2. Materials Process Design and Control Laboratory MODELING THE EFFECTS OF MOLD TOPOGRAPHY ON ALUMINUM CAST SURFACES Lijian Tan and Nicholas Zabaras Materials Process Design and Control Laboratory Sibley School of Mechanical and Aerospace Engineering 188 Frank H. T. Rhodes Hall Cornell University Ithaca, NY 14853-3801 Email: zabaras@cornell.edu URL: http://www.mae.cornell.edu/zabaras/

3. Materials Process Design and Control Laboratory RESEARCH SPONSORS DEPARTMENT OF ENERGY (DOE) Industry partnerships for aluminum industry of the future - Office of Industrial Technologies ALUMINUM CORPORATION OF AMERICA (ALCOA) Ingot and Solidification Platform – Alcoa Technical Center CORNELL THEORY CENTER

4. (b) Ripple formation (c) Non-uniform front growth (a)Surface porosity & surface crack Materials Process Design and Control Laboratory Surface defects in casting Surface defects removed by some post casting process ----- Scalping. These post processes will cause substantial energy and material lost. Surface defects were caused by non-uniform heat extraction, improper contact at metal/mold interface, inverse segregation and meniscus freezing etc.

5. Materials Process Design and Control Laboratory Investigate the effects of mold topography Mold topography Gap nucleation Microstructure Growth pattern Stress evolution Heat transfer Fluid flow For a single aspect, the effect of mold topography may be small. These effects interact each other and may lead to surface defects. Our aim is to establish a (thermo-mechanical) model to incorporate these effects. Segregation Defects Interaction

6. Thermo-mechanical model Materials Process Design and Control Laboratory Shell formation Shell distortion & mold movement Air gap formation Reduction in heat transfer Crack initiation Assuming a sinusoidal mold topography, a study of the effects of wavelength or amplitude on the solidification growth at early times is conducted

7. Definition of the thermal problem Materials Process Design and Control Laboratory Heat conduction in the liquid melt, shell and mold At solid-liquid interface, the Stefan equation is satisfied Before gap nucleation, the thermal resistance is determined by pressure After gap nucleation, the thermal resistance is determined by the size of the air-gap At the mold-shell interface, the thermal resistance is related to the contact pressure or air-gap

8. Materials Process Design and Control Laboratory Deforming FEM A deforming finite element analysis is used to account for phase change. An additional term would appear in the weak (heat or flow) form due to the mesh motion, e.g. Mesh motion is compatible with the interface velocity The freezing interface velocity is computed from the Stefan equation

9. Materials Process Design and Control Laboratory Equilibrium equation (neglect gravity and inertial force) Constitutive law (hypo-elastic) Evolution of plastic strain and state variable Decomposition of total strain Definition of the deformation problem weak form Evolution of thermal strain (driven force)

10. Materials Process Design and Control Laboratory Accounting for the initial stress at the time of solidification The stress at a material point P can be easily computed by proper integration of the hypo- elastic law:  t* should be also used for integration of the following derivatives: Solid created during the time step  t Original solid shell Current interface Previous interface

11. Materials Process Design and Control Laboratory Mold/solid shell contact and friction algorithm Contact between mold and shell is the key of this thermo-mechanical model (a) Deformation affects heat transfer through the contact between mold and shell (b) Contact traction is unknown in the weak form of the deformation problem Use augmentation (Uzawa’s method) to calculate the contact traction (4 steps) (a) Initialize the multipliers, λ N, λ T. (b) Start a nested iteration to solve the displacement with contact forces governed by: (c) Update the Lagrange multipliers (d) Return to the second phase, till converged

12. Gap nucleation time: effects of wavelength At the very early stages of aluminum solidification, the contact pressure between mold and solid shell will drop at the trough due to thermal stress development. When this contact pressure drops to zero, gap nucleation is assumed to take place. For rigid mold (with an topography amplitude=1 µm, wavelength=1-4 mm), under liquid pressure 8000 Pa, the gap nucleation time is in the order of seconds Physical Conditions: Liquid pressure P=8000 Pa Thermal resistance at mold-shell interface R=10 -5 m 2 o C sec J -1 Materials Process Design and Control Laboratory

13. Gap nucleation time: effects of mold conductivity Mold conductivity affects gap nucleation time The higher the conductivity, the quicker the gaps nucleate from the mold surface In this calculations, the deformation of the mold is neglected to illustrate the effects of mold conductivity. Physical conditions: Liquid pressure P=10000 Pa Mold thickness h=0.5 mm Thermal resistance at mold-shell interface R=10 -5 m 2 o C sec J -1 Wavelength=2 mm Materials Process Design and Control Laboratory

14. When the wavelength is relatively small, the evolution of the contact pressure at the trough is mainly affected by the conductivity of the mold, i.e. the deformation of the mold does not play a crucial role Gap nucleation time: effects of mold material ( deformable mold ) Physical Conditions: Liquid pressure P=10000 Pa Mold thickness h=0.5 mm Thermal resistance at mold-shell interface R=10 -5 m 2 o C sec J -1 Wavelength=10 mm, (20 mm, 30 mm in the next two slides) Materials Process Design and Control Laboratory

15. As the wavelength increases, the P tr -t line is about to show a “turn-around” pattern (i.e. the pressure not reaching zero values). This is defined as the `critical wavelength’ in the analytical studies of L. Hector. From this figure, we note that the critical wavelength is slightly above 20 mm. In Hector’s analytical study, the critical wavelength is 16.60 mm, for iron mold and 14.03 mm for lead mold under the same conditions. Gap nucleation time: effects of mold material ( deformable mold ) Materials Process Design and Control Laboratory

16. When the wavelength is greater than the critical value, the P tr -t curve shows a turn- around pattern before the contact pressure reaches zero Gap nucleation time: effects of mold material ( deformable mold ) Materials Process Design and Control Laboratory The pressure would not decrease to 0 for an iron or lead mold, so a large wavelength is preferred. In practice, we can never obtain a such a smooth mold topography with amplitude 1 µm and wavelength 30 mm.

17. Shell thickness at gap nucleation time The shell thickness at gap nucleation time plays an important role in deformation. The thicker the shell, the more its ability to prevent distortion or warping. From our calculations, high melt pressure is the preferred option to achieve larger shell thickness at gap nucleation time. Materials Process Design and Control Laboratory

18. Shell growth after gap nucleation After gap nucleation, the heat flux between mold and shell is determined by the contact condition Gap formation substantially affects heat transfer from the mold to the shell Conclusion A smaller wavelength is preferred as the growth pattern will become stable faster Materials Process Design and Control Laboratory 1mm 5mm Growth front Alcoa chill cast experimental results V cast = 25mm/s

19. Fluid flow Materials Process Design and Control Laboratory A = 1 mm λ = 10 mm A = 0.232 mm λ = 1 mm Two cells will be formed within each wavelength As solidification proceeds, these cells would be merged into a global circulation

20. Effects of fluid flow Materials Process Design and Control Laboratory Potential effects: Improve heat transfer rate Changes in solid-liquid front morphology Segregation At the start of solidification, the fluid flow is weak, maximum stream function is only about 2.0. 10 -6 m 2 /s. So its effect to heat transfer and shell growth pattern is small. But its effects on segregation could be substantial. Segregation is one of our current interests. Flow flow at the start of solidification(7ms)

21. Stress development If the mold surface is perfectly smooth, no gap nucleation would occur and stress would develop uniformly. For a sinusoidal mold topography, the development of stress is determined mainly by the temperature gradient. Stress is large near the crest and small near the trough. The gap caused by thermal stress will substantially affect heat transfer. Materials Process Design and Control Laboratory

22. Microstructure Chill surface: λ=1~20mm A=0.232mm Amplitude of growth front ~ mm Gap between mold-shell ~ 10 μm In a macro scale Roughness ( A typical surface after grind ) λ=40R =2~200μm R=0.05~5μm Critical radius of homogeneous nucleation r*(hom) = 2γ/ΔG = 1nm Critical wavelength of heterogeneous nucleation is much larger than critical wavelength r*(het) = r*(hom) /S(θ) ~ μm Resulted surface grain size (H. Biloni) δ=50~200μm (R=5 μm) In a micro scale

23. References “A stabilized finite element method for flow in porous media and solidification systems”, Proceedings of the Seventh U.S. National Congress on Computational Mechanics, presented at the Symposium on ‘Stabilized and Multi-length scale methods’, Seventh U.S. National Congress on Computational Mechanics, Albuquerque, New Mexico, July 27-31, 2003 “A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes”, Nicholas Zabaras and Deep Samanta, International journal of Numerical Methods in Engineering, in press. “A thermomechanical study of the effects of mold topography on the solidification of Aluminum”, Lijian Tan and Nicholas Zabaras, Metallurgical and Materials Transactions B, submitted. Materials Process Design and Control Laboratory “Solidification and macrosegregation of aluminum alloys on uneven surfaces”, Deep Samanta and Nicholas Zabaras, Int. Hournal of Heat and Mass Transfer, in preparation.