ANNUAL REPORT UIUC, August 20, Grade Effects On The Initial Stress, Strain, And Solidification Behavior In Continuously Cast Steels

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1 ANNUAL REPORT 214 UIUC, August 2, 214 Grade Effects On The Initial Stress, Strain, And Solidification Behavior In Continuously Cast Steels Matthew L. S. Zappulla, M.S. Student Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. 1 Problem Statement The goal of this study is to explore the effect of steel grade on initial solidification using a 1D free shrinking slice mode. Free Shrinkage (No contact) Y X Heat Flux Applied Z Y X From symmetry, insulated on 3 non contact faces Generalized Plane Strain imposed on bottom surface and into page Stress-Free end University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 2

2 Governing Equations Heat Conduction Equation (with solidification): H ( T ) T kt ( ) T ρ kt ( ) T = + T t x x y y Equilibrium Equation (small strain assumption): σ ( x) + b o = Rate Representation of Total Strain Decomposition: ε = ε + ε + ε el ie th Constitutive Law (Rate Form of elasticity eqs, No large rotations): 2 σ = D:( ε εie εth ) D = 2 μ I+ (k ) I I 3 Inelastic (visco-plastic) Strain Rate (strain-rate-independent plasticity + creep): 2 ε = T, ε,% C) = : 3 ie f( σ, ε ε Thermal Strain: ie ie ie { ε } = ( α( T)( T T ) α( T) ( T - T )) i ref [ 111 th ref i ] 3 1 σ= σ': σ', σ' = σ trace( σi ) 2 3 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 3 T Grades Of Interest The Liquid is modeled as a Perfectly-Plastic Solid Elastic Modulus: 1E4 [MPa] Poisson s Ratio:.3 [mm/mm] Yield Stress: 1E-2 [MPa] Element Ultra Low [wt%] Low [wt%] Peritectic [wt%] High [wt%] Carbon Aluminum Chromium Copper Manganese Nickel Phosphorus Sulphur Silicon Titanium MidPlane Temp Centerline Temp Liquidus Solidus Mushy Zone Gamma End Alpha Start Delta End/Solidus Delta End/Solidus Gamma Start/Solidus Liquidus % Solidus Solidus Temperature Indicated with Dark Grey University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 4

3 Grade Phase Fractions.3% C (Ultra Low Carbon) γ δ L % C (Low Carbon) γ δ L Degree Mushy 23 Degree Mushy.13% C (Peritectic Carbon) γ δ % C (High Carbon) L γ L 4 Degree Mushy 69 Degree Mushy Heat Flux Data Collected and compiled from available data and the literature Regression curve fit for total heat flux data Avoid instabilities at zero Lower heat flux profile adopted for the Peritectic grade University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 6

4 Applied Heat Flux Applied Heat Flux From symmetry, insulated on 3 non chilled faces = = 1 ( + ) = 2 ( + ) = ( + ) = (1 + ) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 7 Thermal Conductivity [w/m*k] Enthalpy [Kj/kg] Temperature [C] Temperature [C] Temperature & Grade Dependent Properties Density [Kg/m3] Temperature [C] Ultra Low Carbon High Carbon Low Carbon Peritectic Carbon Phase Fraction weighted average for all properties φ = φ f + φ f + φ f + φ f University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 8 Elastic Modulus [GPa] L L δ δ γ γ α α Thermal Conductivity K. Harste, Ph.D. Thesis, Technical University of Clausthal, (1989). Enthalpy K. Harste, Ph.D. Thesis, Technical University of Clausthal, (1989). Thermal Expansion (from Density) K. Harste, Ph.D. Thesis, Technical University of Clausthal, (1989). I. Jimbo and A. Cramb, The Density of Liquid Iron- Carbon Alloys. Metallurgical and Materials Transactions, 24B (1993), No. 1, pg Elastic Modulus H. Mizukami, K. Murakami, and Y. Miyashita, Elastic Modulus of Steels at High Temperature. Tetsu-to-Hagane, 63 (1977), No. 146, pg. S Temperature [ C]

5 Constitutive Equations Stress (MPa) Austenite δ-ferrite 6 4 ε σ, ε Strain Rate = 1-4 s -1 Temperature = 14 C Composition =.45 %wt C 5 1 ε σ, ε Strain (%) Image by L. Hibbeler P.F. Kozlowski, B.G. Thomas, J.A. Azzi, and H. Wang, Simple Constitutive Equations for Steel at High Temperature. Metallurgical and Materials Transactions, 23A (1992), No. 3, pg H. Zhu, Coupled Thermo-Mechanical Finite-Element Model with Application to Initial Solidification. Ph.D. Thesis, University of Illinois at Urbana- Champaign, (1996). Austenite (Kozlowski model III): f3 T 4 1 f2( T) K ε( s ) = f ( C) σ f1 ( T) ε ε exp T 3 f1 ( T) = T 3 f2 ( T) = T 3 f3 ( T) = T f( C) = C C ( ) ( ) δ-ferrite (Zhu modified power law): 1 ( s ) f C ( T ) 4 ( ) = ( C) T University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla ε =.1 σ ( ) 3 (1 + 1 ε) f C m= + n= T.6166 n m Liquid modeled as a Perfectly-Plastic Solid Elastic Modulus: 1E4 [MPa] Poisson s Ratio:.3 [mm/mm] Yield Stress: 1E-2 [MPa] T in Kelvin, σ in MPa, C in weight % C ABAQUS Mesh Implementation Y X Steel Shell Slice Model CPEG4HRT Elements Chilled Edge 4 Elements 4mm Two dimensional Piecewise Linear Continuum Stress/Displacement (C) Generalized Plane Strain (PEG) 4 nodes Reduced (R) Hybrid (H) One-Way Coupled Temperature Displacement (T) Stress Calculation has NO effect on Thermal Calculation Element size =.1mm Z Y X.3mm 3 Elements University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 1

6 Shell Thickness - Solidus 14 Distance From Cooled Edge [mm] Ultra Low Carbon High Carbon Low Carbon Peritectic Carbon [s] University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 11 Temperature Histories University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 12

7 Thermal Strain Behavior University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 13 Elastic Strain Behavior University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 14

8 Plastic Strain Behavior University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 15 Fluid Strain Behavior University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 16

9 Low Carbon Strain Behavior University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 17 High Carbon Strain Behavior University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 18

10 Stress Perpendicular to Solidification Front University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 19 Ultra Low Carbon Strain Behavior University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 2

11 Peritectic Carbon Strain Behavior University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 21 Conclusions Free shrinkage of a 1D continuous casting slice with varying grades was modeled Stress analysis reveals behavior of compression at the surface moving towards tension at the solidification front Uniform total strain Increasingly negative total strain was observed with time Strain first increases (squeezed by shrinking solid) then later decreases (liquid shrinkage) An initial period of negative plastic strain development that does not persist Not seen in the High Carbon Grade, due to the absence of delta ferrite University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 22

12 Future Work Further development of an all encompassing model More grade accuracy by updating the phase diagram model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Matthew Zappulla 23 Acknowledgements Continuous Casting Consortium Members (ABB, Arcelor-Mittal, Baosteel, Magnesita Refractories, Nucor Steel, Nippon Steel, Postech/Posco, Severstal, SSAB, Tata Steel, ANSYS-Fluent) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 24