Multiphysics 2009, Session 2.2 Impact and Explosions, 10 Dec., University of Science and Technology of Lille, France.
Study on Explosive Forming of Aluminum Alloy
Hirofumi Iyama, Kumamoto National College of Technology, Japan
Shigeru Itoh, Shock Wave and Condensed Matter
Research Center, Kumamoto Univ., Japan
Kumamoto National College of Technology
Contents
1. Introduction
・Explosive forming method
2. Experimental method
・Aluminum alloy forming
3. Experimental results
・Deformation shape of aluminum alloy
4. Simulation method
・Simulation model
・Calculation of pressure for explosive and water
・Constitutive equation of aluminum alloy
5. Simulation result
・Pressure contour of water part
・Deformation process and velocity of aluminum alloy
6. Conclusion
Introduction
Explosive Forming
Underwater shock wave
This slide shows, a general explosive forming method.
A metal die and metal plate set underwater, and an explosive sets upper side.
After detonation, an underwater shock wave was generated and propagated towards the metal plate and then hit it.
This metal plate is deformed by shock loading and collides with the metal die.
The feature of explosive forming that allows the die to sufficiently transfer its shape onto the plate is that the spring-back effect is less than with
ordinary forming methods, like punching and hydro bulging.
So, we considered using this method for aluminum alloy forming.
However, the aluminum alloy forming by static methods, such as hydro bulge forming or general punching, is difficult for
the aluminum forming, because the aluminum alloy is little elongation compared with steel.
In order to examine the application of explosive forming, we tried free forming of aluminum alloy as the basis of the study.
Experimental equipment
Aluminum plate： A5052-O
Explosive： SEP
Detonation velocity: 6970m/s
Detonation pressure: 15.9 GPa.
This slide shows an experimental equipment.
The aluminum plate was installed between the metal die and the blank holder, and the explosive was connected to the tip of the electric
detonator . We used a paper container filled with water.
We used explosive SEP, this is a plastic high explosive and is provided by Asahi Kasei Chemical Corp.
Experimental results
φ100
φ105
Explosive mass: 10 [g]
Bulge depth: 39 [mm]
Explosive forming
Press forming
Bulge depth [mm]
Press forming
Bulge depth: 28 [mm]
R4
Press forming equipment
Press type: mechanical press
Press cycle: 35[cycle/min]
Lubrication: HT103
50
40
30
20
10
0
-80
-40
0
Position [mm]
40
Sectional form
These figures show comparative forming results.
In the case of static punching, we used a punch of a 100mm diameter and a metal die has a 105mm diameter hole.
The explosive forming limit, shown in the upper figure, when we used 10g explosive, and the bulge depth was 39mm.
The configuration obtained by static press forming is shown in the lower figure. The maximum bulge depth was 28 mm.
A diagram of the results using the static press method under those from explosive forming is shown in the right hand figure.
Comparison of the two configurations makes it clear that the amount of deformation by explosive forming is larger.
80
Simulation method
Simulation model
(A5052-O)
Explosive mass：10g
FDM: Finite Difference Method (Lagrangian Code)
This slide shows a simulation model for aluminum forming.
The simulation method is FDM: Finite Difference Method by self coding.
z-r coordinate defined as this figure.
Each dimension was determined for the equipment used in the experiment.
Although a paper container was used in the experiment, side wall of water is treated as free surface.
The die was a rigid body.
The surface contact between the water and the aluminum plate was the slide boundary.
Simulation method
Pressure calculation for water
Mie-Grüneisen equation of state
r 0 c0 2
P
1  s 2
G0 

1

 G0 r 0 e


2 

P: pressure
e : internal energy
r0: initial density
r: density
G0： Grüneisen parameter
  1  r0 / r
Mie-Grüneisen parameter
Water
r0
(kg/m3)
C0(m/s)
S
G0
1000
1490
1.79
1.65
In order to calculate the pressure of the water, Mie-Grüneisen equation of state is used.
Parameters of this equation for water are shown in above table.
Simulation method
Pressure calculation of explosive
JWL(Jones-Wilkins-Lee) equation of state


 
 
E
P  A1 
exp(

R
V
)

B
1

exp(

R
V
)




1
2
VR
VR
V




1
2
*
V= r 0(initial density of an explosive )/r (density of a detonation gas)
P*: Pressure
E : specific internal energy
A,B,R１,R２, : JWL Parameter
JWL parameter of explosive SEP
A(GPa)
B(GPa)
R1
R2

365
2.31
4.30
1.10
0.28
The pressure of the explosive part was calculated by using the JWL (Jones-Wilkins-Lee) equation of state.
where A, B, R1, R2 and ω are JWL parameters.
JWL parameter for the SEP are shown in above table.
Simulation method
Constitutive Equation
The constitutive equation of the aluminum plate is described in the following:
 y  72  132 p
0.28
 12.8 P
σy : plastic stress, εp : plastic strain
0.710


ln  p /( 2.0 10  4 )
(MPa)
 p: strain rate.
ε
In order to calculate of stress and strain of the aluminum alloy, we used this constitutive equation included the strain rate hardening.
Simulation results
Pressure contour and history
Presure(MPa)
1000
r
0mm
10mm
20mm
30mm
40mm
50mm
800
600
400
200
0
100
200
Time( s)
300
400
Pressure profile in water cell on the aluminum plate at r=0,10, 20, 30, 40 and 50mm.
Propagation process of underwater shock wave.
This slide shows a propagation of the underwater shock wave by the simulation result. The left hand figure shows the pressure contour. The right hand side
figure shows the pressure history of the element where the water touches the aluminum plate surface at r= 0 to 50mm. From 5 to 10s, the underwater shock
wave produced radiates spherically. The arc of the shock wave reaches the center of the aluminum plate at about 15s.
Simulation results
Pressure (MPa)
Comparison of pressure values of anaysis result and
experimental data
900
800
700
600
500
400
300
200
100
0
Tungsten bar
10
20
30
Distance from tip of the explosive (mm)
Experiment
Simulation
Experimental equipment for the
measurement of pressure of water
This figure shows the comparison of pressure values by the experimental and simulation results.
The horizontal axis is the distance through the water from the bottom of the explosive.
The experimental data was measured using a tungsten bar pasted two strain gages.
When the shock wave through inside this tangsten bar, the shock velocity was measured by strain gages.
And then, from this shock velocity, the puressure is calculated.
From this figure, both pressure values of the underwater shockwave agree well.
Simulation results
Velocity(m/s)
Deformation velocity
350
300
250
200
150
100
50
0
r
0mm
10mm
20mm
30mm
40mm
50mm
0
50
100
150
200
250
Time( s)
300
350
400
This figure shows the deformation z-direction velocity at r= 0 to 50mm.
When the shock wave acting on the central part of the plate is large, the deformation velocity rises rapidly to about 280 m/s.
Movement of the initial velocity increase is from the central part of the aluminum plate gradually toward the perimeter, with the peak value
decreasing as it moves from the central area to the perimeter.
Deformation process
41.8mm
Experiment
: 39mm
This figure shows the deformation process on 20 s time interval . Between 20 and 40s, the deformation appears in the central part of the plate. At
60s the wave has apparently approached the die shoulder, the plate shown as bending down a little around the opening as deformation progresses.
This bulge at the die shoulder continues toward the center, whereupon the central part of the plate projects all at once in a great bulge, with the
aluminum plate over the opening assuming a hemispherical shape in the final stage. The amount of deformation of the aluminum plate from top to
bottom surface at 400s was shown as approximately 41.8mm. In the experimental result, it value was 39mm.
Conclusion
In this research, a numerical simulation was performed on
the free forming of the aluminum alloy plate by explosive
forming method.
1. The propagation process of an underwater shock wave
and the deformation process were simulated.
2. From experimental and simulation results, both pressure
values of the underwater shockwave agree well.
3. Peak velocity at center of the aluminum plate increased
up to about 280m/s.
Simulation results
Time(s)
380
360
340
320
300
280
260
240
220
200
180
160
140
120
100
080
060
040
020
000
Deformation process
Total elongation vs. Strain rate
(Aluminum base alloys)
Numerical Simulation
Simulation model
Comparison of deformation shape
Simulation result
φ120mm
Water
Electric detonator
Explosive(SEP:10g)
Cardboard
Clay
Water level
50mm(Die)
Al alloy sheet
φ100mm
Experimental equipment
Simulation model
Simulation results
Stress distribution
Time: 20 micro sec.
Time: 40 micro sec.
300
Bottom surfce layer
200
Meridial stress(MPa)
Meridial stress(MPa)
300
100
0
-100
100
0
Top surfce layer
-100
Top surfce layer
-200
-300
Bottom surfce layer
200
0
50
r(mm)
-200
100
-300
0
50
r(mm)
100
Above figure shows the distributin of normal stress along to deformation shape of the
aluminum alloy at 20 and 40 s. Black continuous line is top surface layer of aluminum and
red dashed line is bottom surface layer of it. At 20s, the inner part of aluminum alloy within
approxymately 30mm, because the stress value of bottom surface layer is greater than the
top surface layer, the deformation shape of aluminum allloy is formed below. At 40s, on the
part of die shoulder(from 50 to 65mm), because the stress of top surface layer is greater
than the bottom surface layer, the deformation shape is formed convex to above.
Simulation results
Pressure profile
Presure(MPa)
1000
600
400
200
0
1000
Presure(MPa)
r
0mm
10mm
20mm
30mm
40mm
50mm
800
r
0mm
10mm
20mm
30mm
40mm
50mm
800
600
400
200
0
100
50
Time( s)
100
200
Time( s)
300
400
Above figure shows the pressure history of the element of the water which touches the aluminum plate
surface in r= 0, 10, 20, 30, 40 and 50mm.
Introduction
Simulation method
Burn technique for explosive
CJ volume burn method
Conditions in the explosion were determined by calculating its reaction rate W, which is derived
by the following formula
W 1
V0  V
V0  Vcj
V0：Initial specific volume
VCJ：Specific volume of C-J state
The pressure P inside the grating for the explosion is calculated by the following formula:
P  ( 1  W )P*
P*: Pressure calculated from JWL EOS