Flow effects on the dendritic microstructure of AlSi-base alloysSecondary dendrite arm spacing 1.λ...

Flow effects on the dendritic microstructure ofAlSi-base alloys

Lorenz Ratke, Amber Genau, Sonja SteinbachDLR

Institute of Materials Physics in SpaceCologne, Germany

ICSSP-4, Chennai, 2009

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Flow effects on cast microstructures

Effect of fluid flow onmorphology is unkown in a

quantitative sense !

Mass- and heat transport determine the solidified microstructure andits structural features:

- primary dendrite spacing- secondary dendrite arm spacing- eutectic spacing- segregation- specific surface area of the dendritic network- fractal dimension of the branched dendrites- precipitation of intermetallics- ...

Picture from G. ZimmermanACCESS, Aachen


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Therefore the ESA MAP* MICAST was establishedten years ago to achieve

Quantitative understanding of the influence of fluid flow on the developmentand evolution of the microstructure of cast Al alloys.

→ Development of global and microscopical modelsto predict the evolution of the microstructure under the influence of controlled fluid flow

→ Experiments under microgravity conditions (sounding rockets, ISS)diffusive and controlled convective solidification conditions

→ Laboratory experimentsusing forced fluid flow by rotating magnetic fieldsas an experimental parameter

*MAP= Microgravity Application Project


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Objectives of the present study

Microstructure evolution inSome binary AlSi and two ternary AlSiCu alloys without fluid flow (laboratory and microgravity)and with fluid flow induced by RMF

Looking for good microstructural descriptors to catch the flow effects

primary spacing, secondary spacing, specific surface area, fractal dimension

Support (or not) of observations made on other alloyslike AlSiCu, AlSiMg, AlSiFe, AlSiMn...


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Experimental approach: the alloysAl-5wt.%Si, Al-6wt.%Si, Al-9wt.%Si


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AlSi6Cu4 and AlSi9Cu4 alloys

Al-6wt.%Si-4wt.%Cu1: liquid2: fcc-Al at 611.9 °C3: Al-Si eutectic at 563.7 °C4: Al-Si-Al2Cu at 496.7 °(after ThermoCalc, V.Witusiewicz)

Al-9wt.%Si-4wt.%Cu1: liquid2: fcc-Al at 590 °C3: Al-Si eutectic at 569 °C4: Al-Si-Al2Cu at 523 ° C(after ProCast data base)


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Experimental approach: ProcessingDirectional solidification with

constant solidification velocityand

constant temperature gradient ahead of s/l interfaceand

flat isotherms (aerogel crucibles)

Process parameters:-v = 0.015 – 0.15mm/s-G = 3K/mm-fluid flow induced by RMF


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The RMF parameters used

M. Hainke, PhD-thesis, U Erlangen-Nuremberg, 2004

Al-7wt.%Si

Parameters used:- R = 4mm- G = 3 K/mm- vG = 0.1mm/s- B = 1-6mT- f = 50Hz- h = 100mm- Ta ≤ 2500- Re ≤ 50


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Microstructural evaluation

TITAL

Primary dendrite stem spacing λ1 Specific surface area SV=Aαe/V

secondary dendrite arm spacing λ2A

lSi5

, v =

0.12

mm

/s, G

= 3

K/m

m, 0

mT

Note:

!

SV

= 2H with H ="A

"V= average curvature


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Fractal dimension measurement- a descriptor for branching?

Method:• Outline a single dendritic structure in a section• Characterize its interface to the eutectic matrix with a 1pixel interface• Measure the interface length by the box counting method

– boxes needed to cover the whole interface. Vary the box size.• Plot: Interface length as a function of box size• The fractal dimension of the interface is the slope of the straight line in the range of 55 µm to 550 µm• Note: The fractal dimension in a 2D section is that in 3D too.

y = - 0.75x + 5.3

! = 1 + |m| = 1.75

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3 3.5

Log [ Box Size, " (µm) ]

Lo

g [

Nu

mb

er

of

Bo

xe

s,

N("

) ]


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Microstructures


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Typical Microstructures – effect of solidification velocity

B = 0mTv = 0.03mmsG = 3K/mm

AlSi5 AlSi6 AlSi9



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Effect of RMF: macrosegregation


AlSi5 AlSi6 AlSi9

B = 6mT, 50Hzv = 0.03mmsG = 3K/mm


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Flow effect: Macro-segregation in AlSiCu alloys

Al -

6w

t.%S

i - 4

wt.%

Cu

0.03

mm

/s

G =

3K

/mm

Al -

9w

t.%S

i - 4

wt.%

Cu

0.02

mm

/s

G=3

K/m

m

6 mT 6 mT

0 mT0 mT


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Macro-segregation quantitatively

Segregation of Silicon and Coppertowards the sample centre(measurement by EDX in SEM withcalibration standards)

No axial segregation for bothelements measured !

Effect of secondary flows

Modelled for these alloys by Hainkeand Dagner (U Erlangen) and YvesFautrelle (SIMAP/EPM)

AlSi9Cu4, v=0.02 mm/s, B=6 mTAverage of 8 sections along the processinglength


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Microstructure parameters


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Primary spacing AlSi alloys

Primary dendrite stemspacing depends onsolidification velocity as aninverse fourth power, asexpected (LGK)

Fluid decreases theprimary spacing (PDS)Same observations madein AlSiCu and AlSiMgalloys

!

"1

=72#2$%c

0m

LD

l

k

&

' ( (

)

* + +

1/ 4

1

G1/ 2

1

v1/4


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Primary spacing AlSi Observations:1. Increase of of the rate constant

with Si content as expected. Inthe LGK picture

2. and taking into account theeutectic fraction we arrive at

3. Flow reduces the constant term:thus fluid flow is not treatable asan effective diffusion constantenhancer

!

< "1v1/4

> # (DLc0 )

1/ 4

!

"1

=a + b(c

0#c$ )

Gv1/4

a,b = const.(DL,m

L,%,k)


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Primary spacing ↔ fluid flow

General idea:

Tertiary arms become newprimary arms due toconstituional supercoolingenhancement between dendrites

→

primary spacing decreases

Coupling of different effects :- interdendritic convection

- constitutional supercoolingbetween primary stems

- locally varying permeability ofthe mush


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Secondary dendrite arm spacing

1. λ2 follows classicalcoarsening law tf1/3 in thediffusive case

2. with increasing co the SDASdecreases

3. Flow enhances coarseningand a change in kinetics(tf1/3 → tf1/2) !

)cc)(k1(m

)c/cln(DM

e0l

0e

!!

"=

8.62AlSi9

10.36AlSi6

11.24AlSi5

M [µm3/s]Co [wt.%]


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InterpretationFluid flow accelerates dendrite armcoarsening (Stokes type flow aroundsecondary arms from the mush tiptowards the bottom)Boundary layer flow solution (Ratke,Thieringer, Diepers, Beckermann)yields a new kinetic law

!

"2 =1

2M

PR ( fS )#p

D$

%

& '

(

) *

1/ 3

t f = K t f

!

K(B2) = K(B

1)1" c

0(B

1)/ c

e

1" c0(B

2)/ c

e

B2

B1

#

$ %

&

' (

2 / 3

K=5.7 in A357 Kexp= 4.8K=6.3 in AlSi6Cu4 Kexp= 4.9


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Comparison with microgravity results

Results of four µg-experiments with AlSi6:

TEXUS 39, TEXUS 41, Maxus7 andMapheus yield3 values for diffusive growth and2 values for µg+RMF

λ2 follows classical coarsening law tf1/3 inthe diffusive case

Flow enhances coarsening and a changein kinetics as measured in the lab, but notdisturb by natural convection

Further experiments in the MSL of the ISShave started this month (Nov 7th) and willcontinue January 2010.


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Specific surface area Sv – diffusive case

1. Sv independent of sample section2. Identical time relation:

1/Sv ~ tf 1/3

Sv scales with solidification time tf

!

1

SV=1

SV 0+ a " t f

1/ 3

!

"23

= "203

+ BMt f

M =D# ln(ce /c0)

ml (1$ k)(c0 $ ce )

B % 5.5

!

a =B " M(T,c

0,U /v)3

2

2.53

2.68

2.68

aexp

1.81

1.92

1.98

atheo

8.62AlSi9

10.36AlSi6

11.24AlSi5

M[µm3/s]

Co[wt.%]


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Specific surface area Sv – convective case

Also a scaling relation:

1/Sv ~ tf 1/2 ~ λ2

But:All curves fall together!

And one could equallywell fit a cube root law.


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Fractal dimension

Fractal dimension of selected dendrites in cross sections averages of 4 to 20dendrites, mostly 6 to 14.


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Fractal dimension

Bisang U., Bilgram J.H. J. Cryst. Growth 166 (1996) 207-211.Yang A., Xiong Y., Liu L. Sci. Tech. Adv. Mat. 2 (2001) 101-103.Kaye, B.H. A Random Walk Through Fractal Dimensions VCHPublishers, New York 1989.

Unexpected result:

There is no effect offlow on the fractal dimension.

Interpretation?

Observations by others:Xenon dendritesδ = 1.42 ± 0.05, independent ofundercooling and aging time(Bilgram et. al.)

Ni-base superalloysδ= 1.228 – 1.418 (Yang et al)δ increases with solidificationvelocity

For some dendrites, two linear regions wereapparent. After Kaye these are

• structural fractal (δS) = overall morphology

• textural fractal (δT) = surface roughness


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ConclusionsFluid flow created by RMF fields induces in solidification of AlSi and other AlSi-basealloys

Reduced primary dendrite spacingsIncreased secondary dendrite arm spacing and modifies the coarseningkineticsradial macro-segregation of alloying elements (not shown)Cannot be thought as simply enhancing mass transport

Specific surface area of primary phase is less affected by fluid flow than SDASFractal dimension of dendrites not modified by fluid flow

Further experiments with much better statistics concerningSpecific surface area (high resolution micrographs) and fractal dimension arenecessary

Such evaluations are ongoing at the moment

Microgravity experiments provide a convention free environment confirming labresults and building benchmark experiments.Future µg experiments on the ISS and sounding rockets etc. will enlarge the database.

Flow effects on the dendritic microstructure of AlSi-base alloysSecondary dendrite arm spacing 1.λ...

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