Study on Explosive Forming of Aluminum AlloyHirofumi Iyama, Kumamoto National College of Technology, Japan

Shigeru Itoh, Shock Wave and Condensed Matter

Research Center, Kumamoto Univ., Japan

Multiphysics 2009, Session 2.2 Impact and Explosions, 10 Dec., University of Science and Technology of Lille, France.

Kumamoto National College of Technology

1. Introduction・ Explosive forming method2. Experimental method

・ Aluminum alloy forming3. 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 alloy6. Conclusion

Contents

Explosive FormingIntroduction

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 ： SEPDetonation velocity: 6970m/sDetonation 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.

Explosive mass: 10 [g] Bulge depth: 39 [mm]

Press formingBulge depth: 28 [mm]

Experimental results

φ105

φ100

R4

Press forming equipmentPress type: mechanical pressPress cycle: 35[cycle/min]Lubrication: HT103

0

10

20

30

40

50

- 80 - 40 0 40 80 Position [mm]

Bulge depth [mm]

Press form ing Explosive form ing

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.

Simulation modelSimulation method

(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.

P: pressuree : internal energy0: initial density: density0 ： Grüneisen

parameter /10

Pressure calculation for water

Mie-Grüneisen parameter

Mie-Grüneisen equation of state

0 0

(kg/m(kg/m33))CC00(m/s)(m/s) SS 00

WaterWater 10001000 14901490 1.791.79 1.651.65

Simulation method

e

s

cP 00

02

200

21

1

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.

Pressure calculation of explosiveJWL(Jones-Wilkins-Lee) equation of state

VE

)VRexp(VR

1B)VRexp(VR

1AP2

21

1

*

JWL parameter of explosive SEP

0.281.104.302.31365

R2R1B(GPa)A(GPa)

V= 0(initial density of an explosive )/ (density of a detonation gas)P*: Pressure E : specific internal energyA,B,R １ ,R ２ , : JWL Parameter

Simulation method

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.

σy : plastic stress, εp : plastic strain : strain rate.pε

Constitutive Equation

The constitutive equation of the aluminum plate is described in the following:

(MPa))100.2/(ln8.1213272 4710.028.0 pPpy

Simulation method

In order to calculate of stress and strain of the aluminum alloy, we used this constitutive equation included the strain rate hardening.

Pressure contour and history

Pre

sure

(MP

a)

Time(

0mm10mm20mm30mm40mm50mm

s)

r

0 100 200 300 400

200

400

600

800

1000

Propagation process of underwater shock wave.

Pressure profile in water cell on the aluminum plate at r=0,10, 20, 30, 40 and 50mm.

Simulation results

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 10s, the underwater shock wave produced radiates spherically. The arc of the shock wave reaches the center of the aluminum plate at about 15s.

Comparison of pressure values of anaysis result and experimental data

0100200300400500600700800900

10 20 30

Distance from tip of the explosive

Pre

ssur

e

Experiment Simulation

Experimental equipment for the measurement of pressure of water

Tungsten bar

Simulation results

(mm)

(MPa

)

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.

Vel

ocit

y(m

/s)

Time(

0mm10mm20mm30mm40mm50mm

s)

r

0 50 100 150 200 250 300 350 4000

50100150200250300350

Deformation velocitySimulation results

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

41.8mmExperiment: 39mm

This figure shows the deformation process on 20 s time interval . Between 20 and 40s, the deformation appears in the central part of the plate. At 60s 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 400s 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.

000020040060080100120140160180200220240260280300320340360380

Deformation process

Time(s)

Simulation results

Total elongation vs. Strain rate(Aluminum base alloys)

Numerical Simulation

Simulation model

Simulation result

Comparison of deformation shape

Experimental equipment Simulation model

Top surfce layer

Bottom surfce layer

r(mm)

Mer

idia

l str

ess(

MP

a)

Time: 20 micro sec.

0 50 100-300

-200

-100

0

100

200

300

Top surfce layer

Bottom surfce layer

r(mm)M

erid

ial s

tres

s(M

Pa)

Time: 40 micro sec.

0 50 100-300

-200

-100

0

100

200

300

Stress distribution

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 20s, 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 40s, 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 profileP

resu

re(M

Pa)

Time(

0mm10mm20mm30mm40mm50mm

s)

r

0 100 200 300 400

200

400

600

800

1000P

resu

re(M

Pa)

Time(

0mm10mm20mm30mm40mm50mm

s)

r

0 50 100

200

400

600

800

1000

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.

Simulation results

Introduction

Burn technique for explosive

CJ volume burn method

cjVV

VVW

0

01

*P)W1(P

Conditions in the explosion were determined by calculating its reaction rate W, which is derived by the following formula

V0 ： Initial specific volume

VCJ ： Specific volume of C-J state

P*: Pressure calculated from JWL EOS

The pressure P inside the grating for the explosion is calculated by the following formula:

Simulation method