamic and metadynamic recrystallization, grain growth after recrystallization and Nb(C, N) strain induced precipitation. The model uses the initial austenite grain size distribution as input and provides the size distribution of recrystallized and unrecrystallized grains at the entry of any rolling pass. A validation of the model has been carried out in the laboratory by multipass torsion tests. The model is capable of predicting any heterogeneities that may appear in the final microstructure after this kind of processing and that are not well predicted by using conventional models based on mean values. Additionally, it can calculate the deformation history, in terms of the strain accumulated in the austenite, and stress behavior, in terms of the mean flow stress (MFS) corresponding to each deformation pass.

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Pello Uranga

Papers

Dynamic recrystallization behavior covering a wide austenite grain size range in Nb and Nb–Ti microalloyed steels

Effect of austenite microstructure and cooling rate on transformation characteristics in a low carbon Nb–V microalloyed steel

Transition between static and metadynamic recrystallization kinetics in coarse Nb microalloyed austenite

Static recrystallization behaviour of a wide range of austenite grain sizes in microalloyed steels

Modeling of Austenite Grain Size Distribution in Nb Microalloyed Steels Processed by Thin Slab Casting and Direct Rolling (TSDR) Route