THEORY OF ACOUSTIC EMISSION FOR MICRO-CRACKS APPEARED UNDER THE SURFACE LAYER MACHINING BY COMPRESSED ABRASIVE

Transcription

1 THEORY OF ACOUSTIC EMISSION FOR MICRO-CRACKS APPEARED UNDER THE SURFACE LAYER MACHINING BY COMPRESSED ABRASIVE A.K. Aringazin, 1, V.D. Krvchik,, V.A. Skryabin, M.B. Smnov,, G.V. Tarabrin 1 Eurasian National Univrsity, Astana 18, Kazakhstan aringazin@mail.kz Physics Dpartmnt, Pnza Stat Univrsity, Pnza 4417, Russia physics@diamond.stup.ac.ru Institut for Basic Rsarch, P.O. Box 1577, Palm Harbor, FL 468, USA ibr@vrizon.nt Rcivd March 5, 7 On of th possibl mchanisms for acoustic mission of growing micro-cracks undr conditions of th matrial machining by comprssd abrasiv has bn thortically studid. Physical ground of this mchanism is th dislocation crp in th fild of instant contact tmpratur on stag of micro-cutting with apparanc of th wdgshapd cavity. It has bn shown that th nrgy dnsity for radiatd acoustic wav at th momnt whn th cavity is opnd ssntially dpnds on paramtrs of th matrial abrasiv machining. 1

2 1. Introduction Intrst to acoustic mission for micro-cracks is stimulatd by possibilitis to us it in nondstructiv control of mchanical stat of matrial in procsss of its machining or xploitation [1-]. Also th intrst is du to fundamntal aspct which is rlatd to application of th acoustic mission mthod to rsarch micro-cracks growth physical mchanisms [, 4]. Som gnral mthod of analysis of th acoustic mission of arbitrary micro-cracks in th rstrictd lastic solids has bn dvlopd in Rf. [1]. This mthod is basd on th Huygns principl and allows on to dtrmin both th law of motion of micro-cracks dgs undr influnc of applid xtrnal strss and th spctral dnsity of acoustic mission. Howvr, thortical approach dvlopd in Rf. [1] dos not contain any ral physical mchanisms of th micro-cracks apparanc prior to its opning. Invstigations of ths mchanisms ar spcially important to undrstand procsss of machining of matrial by a comprssd abrasiv. Indd, hat procsss which ar initiatd by instant contact tmpratur on th stag of microcutting can stimulat structural changs of th dfcts in matrial surfac layr. Ths changs ar rlatd to motion of dislocations. Bsids, accumulation of dislocations nar to impurity is on of th possibl mchanisms of th formation of micro-cracks [4].. Th thortical modl of acoustic mission Mchanism of acoustic mission for micro-cracks, which ar appard undr procss of dislocation strngthning during micro-cutting in th matrial surfac layr of th machining sampl, has bn thortically invstigatd in this papr within th framwork Huygns principl for lastic matrial. Physical grounds of this mchanism ar rprsntd by th dislocation crp, which is stimulatd by tmpratur puls. As th rsult of this, a numbr of paralll dislocations accumulat nar to obstacl, which is appard as impurity rlas. In th rgion of such accumulation, th wdg-shapd cavity can aris, and this cavity can b a sourc of th micro-crack apparanc. Acoustic mission taks plac in th momnt of th cavity opning; and, as it will b dmonstratd, its spctral dnsity of radiation ssntially dpnds from paramtrs of dislocation crp and from th matrial abrasiv machining. As it is known [5] in th procss of micro-cutting, strong tmpratur pulss can aris. Charactristic tim for this procss is dtrmind by th t

3 man width of micro-ldgs t = Lm υ. For xampl, it quals L m and th man vlocity υ of th abrasiv grain: t = for υ = m/ s and 1 s L m = mcm. As th rsult, dislocations can b rlasd from fixd impurity and undr any critical strss dislocations can drift togthr with an impurity cloud [4]. Estimation of th instant contact tmpratur can b mad in trms of simplst boundary-valu problm with th instant hat sourc F( x, t) = Qδ( x ξ) δ( t τ), whr Q = Mυ πl is th sourc intnsity, M is th man valu of th abrasiv grain mass. It is thn asy to dmonstrat that valu of th instant contact tmpratur can b rprsntd as: Q 1 Λ a t T( x, t) = Arcth + 1 cg π L L, (1) whr th brackts in th lft-hand-sid of Eq. (1) man that (, ) T x t is mant with rspct to th dislocation ffctiv lngth l with th wight function of th Gauss typ N l = Λxp l L πl, whr Λ is th N ( l ) common dislocation lngth in th part matrial, L is th man lngth of dislocation loop, с is th matrial spcific hat, ρ is th matrial dnsity, a is th tmpratur transport cofficint. T x, t for th following numrical valus: Lt us stimat Λ= 6 1 ml, = 6 mcmc, = 46 J kg K, ρ= 78 kg m, Q 1 J m, M = 6,7m for th paramtr of granularity 8, t= t =. Th stimation is T( x t) 1 s, 18K. On can s that th instant contact tmpratur can b as high as th mtal mlting tmpratur [5]. Dislocation can scap th impurity cloud, with subsqunt joint drift in th tmpratur fild, undr any critical strss, which can aris, for xampl, during micro-cutting. Undr ths conditions, th critical drift spd υ can b dtrmind as [4]: ê 8D t = r υ ê, ()

4 whr Dt () = D Q kt ( xt ) xp, is th diffusion cofficint for fixing impurity in fild of th instant contact tmpratur; Q is th diffusion activation nrgy; r is th radius of Kotrll cloud around dislocation loop. ε ê can b writ- Taking into account Eq. (), th critical spd of crp tn as [4]: whr b is th Burgrs vctor valu; 8Dt = bn d r N d ε ê, () is th dislocation dnsity in matrial τ= π ω is th tim priod up to th micro-cracks growth of machining part. As it has bn mntiond abov, during th drift som part of dislocations is joind togthr and can form th wdg-shapd cavity (nar obstacl) [4]. In th rgion of such accumulation, a stabl cavity of lngth Ln = nbcan aris from n dislocations that can lad to apparanc of micro-cracks. Substituting n εê τ, whr bgins and ω is th angular spd for th machining part rotation, w obtain for L : n L 8bN d = b D() t r n τ. (4) As w can s from Eq. (4), th growth valu for th wdg-shapd cavity is dtrmind mostly by th diffusion mobility of impurity, which dcorats dislocation, and also by th dislocation dnsity and of cours by th paramtrs of th matrial abrasiv machining,. υ, ω, um,. Calculation of L n for th following valus: b= 1 m, ω= 5 rad/, s D 1 m /, s Q 1, V, Nd = 1 m, t = 1 s, Dt,8 1 m / s, r =,1 µ ml, 6 µ m, givs Ln,85mm. 11 Thortical approach to th cavity acoustics is basd on th Huygns principl for solid lastic mdia [1] with account of dislocation crp in conditions of th matrial abrasiv machinry. Sinc th cavity is a primary mdium cut, which is opnd by influnc of applid mchanical strsss without chang 4

5 of ffctiv lngth L n such a situation is quivalnt to modl of th instantly sprading micro-crack [1]. Hr, th nrgy dnsity W for radiating acoustic wav, as it has bn dmonstratd arlir [4], is approximatly dtrmind as whr σ σ L ω W n s 6 6 c πρ, (5) is th amplitud of mchanical strss; ω s is th frquncy of th acoustic wav; с е is th limit spd for lowst symmtric Lamb mod [1]. 5 Substituting σ = 1 N/ m, Ln =,85 mm, ω s = MHz, w obtain from Eq. (5) W 8 µ J / m, amd th radiation intnsity is I,5 mw / cm.. Conclusions On of th possibl mchanisms of th micro-cracks apparanc, which is rlatd to dislocation crp initiatd by fild of th instant contact tmpratur on th stag of micro-cutting, has bn dvlopd. Our numrical stimations show that th surfac matrial layr, as th rsult of th micro-cutting procss, gts dislocation strngthning, undr which th wdg-shapd cavity can aris. Also, th acoustic mission taks plac at th momnt whn th cavity is opnd. This can b idntifid xprimntally. Rfrncs [1] V.V. Krylov, Sound radiation by growing cracks, Acoustic Journal 4 (198) [] V.A. Krasilnikov and V.V. Krylov, Introduction to Physical Acoustics (Moscow, Nauka, 1984), in Russian. [] V.D. Krvchik, I.I. Artmov, Modl of th vibrostimulatd acoustic mission for micro-cracks of th dislocation natur, Nw Enginring Tchnologis, No. (5) [4] I.I. Artmov, V.D. Krvchik, Acoustic mission undr conditions of th hiddn micro-cracks growth, Problms of Mchanical Enginring and Machin Rliability, No. 4 (5) [5] A.N. Martynov, Foundations of parts machining mthod by fr abrasiv comprssd by inrtia forcs (Saratov, 1981), P. 1, in Russian. 5