Phase Field Simulation of

Vanadium Carbide Evolution in Steels

M. Stratmann, A. Monas, E. Borukhovich, O.Shchyglo, I.Steinbach

ICAMS, Ruhr-Universität Bochum, Germany

Investigation

Within this work the results of the phase-field modeling of the evolution of Vanadium carbides (VC) are shown. Simulations

are carried out using the multi-phase field method [1,2] implemented in the Open Source library OpenPhase [3]. The

simulation consists of the calculation of the growth rate of VC depending on many factors like concentration, temperature,

size, mobility and transformation stress. Furthermore a multi-component (Fe, V, C) approach on two separate latices is

introduced to better model the complex evolution of the microstructure found in HSLA steels.

Model

This simulations are carried out with the OpenPhase library [4]. It simulates the growth of the

precipitate in an Iron-Vanadium-Carbon system with two sublattices - (Fe,V),(C,Va).The free

energy (1) takes into account the Gibbs free energy provided by CALPHAD databases (9).

Transformation strain is implemented and also has an effect on the flux of alloyed element

atoms (8). The temperature T is constant at 1173 K, surface energy 0.05 J/m², Mobility µ 1010

at.frac-1.

Figure 2: V-C diagram [6], showing the equilibrium phases in thesystem. Highlighted is the cubic phase VC and the simulationtemperature 1173 K. Simulated are nucleation processes, whichcannot be described perfectly by equilibrium diagrams.

References

1) I. Steinbach, Phase-field models in materials science, Modelling Simul. Mater. Sci. Eng. 17 (2009) 073001

2) Zhang, L., & Steinbach, I. (2012). Phase-field model with finite interface dissipation: Extension to multi-component

multi-phase alloys. Acta Materialia, 60(6-7), 2702–2710.

3) www.openphase.de

4) E355 Fine grain steel Benteler Stahl/Rohr

5) Huang, W. (1991). A Thermodynamic Evaluation of the Fe-V-C System. Zeitschrift für Metallkunde, 82(5), 391–401.

6) Lipatnikov, et al. (1999). Phase transformations in non-stoichiometric vanadium carbide. Journal of Physics:

Condensed Matter, 11(163), 163–184.

7) Furuhara et al. (2003). Multiphase Crystallography in the Nucleation of Intragranular Ferrite on MnS+V(C,N) Complex

Precipitate in Austenite. ISIJ International, 43(12), 2028–2037.

8) Oila, A., Bull, S. J. (2009). Atomistic simulation of Fe-C austenite. Computational Materials Science, 45(2), 235–239.

9) Zhang, H., et al. (2012). First-principles study of solid-solution hardening in steel alloys. Computational Materials

Science, 55, 269–272.

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Figure 1: Microstructure of steel of a plain carbon steel a) with a mixed microstructure with pearlite, cementite and ferrite and a microalloyed steel b) with cementite, ferrite and interstitial carbides (VC, NbC, TiC). [4] The fine grains are a result of the lower grain boundary mobility at high temperatures due to the existence of small carbides.

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Figure 3: a) HREM image of a coherent Vanadium carbide [7], with the geometric structure detailed in b). The {111} facets can be easily identified. C) is the realization of the shape, initialized in OpenPhase.

Figure 4: a) HREM image of the grain boundary region between Austenite and VC [7].

Conclusion and Outlook

The phase field method is capable of simulating the complex process of precipitate evolution. Using the CALPHAD method, it is possible to reproduce a realistic precipitate behaviour on the mesoscale.The introduction of sublatices as in [2] was implemented and was essential for the simulation of the multi component system Fe, V, C. Elastic effects play a significant role in the nucleation and evolution of nano-precipitates. Our model recovers the important effects of the strain-field around precipitates.

Further research will involve - the precipitate nucleation via spinodal decomposition in steels- the pinning characteristics of the precipitates- the influence of Vanadium-Carbides on Austenite to Ferrite transition and resulting grain size distribution

Introduction

High Strength Low Alloy (HSLA) - steels play a very important role in the steel industry and are primarily used in construction

and piping. HSLA steels mainly consist of a fine Ferrite grain with few nano/micro-precipitates. These carbo-nitrides have a

variety of positive influences on the micro-structure. They hinder grain-boundary movement (reduce coarsening), act as

nuclei for Ferrite grains during the Austenite/Ferrite transformation and therefore lower the average grain size significantly.

This results in higher strength and higher ductility.

Figure 7: Concentration field around the Vanadium carbide, a) the concentration of Carbon and b) the concentration of Vanadium around the precipitate after 200 ms with fixed Phase field (no growth). Areas of higher and lower concentration are clearly visible and the result of the contribution of the elastic fields to the concentration flux.

Figure 8:Horizontal concentration profile of a) Carbon and b) Vanadium at the interphase region, only influenced by the diffusion and various transformation strains around the particle.

Figure 5: Dependency of elastic constants of austenitic steel on the concentration of alloyed atoms, a) Carbon [8] and b) Vanadium [9].

Figure 6: Stress field around the Vanadium carbide, due to the difference of the lattice parameters between Austenite and VC. Transformation strain: 5%.

-5

0

5

10

15

20

0 5 10 15

GP

a

at.% Carbon

C11

C12

C44

-6

-4

-2

0

2

4

6

8

10

0 2 4

GP

a

at.% Vanadium

C11

C12

C44

2,69

2,7

2,71

2,72

2,73

2,74

2,75

39 44 49

at.

% V

an

ad

ium

x-Coordinate

15% Eigenstrain 5% Eigenstrain 0% Eigenstrain

a

a b

ba

a

a b

Contribution of the elastic strain to the chemical potential:

Calculation of chemical energy with CALPHAD databases [5]:

(9)

(1)

(2)

(5)

(7)

Transport equations:

100 µm 100 µm

ba1

1,5

2

2,5

3

3,5

4

4,5

5

5,5

6

39 44 49

at.

% C

arb

on

x-Coordinate

15% Eigenstrain 5% Eigenstrain 0% Eigenstrain

100 nm 100 nm100 nm

b c

Results

Free energy: