On the asymmetrical material flow in metal specimens under dynamic compression with Hopkinson bars

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On the asymmetrical material flow in metal specimens under dynamic compression with Hopkinson bars

Cong Tu Nguyen

To cite this version:

Cong Tu Nguyen. On the asymmetrical material flow in metal specimens under dynamic compression

with Hopkinson bars. Journal de Physique IV Proceedings, EDP Sciences, 1994, 04 (C8), pp.C8-95-

C8-100. �10.1051/jp4:1994814�. �jpa-00253369�

JOURNAL DE PHYSIQUE IV

Colloque C8, supplkment au Journal de Physique IZI, Volume 4, septembre 1994

On the asymmetrical material flow in metal specimens under dynamic compression with Hopkinson bars

C.H. Nguyen

EMPA Diihendoif, Department 121, Ueberlandstvasse 129,8600 Dubendoif, Switzerland

RksumC: Une modelisation du fluage asymetrique du materiau d'eprouvette durant un essai de compression aux barres dtHopkinson est proposee, basee sur des resultats comparatifs entre la simulation numerique au moyen dtAUTODYN-2D et des essais experimentaux appliqub a des metaux avec differentes structures de phase (cuivre, aluminium, fer et titane). Parmi les trois principales zones de ce fluage, une seule serait valide pour une etude du materiau. La zone non valide du rebord provient d'un fluage de la face avant d'impact de l'eprouvette, qui serait d'abord radial puis, en debordant de ltCcart entre les deux barres, en direction de la face amere de l'eprou- vette. Des observations metallographiques montrent que la microstructure pour le Fe et surtout pour le Ti est peu definissable. Les trois zones de fluage de materiau peuvent 6tre esquissees en suivant les lignes de fluage observees pour 1'Al ou les bandes de cisaillement pour le Ti.

Abstract: Modeling of the asymmetrical material flow in the specimen during a Hopkinson bar compression test is proposed, based on comparative results between numerical simulation using AUTODYN-2D and experimental tests applied to metals with different phase structures (copper, aluminum, iron and titanium). Among three main material flow regions, only one could be consi- dered as valid for a material investigation. The non-valid rim zone results in a flow process at the specimen impact front side, which is at first radial then, when emerging from the gap between the two bars, moves towards the specimen rear face. Metallographic investigations indicate that the microstructure for Fe and especially Ti is hard to define. The three material flow regions can be outlined by following the observed flow l i e s for A1 or shear bands for Ti.

1. INTRODUCTION

During a Hopkinson bar compression test, the cylindrical material specimen, held between the free-flying measurement bars, will deform asymmetrically when being impacted axially on one side and free from reaction on the other. This deformation, which is transmitted from the specimen impact front face to its rear face, would only be possible in dynamical loading conditions, so that equilibrium between the two specimen faces could already be achieved at a very early moment of the flying movement. The defonna- tion level itself would also be increased by speeding-up the loading rate. This study is an attempt to model this asymmetrical material flow in the Hopkinson bar compression specimen, based on comparative results of process numerical simulation and experimental tests with metal specimens.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1994814

C8-96 JOURNAL DE PHYSIQUE IV

2. NUMERICAL SIMULATION OF HOPKINSON BAR COMPRESSION TEST 2.1. Equivalent impact velocity

Calculations of the specimen deformation during a Hopkinson bar compression test were computed using the FD-non-linear dynamic code AUTODYN-2D [I], as the problem is here axisyrnrnetrical. Figure 1 gives details about the optimal choice for the grid of elements used commonly for the deformed specimen as well as for the two elastic bars. These are however defined as three separated subgrids with their own material strength model and with boundary conditions between them. Both faces of the specimen are able to slide (as slaves or moving points) over the respective faces of the bars (as masters or fixed points).

Furthermore, by calculating the high deformation of the elements composing the specimen with an Arbitrary-Lagrangian-Eulerian (ALE) processor, it has been possible to reduce the number of tedious rezoning operations to only one for this problem (at one node on specimen axis, shortly after calculation beginning). As it is difficult to calculate with enough accuracy the whole configuration of the small specimen together with the two bars in their entire length, a much shorter equivalent length for the bars is used here with adequate balancing of the impact energy, i.e., with an equivalent impact velocity taken as 10.5 times higher than the effective one (figure I), including a slight correction in energy dispersion at the impact and through the measurement bars, up to the pressure fiont calculated as attaining to the

specimen.

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(cn.gx.us) NCLE O I : $.BIIBElOg

F & J . - Numerical simulation of the Hopkinson bar compression test (equivalent impact velocity with equivalent bar length, element grids, sliding boundary conditions)

2.2. Influence of material strength model

To study the intluence of dynamical material properties (as input data) in the simulation of the specimen

deformation during Hopkinson bar compression test, calculations have been done with different empi-

rical material strength models. In the AUTODYN-2D library, data from the published models of

Johnson-Cook [2], Steinberg-Guinan [3] and Zerilli-Armstrong [4] are available. Figure 2 gives the cal-

culation results when using these three models for copper, respectively at 10 ps after impact and at

equilibrium (when specimen and bars are no more in contact with each other). The fust mentioned model

seems to give the greatest total deformation of the specimen, very near to what was experimentally

observed, while the last cited model indicates a much more rigid material behaviour.

i :

: Johnson-Cook Model

l o p s Steinberg-Guinan Model 2 5 ~ s &{

97

1 Ops

.

- Comparison of calculation results, at 10 ps after impact resp. at equilibrium, between data from three different dynarnical strength models (for copper)

2.3. Material flow regions

Figure 3 shows pressure curves calculated for some different locations in the material specimen during the whole process of the Hopkinson bar compression test. Except for a region at the specimen rear side near the specimen axis, it seems that all other locations are more or less in depression towards the end of the process, confirming a strong radial component adding to the uniaxial compression and also a presence of an asymmetry between specimen front and rear faces. The calculated duration of about 30 ps for the process seems quite short. The model for asymmetrical material flow in the specimen, illustrated in fi- gure 4, results from an evolution versus time of the calculated deformation form and velocity direction from the grid elements. Three main material flow regions are identified:

- a wide front region #1, which flows first radially then, emerging from the gap between the bars, towards the specimen rear face; this material zone is non-valid with respect to the uniaxial hypothesis; due to this radial flow, one finds, near the specimen axis, a region void of material, which will then disappear at the end of the impact compression process;

- a middle region #2, which alone is valid for a material investigation;

- a small rear region #3, which also flows radially but much later in the process; it also results in the pre- sence of a smaller empty region.

The mean value for the deformation rate in the specimen material, taken from the rates corresponding to

these three flow regions (figure 4), can effectively be considered to be constant during the whole impact

process.

JOURNAL DE PHYSIQUE IV

FjgJ - Pressure curves calculated for different specimen locations during Hopkinson bar compression test, with parts in tension

- Schematical representation of the asymmetrical deformation mode in Hopkinson bar

compression specimen, with constant mean value for the corresponding strain rate

3. EXPERIMENTATION

Hopkinson bar compression tests were conducted using the apparatus in Thoune [5,6] with bars

lOmm x 1 m) and specimens (4 6 rnm x 4 mm) made of four pure metals having different hardnesses and phase structures: copper (OF), aluminum (99.5%), iron (ARMCO) and titanium (ASTM (3.2). As summarised in table 1, these tests were conducted at maximized impact velocities for each material [7], which give a final specimen thickness of about 1 mm, thus corresponding to a high strain rate value of about 5. lo3 s-l when related to a normal process duration of 120 ps (up to 2 . 1 0 ~ s-]with calculated duration of 30 ps).

Table 1: Principal parameters of the Hopkinson bar compression tests

TEST SPECIMEN COPPER ALIIMEWM IRON TITANIUM

Impact velocity ( d s ) 3 5 21 43 44

Hardness before (HV) 40.8 21.1 94.1 132

Hardness after (HV) 11 1 43.7 145 226

As it was not possible to freeze the tests at mid-time, no correlation could be made with calculations for the whole flow process. The specimens could then only be examined after the tests. They show a rim zone, as main part ofthe non-valid flow region #1 in figure 4, having a volume quite comparable to those calculated. Figure 5 shows macrographs of specimens after test for the four metals. Some of the flow regions defined in the proposed asymmetrical model can thus be outlined by following the observed flow lines for Al or shear bands for Ti. One can also notice that the rim zone flows effectively more towards the specimen rear face: this can be a criterion for material dvnarnic as ovvosed to static flow.

&5 - Macrographs of (half of) specimens after Hopkinson bar compression tests, sho-

wing the flow regions of the model delimited by flow l i e s (Al) or shear bands (Ti)

(arrows indicating specimen impact side and direction)

C8-100 JOURNAL DE PHYSIQUE IV

Metallographic investigations were done on these metal specimens to detect differences in their micro- structure after deformation at this high strain rate. In contrast to the microstructure with longitudiial grains for A1 and Cu, the one for Fe and especially Ti is much less defined (with local traces of twinning), probably due to phase transformation under pressure [a]. This total change in the specimen material microstructure is also to be correlated with the high increase in hardness values measured on the spe- cimens after the tests (table 1).

4. CONCLUSION

By using the concept of an equivalent impact velocity, it was possible to calculate the specimen defor- mation during a Hopkinson bar compression test. This deformation could be modelled by three material flow regions with, for two of them, a strong radial component adding to the uniaxial compression, and also the presence of an asymmetry between specimen front and rear faces. Experiments were conducted, at a high (and shown to be constant) strain rate, which confirmed that these flow regions could well be delimited by either flow lines or shear bands. Further work would consist of studying in more detail the differences in microstructure and mechanical properties between these three material flow regions.

Acknowledgements

The author would like to thank Messrs Norman J. Robertson from Century Dynamics for his advice in the calculations and Andreas Rupp fiom EMPA for the metallographical preparation.

References

[I] AUTODYN Users Manual, Century Dynamics, Inc., Oakland, CA (1989).

[2] JOHNSON, G.R., COOK, W.H., 7th 1nt.Syrnp.on Ballistics, The Hague (1983).

[3] STEINBERG, D. J., COCHRAN, S.G., GUNAN, M. W., J.Appl.Phys., 51,3 (1 980).

[4] ZERILLI, F.J., ARMSTRONG, R.W., J.Appl.Phys., 61,65 (1987).

[5] NGUYEN, C.H., Def.Tech.Proc.Ag., Thun, Tech. Rep. 936-40-92-003 (1992).

[6] NGUYEN, C.H., DGM Hauptversammlung, Friedrichshafen (1993) 239.

[7] LICHTENBERGER, A., Ass. DYMAT, Arcueil, Tech. Rep. RE1002187 (1987).

[8] NAULIN, G., ANSARD, J.P., J. Physique, Coll.C3,49,9 (1988) 363.