Niobium and vanadium precipitates (nitrides and carbides) can inhibit the static recrystallization of austenite but this does not happen for Ti, which form nitrides at high temperatures. RPTT diagrams show the interaction between recrystallization and precipitation allowing study the strain induced precipitation kinetics and precipitate coarsening. Based on Dutta and Sellars's expression for the start of strain-induced precipitation in microalloyed steels, a new model has been constructed which takes into account the influence of variables such as microalloying element percentages, strain, temperature, strain rate and grain size. Recrystallization-Precipitation-Time-Temperature (RPTT) diagrams have been plotted thanks to a new experimental study carried out by means of hot torsion tests on approximately twenty microalloyed steels with different Nb, V and Ti contents. Mathematical analysis of the results recommends the modification of some parameters such as the supersaturation ratio (ks) and constant B, which is no longer a constant but a function of ks. The expressions are now more consistent and predict the Precipitation-Time-Temperature (PTT) curves with remarkable accuracy. The model for strain-induced precipitation kinetics is completed by means of Avrami's equation. Finally, the model constructed in isothermal testing conditions, it has been converted to continuous cooling conditions in order to apply it in hot rolling.
The type and amount of microalloying elements play an important role on the shape and the nature of precipitates. However, the impact of some elements that are not considered as authentic microalloying elements is usually underestimated, even though the influence of these elements on chemical composition, size and distribution of precipitates can be even stronger than that of microalloying. This is true for aluminium-killed, V/Nb-microalloyed steels, whose Al content is often higher than 0.020 mass %. VN particles and NbCN are finer than AlN and therefore they have a stronger contribution during hot rolling (Gómez
Crystallographic structure of AlN is hexagonal (h.c.p.). Nitrides and carbides of typical microalloying elements (Nb, V, Ti) have an f.c.c. crystallographic structure and frequently form precipitates which are semi-coherent with the austenitic (f.c.c) matrix. Lattice parameter is slightly higher than that of the austenite (Gladman,
When strain-induced precipitation starts in microalloyed steels, static recrystallization is inhibited for a certain time, normally until the end of precipitation, before proceeding until recrystallization is complete. It is well known that the static recrystallization of microalloyed steels is different before and after strain-induced precipitation. Before, all the elements are in solution and recrystallization kinetics occur in the same way as in low alloy steels, whereby the various alloying elements contribute to delaying recrystallization to a greater or lesser degree (Andrade
The most important reference to predict strain-induced precipitation nucleation as a function of hot deformation variables (strain, strain rate, temperature) is perhaps the expression given by Dutta and Sellars for a time corresponding to 5% of the precipitated volume
In the present work, a precipitation model based on the above is proposed, taking into account the influence of variables such as microalloying element percentages, strain, temperature, strain rate and grain size, and new parameters and relationships are established. New adjustments have been made and in particular the influence of the temperature has been reassessed thanks to the performance of new calculations based on experimental results and new thermodynamic considerations. Although the model will be presented in its entirety, the quantitative influence of the aforementioned variables will simply be summarized, since the model has been recently published in its full version (Medina
Nineteen steels were manufactured by Electroslag Remelting (ESR) in a laboratory unit capable of producing 30 kg ingots. The steels contained various combinations of carbon, nitrogen, and precipitate-forming elements such as V, Nb and Ti. Their compositions are listed in
Chemical composition (mass %), transformation critical temperature (Ar3, at 0.2 K s−1) and austenite grain size (Dγ) at reheating temperature (RT), being Xi=V, Nb, Ti%
Steel | C | Si | Mn | Al | Xi | N | Ar3, °C |
---|---|---|---|---|---|---|---|
V1 | 0.11 | 0.24 | 1.10 | 0.012 | V=0.043 | 0.0105 | 786 |
V2 | 0.12 | 0.24 | 1.10 | 0.012 | V=0.060 | 0.0123 | 782 |
V3 | 0.11 | 0.24 | 1.00 | 0.010 | V=0.093 | 0.0144 | 784 |
V4 | 0.21 | 0.20 | 1.10 | 0.009 | V=0.062 | 0.0134 | 768 |
V5 | 0.33 | 0.22 | 1.24 | 0.011 | V=0.076 | 0.0146 | 716 |
V6 | 0.35 | 0.21 | 1.23 | 0.008 | V=0.033 | 0.0121 | 715 |
V7 | 0.42 | 0.24 | 1.32 | 0.012 | V=0.075 | 0.0200 | 718 |
V8 | 0.37 | 0.24 | 1.42 | 0.012 | V=0.120 | 0.0190 | 721 |
TV1 | 0.55 | 0.29 | 1.06 | 0.000 | V=0.063 Ti=0.019 | 0.0174 | 693 |
TV2 | 0.34 | 0.22 | 1.08 | 0.009 | V=0.055 Ti=0.024 | 0.0182 | 718 |
N1 | 0.11 | 0.24 | 1.23 | 0.002 | Nb=0.041 | 0.0112 | 786 |
N2 | 0.11 | 0.24 | 1.32 | 0.002 | Nb=0.093 | 0.0119 | 786 |
N3 | 0.21 | 0.18 | 1.08 | 0.007 | Nb=0.024 | 0.0058 | 768 |
N4 | 0.21 | 0.19 | 1.14 | 0.008 | Nb=0.058 | 0.0061 | 769 |
N5 | 0.51 | 0.25 | 1.20 | 0.008 | Nb=0.026 | 0.0105 | 674 |
N7 | 0.29 | 0.22 | 1.30 | 0.006 | Nb=0.066 | 0.0062 | 751 |
N8 | 0.20 | 0.20 | 1.0 | 0.006 | Nb=0.007 | 0.0056 | 770 |
N9 | 0.46 | 0.24 | 1.25 | 0.011 | Nb=0.009 | 0.0100 | 704 |
TN1 | 0.21 | 0.22 | 1.18 | 0.007 | Nb=0.028 Ti=0.024 | 0.0060 | 768 |
Torsions specimens were prepared with a gauge length of 50 mm and a diameter of 6 mm. The reheating temperature before torsion deformation varied according to whether the steel was microalloyed with V or Nb, as the solubility temperature of the precipitates depends on their nature and on the precipitate-forming element content. The parameters of torsion (torque, number of revolutions) and the equivalent parameters of tension (stress, strain) were related according to Von Mises criterion (Faessel,
For steels containing vanadium, designated by the letter V, the reheating temperature was 1230 °C for steels V1, V2 and V3 and 1200 °C for the rest, which is sufficient to dissolve vanadium nitrides and carbides. In the case of niobium steels, designated by the letter N, the reheating temperature depended on the carbon, niobium and nitrogen contents, but was always above the solubility temperature of niobium carbonitrides (Turkdogan,
In all cases the testing temperatures (1150–850 °C) were set as the recrystallized fraction was determined and the recrystallized fraction curves drawn, so that the curves finally obtained would include curves where strain-induced precipitation had taken place and curves where it had not, as is discussed below. The recrystallized fraction (
The recrystallized fraction, determined by applying the back extrapolation method, was drawn against time for each testing temperature. The shape of the recrystallized fraction versus time curves were similar for all the V microalloyed steels, it being observed that some curves display a plateau caused by the formation of precipitates which momentarily inhibit the progress of recrystallization (
Variation of recrystallized fraction (Xa) with time (t) for steel V4.
The Nb microalloyed steels showed varying behaviour. Some presented a similar plateau to the V steels as in the case of steels N1, N2, N3, N8 and N9. An example of which is shown for steel N8 in
Variation of recrystallized fraction (Xa) with time (t) for steel N8.
The recrystallized fraction versus time curves were used to plot Recrystallization-Precipitation-Time-Temperature (RPTT) diagrams. The points defining the start and the end of the plateau were taken to plot the curves for the start (Ps) and the end (Pf) of precipitation, respectively.
RPTT diagram for steel V4.
RPTT diagram for steel N8.
At the moment when precipitation starts, whatever the temperature (Ps curve), it is assumed that the precipitated fraction corresponds to a value of 5%. In the same way, when the Pf curve is reached, the precipitated volume is close to 95%. Once the Pf curve has been reached, recrystallization starts to progress again due to fact that the pinning forces exerted by the precipitates are lower than the driving forces for recrystallization.
The RPTT diagrams, and especially the Ps and Pf curves, define a time interval, whatever the temperature, during which the precipitation state (size and precipitated volume) is changing. For times after Pf, the precipitated fraction does not vary but a coarsening of the precipitates occurs due to the effect of Ostwald ripening (Medina
In microalloyed steels several types of precipitates depending if the steel contains vanadium, niobium or titanium, can be seen. The precipitates are generally VN, NbCN, TiN and AlN, respectively. When the steel contains more than one microalloying element, formation of mixed precipitates is possible.
The TEM resolution of vanadium nitrides corresponding to steel V4 was obtained on strained and quenched specimens at a time close to the start of the plateau. The carbon extraction replica technique was used. The electron energy dispersive X-Ray spectrum showed the presence of V and electron diffraction revealed a f.c.c. cubic lattice with a value of a=0.415 nm, in accordance with the reference value found in the literature which is identified as vanadium nitride (
Transmission Electron Microscope (TEM) images of steel used: (a) image showing precipitates for specimen tested at reheating temp.=1100 °C; deformation temperature =850 °C, ɛ=0.35,
Transmission Electron Microscope (TEM) images of steel N4: (a) image showing precipitates for specimen tested at 1025 °C, ɛ=0.35,
The start of the plateau is identified with the start of precipitation and its duration is related with two phenomena that take place simultaneously; namely increases in the precipitated volume and in the size of precipitates. Particle growth occurs by accretion of successive shells of nitrides or carbonitrides and each shell has its specific composition (Maugis and Gouné,
Dutta, Valdes and Sellars (Dutta
The evolution of the precipitate size was studied from the start of the plateau until after its end and the size distributions have served to confirm that the end of the plateau is due to the coarsening of precipitates and consequently to a decrease in pinning forces (Quispe
Precipitates TiN and AlN are of relatively large size and its impact on the recrystallization is very weak due to the large size of these precipitates. TiN precipitates are formed when the steel contains Ti and it takes place at high temperatures. AlN precipitates may form when the steel contains Al as a remain of deoxidation or the percentage of microalloying elements (V, Nb, Ti) are relatively small leaving free nitrogen that could be combined with Al (Medina
In order to find the influence of every deformation variable, namely the strain (ɛ), strain rate (
The value of β was calculated plotting
Plot of
where,
If the steels contained both Nb and V, the parameter
The activation energy (
The activation energy for bulk diffusivity ( Nb-steels: V-steels:
According to Turkdogan, the supersaturation ratio defined by
Nb-Steels:
V-Steels:
The next expression is deduced (Medina
where,
The expressions for
V-Steels:
Nb-Steels:
The next expressions were found (Medina
V-Steels: Δ
Nb-Steels: Δ
V-Ti; Nb-Ti Steels: Δ
In the case of V-steels,
The parameter
Coefficient
V-Steels:
Nb-Steels:
V-Ti and Nb-Ti Steels:
The
Experimental versus calculated parameter
As occurs in other physical phenomena, where a nucleation time is necessary for the phenomenon to start, precipitation obeys Avrami's law and the precipitated fraction can be expressed in the following way (Maugis and Gouné,
where
If in
Expression (17) can be used to determine the value of
V and V-Ti Steels:
Nb and Nb-Ti Steels:
Expressions (18) and (19) indicate that strain-induced precipitation obeys Avrami's law, as in both cases the exponent of parameter
By comparing Eqs. (
V and V-Ti Steels:
By replacing
Experimental and calculated Ps and Pf curves for steel V8.
From
Some examples on the precipitated fraction against the time for isothermal conditions and for cooling conditions are showed in
Precipitated fraction (Xp) against time. Isothermal and cooling conditions. Steel V5. (T=1150 K).
Precipitated fraction (Xp) against time. Isothermal and cooling conditions. Steel V5. (T=1113 K).
A new model for strain-induced precipitation in microalloyed steels has been constructed. At greater strains, the times for the incubation of the precipitates and for complete precipitation are smaller. For larger austenite grain sizes, the times for incubation of the precipitates and complete precipitation are also longer. The model on precipitation kinetics was constructed in isothermal conditions and converted at cooling rate conditions applying the method known as “compensated times”. The cooling conditions could avoid that the precipitation was completed. The incubation time ( The parameter Strain-induced precipitation kinetics obey Avrami's law, where the time necessary for precipitation to finalize (