TENTH INTERNATIONAL ALUMINUM EXTRUSION TECHNOLOGY
SEMINAR AND EXPOSITION
Constitutive Equations for Hot Extrusion of AA6005A,
AA6063 and AA7020 Alloys
Tommaso Pinter1
Mohamad El Mehtedi2
1Almax Mori S.r.l., Mori - Italy2Università Politecnica delle Marche, Ancona - Italy
Introduction Experiments &
Numerical Simulation Results Discussion Future Developments
Schedule (20’)
Necessity to Predict Aluminium Flow & Tool Stress
Poor Availability of Constitutive Equations
Need of Hot Torsion Tests to provide Constitutive Parameters to implement in FEM codes
Validate Constitutive Equations using Industrial Applications
Intentions
Torsion Tests DC homogenized billets
courtesy of Nedal Aluminium B.V.
Specimens r=4mm Pre-Heating: 1 Ks-1 (5
minutes) έ= 0.01-1-10s-1
T=450-500-550-575 °C Water Quenching at ε=30
3
33
2
M( m' n')
R
2
3
N R
L
NMm log/log'
NMn log/log'
Extrusion Why? To establish BCs for numerical
simulations and validate the FEM model How? 50MN (11’’) direct press by ETEM
S.A. What? Transport Profile in AA6005
Extrudate Temperature: 550-560 °C RAM force required: 91% press capacity
Numerical SimulationTransient simulation (51 seconds) with 30 variable time steps for a total CPU time 76 hours.
T Workpiece: 460 °C Billet Taper: 20 °C/m T Die: 480 °C T Container: 430 °C Ram Speed: 3 mm/s HTC die/workpiece: 500
W/m2K HTC container/billet: 3000
W/m2K
Results - Laboratory
0
10
20
30
40
50
60
70
0 1 2 3 4 5 6 7 8 9 10equivalent strain
equ
ival
ent
stre
ss [
MP
a]
450°C 500°C550°C 575°C
1 s-1
10 s-1
0.01 s-1
AA 7020
0
10
20
30
40
50
0 5 10 15 20 25 30 35 40equivalent strain
equ
ival
ent
stre
ss [
MP
a]
450°C 500°C550°C 575°C
1 s-1
10 s-1
0.01 s-1
AA 6063
0
10
20
30
40
50
0 5 10 15 20 25 30equivalent strain
equ
ival
ent
stre
ss [
MP
a]
450°C 500°C550°C 575°C
1 s-1
10 s-1
0.01 s-1
AA 6005
Results - Laboratory
Alloy n QHW [J/mol] A [sec-1] α [MPa-1]
AA 6063 5.12 204078 6.67E+12 0.045
AA 6005A 5.16 182798 9.84E+9 0.053
AA 7020 5.37 232568 7.86E+13 0.038
n
p HWε A sinhα σ exp( Q / RT)
0.001
0.01
0.1
1
10
100
0.1 1 10
sinh(a)
450°C
500°C
550°C
575°C
AA6063
n= 5.1
a= 0.045
0.001
0.01
0.1
1
10
100
0.1 1 10
sinh(a)
450°C
500°C
550°C
575°C
AA6005
n= 5.1
a= 0.052
0.001
0.01
0.1
1
10
100
0.1 1 10
sinh(a)
Str
ain
rate
[1/
s]
450°C
500°C
550°C
575°C
AA7020
n= 5.3
a= 0.038
Results - Laboratory
1.E+10
1.E+11
1.E+12
1.E+13
1.E+14
1.E+15
1.E+16
1.E+17
1 10 100
Peak flow stress (MPa)
Z (
1/s)
AA 7020
AA6063
AA6005
Q= 206 kJ/mol
)RT/Qexp(Z HW
Results - Simulation Good correspondence of
Temperature and profile Deformation
RAM force overestimated (flow stress not dependent on strain)
Extrudability Data were normalized in respect of AA6005A peak force
Results - Simulation
0.50.60.70.80.9
1.01.11.21.31.4
0 10 20 30Ram Displacement [mm]
Nor
mal
ized
Ram
For
ce 7020
6005A
6063
Results - SimulationTemperature Comparison
460
465
470
475
480
485
490
495
500
0 10 20 30 40 50
Extrusion Time [sec]
Tem
per
atu
re [
°C]
. 7020
6005A
6063
Discussion The peak stress values of the AA6005 alloy are
close to AA7020 for low Z-values, while in the high-Z regime, the stresses were closer to the AA6063 values.
The simulation results show that to extrude the same profile in alloy AA6063, a ram force 17% lower than that used in AA6005, is required.
The implementation in FEM codes of a relationship where flow stress (σ) is dependent on the strain (ε) seems mandatory to properly predict the die behavior under working conditions.
Future Developments
Implement an ε dependent constitutive equation (Hansel – Spittel)
Validate the model in respect of the Ram Force Vs Time
Simulate the real pressure map on the tool
Give accurate indication of die stress
New Equations in HX
In the Hansel-Spittel equation the flow stress () dependence on strain and strain rate is described by the expression:
where A and mi are material parameters and T is the
absolute temperature.The first 8 coefficients and A were calculated thanks to a
linear regression of all the flow stress experimental data obtained for alloy AA6005A while m9 has been settled equal to zero.
0 3 7 10 13 16 20 23 26 30 33 36 39 43 46 49 52 56 59 62 660
10
20
30
40
50
60
70
Hansel & Spittel
ExperimentalPredicted TransientPredicted Steady
Time [s]
RAM
For
ce [M
N]
0 5 10 15 20 2510
15
20
25
30
35
40
Experimental Theoretical
σ
ε
Results
Almax-Mori & Alumat
Alumat S.r.l.Via Lisbona 924040 Ciserano (BG)
[email protected] www.alumat.it
Almax-Mori S.r.l.Via Matteotti 1338065 Mori (TN)
[email protected] www.almax-mori.it