Introduction
Experiments
Procedure
Steel | C | Mn | Si | Cr | P | S |
---|---|---|---|---|---|---|
A | 0.09 | 1.42 | 0.1 | 0.35 | 0.011 | 0.01 |
B | 0.15 | 1.5 | 0.4 | 0.2 | 0.01 | 0.01 |
Test | Heating | Cooling | Microstructure | ||
---|---|---|---|---|---|
Temperature, °C | Time, s | Temperature, °C | Time, s | ||
1 | 780 | 60 | 20 | Water | F + B + M |
2 | 810 | 1200 | 20 | Water | F + B + M |
3 | 810 | 0 | 20 | Water | F + B + M |
4 | 810 | 10 | 20 | Water | F + B + M |
5 | 810 | 10 | 710-20 | Water | F + B + M |
6 | 810 | 10 | 450 | 1200 | F + B |
Results
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Cycle 1 (Fig. 3): Microstructure is composed of ferrite (75%) with the grain size of 5.8 μm and hard constituents. The latter are in the form of grains containing bainite and martensite of the average size of 5.3 μm.
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Cycle 2 (Fig. 4): As in cycle 1, the microstructure is composed of ferrite (72%) and hard constituents in the form of complex grains containing bainite and martensite. Volume fraction of bainite is larger than in cycle 1. This is due to increase of austenite volume fraction and decrease of carbon content in this phase after long time at 810 °C.
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Cycle 3 (Fig. 5): The sample was heated to 810 °C, held for 10 s and then quenched right after this temperature was reached. The microstructure contained 75% of ferrite with the grain size of 4.0 μm and hard constituents bainite and martensite. Volume fractions of these two phases were similar and the average size was 5.3 μm.
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Cycle 4 (Fig. 6): The sample was maintained at 810 °C for 10 s. The microstructure is similar to the sample after cycle 3. Volume fraction of ferrite was 73% with the grain size of 5.3 μm.
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Cycle 5 (Fig. 7): After maintaining the sample at 810 °C for 10 s, it was subjected to two step cooling, slow and fast. During slow cooling austenite was transformed into ferrite and carbon content in austenite increased. In consequence martensite was the main hard constituent. Small amount of bainite was observed, as well. Volume fraction of ferrite was 74% with the grain size of 6.2 μm.
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Cycle 6 (Fig. 8): After maintaining at 810 °C for 10 s the sample was cooled to 450 °C and maintained at that temperature for 1200 s. At the beginning of cooling about 50% of ferrite remained in the microstructure. The total volume fraction of ferrite after cooling was 80%. The whole remaining austenite was transformed into bainite. Coagulation of the cementite particles followed.
Models
Basic Equations
\(X = 1 - \exp ( - kt^{n} )\) (1) |
\(k_{\text{f}} = \frac{{a_{5} }}{{D_{\upgamma } }}\exp \left[ { - \left( {\frac{{T - A_{{{\text{e}}3}} - \frac{400}{{D_{\upgamma } }} + a_{6} }}{{a_{7} }}} \right)^{{a_{8} }} } \right]\)
\(k_{\text{b}} = a_{23} \exp \left( {a_{22} - 0.01a_{21} T} \right)\)
|
\(\uptau_{\text{P}} = \frac{{a_{9} }}{{\left( {A_{{{\text{e}}1}} - T} \right)^{{a_{11} }} }}\exp \left[ {\frac{{a_{10} }}{R(T + 273)}} \right]\)
|
\(\uptau_{\text{b}} = \frac{{a_{17} }}{{\left( {B_{\text{s}} - T} \right)^{{a_{19} }} }}\exp \left[ {\frac{{a_{18} }}{R(T + 273)}} \right]\)
|
\(B_{\text{s}} = a_{20} - 425[{\text{C}}] - 42.5[{\text{Mn}}] - 31.5[{\text{Ni}}]\)
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\(M_{\text{s}} = a_{26} - a_{27} C_{\upgamma }\)
|
\(F_{\text{m}} = \left( {1 - F_{\text{f}} - F_{\text{p}} - F_{\text{b}} } \right)\left\{ {1 - \exp \left[ { - 0.011\left( {M_{\text{s}} - T} \right)} \right]} \right\}\)
| |
\(c_{\upgamma \upalpha } = c_{\upgamma \upalpha 0} + c_{\upgamma \upalpha 1} T\) (2) |
\(c_{\upgamma \upbeta } = c_{\upgamma \upbeta 0} + c_{\upgamma \upbeta 1} T\) (3) |
\(B_{1}^{2} \frac{{d^{2} X}}{{dt^{2} }} + B_{2} \frac{dX}{dt} + X = f\left( T \right)\) (4) |
\(B_{1} = a_{4} \exp \left[ { - a_{5} \left( {A_{e3} - T} \right)} \right]\)
\(B_{2} = \left\{ {a_{6} \exp \left[ { - \left( {\frac{{a_{7} - T}}{{a_{8} }}} \right)^{2} } \right]} \right\}^{ - 1}\)
|
\(f(T) = \frac{{F_{f} }}{{F_{f\max } }}\)
|
\(F_{f\max } = 1 - \frac{{\left( {c - c_{\upalpha } } \right)}}{{\left( {c_{\text{eut}} - c_{\upalpha } } \right)}}\)
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Identification
a
4
|
a
5
|
a
6
|
a
7
|
a
8
|
a
9
|
a
10
|
a
11
|
a
12
|
a
16
|
---|---|---|---|---|---|---|---|---|---|
1.479 | 7.104 | 145.9 | 36.77 | 2.092 | 1397 | 67.73 | 3.475 | 0.079 | 1.856 |
1.62 | 8.405 | 171 | 72.59 | 2.68 | 21.0 | 0.371 | 0. | 0.276 | 0.834 |
a
17
|
a
18
|
a
19
|
a
20
|
a
21
|
a
22
|
a
23
|
a
24
|
a
26
|
a
27
|
---|---|---|---|---|---|---|---|---|---|
24.17 | 24.89 | 1.698 | 683.3 | 0.006 | 0.187 | 0.518 | 0.462 | 428 | 2.9 |
29.03 | 26.34 | 1.682 | 722.7 | 3.569 | 2.95 | 4.066 | 3.5 | 409.1 | 21.44 |
a
4
|
a
5
|
a
6
|
a
7
|
a
8
|
---|---|---|---|---|
32.98 | 0.0774 | 0.896 | 544.85 | 123.2 |
19.92 | 0.086 | 0.807 | 664.86 | 78.81 |
c
γα0
|
c
γα1
|
c
γβ0
|
c
γβ1
|
---|---|---|---|
4.659 | −0.00554 | −1.1323 | 0.002443 |
19.92 | 0.086 | 0.807 | 664.86 |
Results
Kinetics of Transformation
Industrial Annealing Cycles
Conclusions
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Dilatometric tests confirmed good accuracy of both models as far as prediction of volume fractions of phases in constant cooling rate conditions is considered.
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Experimental simulations confirmed good accuracy of the models for more complex thermal cycles. Discrepancies between calculations and measurements were observed for the cycles where direct quenching from the intercritical region was applied.
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CONT model does not require additivity rule and is more suitable for simulations of complex thermal cycles.
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Capability of the CONT model to simulate the industrial continuous annealing line was confirmed.