Stress Analysis of Dendritic Microstructure During Solidification. Introduction

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1 ANNUAL REPORT 2012 UIUC, August 16, 2012 Stress Analysis of Dendritic Microstructure During Solidification Lance C. Hibbeler (Ph.D. 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. Hibbeler 1 Introduction Hot tearing is a solidification defect that leads to poor product quality at best and a breakout at worst The averaging inherent to traditional macro-scale models prevents study of the details of hot tear formation and propagation This work explores the hot tearing phenomenon by combining macro-scale information with a detailed model of the morphology of the solidification front University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 2

2 Shell Surface Stress (MPa) Previous Work Large Scales Simulations of entire caster Maximum Shell Stress (MPa) mm Outer Funnel Width 950 mm Outer Funnel Width s Distance from Mold Centerline (mm) 4 s 6 s 8 s 10 s 8 s 10 s 4 s 6 s 750 mm Outer Funnel Width 950 mm Outer Funnel Width Thermomechanical model of funnel molds Hibbeler and Thomas 2 s Distance from Mold Centerline (mm) Multiphysics model of beam blank Koric, Hibbeler, Liu, and Thomas University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 3 Previous Work Intermediate Scales Detailed simulation of a surface defect ε = c ε ΔT B Won et al., MMTB 2000 Contours of inelastic strain Δ T = T( f = 99%) T( f = 90%) B s s Damage Index Distance from Shell Surface (mm) H Jasti University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler ε( fs = 99%) ε( fs = 90%) ε = t( f = 99%) t( f = 90%) D = ε ε s ε = ε( f = 99%) ε( f = 90%) dmg s s dmg c Likely form a hot tear s 0.75mm Dis with HF drop to 20% at crack 0.75mm Dis over 4 secs and HF drop to 50% at crack during same 4 secs

3 Semi- or Analytical models Previous Work Small Scales Rappaz, Drezet, and Gremaud, MMTA 1999 Monroe and Beckerman, MSEA 2005 Mushy zone RVE models Vernede, Dantzig, and Rappaz, Acta Mat Phillion, Cockcroft, and Lee, MSMSE 2009 Sistaninia, Phillion, Drezet, and Rappaz, Acta Mat University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 5 Previous Work Room for Improvement Previous work covers mostly: Aluminum alloys Equiaxed/globular grains Mushy zone frozen in time Macro- or meso-scale need liquid+solid averaging Oversimplified material models solid, liquid or both Present work is concerned with: Commercial steel alloys Entire solidification history surface and columnar zones Microscale no averaging Proper material models Relate microscale information to macroscale quantities University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 6

4 Background Different break-out risk is observed during production, which is believed to be due to hot cracking in the first solid shell inside the caster: 2 > 1 >> 3 Table 1: Typical chemical composition of three steel grades Steel C Mn V Nb N (ppm) grade (wt %) (wt %) (wt %) (wt %) aim max 1 LCAK LR-HSLA HSLA B. Boettger et al., MCWASP XIII University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 7 RDG Criterion for Steels This is in contradiction to the empirical finding 2 > 1 >> 3 But why 3 << 2??? B. Boettger et al., MCWASP XIII University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 8

5 Modeling Approach CON1D+ Plant Data Casting Conditions Mold heat transfer data under ideal taper Microstructre Phase field calculations CON1D+ MICRESS Macro Slice Model Bulk thermal and mechanical response Micro Slice Model Detailed mechanical behavior in mushy zone ABAQUS CON1D+ ABAQUS ABAQUS Macro Caster Model Overall thermal and mechanical response, evaluate for hot tearing University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 9 Calibrated Heat Flux Profile Casting speed = 4.8 m/min B. Santillana University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 10

6 Microscale Domain 200,000 4-node elements, 0.3-μm square x 333 μm y Fixed edge, u y = 0, σ xy = 0 Fixed edge, u x = 0, σ xy = 0 Solid Liquid 66 μm Free edge, σ xx = 0, σ xy = 0 Generalized plane strain edge, u y = uniform, σ xy = 0 Out-of-plane assumption: generalized plane strain u z = uniform Phase field calculated with MICRESS by B. Boettger University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 11 Explicit FEM Get accelerations from force balance Integrate to get half-step velocity Integrate at half-step to get displacement Critical time step Dilational wave speed (approx m/s) Efficiencies from: No Newton iterations (no matrix solve) Lumped mass matrix (no matrix solve) Mass scaling make density large to increase critical step size University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 12

7 Modeling Issues Using the traditional quasi-static approach, the 2D simulation with previously-described conditions always crashes with the formation of solid material An alternative approach, which explicitly integrates the full force balance, is more numerically stable Mass scaling technique increases critical time step size Explicit marching scales well across processors No generalized plane strain elements; must work in 3D See (Koric, Hibbeler, and Thomas, IJNME 2009) for more detail University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 13 Modeling Issues Imposing the generalized plane strain constraint prevents parallelization (in ABAQUS/Explicit) Efficient solution to this problem is to calculate the shrinkage in a macroscale model and impose timedependent boundary conditions x Other BCs mimic 2D case y z Top face fixed in z 200,000 8-node elements, 0.3-μm cube University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 14

8 Material Models Liquid: Stress (MPa) Elastic, perfectly plastic (500 Pa yield stress) To be improved to Newtonian fluid (viscosity increases critical t) Solid: Zhu (ferrite) or Kozlowski III (austenite) Austenite δ-ferrite Strain Rate = 10-4 s -1 Temperature = 1400 C Composition = %wt C 1 ( s ) f C ( T ) 4 ( ) = ( C) T 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 Strain (%) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler ε = 0.1 σ ( ) 300 ( ε) f C m= + n= T n m Zhu Kozlowski Macroscale Model Thermal Boundary Conditions Insulated Insulated Prescribed heat flux Insulated Material properties from CON1D Mechanical Boundary Conditions Zero perpendicular displacement Domain Zero perpendicular displacement Equal perpendicular displacement Stress-Free Solid material Liquid material University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 16

9 Macroscale Model Results University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 17 Macroscale Strain History Total strain Input this data into microscale model Noise corresponds to nodes turning solid Total Strain Rate Component of strain perpendicular to solidification direction University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 18

10 Microscale Domain Temperature and Carbon Concentration 0.10 s 66 μm 0.15 s 0.20 s B. Boettger 0.25 s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 19 Total strain in vertical direction Microscale Deformation Preliminary Results Strain concentrations in liquid regions Most motion occurs in liquid Peak negative pressure in roots of secondary arms Insufficient feeding can lead to porosity Fraction Liquid Pressure stress Negative pressure means material in tension University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 20

11 Stress in vertical direction Microscale Deformation Preliminary Results Consequences to be determined Fraction Liquid von Mises stress University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 21 Microscale Deformation Preliminary Results Total strain in horizontal direction Stress in horizontal direction University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 22

12 Modeling Issues Even ABAQUS/Explicit has trouble with the formation of the first solid material, but the explanation is more evident than with /Standard: The large step-change in stiffness causes the critical time step to be violated The mass scaling must be readjusted, frequently, to account for the change in stiffness as temperature and phase evolve University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 23 Future Work Simulations of many dendrites will reveal statistically significant data that is useable for macroscopic models B. Boettger University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 24

13 Conclusions Modeling effort underway to predict hot tearing from small-scale phenomena Preliminary efforts look promising Future studies based on very large phase field simulations University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lance C. Hibbeler 25 Acknowledgements Continuous Casting Consortium Members (ABB, ArcelorMittal, Baosteel, Tata Steel, Goodrich, Magnesita Refractories, Nucor Steel, Nippon Steel, Postech/Posco, SSAB, ANSYS-Fluent) Dr. Bernd Boettger, ACCESS e.v. See (Boettger, Apel, Santillana, and Eskin, MCWASP XIII) for more detail National Center for Supercomputing Applications (NCSA) at UIUC Forge cluster Dassault Systemes (ABAQUS parent company) University of Illinois at Urbana-Champaign MechSE Metals Processing Simulation Lab Lance C. Hibbeler 26