DEVELOPMENT OF THE HOPKINSON BAR FOR TESTING LARGE SPECIMENS IN TENSION

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DEVELOPMENT OF THE HOPKINSON BAR FOR TESTING LARGE SPECIMENS IN TENSION

C. Albertini, P. Boone, M. Montagnani

To cite this version:

C. Albertini, P. Boone, M. Montagnani. DEVELOPMENT OF THE HOPKINSON BAR FOR TEST- ING LARGE SPECIMENS IN TENSION. Journal de Physique Colloques, 1985, 46 (C5), pp.C5-499- C5-503. �10.1051/jphyscol:1985563�. �jpa-00224795�

JOURNAL DE PHYSIQUE

Colloque C5, suppl6ment a u n08, Tome 46, aoDt 1985 page C5-499

DEVELOPMENT OF THE HOPKINSON BAR FOR T E S T I N G LARGE SPECIMENS I N T E N S I O N

C. A l b e r t i n i , P.M. ~ o o n e ' and M. Montagnani

Commission o f t h e European Communities, Joint Research Centre, l s p r a Establishment, 21020 Ispra IVa'a), I t a l y

+ ~ n i v e r s i t ~ of Ghent, Belgium

Rbum6 - On decrit une barre de pression pour grandes charges caractkrisee par deux impul- sions symetriques engendrees aux deux extrBmitCs de la barre, et la mkthode & utiliser pour I'interprbtation des signaux. On donne les premiers resultats obtenus avec des iprouvettes de grandes dimensions en utilisant des techniques optiques de mesure.

Abstract - A hlgh load pressure bar characterized by symmetric pulses coming from the two ends is described together with a method for interpretation of signals. First results obtained by testing large specimens using optical techniques are reported.

The Hopkinson bar has been used among others by Campbell and Harding [ l ] , Lindholm [2], Nicholas 131, Ellwood, Griffith and Parry [4] in tension tests, where the momentum was generated by a projec- tile. Higher pulse durations have been obtained with the system developed by Albertini and Montagnani

[S], where the momentum is generated by the release of mechanical energy stored in a pretensioned bar.

By this system, using test pieces of small dimension (about 7 mm2 cross section, Fig. l ) , tension tests were performed up to rupture with ductile materials having a total elongation of 50% or more, with a pulse duration of about 2 ms. A characteristic record of a test is shown in Fig. 2. In this case the dura- tion of the test corresponds to a length of the prestressed bar of 2 m. The contribution of the specimen shoulders has been taken into account on the basis of the assumption that the specific volume of the material remains constant during the test. The correction of the active length of the specimen is given by the following expression:

1 = length including the two shoulders AI-AIo

(1) 1; = corrected active length 1; = 1, + ---

A ~ o / ~ o 1, = nominal active length

A 0 A increments of the lengths l. and 1.

More recently we have measured the deformation of active length and shoulders of a specimen hqving l. = 7 mm by optical microscopy (Fig. 3), and a correction of the contribution of the end pieces during the whole deformation process has been found. Two pretensioned bar systems can be coupled for acting on a specimen placed in between the two bar systems, as shown in Fig. 4. This double system, by equal pretensioning, guarantees perfect load equilibrium across the specimen and permits to double the maxlmum strain rate obtainable from one system. Furthermore, the double Hopkinson bar system can be analysed by the same procedure reported by Kolsky [6] and Davies [7] with minor modifications [a]. The Hopkinson bar is shown schematically in Fig. 4, for the case of the waves which propagate, in opposite directions, along two half bars. Let us assume that the two incident waves which propagate in the two half bars, 1 and 2, have the same amplitude and duration, and that the instants in which wave 1 arrives at aa and wave 2 at bb are coincidental. Let us also assume that the position of the SGl and SG2 strain gauges are symmetrical to the specimen, whose length is usually small, so that the time the wave takes t o travel across it is small compared t o the duration of the two waves With the above mentioned hypothesis, the readings taken from SG1 and SG2 are identical and, therefore, only one of them will be referred to.

The previous considerations are valid for E R sign, which is opposite t o the €1 sign, as the same configu- ration indicated in Fig. 4 is assumed. Let us assume now that the time taken by the wave t o cross the specimen is insignificant. The €1 strain incident wave arrives a t edge aa (generating the insurgence of a reflected strain wave eR) at the same instant as the ET transmitted strain wave generated by the wave

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985563

C5-500 JOURNAL DE PHYSIQUE

propagation in bar 2. The displacement of the edge, aa, is given by [2,6,7]:

where EI and ET have the same sign, which is opposite to the sign of ER. Similarly, the displacement of the edge, bb, is given by:

Ub = -Co f t (EI - ER - eT)dt = -Ua (3) Therefore, average strain and strain-:te in the specimen are:

and

It must be remembered that the half bars remain in an elastic field and the effects of the two waves overlap. Imagine, to be more precise, that we first consider only the incident wave in half bar 1 (which generates in SGl the signals connected to EI and EI + ER) and then, being the specimen de- formed by the effect of wave l, the effect of the incident wave, in half bar 2 (which generates in SGl the signal connected to ET). With this scheme the ET which appears in (2) to (5) is completely assimilated to the strain wave transmitted, as found in the usual Hopkinson bar scheme with a single incident wave. As regards the readings obtained at SGl (and SG2), we can state that in the time in- terval -tl + t the signal read is proportional to (cI + ^{E R} + ET) (Fig. 4). AS regard the forces on the aa and bb edges of the specimen one has:

F, = EA (cI + ^{E R}

+

where E bar Young modulus, A bar cross section, A s ecimen cross section'

0 P

Measurements X, Y at SG1 which are available, are grven by the following (excepting a propor- tionality coefficient depending on the nature of the strain-gauge and the bar):

X = €1 (interval: -tl + 0) Y = E I

+

+

(4), (5) and (7) expressed as a function of the two measurements X and Y become:

As can be seen, although the two measurements X and Y do no; permit the separate determination of all three strains EI, ER, ET, they are sufficient t o determine E , E,, as

In order t o extend the application of the results obtained o n small specimens t o the calculation of real size structures, these results must be checked by tests o n large specimens, in order to verify the effect of dimension and of the non-homogeneous distribution of defects on materials damaged by creep, fatigue, welding, etc. :Ye have, therefore, designed o n the same principle as the former device a ma- chine [9] in which the mechanical energy necessary for deforming and rupturing the specimen is stored in two steel cables, each 100 m long, able t o develop a load of 5 MN. The two opposite symmetric pulses generated by the discharge of the two cables are directly transmitted t o the specimen with the intermediate action of a short transmission bar. The reflected pulses are taken away by the same cables, avoiding any disturbances of the specimen. The synchronous generation of the two pulses is made pos- sible by the use of electric detonators with a response time better than 1 ps, which break the fixations securing the cables up to the moment of the test. This synchronous action permits the extension of the machine t o biaxial testing by the simultaneous action of four cables.

The design of the machine began in 1979 and its construction ended in 1982. In 1984 tests have been performed on austenitic stainless steels, after having developed in static tests the method for mea- suring deformations. One of the specimens presently investigated is shown in Fig. 5. This specimen is connected to the machine by a cross head connection. At present it is not yet possible to use fully the interpretation of signals

which we have discussed before Ceqs. 8 t o 10) due to the rise time of the load (about 350 ps) which does not permit t o discriminate incident, reflected and transmitted pulses. Actually improvements

in the clamp mechanism in order to obtain a rise time less than 100 ps, and supplementary measure- ments directly on the specimen of load and deformation have been studied.

The measurement of the load acting on the specimen is done consequently in two different areas (Fig. 6), and repeated two times symmetrically in the two driving sections. The first measurement is performed on the driving rod, o n the mountain side of the specimen. This measurement is done by a strain gauge station (SGII), calibrated by a dynamometer. Because of the influence of the cross head connection on the load acting on the specimen, a second measurement area is chosen on the specimen itself (SGI). Also this measurement is performed by a strain gauge station. The measurement of the force is calibrated in previous static tests. A preliminary calibration is given in Fig. 7. This calibration pro- cedure will have to be validated for specimens of different materials and different loading conditions. It has to be noted that the area chosen for the measurement on the specimen is a n area of minor deformation of the specimenj where the material remains mostly elastic during the whole deformation process up to rupture. In Fig. 8 is given the observation of the strain field of this area by a Moire interferometry [10], measurement obtained after rupture of the specimen. Due t o the sensitivity of the Moire (a grid of 63 lineslcm was used) it can be observed that the bulk deformation of the measurement area remains in the order of 0.001 total elongation, because in this area no displacement fringes are observable.

This Moire method, applied to the specimen active length, permits also the observation of the defor- mation of the specimen during the test. A record of the Moire pattern is given in Fig. 9, where several Moire grids of different sensitivities and directions were applied o n the specimen front surface and on the specimen side surface. Records of the measurements of the load obtained by strain gauge stations are also given in Figs 10 (SGI) and 11 (SGII). Due to the rise time obtained in these tests it was possible to perform tests with a strain rate of i = 25-50 /S. Higher strain rates can be obtained with shorter rise time of the pulse and avoiding, by a new design of the specimen, the cross head connection.

ACKNOWLEDGEMENTS

Mr. G. Verzeletti and his team have operated the high load testing device and recording instruments.

Mr. G. van der Steen of the University of Ghent and Mr. E.V. Pizzinato of JRC have collaborated in the Moire application.

REFERENCES

[l] Harding, J., Wood, E.O. and Campbell, J.D., ^J. Mech. Engng. Sci., 2 (1960) 88.

[2] Lindholm, U.S. and Yeakley, L P , (1968) Exp. Mech., 8, 1.

[3] Nicholas, ^T. (1980a) Exp. Mech., 21, 177.

[4] Ellwood, S., Griffiths, L.J. and Paw, DJ., J. Phys. ^E.: Sci. Instrum., Vol. 15 (1982).

[S] Albertiii, ^C., Montagnani, M,, Inst. of Physics, Conf. Ser. No. 21,22.

[6] Kolsky, H., Stress waves in solids, Dover Pub. 1963.

[7] Davies, ^R.M., A critical study of the Hopkinson pressure bar, Phil. Trans. Roy. Soc. London, Ser. A, 240,375 (1948).

[8] Benuzzi, E., Cesari, F., ENEA D.R.V., Bologna, Italy, Numerical analysis of wave-propagation in a biaxial specimen.

[9] Alberti~u, C., Montagnani, M,, Inst. of Physics, Conf. Ser. No. 47, 25.

[l01 Boone, P.M. et al., Application of specimen-grid Moire techniques in large scale steel testing, Optical Engineering, July-August 82, Vol. 21, No. 41615.

F#g 1 SPECIMEN RECORD OF A TEST WITH A MODlFlED HOPKINSON R g 3 CORRECTION OF THE CONTRIBUTION OF END

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