2008 International ANSYS Conference

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1 2008 International ANSYS Conference Ultrasonic Model Development and Applications to Ingot Casting Processes Laurentiu Nastac 1 and Yi Dai 2 1 Concurrent Technologies Corporation Pittsburgh, PA, USA 2 Ansys Inc., Lebanon, NH, USA 2008 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary 1

2 Outline Objective Solidification Structure Management Techniques Electromagnetic stirring (Grain structure and columnar-toequiaxed (CET) predictions) Ultrasonic treatment (UST) Preliminary Analysis on Grain Refinement with Ultrasound (Direct Method) Quick Ultrasonic Modeling Technique (Indirect Method) MMNC Processing using UST Dispersion of Nanoparticles in Molten Alloys A Modeling Strategy for Simulation of the MMNC Process Assisted by Ultrasonic Cavitation 2008 ANSYS, Inc. All rights reserved. 2 ANSYS, Inc. Proprietary

Objective Develop an ultrasonic modeling tool in Fluent to assist in the scale up of the following processes: An ultrasonic technology to significantly refine the solidification microstructure of

3 Objective Develop an ultrasonic modeling tool in Fluent to assist in the scale up of the following processes: An ultrasonic technology to significantly refine the solidification microstructure of castings and ingots A nanotechnology-assisted by ultrasonic cavitation to manufacture metal-matrix-nano-composite (MMNC) castings with enhanced mechanical properties (see some lab results in the table below) Comparison of mechanical properties between MMNC (A356+1% nano-sic) and 356 * * X. Li, Research Progress on Ultrasonic Cavitation based dispersion of nanoparticles in Al/Mg melts for solidification processing of bulk lightweight metal matrix nanocomposites, TMS ANSYS, Inc. All rights reserved. 3 ANSYS, Inc. Proprietary

4 Solidification Structure Management Electromagnetic stirring (demonstrated) Ultrasonic vibration (viable) Bulk micro-chilling Mechanical vibration Composition control (low impurity content) Mold rotation Control of heat extraction rate 2008 ANSYS, Inc. All rights reserved. 4 ANSYS, Inc. Proprietary

Electromagnetic Stirring * 3 I Lorentz Force: F em = J B Current Density: ( ) r J r = exp - 3 2 π r e r 1 2 3 η V I Joule Heating: Q em = J J ( ) r

magnetic flux density; σ electric conductivity * L. Nastac et al.

5 Electromagnetic Stirring * 3 I Lorentz Force: F em = J B Current Density: ( ) r J r = exp π r e r η V I Joule Heating: Q em = J J ( ) r Heat Flux: q r = exp - 3 σ 2 2 π r e re r e effective radius; η torch efficiency; V and I torch voltage and current J electric current density; B magnetic flux density; σ electric conductivity * L. Nastac et al., Magnetohydrodynamics in PAM Processed Ti-6Al-4V Ingots,"Modelling of Casting, Welding, and Advanced Solidification Processes X", San Destin, Florida, May ANSYS, Inc. All rights reserved. 5 ANSYS, Inc. Proprietary 2 2 e

Electromagnetic Stirring Ti-17 Ingots V, m/s 2-D velocity contour 2-D velocity

7 Grain Structure Stochastic Modeling in PAM Ingots Boundary conditions Modeling of columnar growth for constant G/V ratio t + δt t t + δt t R = R + ( V sin α ) δt X = X + ( V cos α) δt c c c c c c Radiation heat loss Plasma torch Gaussian heat flux Angle of growth α = tan 1 G G m x m r h s Ingot h s Growth direction probability p α = 1 (1 m ) α π /4 n π 0 α 4 δt = a 2 V c h b R and X columnar front position; t time; δt time step m G x and m G r local temperature gradients in the mushy zone V c growth velocity of the columnar front; a mesh size m and n parameters that control growth direction of columnar grains 2008 ANSYS, Inc. All rights reserved. 7 ANSYS, Inc. Proprietary

9 Prediction of Columnar-to- Equiaxed Transition G COL / 3 ( ) T N Δ n g 1 Δ T c Δ T c G N g EQ ( grain size) / 3 ( ) T N Δ 1 n Δ Tc g Δ T c = 8 Γ Δ T m c L ( 1 k ) D L C L V 1 / 2 G COL = Temperature gradient for columnar structure G EQ = Temperature gradient for equiaxed structure ΔT C = constitutional undercooling ΔT N = nucleation undercooling N g = grain density Γ = Gibbs-Thomson coefficient m L = average liquidus slope k = average partition coefficient C L = average liquid concentration D L = liquid diffusivity V = front velocity 2008 ANSYS, Inc. All rights reserved. 9 ANSYS, Inc. Proprietary

10 Analysis on Grain Refinement with Ultrasound (Direct Method) Flow induced by ultrasound: Ultrasonic Probe of D=20 mm A = 10 microns f = 17.5 KHz) Liquid Pool 2008 ANSYS, Inc. All rights reserved. 10 ANSYS, Inc. Proprietary

$Volume fraction (vapors) 2008 ANSYS, Inc.$

15 Quick Ultrasonic Modeling Technique (Indirect Method) Solve the acoustic field analytically using Rayleigh integral method and Helmholtz reduced wave equation: 2 2 ϕ ( p) + k ϕ ( p) = 0 ϕ ( p) = velocity potential k = 1/ 3ω / c k = magnitude of the wave vector Ultrasonic Pressure (P UT ) Ultrasonic Force 5.0E E E E+06 P, pa 3.0E E E E F (dp/dx), N/m3 2.0E E E E E E E E E+06 r, m -1.5E E+06 r, m Ultrasonic Pressure (P) of spherical waves as a function of the distance (r) from the ultrasonic probe for a Ti-6-4 alloy Ultrasonic volumetric force (P) of spherical waves a a function of the distance (r) from the ultrasonic probe for a Ti-6-4 alloy 2008 ANSYS, Inc. All rights reserved. 15 ANSYS, Inc. Proprietary

16 Quick Modeling Technique (Cont.) Ultrasonic Intensity Ultrasonic Heating 5.0E E+08 Iav, W/m2 4.5E E E E E E E E+06 RMS-Q, W/m3 8.0E E E E E E E E E E r,m 0.0E r, m RMS ultrasonic intensity (I av ) of spherical waves as a function of the distance (r) from the ultrasonic probe for a Ti-6-4 alloy RMS rate of ultrasonic heating for (Q) of spherical waves as a function of the distance (r) from the ultrasonic probe for a Ti-6-4 alloy Use Q as a source term in energy equation Use F as a source term in momentum equation 2008 ANSYS, Inc. All rights reserved. 16 ANSYS, Inc. Proprietary

17 2008 ANSYS, Inc. All rights reserved. 17 ANSYS, Inc. Proprietary Cavitation Bubble Dynamics Noltingk-Neppiras Model (modified Rayleigh model) to predict the cavity time-evolution in an acoustic field: P UT : Acoustic pressure distribution (predicted) Possible model improvements: - Herring-Flinn: allows for liquid compressibility and viscosity - Kirkwood-Bethe-Gilmore model: allows for cavity motion and free enthalpy change at the surface of a spherical cavity = γ σ σ ρ R R R P R P P P dt dr dt R d R L L UT v L

18 Ultrasonic Treatment: Prediction of Microstructure 2 mm x 9mm 20 mm x 90mm 2 mm x 9mm G E = 5x10 +7 nuclei/m 2 G G E = 5x10 +9 nuclei/m 2 E = 5x10 +9 nuclei/m 2 W/o UST With UST 2008 ANSYS, Inc. All rights reserved. 18 ANSYS, Inc. Proprietary

19 MMNC Processing using UST Dispersion of Nanoparticles in Molten Alloys Traditional processing methods (high energy ball milling, rapid solidification, electroplating, sputtering, etc.) are neither reliable nor cost effective. Traditional methods could not be used successfully for mass production and net-shape fabrication of complex structural components with reproducible properties and uniform structures. Ultrasonic cavitation based dispersion of nanoparticles into a liquid alloy was proven to be best suited for manufacturing of metal-matrix-nano-composite (MMNC) castings* UST modeling capability is needed to scale up the nanotechnology for manufacturing of cast MMNCs. * X. Li, Research Progress on Ultrasonic Cavitation based dispersion of nanoparticlesin Al/Mg melts for solidification processing of bulk lightweight metal matrix nanocomposites, TMS ANSYS, Inc. All rights reserved. 19 ANSYS, Inc. Proprietary

MMNC Processing using UST Dispersion of Nanoparticles in Molten Alloys UST induced phenomena that are involved in dispersing the nanoparticles: Ultrasonic cavitation (P>1000 atm and T>5000K) Shock

20 MMNC Processing using UST Dispersion of Nanoparticles in Molten Alloys UST induced phenomena that are involved in dispersing the nanoparticles: Ultrasonic cavitation (P>1000 atm and T>5000K) Shock force Acoustic streaming Phase interactions (A356 liquid-a356 vaporsnanoparticles-agglomerates): Brownian motion (Langevin model) Surface tension (Young-Laplace model) Drag (Schiller-Naumann model) Heat (Ranz-Marshall model) Mass (Schnerr-Sauer cavitation model) Li s dispersion model Alloy melt P D = 650 atm Van der Waals forces Capillary forces 2008 ANSYS, Inc. All rights reserved. 20 ANSYS, Inc. Proprietary

21 Length Scales in MMNC Modeling Micro ( μm) Macro (1 mm 1 m) Nano (1 100 nm) Meso ( μm) University of Wisconsin: Exp. work CTC: UST modeling 2008 ANSYS, Inc. All rights reserved. 21 ANSYS, Inc. Proprietary

22 A Modeling Strategy for Simulation of the MMNC Process Assisted by Ultrasonic Cavitation Multiphase Eulerian model A356 liquid primary phase A356 vapors secondary phase (typically 1 micron bubble size) Agglomerates of nanoparticles secondary phase (typically 1-10 microns in size) Individual nanoparticles (after separation) - secondary phase (typically nm in size) Phase interaction models (see slide 19) An instantaneous volumetric phase change (Agglomerates=>individual nanoparticles) takes place in the cavitation area); - Individual nanoparticles are spread uniformly by the shock force in all directions over a predetermined distance - Acoustic streaming helps further spreading the nanoparticles inot the bulk liquid 2008 ANSYS, Inc. All rights reserved. 22 ANSYS, Inc. Proprietary

23 Concluding Remarks and Future Work UST is a promising technology to improve the solidification structure and mechanical properties of ingots and castings (steel, Mg, Ti, Al and superalloys) Ultrasonic cavitation based dispersion of nanoparticles into a liquid alloy is best suited for manufacturing of metal-matrix-nano-composite (MMNC) castings UST modeling technology is currently used to scale up a nanotechnology to manufacture MMNC A356 castings R&D work is required to further develop, refine and integrate the UST and microstructure models in commercial M&S tools 2008 ANSYS, Inc. All rights reserved. 23 ANSYS, Inc. Proprietary

25 Classification of Modeling Techniques Model Generation Macro- Modeling Micro- Modeling Overall Chronology First Deterministic None Deterministic present Second Deterministic Deterministic Deterministic present Third Deterministic Stochastic Stochastic present Stochastic / Fourth None Probabilistic Probabilistic present 2008 ANSYS, Inc. All rights reserved. 25 ANSYS, Inc. Proprietary

ICME * : Paradigm to Enable Integration of Manufacturing and Design via

eutectics, etc. Secondary Phases carbides, eutectics, porosities, etc.

spacing interlamellar spacing in eutectics and eutectoids GRAIN AND PARTICLE

Orientation Co-Simulation Engine STRUCTURAL TRANSITIONS Semi-Empirical Neural

grains Material Modeling Yield Strength Hardness Fatigue Creep Fracture

Modeling * J. Allison, D. Backman, and L. Christodoulou et al.

26 ICME * : Paradigm to Enable Integration of Manufacturing and Design via Materials Models Design Modeling AMOUNT OF PHASES Primary Phases γ, δ, eutectics, etc. Secondary Phases carbides, eutectics, porosities, etc. Process Modeling PREDICTION OF STRUCTURE INTERPHASE SPACING dendritic arm spacing interlamellar spacing in eutectics and eutectoids GRAIN AND PARTICLE SIZE Coarsening Coalescence Continuous Nucleation Grain Growth and Orientation Co-Simulation Engine STRUCTURAL TRANSITIONS Semi-Empirical Neural Networks gray-to-white in cast iron columnar-to-equiaxed small grains-tolarge grains Material Modeling Yield Strength Hardness Fatigue Creep Fracture Toughness Deterministic Approaches Probabilistic Approaches Stochastic Modeling * J. Allison, D. Backman, and L. Christodoulou et al., Integrated Computational Material Engineering, JOM, November ANSYS, Inc. All rights reserved. 26 ANSYS, Inc. Proprietary

27 Solidification Map Development: Deterministic Numerical Analysis / Experiments Casting Conditions -superheat -mold condition -casting geometry -withdrawal rate -power input Solidification Conditions -liquid-solid (L/S) interface velocity -temperature gradient at T L -local cooling rate at T L -bulk and surface nucleation -fluid flow near the L/S interface Mechanical Properties Solidification Structure Macrostructure -grain size and direction -grain morphology Microstructure -spacing -secondary phases 2008 ANSYS, Inc. All rights reserved. 27 ANSYS, Inc. Proprietary

Numerical Simulation of Solidification Structure Formation during Continuous Casting in Fe 0.7mass%C Alloy Using Cellular Automaton Method

, pp. 903 908 Numerical Simulation of Solidification Structure Formation during Continuous Casting in Fe 0.7mass%C Alloy Using Cellular Automaton Method Minoru YAMAZAKI, 1) Yukinobu NATSUME, 1) Hiroshi