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Presentation title – Presenter/ref. - 17 June 2016 - p.1Presentation title – Presenter/ref. - 17 June 2016 - p.1

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Numerical Modeling of Zirconium Alloys Hot Extrusion

Alexis Gaillac, Pierre Barberis

18th ASTM Int'l Symp on Zr in the Nuclear Industry

16-19 May 2016 – Hilton Head Island - USA

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Numerical Modeling of Zirconium Alloys Hot Extrusion - Alexis Gaillac - p.3

18th Int'l Symp on Zr in the Nuclear Industry - 16-19 May 2016 – Hilton Head Island - USA

Outline

Introduction

The Hot extrusion process

Numerical modeling of Zr manufacturing processes

Description and validation of the models

Analytical and Finite Element model

Recrystallization model

Validation of the models

Applications

Extrusion loads

Recrystallization

Lubricants and tools optimization

Conclusion

© AREVA NP – Property of AREVA NP

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Outline

Introduction







Applications

Extrusion loads

Recrystallization


Conclusion


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Tubes hollows

With suitable geometry

for cold pilgering

Without surface defects

Without microstructural

heterogeneities

IntroductionThe Hot Extrusion process


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Direct hot extrusion through a conical die

Billets machined from forged bars

Extrusion temperature = 600°C

Extrusion ratio = 10

IntroductionThe Hot Extrusion process


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IntroductionNumerical modeling of Zr manufacturing processes

Since the 1990’s, AREVA NP uses numerical modeling for

a mastering of the whole Zr manufacturing processes.

Extractive metallurgy

VAR Melting

Forming processes

(Forging, Extrusion, Rolling, … )

Heat treatments, Quenching

US Inspections

VAR Melting

ASTM STP 1529, Chengdu 2010

Cold Pilgering

ASTM STP 1354,

Toronto 1998

J. Mater. Process.

Technol., Vol. 117, 2006

Quenching

ASTM STP 1543,

Hyderabad 2013

Resistance Butt

Welding

ASTM STP 1543, Hyderabad 2013


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IntroductionNumerical modeling of Zr Hot Extrusion

For Hot Extrusion, the purpose of numerical modeling is to :

Better understand the effect of extrusion parameters on the

Extrusion load

Microstructural evolutions during extrusion

Stresses and temperatures applied to the tools

Check the capability of extrusion press and tools for a new configuration

Optimize extrusion parameters for a given material and geometry, in order to

ensure a good quality of the extruded products


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Outline

Introduction







Applications

Extrusion loads

Recrystallization


Conclusion


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Analytical Model (AM)

First simple estimation for extrusion load

Isothermal and homogeneous deformation of the billet is assumed

𝐹 = 𝐹𝑑 + 𝐹𝑓

𝐹𝑑 = 𝜋. 𝑅𝑜𝑏2 − 𝑅𝑖𝑏

2 . 𝜎0. ln 𝜆

𝐹𝑓 = 2. 𝜋. 𝑅𝑜𝑏 + 𝑅𝑖𝑏 . 𝐿𝑏. 𝜎0.ഥ𝑚

3

𝜆 =𝑅𝑜𝑏2 − 𝑅𝑖𝑏

2

𝑅𝑜𝑡2 − 𝑅𝑖𝑡

2

Extrusion load

Deformation load

Friction load

Reduction ratio


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Analytical Model (AM)

First simple estimation for extrusion load

Isothermal and homogeneous deformation of the billet is assumed

Strain rate

(s-1)

Flow stress (MPa) at Temperature (°C)

500 600 700 800

0.1 224 165 104 74

1 240 180 132 96

10 257 196 169 127

𝑇𝑒𝑥𝑡𝑟𝑢𝑠𝑖𝑜𝑛 =𝑇𝑖𝑛𝑖𝑡 + 𝑇𝑚𝑎𝑥

2

𝑇𝑚𝑎𝑥 = 𝑇𝑖𝑛𝑖𝑡 +ln 𝜆 . 𝜎0𝜌. 𝐶𝑝

𝐹𝑑 = 𝜋. 𝑅𝑜𝑏2 − 𝑅𝑖𝑏

2 . 𝜎0. ln 𝜆

𝐹𝑓 = 2. 𝜋. 𝑅𝑜𝑏 + 𝑅𝑖𝑏 . 𝐿𝑏. 𝜎0.ഥ𝑚

3

Average flow

stress from

torsion and

compression

tests (Zircaloy-4)


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Finite Element Model (FEM)

2D thermo-mechanical coupled model, Forge NxT software

Initial geometries and meshing


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Geometries and meshing during extrusion


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Flow stress as a function of temperature, strain and strain rate

From torsion and compression tests (Zircaloy-4)


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Recrystallization Model

Model developed by Gaudout [1] and based on the

Gourdet-Montheillet [2] and Avrami [3] approaches

From FEM results (temperature, strain and strain rate)

Dynamic microstructure fragmentation during extrusion (Gourdet-Montheillet)

Post-dynamic grain growth during cooling of the extruded tube (Avrami)

The result is a recrystallized volume fraction ( = surface fraction of equiaxed

grains on the micrographs)

Model parameters were fitted on recrystallized volume fraction after torsion

tests and heat treatments

Schematic representation of the

microstructure during fragmentation [1].

Thick lines are grains boundaries

(crystallographic misorientation > 15°),

fine lines are sub-grain boundaries.


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Extrusion loads

Calculated loads are consistent with experimental one

Extrusion load (T)

Experimental Finite Element Model Analytical Model

Min 1600

Max 18001700 1667

Experimental loads

for Zircaloy-4 tubes


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Temperature

Calculated temperatures are consistent with experimental ones


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Recrystallization

Recrystallized volume fraction ( = surface fraction of equiaxed grains on

the micrographs) after small scaled extrusion tests and heat treatments

Rather good agreement between numerical results and experimental ones


Figures from Gaudout [1]

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Outline

Introduction







Applications

Extrusion loads

Recrystallization


Conclusion


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Extrusion loads

Extrusion load curve can be decomposed into 4

sequences and explained using FEM results


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Extrusion loads



Filling of the gaps between billet and tools


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Extrusion loads




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Extrusion loads



Peak load (lower temperature and maximum flow stress because of

lower strain), front end of the tube exits the die


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Extrusion loads




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Extrusion loads



Maximum temperature and minimal load, then pseudo-steady-state


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Extrusion loads




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Extrusion loads



Rising load due to the chilling effect of the tools


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Recrystallization at front end

RX ratio = surface fraction of equiaxed grains

Outer surface: RX ratio = 95% Mid-thickness: RX ratio = 70%

300mm from front end = steady-state microstructure


R

L

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Recrystallization at front end

Results from the FEM + recrystallization model

Consistent with experimental ones

RX ratio lower at front end because of lower strain

Following our experience, to avoid cracks or voids during pilgering,

necessary discarded length (RX<50%) is about 100 mm

This model is validated and can be applied to new extrusion configurations


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Choice of the right tools materials and lubricant

Mandrel: up to 700 MPa at 600°C

Die: up to 680°C at the end of extrusion

Lubricant: temperature range 450 – 650°C


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Outline

Introduction







Applications

Extrusion loads

Recrystallization


Conclusion


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Conclusion

Conclusion

Models are validated regarding to experimental data

For the standard extrusion configuration, models give better

understanding of the effect of process parameters on the

Extrusion load

Microstructural evolutions during extrusion

Stresses and temperatures applied to the tools

For new configurations (reduction ratio, extruded material, …),

models are great tools to

Check the capability of extrusion press and tools

Optimize extrusion parameters for a given material and geometry, in

order to ensure a good quality of the extruded products


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Thanks

Any questions ?


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