A Novel 3D Finite Element Simulation Model for the Prediction of the Residual Stress State after Shot Peening

Transcription

1 A Novl 3D Finit Elmnt Simulation Modl for th Prdiction of th Rsidual Strss Stat aftr Shot Pning M. Zimmrmann, V. Schulz, H. U. Baron, D. Löh nstitut for Matrials Scinc and Enginring, Univrsity of Karlsruh MTU Aro Engins, Munich ABSTRACT 3D Finit-Elmnt shot pning modls known from litratur do not tak into account componnt thicknss as a gomtric paramtr influncing th rsidual strss stat aftr shot pning. Hnc classic approachs and a nw approach of modl constraints wr invstigatd for thir capability to contribut to a ralistic prdiction of th rsidual strss stat aftr shot pning. Th numrical rsults obtaind wr compard with x-ray masurmnts. Th strain rat dpndnt dformation bhavior of th invstigatd and agd matrial N78 was takn into account using an lasto-viscoplastic matrial modl with combind isotropic and kinmatic hardning. t was found that a small thicknss has no influnc on th comprssiv rsidual strsss in th surfac rgion but grat influnc on th tnsil rsidual strsss prsnt in dpr rgions. Th nw approach of modl constraint taks into account dflction ffcts and yilds to a vry good accordanc with xprimntal rsults. KEY WORDS Shot Pning, simulation, matrial modling, N78, curvd surfacs NTRODUCTON Comprssiv rsidual strsss ar inducd during shot pning in th surfac nar rgions of tratd componnts and ar balancd by an almost constant tnsil rsidual strss fild in gratr dpths (Mnig, ). For bulky componnts th tnsil strsss ar small bcaus of th availabl thicknss on which th comprssiv strsss ar balancd. Howvr sinc shot pning is also applid on rathr thin componnts such as turbin blads, it can b assumd that largr tnsil rsidual strsss can b found in th innr componnt rgions rprsnting a potntial risk to crack initiation during srvic. Hnc thicknss has to b takn into account as a gomtric paramtr influncing th rsidual strss stat of a componnt. Sinc tnsil rsidual strsss ar locatd in th dpr rgions of a componnt thir xprimntal dtrmination by x-ray or nutron masurmnt is quit costly. Hnc FE simulation of shot pning is an intrsting approach of analyzing th componnt thicknss as a gomtric paramtr. On this account th motivation of this work ariss to find a suitabl typ of boundary condition, which is capabl to ralistically dscrib th influnc of componnt thicknss on th rsidual strss stat. METHODS Exprimntal Procdur n ordr to analyz th gomtry paramtr thicknss on th rsidual strss stat xprimntally and to provid xprimntal data for th comparison with th simulation modl a tst spcimn faturing thr sctions of diffrnt thicknss (cp. Figur ) was tratd with an air blast machin (typ Baikr) with th following pning paramtrs: mass flow.83 kg/s, impact angl = 8, shot mdia

2 CCW3 with a masurd man diamtr of.89 mm and a hardnss of 55 HV, air prssur bar, covrag 98 %. Th man shot vlocity was dtrmind by mans of an optical masuring systm providd from KSA (Wüstfld, 5) to 3 m/s. Th impact angl is dfind according to Figur. Th matrial of th tst spcimn was ag hardnd N78 (hardnss 45 HV; R p. MPa). Th rsidual strsss aftr shot pning wr masurd by x-ray diffraction on th {3}-intrfrnc lin using Mn-K-radiation. Th masurd intrfrnc paks wr valuatd according to th sin mthod, using a Young s Figur : Tst spcimn gomtry, coordinat systm and positions of sparation. modulus of E 3 = MPa and a Poisson s ratio of 3 =.3. Masurmnts in dpth wr prformd by succssiv lctro polishing of a circular ara with a diamtr of 5 mm. Strss rlaxation du to th matrial rmoval by lctro polishing was not takn into account, sinc th rmovd ara was small. Th tst spcimns wr sparatd aftr th shot pning tratmnts at th positions shown in Figur in ordr to nabl th x-ray diffraction masurmnt in th x-dirction at th tst spcimn sctions with a thicknss of 5 and mm. Aftr th tratmnts th tst spcimn sction with a thicknss of mm was slightly bnt around th y-axis and aftr th sparation also around th x-axis. Shot Pning Modl Th shot pning modl consists of a 3-dimnsional rctangular body of arbitrary thicknss and quadratic bas and is basd on th work of (Schwarzr, 3). ABAQUS/Explicit is usd for th dynamic analysis of th shot impacts on th surfac taking into account inrtia ffcts. Th msh is st up by 8-nod linar brick lmnts with rducd intgration and hourglass control. Th lmnt siz of a surfac lmnt is adjustd to /5th of th dimpl diamtr producd by a singl shot impact for th givn shot diamtr and vlocity. Th problm of damping of inducd and intrnally rflcting strss wavs in th modl is solvd using so-calld infinit Figur : Shot arrangmnt and valuatd ara to calculat th rsidual strss profil; numbrs indicat th impact ordr of th shots. lmnts surrounding th facs of th rctangular body. Ths spcial typs of lmnts lad to a minimization of th rflction of dilatational and shar wavs into th body during th analysis and do not affct th strss stat of th modl whn static quilibrium is rachd (ABAQUS manuals, 7). Th stl shots ar modld by half sphrical rigid surfacs with paramtrizd diamtr, vlocity, and dirction. Th physical proprtis of a full sphr ar assignd to th rigid surfacs by conncting ach on of thm to a point mass and a rotary inrtia lmnt locatd in th cntr of th sphrs. sotropic Coulomb friction btwn th shots and th surfac of th plats is assumd with a constant friction cofficint µ =.4. Th stochastic impact ordr of th shots on th tratd surfac is modld by a dimpl pattrn of full covrag of th ntir modl surfac with th impact ordr and shot arrangmnt shown in Figur providing an axis-symmtric rsidual strss stat in th cas of an impact angl = 9. Th rsidual strsss from th simulation ar dtrmind according to (Schwarzr, 3) with an avraging tchniqu whr th rsidual strsss of th lmnts lying within th gray markd circular ar avragd for vry dpth layr.

3 Boundary Conditions Thr typs of boundary conditions wr invstigatd in this study. Th first typ corrsponds to th boundary condition usd by (Schwarzr, 3) whr th latral facs of th modl ar not constraind and th modl s bas is fixd in z-dirction (cp. Figur 3 a). Th scond typ is th classic approach applying symmtric boundary conditions to th latral facs and th third and nw typ of boundary condition aims to modl a small sction of an initially flat plat with a dfind thicknss whr dflction can occur dpnding on th thicknss and th pning intnsity. Th latral facs of th modl ar forcd to b prpndicular to th surfac as wll to th bas by a kinmatic coupling constraint of th latral facs in normal dirction with 4 rfrnc points surrounding th modl according to Figur 3 b). Control of dflction is stablishd by constraining th rotational dgr of frdom of th rfrnc points. This is important whn dflction is omittd du to gomtrical constraints lik for instanc th dflction of th mm thick sction of th tst spcimns around th x axis during th shot pning tratmnt. a) b) Figur 3: Boundary conditions with a) fr and b) constraint latral facs. Matrial Modl To tak into account th Bauschingr ffct and strain rat snsitivity of agd N78 a combind isotropic/kinmatic lasto-viscoplastic matrial modl is usd for th shot pning simulation and was implmntd into ABAQUS/Explicit as a usr dfind subroutin. This matrial modl is an xtndd vrsion of th unifid constitutiv matrial modl proposd by (Ramaswamy, 99) and consists of a st of ordinary partial diffrntial quations, which ar prsntd in rat form: & & &,,, E & & & () n S Z & D xp 3K K () &, a & a &,, &, a & a &, 3, m 3, m (3, 4, 5) Z& m( Z Z ) & (6) with K ( S )( S ) and & & & bing th scond invariants of th 3 dviatoric ovrstrss tnsor and inlastic strain rat tnsor. E Equation () is th gnral kinmatic quation combining lastic and inlastic strain to total strain. Th inlastic strain rat & is calculatd by th flow quation () as a function of dviatoric strss S and two stat variabls, namly th back strss and th scalar drag strss Z. Strain rat snsitivity is govrnd by th modl paramtrs D, corrlating with th maximum inlastic strain rat of th matrial, and n. Th xtnsion of th matrial modl from (Ramaswamy, 99)

4 consists in a dcomposition of th back strss into two back strss trms and, which dvlop according to quation (4) and (5) during inlastic dformation. This dcomposition yilds to a bttr dscription of th cyclic dformation bhaviour of th matrial (Lmaitr, 999) by mans of th matrial modl paramtrs a, a,,m, and, m. Equation (6) is th volution quation of th drag strss Z. m and Z ar matrial modl paramtrs and & is th ffctiv inlastic strain rat. Th procdur to dtrmin th matrial modl paramtrs is dividd into two stps. n th first stp th paramtrs n govrning th strain rat snsitivity and th initial flow strss of th matrial rprsntd by th paramtr Z Z ( ) wr dtrmind on th basis of comprssion tsts carrid out at strain rat rgims ranging from -3 to +4 /s with th mthod of last squars. D was st to 6 /s. Th rmaining matrial modl paramtrs ( a, a,, m,, m, m and Z ) dscrib th dformation and hardning bhaviour and wr fittd in a scond stp of th matrial modl paramtr dtrmination procdur by mans of th commrcial softwar (Fitt) on basis of strain controlld push pull tsts, which provid information about th dformation bhaviour during cyclic loading conditions. RESULTS AND DSCUSSON A comparison with xprimntal data validats th capability of th matrial modl to account for strain rat snsitivity for all masurabl strain rat rgims and for th Bauschingr ffct during cyclic loading conditions (Zimmrmann, 8). Consquntly a matrial modl is providd to th shot pning simulation that should mt th rquirmnts for ralistically dscribing th matrial bhavior of a componnt during shot pning. n ordr to invstigat th capability of th thr typs of boundary conditions to ralistically constrain th simulatd body for diffrnt thicknsss simulations with th 3 typs of boundary conditions wr carrid out with a modl thicknss of and 5 mm. Th calculatd rsidual strss dpth profils ar compard to th xprimntal masurmnts in Figur 4. Th symmtric boundary conditions yild to a good prdiction of th comprssiv rsidual strsss clos to th surfac. Howvr th calculatd rsidual strss dpth profil is unbalancd sinc no tnsil rsidual strsss ar prsnt. This shortcoming is du to xtrnal nodal forcs on th latral facs rprsnting th infinit latral xtnsion. Hnc th calculatd strss stat with symmtry boundary conditions on th latral facs is not intrnally quilibratd and thrfor unralistic if small thicknsss ar invstigatd. n th cas of laving th latral facs unconstraint a qualitativly and quantitativly satisfying accordanc to th xprimntal rsults is achivd for a thicknss of mm. Howvr for a thicknss of 5 mm th comprssiv rsidual strsss in th surfac rgion ar strongly undr- and th tnsil rsidual strsss strongly ovrstimatd. This ffct is du to th smallr stiffnss in th dg nar rgions of th modls surfac lading to an out squzing which is shown in Figur 5. Ovrcoming ths disadvantags th kinmatic coupling constraint supprsss th squz out ffct and nforcs th inducd comprssiv rsidual strsss to b balancd with tnsil rsidual strsss lading to a bttr accordanc of th numrical rsults with th xprimntally masurd profils.

5 a) RS [MPa] x modl: symmtry cll fr facs kinmatic constraint xp.: x-ray N78 pning paramtrs: shot vlociy 3 m/s shot diamtr.89 mm impact angl 8 covrag % thicknss mm dpth [mm] b) modl: symmtry cll fr facs RS [MPa] x xp.: kinmatic constraint x-ray N78 pning paramtrs: shot vlociy 3 m/s shot diamtr.89 mm impact angl 8 covrag % thicknss 5 mm dpth [mm] Figur 4: nflunc of boundary conditions on th calculatd rsidual strss dpth profils for a thicknss of a) and b) 5 mm. n Figur 6 th capability of th nw typ of boundary condition dscribing th influnc of thicknss on th rsidual strss stat aftr shot pning is shown. Th simulations of a thicknss of 5 and mm wr carrid out supprssing th dflction of th rctangular body around th y axis during th shot impacts, which should rprsnt th gomtrical stiffnss of th tst spcimn. Th sparation of th 5 Figur 5: Scald msh dformations with fr facs (cut viw). and mm thick tst spcimn sctions and th corrsponding strss rlaxation is takn into account by rlasing th rotational constraint of th rfrnc nods linkd to th latral facs normal to th y dirction aftr th shot impacts. Th rsults show that in x-dirction no influnc of th thicknss on th surfac and maximum comprssiv rsidual strsss can b obsrvd. Howvr, in y-dirction th surfac and maximum comprssiv rsidual strsss for a thicknss of mm ar smallr. This ffct can b attributd to th strss rlaxation du to th sparation of th tst spcimn. n both dirctions incrasing tnsil rsidual strsss can b obsrvd with dcrasing thicknss. Th prdictd tnsil rsidual strsss for a thicknss of mm ar ovrstimatd in comparison to th x-ray masurmnts. Howvr, strong strss rarrangmnt ffcts du to lctro polishing of such a thin tst spcimn ar likly to dcras th masurd tnsil rsidual strsss and to b th rason of this dviation. RS [MPa] x mm thicknss x-ray modl 5 mm thicknss x-ray modl mm thicknss x-ray modl N78 pning paramtrs: shot vlociy 3 m/s shot diamtr.89 mm impact angl 8 covrag % dpth [mm] RS [MPa] y mm thicknss x-ray modl 5 mm thicknss x-ray modl mm thicknss x-ray modl N78 pning paramtrs: shot vlociy 3 m/s shot diamtr.89 mm impact angl 8 covrag % dpth [mm] Figur 6: Masurd and simulatd rsidual strss dpth profils for diffrnt thicknsss.

6 CONCLUSONS Th influnc of componnt thicknss on th rsidual strss stat aftr shot pning was analyzd xprimntally by x-ray diffraction masurmnts at a shot pnd tst spcimn faturing diffrnt thicknsss and numrically by 3D FE simulations using thr diffrnt approachs for constraining th modl boundaris. t was found that with th classic approach of symmtric boundaris at th latral modl facs th influnc of thicknss is compltly nglctd and th rsidual strss dpth profil is unbalancd. Laving th latral facs fr lads to squzing ffcts at th dgs of th modl surfac and to unralistic strss stats. Constraining th latral facs to b prpndicular to th surfac as wll to th bas of th modl lads to th incorporation of dflction ffcts and to ralistic simulation rsults bing in vry good accordanc to th xprimntal rsults. Th analysis of th influnc of thicknss on th rsidual strss stat showd that dcrasing thicknss dosn t affct th comprssiv rsidual strsss in th surfac rgion but lads to a shift of th zro crossing to th surfac and to highr tnsil rsidual strsss in gratr dpths. On basis of this obsrvation it can b concludd that th rsidual strss distribution can b diffrnt vn whn th inducd plastic dformations ar idntical. This mans that th rsidual strss distribution not only dpnds on th plastic dformation fild but also on th gomtrical constraints. ACKNOWLEDGMENTS Th simulations wr prformd on th national supr computr HP XC4 at th Scintific Suprcomputing Cntr Karlsruh undr th grant numbr FESSPP. Th authors gratfully acknowldg th financial support from th Europan 6th Framwork Programm through th rsarch projct VERD (Virtual Enginring for Robust manufacturing with Dsign ntgration; REFERENCES ABAQUS Analysis Usr s Manuals (7), vrsion 6.7, nfinit lmnts, Sction... Fitt, Lmaitr, J. & Chaboch, J. (99), Mchanics of solid matrials, Cambridg Univrsity Prss, st dition, pags Mguid, S. A.; Shagal, G. & Stranart, J. C. (7), 'Dvlopmnt and Validation of Novl FE Modls for 3D Analysis of Pning of Strain-Rat Snsitiv Matrials', Journal of Enginring Matrials and Tchnology 9(), Mnig, R.; Pintschovius, L.; Schulz, V. t. al. (), 'Dpth profils of macro rsidual strsss in thin shot pnd stl plats dtrmind by X-ray and nutron diffraction', Scripta Matrialia 45, Ramaswamy, V. G.; Stouffr, D. C. & Lafln, J. H. (99), 'A Unifid Constitutiv Modl for th nlastic Uniaxial Rspons of Rné 8 at Tmpratur Btwn 538 C and 98 C', Journal of Enginring Matrials and Tchnology, Schwarzr, J.; Schulz, V. & Vöhringr, O. (3), 'Evaluation of th nflunc of Shot Pning Paramtrs on Rsidual Strss Profils using Finit Elmnt Simulation', Matrials Scinc Forum 46-43, Wüstfld, F.; Linnmann, W.; Kittl, S. t al. (5), On-Lin Procss Control for Shot Pning Applications, in 'Procdings of th Ninth ntrnational Confrnc on Shot Pning'. Zimmrmann, M.; Klmnz, M.; Schulz, V. & Löh, D. (8), 'Numrical Studis on th nflunc of Thicknss on th Rsidual Strss Dvlopmnt During Shot Pning', High Prformanc Computing in Scinc and Enginring: Transactions of th High Prformanc Computing Cntr, Stuttgart (HLRS), submittd.