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., JapanMultiphysics 2009, Session 2.2 Impact and Explosions, 10 Dec., University of Science and Technology of Lille, France. Kumamoto National College of Technology
1. IntroductionExplosive forming method2. Experimental methodAluminum alloy forming3. Experimental resultsDeformation shape of aluminum alloy4. Simulation methodSimulation modelCalculation of pressure for explosive and waterConstitutive equation of aluminum alloy5. Simulation resultPressure contour of water partDeformation process and velocity of aluminum alloy6. ConclusionContents
Explosive FormingIntroductionThis 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 equipmentAluminum plate A5052-OExplosive 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 resultsPress forming equipmentPress type: mechanical pressPress cycle: 35[cycle/min]Lubrication: HT103These 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 methodExplosive mass10gFDM: 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.
Pressure calculation for waterMie-Grneisen parameterMie-Grneisen equation of stateSimulation methodIn order to calculate the pressure of the water, Mie-Grneisen 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 JWL parameter of explosive SEPV= r 0(initial density of an explosive )/r (density of a detonation gas)P*: PressureE : specific internal energyA,B,R,R,w : JWL ParameterSimulation methodThe pressure of the explosive part was calculated by using the JWL (Jones-Wilkins-Lee) equation of state.where A, B, R1, R2 and are JWL parameters.JWL parameter for the SEP are shown in above table.
Constitutive Equation The constitutive equation of the aluminum plate is described in the following: Simulation methodIn order to calculate of stress and strain of the aluminum alloy, we used this constitutive equation included the strain rate hardening.
Pressure contour and historyPropagation process of underwater shock wave. Pressure profile in water cell on the aluminum plate at r=0,10, 20, 30, 40 and 50mm. Simulation resultsThis 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 10ms, the underwater shock wave produced radiates spherically. The arc of the shock wave reaches the center of the aluminum plate at about 15ms.
Comparison of pressure values of anaysis result and experimental data Experimental equipment for the measurement of pressure of waterTungsten barSimulation 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.
Distance from tip of the explosive
Distance from tip of the explosive
Deformation velocitySimulation resultsThis 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 processExperiment: 39mmThis figure shows the deformation process on 20 ms time interval . Between 20 and 40ms, the deformation appears in the central part of the plate. At 60ms 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 400ms 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.
Deformation processTime(ms)Simulation results
Numerical SimulationSimulation model Simulation resultComparison of deformation shape
Experimental equipmentSimulation model
Stress distribution Above figure shows the distributin of normal stress along to deformation shape of the aluminum alloy at 20 and 40 ms. Black continuous line is top surface layer of aluminum and red dashed line is bottom surface layer of it. At 20ms, 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 40ms, 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 profileAbove 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
Burn technique for explosiveCJ volume burn method Conditions in the explosion were determined by calculating its reaction rate W, which is derived by the following formula V0Initial specific volume VCJSpecific volume of C-J stateP*: Pressure calculated from JWL EOSThe pressure P inside the grating for the explosion is calculated by the following formula: Simulation method
*Thank you Mr. Chairman.Im Hirofumi Iyama, Yatsushiro National College of Technology, from Japan.Id like to talk about Numerical Simulation of Sheet Metal Forming Using Underwater Shock Wave.*Contents of this presentationThe first, Introduction, I will explain the basis of explosive forming.The second, experimental method, the aluminum alloy formingwas carried out. The aluminum alloy is used as the parts of car.