Maximum Casting Speed for Continuous Casting Steel Billets
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1 ISS Conference, Nashville, TN Maximum Casting Speed for Continuous Casting Steel Billets Chunsheng Li and Brian G. Thomas Department of Mechanical & Industrial Engineering University of Illinois at Urbana-Champaign March 12, 22 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 1
2 Objective Analyze bulging below the mold for unsupported billet/bloom casting due to ferrostatic pressure for different casting speeds. Determine critical casting speed to avoid cracks as a function of section size and mold length. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 2
3 Continuous Casting Billet after Breakout Showing Off-corner Sub-surface Crack Off-corner crack due to excessive bulging University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 3
4 Model Description Stepwisely coupled 2D slice finite element thermal stress model Temperature dependent thermal and mechanical properties Treat liquid elements with nearly zero yield strength to make it deform freely under shear stress Phase fractions from non-equilibrium Fe-C phase diagram for plain carbon steels Efficient contact algorithm between mold and shell surface 2-D generalized plane strain to give 3D stress/strain state total elastic thermal inelastic flow & ε = & ε + & ε + & ε + & ε Unified elastic-visco-plastic constitutive model Robust alternating implicit-explicit time integration scheme University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 4
5 Heat Transfer Model Validation Sec. 5 Sec. 1 Sec. 2 Sec. 4 Sec. Lines: Boley & Weiner Analytical Solutions Symbols: CON2D Predictions Time Step Size:.1 ~.1 Sec. Mesh Size:.3 ~ 2. mm Distance to the Chilled Surface (mm) Lines: Boley & Weiner s analytical solution* Symbols: CON2D computation results * J. H. Weiner and B. A. Boley, J. Mech. Phys. Solids, 1963, Vol. 11, pp University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 5
6 Stress Model Validation Sec. 5 Sec. 1 Sec. 2 Sec. 4 Sec. Lines: Boley & Weiner Analytical Solutions Symbols: CON2D Predictions Time Step Size:.1 ~.1 Sec. Mesh Size:.3 ~ 2. mm Distance to the Chilled Surface (mm) Lines: Boley & Weiner s analytical solution* Symbols: CON2D computation results * J. H. Weiner and B. A. Boley, J. Mech. Phys. Solids, 1963, Vol. 11, pp University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 6
7 Constitutive Model Behavior Lines: 1 γ δ + γ δ δ + L Constitutive Model Predictions Symbols: Wray measurements * 1.1 ELEC FE - 2.3x1-2 (s -1 ) ELEC FE - 2.8x1-5 (s -1 ) FE.28%C - 2.3x1-2 (s -1 ) FE.28%C - 2.8x1-5 (s -1 ) FE.44%C - 2.3x1-2 (s -1 ) FE.44%C - 2.8x1-5 (s -1 ) FE 3.%Si - 2.3x1-2 (s -1 ) FE 3.%Si - 2.8x1-5 (s -1 ) dε/dt 2.3x1-2 (s -1 ) dε/dt 2.8x1-5 (s -1 ) Temperature ( o C) * P. J. Wray, Met. Trans, A, V7A, 1976, P mm 3.2mm University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 7
8 Non-equilibrium phase diagram* of plain carbon steels ** used in CON2D δ+l δ+γ+l Liquid Temperature, o C δ δ+γ γ ZST(exp.)[2] 135 ZDT(exp.)[2] Fe-C equilibrium diagram present FDM simple model f S = *Young Mok WON et. al., Effect of Cooling Rate on ZST, LIT, ZDT of Carbon Steels Near Melting Point, ISIJ International, Vol. 38, 1998, No. 1, pp **Other Steel Components: 1.52%Mn,.34%Si,.15%S,.12%P University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 8 γ+l Carbon Content, wt% f S =. f S =.75
9 Hot Tear Fracture Criterion Crack Criterion: Fracture occurs when ε D > ε Dc Damage Strain,ε D 99% Solid ε D =Σ ( inelastic flow ) 9% Solid ε + ε ** This is the empirical equation by Y.M. WON et. al. based on many published measurements. [Met. Trans. B, Vol. 31B, August, 2] Damage threshold,ε Dc** ε Dc ij where :.2821 = & ε T ij B T = T( f =.9) T( f =.99) B s s o for.27% C steel T = 9 C B University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 9
10 Mold Heat Flux Data 5 Kapaj[1] Wolf fitted Eqn for slag casting: 7.3*t(s) -.5 [2] Wolf fitted Eqn for oil casting: 9.5*t(s) -.5 [2] Thin Slab [3] Brimacombe fitted Eqn: t(s).5 [4] C LI fitted Eqn for Slab casting: 4.5*t(s) -.33 [5] C LI fitted Eqn for Billet Casting t -.54 Lorento fitted Eqn: 1.4*Vc(m/min).5 with 7mm Mold [6] Other Sources:.1%C, Billet Other Sources- Slab? Heat Flux (MW/m 2 ) Dwell Time (s) Time Below Meniscus (sec.) [1] Kapaj N., Pavlicevic M. and Poloni A., 84th Steelmaking Conf. Proc., Baltimore, MD, ISS, p67 [2] Wolf M.M., I&SM, V.23, Feb., 1996, p47 [3] Park J.K., Samarasekera I.V., and Thomas B.G. et al, 83th Steelmaking Conf. Proc., Warrendale, PA, ISS, p13 [4] Brimacombe J.K., Canadian Metallurgical Quarterly, V.15, N.2, 1976, p17 [5] Li C. and Thomas B.G. Brimacombe Memorial Symposium, Vancouver, Canada, 2, p17 [6] Lorento D.P. unpublished paper University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 1
11 Parametric Study Vary: Casting speed for given section size and mold length until failure criterion is just exceeded Assume: Unique heat flux profile down mold Ideal mold operation to achieve uniform heat flux around mold parameters Ideal spray zone managed to produce no change in surface temperature below mold exit University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 11
12 Conditions of Parametric Study Material Composition (wt%) Billet Total Mold Length (mm) Taper (%/m) Time of Turning on Ferrostatic Pressure (sec.) Mesh Size (mm x mm) Node Number Element Number Time Step (sec.) Pouring Temperature ( o C) Solidus Temperature ( o C) Liquidus Temperature ( o C) 7% Solid Temperature ( o C) (Shell Thickness) 9% Solid Temperature ( o C) (Damage strain accumulation begins).27c, 1.52Mn,.34Si,.15S,.12P 12x12, 175x175, 25x25 5, 7, 1 6, 8, (on both faces).3.1x1. (at surface), 1.4x1. (at center) 7381(s12), 1797(s175), 15433(s25) 72(s12),156(s175),1512(s25).1 ~ University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 12
13 Surface Temperature History Mold Exit TEMPERATURE(C) TEMPERATURE(C) - Horizontal Face Center TEMPERATURE(C) - Vertical Face Center TEMPERATURE(C) - Corner TEMPERATURE(C) TEMPERATURE(C) - Horizontal Face Center TEMPERATURE(C) - Vertical Face Center TEMPERATURE(C) - Corner DISTANCE-BELOW-MENISCUS(mm) DISTANCE-BELOW-MENISCUS(mm) 12x12 12x University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 13
14 Shell Thickness History SHELL-THICKNESS(mm) SHELL-THICKNESS(mm) - Center SHELL-THICKNESS(mm) - Corner DISTANCE-BELOW-MENISCUS(mm) SHELL-THICKNESS(mm) SHELL-THICKNESS(mm) - Center SHELL-THICKNESS(mm) - Corner DISTANCE-BELOW-MENISCUS(mm) 12x12 12x University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 14
15 Temperature Contour with Distorted Shape (Mold Exit) Y(mm) 6 TEMPERATURE(C) Y(mm) 6 TEMPERATURE(C) mm 1 8.1mm X(mm) X(mm) 12x12 12x Time from Meniscus (sec.) 19.1 Time from Meniscus (sec.) 8.4 Distance below Meniscus (mm) 7 Distance below Meniscus (mm) 7 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 15
16 Stresses in XY Plane (2 mm Below Mold Exit) σy σ-8y σx 3-4 Y(mm) 4 σx 3 Y(mm) X(mm) X(mm) 12x12 12x Time from Meniscus (sec.) 24.6 Time from Meniscus (sec.) 1.8 Distance below Meniscus (mm) 9 Distance below Meniscus (mm) 9 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 16
17 Total Strains in XY Plane (2 mm Below Mold Exit) Y(mm) ε y ε x Y(mm) ε y ε x X(mm) X(mm) 12x12 12x Time from Meniscus (sec.) 24.6 Time from Meniscus (sec.) 1.8 Distance below Meniscus (mm) 9 Distance below Meniscus (mm) 9 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 17
18 Damage Strain in XY Plane (2 mm Below Mold Exit) Y(mm) ε x Y(mm) ε x 1 ε y 1 ε y X(mm) X(mm) 12x12 12x Time from Meniscus (sec.) 24.6 Time from Meniscus (sec.) 1.8 Distance below Meniscus (mm) 9 Distance below Meniscus (mm) 9 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 18
19 Bulging Histories and Effect of Casting Speed Vc = 2.2m/min Vc = 4.6m/min 5 DISPLACEMENT (mm) Vc = 4.8m/min Vc = 5.m/min Vc = 6.m/min Maximum Bulging V (mm) Maximum Bulging U (mm) Vc = 1.m/min DISTANCE-BELOW-MENISCUS(mm) x12 7 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 19
20 Critical Casting Speed to Avoid Cracks (WML = 5mm) (WML = 7mm) (WML = 1mm) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 2
21 Critical Casting Speed Due to 1mm Maximum Bulging 6 5 Maximum Casting Speed - WML=5mm (m/min) Maximum Casting Speed - WML=7mm (m/min) Maximum Casting Speed - WML=1mm (m/min) Section Size (mm) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 21
22 Conclusions Parametric study was performed to investigate the maximum casting speed for different square sections sizes and mold lengths with uniform heat flux around the mold perimeter. Excessive bulging below mold exit may generate subsurface off-corner longitudinal cracks due to hinging. Bulging criterion (4~1 mm maximum) and the hot tearing damage criterion indicate the same critical casting speed. Larger section size leads to slower casting speed limit. Longer mold increases casting speed limit. Productivity benefit from larger section size is partially canceled out by its slower casting speed limit. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 22
23 Future Applications Continuing model developments and validation Further maximum casting speed investigations: Effect of mold distortion Effect of mold taper Effect of spray cooling pattern Effect of steel composition (Fully δ or γ stainless steels) Ideal taper prediction which will help to achieve higher casting speeds University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Chunsheng Li 23
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