STUDY OF THE PLASTIFICATION OF METALLIC TARGETS SHOCKED BY A LASER PULSE OF HIGH ENERGY

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1 JOURNAL DE PHYSIQUE Colloque C3, Supplbment au no9, Tome 49, septembre 1988 STUDY OF THE PLASTIFICATION OF METALLIC TARGETS SHOCKED BY A LASER PULSE OF HIGH ENERGY P. BALLARD', J. FOURNIER', R. FABBRO", J. FRELAT' ' and L. CASTEX" '* Laboratoire dlutilisation des Lasers Intenses, Ecole Polytechnique, F Palaiseau Cedex, France 'PSA Etudes et Recherches, Centre Technique Citroen, F Velizy, France t. Laboratoire d'vtilisation des Lasers Intenses, Ecole Polytechnique, F Palaiseau Cedex, France "'~aboratoire de Mecanique des Solides, Ecole Polytechnique, F Palaiseau Cedex, France ***. Laboratoire de MGcanique des Materiaux et Diffractometrie X, Ecole Nationale d'drts et Metiers, 24, Rue Pinel, F Paris, France Resume L'interaction d'un pulse laser de forte energie avec une czble metallique conduit h la propagation d'une onde plastique dans cette derniere qui y induit des contraintes residuelles superficielles de compression. Nous avons develop@ un dele simple pennettant de correler l'epaisseur de la zone affectee plastiquement A l'rmpulsion comuniquee h la cible. Abstract The interaction between an intense laser pulse and a metallic target generates a plastic wave which induces compressive superficial residual stresses. on the basis of a simple model, we try to correlate the thickness of the plastically affected zone ( P.A. 2. ) to the impulse momentum induced in the target. I. Introduction Recent studies (1) have proved that a pulsed laser can induce compressive residual stresses due to pure mechanical effects. This can be easily explained : the interaction between the pulse and the target creates a high pressure plasma which induces a plastic Weinthetarget. This process canbecomparedtoshot-peeningandcould improve inthe Same way materials fatigue behaviour. The object of this paper is to analyse the dynamic plastification of materials. -rimentally, whenirradiatingametallictarget, we canmeasuretwoparameters :the hxjuli3e mmntum transferred to the target and the thickness of the P.A.Z. We pressnt here a mdel which allows to correlate these parameters. 11. Dynamic plastic analysis 'Phe problem is studied under the following assumptiens.. The material is elastic perfectly plastic and obeys to a Von Mises Criteria.. The result oftheinteraction is apulse ofpressure appliedtothesurfaceof the sample. This pulse is supposed to be spatially and temporally uniform.. The physical parameters ln target are only function of the depth (monodimensional study), displacements can only be longitudinal. Article published online by EDP Sciences and available at

2 JOURNAL DE PHYSIQUE Notat ions A, p : target Lam4 constants P Y : target density i uniaxial traction elastic limit ores : lateral component of the residual stress tensor P : pressure applied to the surface of the sample,, P : maximum value of this pressure T : pressure duration. AMlysis of the loading/unloading of a volume element Loading : the use of the Von Mises Criteria gives :. When P increases from 0 Yo Y (1 + A/2p) : elastic loading. When P increases from Y (1 + A/2p) to P-: plastic loading. Unloadinq We must examinate two cases : 1) P- Q 2Y (1 + A/2/l) The unloading is entirely elastic.. When P decreases from,, P to Pmax -2Y (1 + A/2p) : elastic unloading. When P decreases from P- -2Y ( 1 + A/2p) to 0 : plastic unloading. Thus we can calculate the effect of this loading/unloading process on the final stateofthe element. We findthat the lateralcomponent oftheresidualstresstensor is not necessary to be zero. Its value depends on the amplitude,, P of the loading/unloading process ( fig. 1 ). Fig.1 : Residual stresses function of the amplitude of a loadinglunloading process.

3 ~g~pric analysis First, we have to analme the propagation of a loading/unloading wave. mt, in such a material there are two celerities of wave8 depending on the reginre (elaatic or plastic ). This implies that the shape of the wave undergoes an evolution while propagating ( Pig. 2 ). Fig.2 : Evolution of the shape of the stress wave in the target at different instants. This analysis allows to estimate the thickness of the P.A.2 (which is the depth after which the wave is purely elastic). We findthat if~~ishighenough, thisthickness P is asymptoticallyequalto: It shows that the optimum of the treatmsnt is obtained for the maxrmal Value of the impulse momentum transferred to the target. We have compared this model to simulations made with a dynamic elastic-plastic finite elements code r it shows that the shape of the temporal law of the pressure applied to the surface of the sample has practically no influence on the size of the P.A.Z. Thus we can replace in the formula P-. T by : This has been compared as well to experiments.

4 C3-404 JOURNAL DE PHYSIQUE 111. Measurement of the impulse momentum Let's suppose we irradiate by laser a cylindar on its entire basis. This communicates an impulse momentum t o the sample. If we let the sample fly, we can measurn its speed and thus the impulse momentum. Indeed, we have : I I P (t) dt = p.e.u p : density o : thickness of the sample v : sped of ejection Practically, we used a stroboscop and a camera (fig. 3) Fig. 3 : Photograph or a copper cylindar irradiated by a laser pulse. This give a practical mean to adlust the laser parameters in order to find an optimum of the impulse momentum (equal to P- T) and, so, to reach the optimum of the size of the P A 2. N. Measurement of the thickness of the P A 7, Usingxraysdiffraction, wecanmeasure residual stresses on a samplesurface. If we polish this sample step by step, we can obtain the shape of the residual stresses distribution.

5 Daplh lo m Fig.4 : Residual stresses in a sample of 35tD4 V. Experimental results synthesis We have measured the length of the P.A.Z and the impulse momentum (P.7) for different values of the laser intensity. This has been done with laser pulse8 of twu durations : 3 ns and 30 ns. On fig. 5, we have located the experimental point8 on a e. T, 8 plane. Fig.5 : Comparison of Lhe model with experimental results. These points are approximatively on a line, as predicted by the model, but the slope of this line is different from the theoric one. Moreover, orders of magnitude an?

6 JOURNAL DE PHYSIQUE in agreement but the theoric values of the size of the P.A.2 are over estimated. All these observations might be explained by the fact that we neglected visquow dissipation. And, the higher the strain rate (and the P.T) is, the most important it must be. This could explain the respective positions of the two lines as well as the difference of slope. VI. Conclusion There are slight differences between theory and experiment, but the model gives very interesting qualitative results :. As far as plastification is concerned P- and T are equivalent.. The more dense and fragile (Y high) a material is, the thiner the P.A.2 1s. Moreover, this study gives a practical mean to adjust the laser parameters in order to maximise the size of the P.A.Z. (1) J. WURNIER, Etude Experimentale des ondes de choc engendrees par laser pulse de forte energie, CRAs 304 (1987). (2 ) N. CRISTESCU, dynamic plasticity, North Rolland publishing company ( 1967 ).