STUDY ON 2-D SHOCK WAVE PRESSURE MODEL IN MICRO SCALE LASER SHOCK PEENING

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1 Study Rev. Adv. on -D Mate. shock Sci. wave 33 (13) pessue model in mico scale lase shock peening 111 STUDY ON -D SHOCK WAVE PRESSURE MODEL IN MICRO SCALE LASER SHOCK PEENING Y.J. Fan 1, J.Z. Zhou, S. Huang, W. Wang, D.H. Wei, J.R. Fan and B. Gao 1 School of Mechanical Engeneeeing, Jiangsu Univesity of Science and Technology, Zhenjiang, Jiangsu 13, China School of Mechanical Engineeing, Jiangsu Univesity, Zhenjiang, 113, China Received: Octobe 17, 1 Abstact: Lase-induced shock pessue in mico scale lase shock peening (LSP) is the key to numeically analyze the stengthening effect of the tagets. In ode to establish the model of shock wave pessue loading in LSP pocess, a easonable simplification was conducted accoding to the shock wave popagation theoy. -D pessue distibution along the adial and axial diection at diffeent time was modeled based on theoy of ellipsoidal wave popagation, compehensively consideing popeties of shock wave popagation in time and spatial distibution and geometic featues of ellipse. Numeical simulations of LSP with single point unde 1-D and -D pessue loading wee caied out to investigate the influence of loading in adial diection on esidual stess distibution. The esults showed that esidual stess distibution unde -D pessue loading was obviously diffeent fom the 1-D case, so effect of pessue in adial diection duing the popagation of shock wave should not be ignoed in LSP pocess. -D shock wave pessue model lays a theoetical basis fo accuate loading of shock wave pessue in the simulation of LSP. 1. INTRODUCTION Lase shock peening (LSP) has been the most effective and widely used method of intoducing compessive esidual stesses into the suface of metals to impove fatigue pefomance since 196s [1-3]. The pevious eseaches wee focused on the teatment of maco-components with lase beam diamete at the ode of millimete. Lase shock wave pessue model was theoetically studied by R. Fabbo [4], in which 1-D spatial unifom wave model based on the assumption that shock wave popagates in one diection was poposed. Mico lase shock peening (LSP with lase beam diamete at the ode of micon can modify suface popeties and enhance the fatigue life of mico scale components. Howeve, the lase beam size in LSP is the same ode of the enegy ablative laye thickness, popagation of shock wave induced by LSP has geat diffeence with LSP in many aspects. As a Coesponding autho: Y.J. Fan, fanyujie@tom.com peliminay study, Yao et al. [5] pesented an impoved 1-D pessue model fo LSP pocess based on lase-suppoted combustion wave theoy, and non-unifom distibution in adial diection was consideed in spatial expansion effects, but the model adial diection and was difficult to solve. In fact, significant diffeence between LSP and LSP is size effect. Since the diamete adopted in LSP is at the ode of micon equal to the thickness of enegy ablative laye, shock waves popagate along both adial and axial diections, so 1-D pessue model is no moe applicable, effect of pessue in axial and adial diections on mico plastic defomation must be consideed in the model of LSP. In this pape, -D shock pessue distibution was investigated based on theoy of ellipsoidal wave popagation. Compehensively consideing popeties of shock wave popagation in time and spatial

2 11 Y.J. Fan, J.Z. Zhou, S. Huang, W. Wang, D.H. Wei, J.R. Fan and B. Gao distibution and geometic featues of ellipse, spatial pessue distibution in adial diection at diffeent time was deived, and -D pessue loading was modeled. In ode to investigate the influence of the loading in adial diection on esidual stess distibution, simulations of LSP with single point unde 1-D and -D pessue loadings wee conducted espectively and the esults wee compaed.. 1-D PRESSURE MODEL The spatially unifom shock pessue P(t) elates to the spatially non-unifom shock pessue as [5] P(, t ) P ( t) exp, R (1) whee is the adial distance fom the cente of the lase beam, and R is adius of lase beam. P(t) is pessue at cente of lase beam at time t. P(,t) can be solved numeically fom the above equations. The values of P(,t) ae then used as dynamic load in the stess analysis. The impoved shock pessue model took into account the adius of shock wave changing with time as follows [6] t T z P P 1D,, T t T t T R R P P t / T 1D,, R R t / T 4,5 1/ P P t / T T / t 1D z z,, z 1/ 4 / 5 R R T / T T / t z z 4 / 5 6 / 5 () whee P 1D is the plasma pessue fom 1-D model descibed above, T is the time that aefaction wave popagates into the plasma fom the edge at the sound speed of the plasma, theefoe T = R /a, whee R is adius of lase beam and a is the sound of speed. Axial elaxation stats afte the lase pulse teminates, thus the chaacteistic time fo axial expansion is T z = T p, whee T p is pulse duation. 3. CHARACTERISTIC OF SHOCK WAVE PROPAGATION IN WATER Plasma shock wave induced by lase in ai is ceated by the extenal expansion of plasma with high tempeatue and pessue and popagates as Taylo model. When the inteaction between high powe lase and enegy ablative laye unde constaint of wate duing LSP pocess, lase induced plasma Fig. 1. Fomation couse of shock wave in wate, coutesy of D. X. Chen. shock wave is poduced. Fig. 1 shows fomation couse of shock wave in wate [7]. Self-focusing of lase is easie caused in wate than ai, especially impuity in focusing aea makes the beakdown theshold of liquid geatly deceased, which induces elongate of plasma shock wave along the diection lase incidents at pimay, with the lage enegy and the shote pulse duation the moe significant tend. Fo the LSP pocess, ellipsoidal wave theoy [7] was poposed to descibe popagation of plasma shock wave in wate, which assumed that popagation law of wave font along shot axis submits to Fomula (3), consideing popagation of shock wave is in the same diection with shock wave velocity along shot axis R. n 1 b b( t ) M c t b 1 1 exp, M c t (3) whee b is initial adius along shot axis of ellipsoidal wave, M is the maximum Mach numbe along shot axis, c o is sound speed in wate. 4. -D SHOCK PRESSURE MODEL Accoding to chaacteistics of popagation of shock wave, ellipsoid-based model of shock wave pessue can be analyzed as follows. Any point (x,y,z) on the ellipsoid suface as shown in Fig. can be pojected onto the -D plane. Fom the geometic featues of ellipse shown in Fig.3, we can get the elations (4) z a 1, a b c b a z b z, b ( t ), (4)

3 Study on -D shock wave pessue model in mico scale lase shock peening 113 Fo any point a b,, b we have Fig.. Ellipsoidal wave model at time t. whee a and b ae function of time, b is adius of wave font along shot axis and expessed by Fomula (3), a is adius of wave font along long axis. K t P a (, ), z P b b (5) whee P is pessue in adial diection and P z is pessue in axial diection, K (t,) is P /P z atio of any point of wave font. Accoding to ef. [7] when the popagation time of shock wave is 18 ns (a = 13 um, b = 81 um), K() can be deived K( ) (6) This expession can be numeically shown as Fig. 4, it can be seen that effect of pessue in adial Fig. 3. Section of ellipsoidal wave acoss Z axis. Fig. 4. Spatial distibution of K() at 18 ns.

4 114 Y.J. Fan, J.Z. Zhou, S. Huang, W. Wang, D.H. Wei, J.R. Fan and B. Gao Fig. 5. Changes of K() along adial diection at diffeent time. Fig. 6. Pessue loading cuve of shock wave. diection is zeo at the cente of lase beam and inceases with the incease of distance to the cente of lase beam. Fig. 5 shows diffeent changes of K() along adial diection at time 3 ns, 7 ns, 1 ns, and 18 ns, espectively, it is clea that effects of pessue in adial diection incease with popagation of wave font. Assuming that spatial pessue distibution along long axis obeys Gaussian distibution [6], then P can be deived P K ( t, ) P( t )exp. R ( t ) (7) Fo the LSP pocess, -D pessue model must be modified as P BP, P AP, (8) z z whee A B a a b b b b a b b,. Fig. 6 shows pessue loading cuves of shock model, line and 3 ae the modified pessue cuve along axial and adial diection espectively, whee A =.8, B =.6. Spatial distibution of P z at 18 ns was obtained (shown in Fig. 7) accoding to Ref. [7], it is shown that the pessue eaches maximum value at the

5 Study on -D shock wave pessue model in mico scale lase shock peening 115 Fig. 7. Spatial distibution of shock wave along axial diection. cente of lase beam and deceases with the incease of distance to the cente of lase beam. Spatial distibution of P can be defined by the intoduction of coefficient D(t,) D( t, ) K ( t, )exp, R ( t ) Table 1. Coefficient of D (t, ) at diffeent time. Time (ns) A B C (9) whee D(t,) is function of time and adius. Spatial distibution of P at 3 ns, 1 ns, and 18 ns ae shown in Fig. 8 espectively, it can be seen that thee is no effect of P at the cente of lase beam, it inceases with incement of distance to the cente of lase beam and deceases with popagation of shock wave at the same action egion. Accoding to the diffeent spatial distibution of P, D(t,) can be expessed as D( t, ) A( t) B( t )exp C( t ) * R( t), (1) whee A(t), B(t) and C(t) ae function of time shown in Table 1, espectively, R(t) is popagation distance of ellipsoidal wave font along adial diection at time t. 5. SIMULATION BASED ON -D PRESSURE MODEL 5.1. Establishment of finite element model 3 was chosen in the simulation, lase beam diamete was 1 m, and lase enegy was 1 mj. In the following stess analysis, stain ate and ate effect on yield stength wee consideed while tempeatue was taken as oom tempeatue, mateial was assumed as isotopic and homogeneous and obeyed Von fo the high stain ates (1 6 s -1 ). Shock pessue model was detemined by fomula (8). To compae pessue loading influence on esidual stess distibution, simulations with 1-D and -D pessue model wee conducted, espectively. 5.. Results and discussion Distibutions of esidual stess S 11 fo a single shock peening unde diffeent pessue loading ae shown in Fig. 9. As seen that compessive esidual stess distibutes in a wide egion unde both loading model, the maximum esidual stess is on the top suface with -D pessue model but sub-laye fo 1-D pessue loading. Distibution of esidual stess S 11 in adial diection is shown in Fig.1a. It can be seen that distibution of S 11 is nealy same when the distance to cente exceeds 1 mm but geatly diffeent within 1 mm. At suface, the magnitude of S 11 is maximum at the cente of lase beam unde -D pes-

6 116 Y.J. Fan, J.Z. Zhou, S. Huang, W. Wang, D.H. Wei, J.R. Fan and B. Gao Fig. 8. Spatial distibution of adial pessue coefficient at diffeent times: (a) 3 ns, (b) 1 ns, (c) 18 ns. Fig. 9. Stess nephogam unde diffeent load model: (a) S 11 unde 1-D pessue loading, (b) S 11 unde -D pessue loading.

7 Study on -D shock wave pessue model in mico scale lase shock peening 117 Fig. 1. Influence of distibution of esidual stess unde diffeent pessue loadings: (a) S 11 in adial diection, (b) S 11 in axial diection. sue loading, below the top suface about 3 m, distibution of S 11 ae nealy same unde both pessue models and below the top suface about 6 m, magnitude of S 11 unde 1-D pessue loading is geatly lage than that unde -D pessue loading. The esults indicate that suface wave takes geat effect on the distibution of suface esidual stess in mico scale, the eason is the convegence of suface wave induces the incease of plastic stain in evesal diection and the decease of stess magnitude. Unde the condition of -D pessue loading, suface wave popagates outwad along adial diection with the effect of pessue in adial diection and the maximum magnitude of S 11 is ceated at the cente of lase beam. Distibution of esidual stess S 11 in axial diection is shown in Fig.1b, it is clea that influence of depth unde 1-D pessue loading is much lage. The eason is that all enegy was assumed to convet into pessue effect in axial diection unde 1-D pessue model. 6. CONCLUSIONS Reasonable simplified -D model of shock wave pessue in LSP pocess was built, spatial distibutions of pessue in adial and axial diections at diffeent time wee investigated espectively, and the loading mode of shock wave pessue was concluded. The numeical simulations show that pessue in axial diection plays a dominant ole neaby the cente of lase beam, while pessue in adial diection is almost zeo at cente of lase beam and inceases with inceasing of adial distance. Pessue in adial diection plays a dominant ole when

8 118 Y.J. Fan, J.Z. Zhou, S. Huang, W. Wang, D.H. Wei, J.R. Fan and B. Gao the distance eaches a theshold value. The esults indicate that distibution of esidual stess in width and depth is obviously diffeent unde two pessue models, the distibution of esidual stess fom -D pessue loading is much close to the eal situation, in ode to pecisely simulate and analyze the LSP pocess it is necessay and impotant to intoduce -D pessue loading model. ACKNOWLEDGEMENTS The eseach was suppoted by the National Natue Science Foundation of China (No.56759), the Doctoal Pogams Foundation of Ministy of Education of China (NO.8994), Key pogam of Natue Science Foundation fo Univesity of Jiangsu Povince (No.8KJA46), Natue Science Foundation of Jiangsu Povince (NO. BK919), Poject of Jiangsu Povince Key Laboatoy of photon (GZ16), and Jiangsu Univesity of Science and Technology (no. 6351). REFERENCES [1] P. Peye, X. Schepeeel, L. Bethe and R. Fabbo // Suf. Eng. 14 (1998) 377. [] C.A. Lavendea, S. Hong, M.T. Smith, R.T. Johnson and D. Lahman // Jounal of mateials pocessing technology 4 (8)486. [3] A. Chahadehi, F.P. Bennan and A. Steuwe // Engineeing Factue Mechanics 77 (1) 33. [4] R. Fabbo, J. Founie and P. Ballad // J. Appl. Phys. 68 (1995) 755. [5] S. Vukelic, Y. Wang, J.W. Kysa and Y.L. Yao // J. Manuf. Sci. Eng. 131 (9) [6] W.W. Zhang and Y.L. Yao // Jounal of Manufactuing Pocesses 3 (1) 18. [7] X. Chen, Studies on mechanisms of the inteaction between high-powe lase and matte in wate (Nanjing Uinvesity of Science & Technology, Nanjing, 4).