Contribution to modelling the effect of explosive on accelerated material in explosion welding.

Benak, Michal ; Taraba, Bohumil ; Turna, Milan 等

1. INTRODUCTION

Explosion welding is a process of solid state welding, where bonding of materials occurs due to effect of dynamic impact of accelerated and stable material. The power for acceleration of material is attained from burning of explosive. Welded joint is characterised with an undulated boundary of both materials. Knowing of kinematic parameters of welding is a precondition for a proper selection of basic welding parameters. Computer modelling is an efficient way how to predict the kinematic parameters of welding process. Review of actual publications has shown that the explosion welding process was modelled by different methods and it is not clear what modelling procedure was employed for modelling the effect of burning explosive on the surface of accelerated material. The presented contribution has character of numerical experiment, where three ways of placing the effect of pressure of combustion products on accelerated material were applied: force proper, normal effect of pressure on the surface of accelerated metal and discretisation of pressure from combustion products on the forces in the nodes of generated mesh. Two process parameters were studied: flight velocity of accelerated material and the dynamic angle of collision. Modelling of explosion welding process was performed by use of ANSYS software.

2. THEORETICAL BACKGROUND

The theoretical principles refer to kinematic parameters of process. A parallel configuration of welded materials is considered, Fig. 1 (Turna).

[FIGURE 1 OMITTED]

The burning explosive acts on the surface of accelerated material in the plane of detonation front (Chapman-Jougett plane) by pressure [p.sub.cj]. The pressure of expanding combustion products drops exponentially with time, according to the relationship (Turna)

[p.sub.t] = [p.sub.cj]exp(-t / [tau]), [Pa] (1)

where t is time [s], [tau]--time constant, which depends of the explosive type [s], [p.sub.cj] is the pressure in the Chapmann-Jouguet plane. The cladding plate velocity w0 bisects the angle between the initial plate and the deformed plate orientation (Akkari-Mousavi)

[w.sub.0] = 2 [w.sub.d] sin([beta]/2), [m.[s.sup.-1]] (2)

where [w.sub.d] [m.[s.sup.-1]] is the velocity of detonation front, [beta] [[degrees]] is the bend angle.

3. EXPERIMENTAL

Aluminium was welded with structural carbon steel in experimental conditions. Thickness of aluminium material was 4 mm, while the thickness of steel plate was 20 mm and the spacing distance (stand off) between the materials was 8 mm. The parameters attained from the experiments were as follows (Nesvadba):

[p.sub.cj] = 1.14 GPa,[w.sub.d] = 1536 m.[s.sup.-1], [tau] = 4.49 [micro]s, [w.sub.d] = 372 m.[s.sup.-1], [beta] = 13.9[degrees].

4. NUMERICAL SIMULATION

The numerical simulation of process had the character of numerical experiment. The geometric model of process was the same for all analysed loading modes, Fig. 2. Owing to great size of welded materials, two-dimensional model was applied. The solved task was non-stationary and non-linear. Impact of materials welded was solved as a standard contact task, regardless the material environment between the plates.

[FIGURE 2 OMITTED]

Material models were regarded as elasto-plastic with kinematic strengthening, Tab. 1 (Ansys Theoretical Manual).

Simulation models differed in the way of modelling the surface loading of the accelerated material. Three simulation models were created:

* model No.1--material was loaded in Chapmann-Jouget plane with an equivalent force, which corresponded to pressure effect of combustion products, Fig. 3, Fig. 4.

* model No.2--material was loaded with pressure, reducing with time, Fig. 5,

* model No.3--pressure effect was modelled with force components [F.sub.y] and [F.sub.x], Fig. 6. The solution was achieved by iterative method.

Modelling of loading moving over the surface of accelerated material was solved by use of time functions (Array parameters) (Ansys).

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

5. ATTAINED RESULTS

The results from numerical experiment are shown in Figs. 7 to 9. Pictures show the deformed shapes of materials and the velocity fields in vector images with values given in selected points. The sought bend angle was determined from the geometry of deformed shape.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

Comparison of values of dynamic angle of collision [beta] from experiment and from computer modelling is shown in Table 2.

6. CONCLUSIONS

Numerical analysis has shown that the processes with time base at the level of microseconds can be modelled by computer. Three ways of pressure application from combustion products of a burning explosive on accelerated material were analysed in form of numerical experiment. Application of an isolated force has shown that the loading effect on material surface was very intense. It resulted in material impact velocities with the values around 500 m.[s.sup.-1] and bend angle [beta]= 18.7[degrees]. Surface loading by pressure (model No. 2) resulted in finding, that the normal acting of pressure on surface is related only to non-deformed generated net. There does not exist shifting force in x axis direction during flight, at model No. 2, and the achieved impact angle was smaller than that measured at experiment. The flight velocities were lower than those found out in experiment (around 340 m.[s.sup.-1]). Model No.3 can be considered acceptable, with very good measure of agreement with experiment. The velocity field corresponds to flight velocity from experiment and the impact angle differed from that measured by only 0.2[degrees].

The given results have shown that computer modelling allows to predict the kinematic parameters of explosion welding process. The most suitable way of placing the load on the surface of accelerated material seems to be application of method according to model No. 3.

7. ACKNOWLEDGEMENT

The research has been supported by VEGA MS and SAV of the Slovak Republic within the project No. 1/3191/06 and 1/0721/08.

8. REFERENCES

Akkari-Mousavi, S.A.A., Barret, L.M., Al-Hassani, S.T.S. (2008). Explosion welding of metal plates. Journal of materials processing technology. 202 224-239

Ansys Theoretical Manual. (2005). Release 10.0, SAS IP, Inc.

Nesvadba, P. (2006). Explosion welding and allied processes. Professional consultations. VUPCH. Explosia. Pardubice--Semtin

Turna, M. (1989). Special welding processes. Explosion welding. Alfa. Bratislava

*** Referativnyj zurnal "SVARKA". (2005). Solid state welding. Explosion welding. Moscow

Tab. 1. Elastic-plastic material models (used values)

Properties Aluminium Steel

Density [rho] [kg.[m.sup.-3]] 2720 7850
Elastic modulus E [GPa] 76 210
Poisson's ratio 0.34 0.30
Yield stress [R.sub.e] [MPa] 145 310
Tangent modulus [E.sub.t] [MPa] 25 763
Friction coefficient Aluminium-Steel [mu] = 0-6

Tab. 2. Bend angle values, experiment vs. modelling

 Experiment Model No 2. Model 3. Model

[beta][[degrees]] 13.9 18.7 12.4 13.7