USING THE INCREMENTAL HOLE-DRILLING TECHNIQUE FOR MEASURING RESIDUAL STRESSES IN FIBRE-REINFORCED POLYMER COMPOSITES

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1 USING TH INCRMNTAL HOL-DRILLING TCHNIQU FOR MASURING RSIDUAL STRSSS IN FIBR-RINFORCD POLYMR COMPOSITS J.P. Nobre 1*, A.C. Batsta, A. Nau 3, W. Van Paepegem 4 and B. Scholtes 3 1 CMDRX, Department of Mechancal ngneerng, Unversty of Combra, Rua Luís Res dos Santos, Pólo II, Combra, Portugal CMDRX, Department of Physcs, Unversty of Combra, Rua Larga, Pólo I, Combra, Portugal 3 IfW, Insttute of Materals ngneerng, Kassel Unversty, Sophe-Henschel-Haus, Mönchebergstr. 3, Kassel, Germany 4 MMS, Mechancs of Materals and Structures, Ghent Unversty, Snt-Petersneuwstraat 41, 9000 Gent, Belgum *correspondng author: joao.nobre@dem.uc.pt Keywords: hole-drllng method, resdual stresses, drllng stresses, polymer-matrx compostes (PMCs). Abstract The Incremental hole-drllng technque (IHD) seems to be a promsng technque, among the destructve (relaxaton) technques, to determne n-depth non-unform resdual stresses n fbre-renforced polymer compostes. Hence, vald theoretcal approaches for IHD resdual stress determnaton n composte lamnates, based on a set of stran-depth relaxaton curves, are needed. Nevertheless, the nfluence of the drllng process tself on the ntal resdual stress state,.e. exstng pror to hole drllng, must be verfed frst. In ths work, the IHD resdual stress evaluaton procedures n composte lamnates wll be revewed and an orgnal hybrd expermental-numercal methodology wll be used to quantfy the resdual stran nduced by the drllng process. Thus, resdual strans nduced by ultra-hgh speed drllng processes on carbon-epoxy lamnates (CFRPs) have been quantfed. The results seem to show that IHD technque can be mproved to be successfully appled for measurng resdual stresses n CFRPs. 1 Introducton Mechancal performance of the polymer matrx compostes can be hghly nfluenced by the resdual stress state, whch can have a benefcal or detrmental effect. Warpage, nterface debondng and matrx mcrocrackng are examples of detrmental effects caused by resdual stresses, whch can reduce the stffness, the strength and lfe of the composte component [1,]. The study and the knowledge of ts exact nfluence on composte systems mply the accurate determnaton of the resdual stress state. In the case of orthotropc materals, such as advanced lghtweght, hgh-performance carbon-fbre renforced polymers (CFRP), or glassfbre renforced polymers (GFRP), the hole-drllng method seems to be a promsng technque to determne resdual stresses snce, n these cases, the usual non-destructve methods cannot be appled or have hghly restrctve applcaton [1,3-5]. 1

2 Ths technque bascally conssts on drllng a small hole n the surface of the test materal and measurng the surface stran produced by the local stress relaxaton nduced by the hole (typcally 1 to 5 mm dameter) on the exstng resdual stress feld. Hole-drllng technque was orgnally developed for sotropc materals [6] and later for orthotropc materals [3,4]. In the case of sotropc materals, based on the theory of lnear elastcty, the well known Krsch s soluton can be used to relate the measured stran relaxaton feld wth the exstng resdual stresses pror to the hole-drllng. Apart the hgher mportance to fnd the best theoretcal approach to determne resdual stresses from a set of n-depth stran relaxaton curves, n the case of fbre-renforced polymer compostes, t s necessary frst to verfy the nfluence of the drllng operaton tself on the ntal resdual stress state exstng pror to hole drllng. In ths work the resdual stress evaluaton procedures for IHD technque, for ts applcaton to composte lamnates, wll be revewed and the effect of the drllng process tself on the stress state exstng pror to hole drllng wll be studed usng a new hybrd expermental-numercal methodology. Ths methodology allows the resdual stran nduced by the drllng process to be quantfed. Ths way, the applcablty of the IHD technque for measurng resdual stresses n fbre-renforced polymer compostes could be evaluated. IHD Resdual Stress valuaton Procedures for Composte Lamnates Fgure 1 shows a schematc representaton of ASTM type A stran-gauge rosette [7] to be used n hole-drllng resdual stress measurements. When a hole s drlled nto a test materal at centre of the rosette, the Krsch's soluton allows the surface radal stran relef ( r ), n drecton relatvely to L axs, to be related to the releved stresses ( L, T and ) by the relatonshp: B cos C sen A. (1) r L T L T Fgure 1. ASTM type A stran-gauge rosette for the hole-drllng method [7], showng reference axs for equaton (1), also consderng the prncpal lamnate axs system L-T. The constants A, B and C depend on the materal propertes, the rosette geometry, the hole dameter and the hole depth. It can be determned expermentally or numercally. All resdual stress evaluaton procedures for sotropc materals are based on ths equaton [8]. For these materals C = B. Thus, some authors proposed resdual evaluaton procedures for orthotropc materals based on ths trgonometrc-based equaton, e.g. [4,9], for whch C wll be ndependent from A and B. However, Schajer and Yang [3] have shown that the dsplacement feld around a hole n a stressed orthotropc plate does not have such smple trgonometrc form and, therefore, the applcaton of equaton (1) to orthotropc materals can lead to erroneous results. In addton, based on Smth s work [10], they proposed an evaluaton procedure for determnaton of unform resdual stress feld n some class of orthotropc materals. More recently, Paglaro and Zuccarello [11], followng the work of Schajer and Yang [3], mplemented an alternatve formulaton for analyss of the resdual stresses on

3 orthotropc lamnates. In complex cross-ply or angle-ply orthotropc lamnates, elastc propertes of the materal change suddenly from ply to ply and, consequently the resdual stresses could not be unform through the depth. Usng a formulaton smlar to Schajer and Yang [3] for unform orthotropc materals, those authors extended the method to the analyss of the through thckness non-unform resdual stresses (not equlbrated) n a generc orthotropc lamnate due to n-plane ntal loads, as those n a tensle calbraton test. Shortly, although the resdual stresses are not unform through the lamnate thckness, the resdual strans are unform (consderng the n-plane loadng) and smple relatonshps between surface relaxed stran and resdual stresses can be detected by usng the Classcal Lamnate Theory. The relatonshp that allows the user the evaluaton of the resdual stresses components n each ply, from the relaxed strans measured on surface, can be determned by solvng the Paglaro-Zuccarello s equaton [11]: L, T,, 1 3 ~ 1 1 C 1,,.., n. () Where {e 1, e, e 3 } T s the vector contanng the surface stran relaxaton values measured by the stran-gauges 1, and 3, respectvely (see Fgure 1), whch stran-gauge 1 was algned wth the prncpal lamnate axs L. { L,, T,,, } T contans the stresses exstng n a gven ply, relatvely to prncpal lamnate system L T. [] s the stffness matrx of the th ply n the prncpal lamnate system L T gven by: L 1TL ~, T T T 1,,..,n 1 TL L, G T 1TL 1TL T, G L, G G G. (3) Where L, T,, TL L,, T, and G are the elastc propertes of the th ply n the prncpal coordnate system L T of the lamnate, whch s, n general, dfferent from the prncpal coordnate system 1 of each ply/fbre. [] s a dmensonless stffness matrx gven by: G. (4) Where, and are dmensonless elastc constants, gven by: L ; T G G ;. (5) T 3

4 Beng L, T, and G the elastc propertes of an equvalent homogenous orthotropc materal, havng the same n-plane elastc behavour of the composte lamnate to study, whose elastc propertes can be related to those of each ply by usng the well-known relatonshps of the Classc Lamnate Theory (C). Note that, n the case of an undrectonal lamnate, [] = L.[], and equaton can be smplfed. Fnally, [C] s the matrx of the so called dmensonless nfluence coeffcents c j (,j=1,), or calbraton coeffcents, gven by: c11 c1 0 C c1 c c3. (5) c31 c3 0 Where each coeffcent c j can be determned numercally, or analytcally usng the approach proposed n reference [11]. The complances c 13 and c 33 equal zero, f the drectons of the rosette, correspondng to stran-gauge 1 and 3, concde wth the prncpal elastc drectons L- T of the orthotropc materal, respectvely as shown n fgure 1 ( 1 =0, =135 and 3 =70 ). If the same rosette s nstalled wth gauge 1 algned wth the cross materal drecton T,.e., 1 =90, =5 and 3 =0, equaton stll apples f 1 s changng wth 3 and c 3 replaced by c 3. Thus, the applcaton of the hole-drllng method to a gven orthotropc materal nvolves seven dstnct calbraton coeffcents. In partcular, f the orthotropc materal s balanced (.e., L = T and then =1), due to symmetry t follows that c 11 =c 3, c 1 =c 31, c 1 =c and the number of coeffcents wll only be four. In addton, for an sotropc materal =1/[(1+ )] and c 11 =c 3 ; c 1 =c 31 ; c 1 =c =(c 11 +c 31 )/=(c 1 +c 3 )/, so that the number of ndependent calbraton coeffcents reduce to two. In fact, n ths case, equaton 1 can be rewrtten usng the three stran relaxaton values measured for each strangauge of the rosette, as follows: 1 A B A 3 A B A B A A B 0 L B T 0. (6) The theoretcal background presented above represents the best theoretcal approach to determne resdual stresses n each ply of a gven composte lamnate, after measurng the surface strans releved by hole-drllng. However, the presented theory was developed to analyse the resdual stresses on orthotropc composte lamnates, caused by ntal n-plane loads. It cannot be appled for measurng n-depth non-unform resdual stresses yet. Some addtonal work must be performed frst. Nevertheless, to apply the IHD technque to composte lamnates t s necessary, prevously, to verfy how the cuttng process can modfy the stress state exstng n the composte lamnate before drllng. In the followng, the results of a methodology developed to quantfy the nduced drllng strans wll be presented [1]. 3 valuatng the nduced drllng strans The resdual strans nduced by drllng operaton n fbre-renforced polymer compostes, due to thermo-mechancal phenomena related to cuttng process, can affect ether the functonal behavour n servce of the composte lamnate or the accuracy and relablty of the holedrllng resdual stress measurement technque. The hybrd expermental-numercal methodology presented n Fgure allows the determnaton of nduced drllng strans. Shortly, the methodology conssts on drllng, ncrementally, specmens subjected to a gven 4

5 dfferental appled stress, usng purpose-bult tensle devces. Thus, a set of stran-depth relaxaton curves can be determned expermentally. Next, a numercal smulaton of the whole expermental procedure s carred out usng the fnte element method, allowng a set of deal set of stran-depth relaxaton curves to be determned. The drect comparson between the expermental and numercal curves enables the determnaton of the effect of the drllng process,.e., the quantfcaton of the nduced drllng strans. Fgure. Flowchart of a hybrd expermental-numercal methodology to determne nduced drllng strans and to optmze the hole-drllng process In ths work a carbon-epoxy composte lamnate was selected as test materal. The specmens were manufactured n an autoclave usng carbon-epoxy prepreg (M55j/M18) as raw materal, usng dfferent stackng sequences. Table 1 shows the specmens used and table the elastc propertes of sngle lamna. Carbon-epoxy lamnate Specmens [mm 3 ] Ply thckness [m] Depth Increments per ply Increment s depth [m] [0º] 4 165x5x [0º /90º ] s 165x30x [0º/90º] 5s 80x8x Table 1. Composte lamnate specmens for tensle tests 11 = 33 G 1 = G 13 G 3 [GPa] [GPa] [GPa] [GPa] 1 = 13 3 = 3 1 = Table. lastc propertes for the carbon-epoxy lamna (obtaned accordng to [13]) The drllng process under evaluaton was the ultra-hgh speed mllng usng a turbne powered by compressed ar, a process commonly used wth hole-drllng equpments for measurng resdual stresses n metallc materals. In a prevous work [14] ths process showed to gve better results than tradtonal CNC machnng. Here, the presented results are only for normal drllng, even f orbtal drllng processes could even lead to better results,.e., decreasng the nduced drllng strans. Table 3 shows the most mportant drllng parameters used n the tests. 5

6 Ar pressure [bar] WC mll dameter [mm] Cuttng speed [ms -1 ] Rotaton speed [rpm] Feed rate [mm/mn] ~4 80,000 << ~18 10,000 <<0.01 Table 3. Ultra-hgh speed drllng parameters (UHSM) Followng the flowchart of Fgure 1, durng the expermental calbraton tests, the composte specmens were loaded as shown n Fgure 3. Fgure 3. Loadng condtons durng tensle tests. ach depth ncrement was always drlled for mn. Durng the expermental calbraton test, each depth ncrement was always machned for the mnmum appled load. A specal 1.6 mm dameter WC hard coated mllng cutter of sx blades n nverted cone, usually employed n IHD applcatons, has been used. After each ncremental depth machned, the stran data were recorded and the specmen loaded tll maxmum load, where the stran data were recorded agan. Ths process was systematcally repeated untl the total hole depth was reached ( half hole dameter). At least two depth ncrements by each ply were consdered. Thus, a set of expermental stran-depth relaxaton curves were obtaned for each case. Followng the flowchart of Fgure, the experments were then smulated by fnte elements (FM) usng ANSYS APDL code [15]. The model uses quadratc 0 nodes 3D layered sold elements SOLID186 and has been parameterzed to be appled to dfferent stackng sequences and orentaton of the ples, mnmzng the changng of APDL scrptng see Fgure 4. Fgure 4. Fnte element meshes for hole smulaton n tensle specmens of CFRP undrectonal lamnates [0º] 4, also showng the relatve poston of the stran-gage grds (left) and CFRP cross-ply lamnates [0 /90 ] s (rght) 6

7 Durng the processng phase, the hole drllng was always smulated, ncrementally, at the centre of the FM model usng brth and death ANSYS code features [15], beng the thckness of each depth ncrement equal to the mposed durng the expermental tests. 4 Results and Dscusson Fgure 5 shows stran-depth relaxaton curves, n the drecton of the appled stress and n the cross drecton, obtaned durng the expermental tests on the [0º] 4 lamnate. The results usng the two drllng condtons (table 3), are compared wth deal ones determned by FM. Fgure 5. Comparson between expermental and numercal stran-depth relaxaton curves for CFRP undrectonal lamnates [0º] 4, subjected to calbraton stress of 65 MPa (drecton of the appled stress (left) and cross drecton (rght)). xpermental UHSM condtons are presented n table 3. It can be seen that better results are obtaned when cuttng speed ncreases from 18 m.s -1 to 4 m.s -1 (.7 bar to 4 bar). A smlar behavour s obtaned for cross-ply lamnates. Fgure 6 shows the stran-depth relaxaton results obtaned on [0º/90º] 5s lamnate for 18 m.s -1 (.7 bar) and [0 /90 ] s for 4 m.s -1 (4 bar), n the longtudnal drecton. The expermental and numercal stran-depth relaxaton curves for 4 m.s -1 (4 bar) present an excellent agreement. Fgure 6. Comparson between expermental and numercal stran-depth relaxaton curves for CFRP cross-ply lamnates [0 /90 ] 5s, subjected to a calbraton stress of 75 MPa (left) and [0 /90 ] s, subjected to a calbraton stress of 15 MPa (rght). xpermental UHSM condtons are presented n table 3. As shown n Fgure 6, the stran relaxaton measured at surface can be studed consderng a contnuous behavour, although the stresses exstng n each ply could present a dscontnuous behavour between ples. Ths calculaton, however, s under study yet, usng equatons presented n secton. Nevertheless, even f some expectable dfferences arse, between expermental and numercal curves, the results are very encouragng relatvely to the future mprovement of the IHD technque for ts applcaton to CFRPs. 7

8 5 Conclusons The state-of-the-art for IHD resdual stress evaluaton on composte lamnates was presented. However, the effect of the nduced drllng strans must be analysed before any further development of IHD resdual stress evaluaton procedures. Thus, nduced drllng strans n undrectonal and cross-ply CFRP lamnates were determned for two ultra-hgh speed drllng processes. These drllng processes, combned wth very slow feed rate, led to relatvely low nduced drllng strans, especally for the hghest cuttng speed used n the tests. The comparson between expermental and numercal stran-depth relaxaton curves has shown that the ncremental hole-drllng can be successfully mproved for ts applcaton to the CFRP lamnates. In addton, very good geometrcal hole shape, wthout appearance of delamnaton, has been observed. In ths context, the hybrd expermental-numercal methodology used can be of great help to mprove drllng processes and parameters on CFRPs. Acknowledgments The authors gratefully acknowledge the fnancal support of German Research Foundaton (DFG), Project SFB TRR30, whch made ths work possble. J.P. Nobre and A.C. Batsta also acknowledge the fnancal support of the uropean Regonal Development Fund (RDF) through "Programa COMPT" and Portuguese natonal funds through FCT under the projects PestC/FIS/UI0036/011 and PTDC/MS-TC/1860/01. References [1] Benedkt, B., Predeck, P., Measurement of resdual stresses n fber-renforced compostes based on X-ray dffracton. Adv. n X-ray Anal., Vol. 45, pp. 18-4, 00. [] Zhao, L., Warror, N. A., Long, A. C., Analyss of resdual stress n fbre-renforced polymer compostes. Proc. 16th Int. Conf. on Composte Materals, Kyoto, Japan, 007. [3] Schajer, G. S., Yang, L., Resdual-stress measurement n orthotropc materals usng the hole-drllng method. xpermental Mechancs, Vol. 34, pp , [4] Scot, O., Gong, X., Cherouat, A., Lu, J., Determnaton of resdual stress n composte lamnates usng the hole-drllng method. J. of Comp. Mat., Vol. 37, pp , 003. [5] Schajer, G., Hole-drllng resdual stress measurements at 75: orgns, advances, opportuntes. xpermental Mechancs, Vol. 50, pp , 010. [6] Bjak-Zochowsk, M., A sem-destructve method of measurng resdual stresses. VDI- Berchte, Vol. 313, pp , [7] ASTM , Standard test method for determnng resdual stresses by the holedrllng stran-gage method. Annual Book of ASTM Standards, pp. 1-1, 008. [8] Schajer, G., Flaman, M. T., Roy, G., and Lu, J., Hole-drllng and rng core methods. In: Lu, J., d., Handbook of Measurement of Resdual Stresses, SM, pp. 5-34, [9] Lake, B., Appl, F., Bert, C., An nvestgaton of the hole drllng technque for measurng resdual stress n orthotropc materals. xp. Mech., Vol. 10, pp , [10]Smth, C. B., ffect of ellptc or crcular holes on the stress dstrbuton n plates of wood or plywood consdered as orthotropc materals, USDA Forest Prod. Lab., pp. 1-5, [11]Paglaro, P., Zuccarello, B., Resdual stress analyss of orthotropc materals by the through-hole drllng method, xp. Mech., Vol. 47, pp , 007. [1]Nobre, J. P., Stffel, J.-H., Nau, A., van Paepegem, W., and Scholtes, B., valuatng nduced drllng strans n fbre-renforced polymer compostes. Part I: A hybrd expermental-numercal methodology. Submtted to Compostes Scence and Technology. [13]ASTM-D3039-D3039M-08, Standard Test Method for Tensle Propertes of Polymer Matrx Composte Materals. ASTM Internatonal, West Conshohocken, PA, 008. [14]Nobre, J. P., Stffel, J., Paepegem, W., Nau, A., Batsta, A., Marques, M., Scholtes, B., Quantfyng the drllng effect durng the applcaton of ncremental hole-drllng technque n lamnate compostes, Materals Scence Forum, Vol. 681, pp , 011. [15] ANSYS, I. (010). Release 11.0 Documentaton for ANSYS, SAS IP, Inc., Houston. 8