EXPERIMENTAL AND NUMERICAL STUDY OF DEBONDING IN COMPOSITE ADHESIVE JOINTS

Transcription

1 6 TH NTERNATONAL CONFERENCE ON COMPOSTE MATERALS EXPERMENTAL AND NUMERCAL STUDY OF DEBONDN N COMPOSTE ADHESVE JONTS Rosen T. Tenhev, Brian. Falzon mperial College, London, UK Keywords: interfae elements, deohesive zone, mixed mode, DCB, ELST Abstrat The mode and mode fratre properties of the FM- adhesive bond between 5HS/RTM6 laminates are determined experimentally by DCB and ELS test. The rak propagation is stdied nmerially by means of interfae elements based on the deohesive zone model. The latter is haraterized by material degradation, whih is sally assmed to be linear. n the present stdy it is shown that if a non-linear material degradation is sed with an inreased magnitde of the interfae relative displaement at failre it is possible to model more orretly the experimentally observed signifiant non-linear behavior before the start of rak propagation. An adhesive stepped flsh joint is stdied experimentally and nmerially. A mixed mode interation riterion is sed together with the nonlinear material degradation of the interfae. Sensitivity stdies are performed to stdy the inflene of the parameters defining it. ntrodtion Experimental stdies have shown that an adhesive stepped flsh joint may derease the load arrying apaity by p to % []. The failre mode is a ombination of adhesive failre and omposite adhesive srfae debonding. Sine the adhesive layer is very thin, ompared to a typial laminate thikness, the failre proess an be modelled as a rak propagation problem. An established nmerial strategy is to make se of an interfae finite element that is based on the deohezive zone approah []. n this paper the identifiation of ertain parameters of the interfae element onstittive law, related to the deohesive zone, is disssed. This enables the finite element analysis to predit more arately the experimentally observed non-linear behavior at the initiation of rak propagation. The non-linear interfae onstittive law is sed to analyse a stepped flsh joint. Fratre Properties - Experimental Stdies The rak propagation throgh an adhesive bond was stdied for mode on doble antilever beam (DCB) speimens, and for mode on end load split (ELS) speimens [].. Mode, DCB test The loading and deformation of a DCB speimen are shown in Fig.. The dimension, in mm, are: L=., B=., h=.9, =9., a =. The separation d of the antilever arms is measred by an LVDT. raph paper was bonded along the length of the adhesive interfae to measre the propagation of the rak. The latter was observed and reorded by a travelling zoom amera. Still shots of the rak propagation for one speimen are presented in Fig.. t an be seen that the rak grows either by a single rak propagation or the propagation and oalesene of several raks. d F F Crak a a Loading bloks Adhesive film L Fig.. DCB test. Speimen and free body diagram. h B

2 ROSEN T. TENCHEV, B.. Falzon t was observed that the rak patterns at the front and bak srfaes are not the same, whih means that the rak front is not a straight line and it may not traverse the whole width of the speimen. To model the derease of the stiffness of the adhesive interfae these pathes an be smeared into a softening deohesive zone Fore [N] Speimen Single rak front Displaement, d [mm] Fore [N] Speimen Speimen Speimen Mlti fronts: a deohesive zone. Fig.. DCB tests. Crak propagation Speimen 5 Speimen Displaement, d [mm] Fig.. DCB tests. Fore-displaement response. 6 The measred fore-displaement response dring rak propagation of six speimens is shown in Fig.. The graphs are not smooth bease the rak propagates in disrete steps. The rak length growth is visally reorded together with the fore-displaement measrement display. Based on beam theory [] the energy release rate an be ompted by three formlas, Eqs.. Analytially the three variables (fore F, displaement d, and rak length a) are not independent and the formlas will give the same reslts for. ( Fa) = B E (a) Fd = B a (b) = B F d E () The laminate s elasti modls in bending was experimentally determined on intat antilever speimen to be E b = 6 Pa. Varios tehniqes for orreting beam theory (ompliane orretions for root rotation, large displaements, et., []) were onsidered bt the hange in the reslts was insignifiant when ompared to the large osillations in Fig.. The fator that had the biggest inflene (bt still less than %) was the hange of the fore moment arm de to the rotation of the loading bloks. Hene all these orretions are omitted here for simpliity. The energy release rates are ompted by Eq. a, b and and the reslts for for speimens are presented in Fig.. The reslts ompted by the three formlas are averaged. These averaged reslts are linearly interpolated (bease for eah speimen the reorded data is for different d and F) and averaged again. The final resistane R rve is presented in Fig. 5. A steady state vale of =. [] is well defined. The rak initiation vale is lower (, =.6 ), whih agrees with other experimental data [5].. Mode, ELS test The same speimen, shown in Fig., is sed for mode ELS tests. The loading and the spports are aording to the free body diagram shown in Fig. 6. Five speimens were tested: three with initial rak length a = mm; one with a = mm and one

3 EXPERMENTAL AND NUMERCAL STUDY OF DEBONDN with a =5 mm. The fore displaement (F-d) graphs are shown in Fig []. Speimen Speimen =. Crak length, a [mm].8, =.6. [] Speimen Speimen Crak length, a [mm] Fig.. ompted by Eqs a, b and. [] Crak length, a [mm] Fig. 5. Fratre toghness, R rve. The eqations for ompting the energy release rate, derived from beam theory [], are: FL 9 B = d Eh EBh F Fore [N] 6 a = mm 9 Fa = Eh B Displaement, d [mm] Fore [N] 6 a = mm a = 5 mm (a) (b) Displaement, d [mm] Fig. 7. ELS test. Fore-displaement response. The reslts based on Eq. a for the five tested speimens are plotted in Fig. 8a. The R rve, after the two step averaging sed in the previos setion (i.e. averaging reslts from Eq. a and Eq. b for all speimen and then averaging the interpolated rves) is plotted in Fig. 8b. The basi differenes between the experimental mode reslts and mode is that the mode foredisplaement response show less osillations bt there is no well defined platea vale for. The reason for this is most probably the frition fores and a possible interloking of the exposed fiber bndles along the already delaminated rak srfaes. A vale for between 5 and 6 [], based on the graphs in Fig. 8a, will be sed in later analytial and nmerial allations. The energy release rate at rak initiation is estimated to be, =.5. [] 8 a [] 8 b d F 6 6 a L = mm 5 5 Displaement, d [mm] Crak, a [mm] Fig. 6. ELS test. Free body diagram. Fig. 8. ELS test. Energy release rate,

4 ROSEN T. TENCHEV, B.. Falzon. Experimental v. beam theory reslts n Fig. 5 and Fig. 8 it an be seen that dring the initial stages of rak propagation the energy release rates depend on the rak length. n analytial and nmerial analysis, and, are defined as material properties independent of any geometry dimensions. How well the analytial beam theory soltion mathes the experimental reslts, when onstant vales for, and, are sed, is presented in Fig. 9. t an be seen that there is good agreement dring the rak propagation bt the nonlinear behavior shown dring the initiation of rak growth annot be modeled arately. The finite element interfae elements, sed in the analyses, are based on the onept of a deohesive zone. The physial existene of sh zone an be deded from the mltirak pattern in Fig.. f sitable parameters that define the deohesive zone are sed, it is possible to improve on the nmerial predition of rak growth initiation. Fore [N] 6. nterfae elements A D interfae element [6, 7] is shown in Fig.. t has either two or three pairs of nodes depending on whether it onnets linear or qadrati elements, respetively. t has zero thikness h so nodes and have idential oordinates and similarly for nodes and. Eah node has two degrees of freedom, normal and tangential. The relative displaements = vtop vbot and = represent delamination in mode and top bot,=.,= Displaement, d [mm] a Fore [N] 6 a = mm a = 95 mm,=5 b Displaement, d [mm] Fig. 9. Experimental (solid blak line) and beam theory (broken red line) reslts. (a) Mode, DCB test; (b) Mode, ELS test. mode, respetively. The bond between a node pair of the interfae is ompletely severed when the energy amlated dring their relative displaement reahes the ritial energy release rate v = d () The initial penalty stiffness K = t / has to be sffiiently large to orretly model the predelamination response as well as to enfore the no penetration ondition when the relative displaement is in a losing mode. The interfae onstittive law is sally assmed to be bilinear. Other formlations, with a smooth transition at t to avoid nmerial problems, have been also sed [8]. The shape of the softening rve and the magnitde of the ritial relative displaement (provided that the area below the rve remains eqal to ) have no inflene on the predition of v Top h= Bottom v L v the rak propagation. Small vales of are sed when reslts are heked against analytial beam theory soltions, whih does not onsider deohesive softening. Experimental data shows a signifiant non-linear behavior jst before the initiation of rak propagation, Fig. 9, whih an be explained by the development of an extensive deohesive zone. n the present stdy it will be shown how modifying the magnitde of the ritial relative displaement and the shape of the softening rve, while regarding as onstant material property, an improve the nmerial modeling of the rak propagation initiation and sbseqent growth. To stdy the delamination initiation and propagation, a finite element software has been developed by the athors. t is based on a psedotransient formlation [7], whih ses the seant t K ( D) K = Fig.. nterfae finite element and its onstittive law

5 EXPERMENTAL AND NUMERCAL STUDY OF DEBONDN stiffness modls and avoids sprios osillations in the soltions [6], typial of other more onventional soltion strategies.. nterfae onstittive law The strain softening interfae onstittive relationship, for mode as well as mode, may be given by a power law t if k ( ) = t if < < C if () The energy release rate, when the energy of the elasti deformation is ignored (i.e. = sine ), is: k k = t t( ) t + k + k+. Comparison of FE and experimental reslts (5) Finite element analyses (FEA), sing the experimental vales for the ritial energy release rates, have been arried ot to determine the most sitable vales for k and in Eq. and Eq. 5). Comparisons of the experimental reslts with the orresponding FEA reslts and beam theory reslts are presented in Fig. and Fig. for the DCB and ELS test, respetively. Fore [N] 5 =. Speimen Fore [N] 5 Speimen 5 FEA Experiment 5 5 = Speimen Speimen Displaement, d [mm] 5 5 Displaement, d [mm] Fig. DCB mode tests. Blak line Experimental reslts, Red dash lines Beam theory reslts, =.6 and =. Ble line Finite element reslts, =. 5

6 ROSEN T. TENCHEV, B.. Falzon Fore [N] 6 Beam theory, =5 a =95 mm, =6 Displaement, d [mm], =5 Fig.. ELS mode tests. Experiment Blak line Experimental reslts, Red dash lines Beam theory reslts, Ble, reen line Finite element reslts. 6 5 Fore [N] t, = 5 MPa t, = 5 MPa t, = MPa Experiment Displaement, d [mm] Fig.. ELS tests. nflene of, and k. t, = 5 MPa :, =.67 mm; k =. t, = MPa :, =. mm; k =. t, = 5 MPa :, =. mm; k =. The fratre toghnesses are determined from the experimental data, Fig. 5 and Fig. 8. The power law oeffiient k and the relative displaements at failre, and, are determined to best fit the experimental reslts, Fig. and Fig. 7. The interfae strength t, and t, are ompted from Eq. 5. They shold be regarded as the interfae strength, in the orresponding mode, of the adhesive bond system: omposite laminate 5HS/RTM6 and adhesive FM-. The set of the interfae material properties, sed in the analyses, is given in Table. n Fig. the line a = 95mm stands for beam theory reslts at fll delamination. Sine the experimental reslts, Fig. 8, does not show a well defined stationary vale for the fratre toghness FEA reslts with =5. and =6. have been ompted to show a range of aeptable vales for. Table. nterfae material properties t, MPa t, MPa, mm, mm k n Fig. a sensitivity stdy is performed for the ELS mode tests by varying the interfae strength t,, whih is ompted from the predefined set of vales for, and k. The fratre toghness is kept onstant at, = 5 N / mm. All reslts may be onsidered eqally aeptable. Ths, it is not possible from one experiment to determine a niqe set of vales for, and k (and similarly for the orresponding parameters in ase of mode loading) that may be regarded as interfae material properties. 5. Mixed-mode formlation The interfae element onstittive law, Eq., may be written in terms of a single damage variable D, for mode loading as K, if D D K if < D < ( ) =, if D and similarly for mode. The damage variable is D k = (6) (7) 6

7 EXPERMENTAL AND NUMERCAL STUDY OF DEBONDN where the relative displaements, in ase of mixed mode loading, are ompted as follows: Eqivalent mixed-mode relative displaement: ( ( ) ) α α max, α = + (8) whih an be derived [6] from the mixed mode riterion α + = in whih sally α. α (9) Damage initiation threshold - derived from the qadrati strength riterion: = +,, Eqivalent mixed mode relative displaement at failre: α α α = + () () whih an be derived from Eq. 9., written as α α α = + 6. Nmerial example () The finite element model of a repaired opon that was tested experimentally is shown in Fig.. The longitdinal ross setion is modeled as D plane strain problem. Symmetry is taken into aont. The plies are modelled by a single layer of orthotropi elements. The top over plate is modeled by two elements per ply to aptre better the edge effets in its tapered part. The /9 plies have stiffness of E x =67 Pa, the ±5 plies E x =6 Pa. The properties in the z diretion orrespond to the throgh thikness properties of the laminate. The properties of the interfae are those given in Table. The fore-displaement response is presented in Fig. 5. The load at failre is predited to be maxp=5.5 kn and it is in exellent agreement with the experimental failre loads, whih were in the range P =5. kn to P = 5.8 kn. y x 5 mm mm 88 mm 6 mm 6 mm t =.9 mm z (axis of symmetry) /9 plies ±5 plies P x nterfae elements Fig.. A repaired opon: Photo, Shemati ross setion; Finite element D (half) model. 7

8 ROSEN T. TENCHEV, B.. Falzon 5 5 P [kn] 5 max P = 5.5 kn Fig. 5. Fore-displaement response. [mm] A sensitivity stdy is performed by varying the interfae deohesive zone parameters that are not determined diretly by experiments: k and, (or t,, t,, whih are interrelated via Eq. 5 for a fixed fratre toghness). The ritial energy release rates =. N / mm and = 5. N / mm are kept onstant. The reslts are presented in Fig. 6A, as fntion of, and in Fig. 6B - as fntion of k. The failre load inreases with the inrease of the interfae strength t, and t, as well as with the derease of the relative displaement at failre and,. t an be seen that the experimental failre load an be predited by several sets of vales for these parameters. 5. Conlsions The mode and mode fratre properties of the FM- adhesive bond between 5HS/RTM6 laminates were determined experimentally by DCB and ELS tests, respetively. The fratre toghness in mode is initially inreasing with the inrease of the rak length and then onverges to a onstant vale =.. n mode a signifiant dependene of on the rak length was observed, whih was most probably de to the frition fores and interloking of the fibre bndles of the raked rogh srfaes. n sbseqent nmerial analyses a vale of = 5. was sed. The rak propagation was stdied nmerially by means of interfae elements based on the deohesive zone model. t was shown that beam theory and FE analyses, sing onventional interfae onstittive law with linear material degradation, old be sed to analyse the steady rak propagation. However, a signifiant non-linear behavior was observed before the initiation of the rak propagation, whih old only be modelled if a non-linear material degradation was sed with an inreased magnitde of the interfae relative displaement at failre. An adhesive stepped flsh joint was stdied experimentally and nmerially. A mixed mode interation riterion was sed together with the nonlinear material degradation of the interfae. The agreement between the experimental and nmerial P [kn] 5 5 A 5 5 P [kn] B Experiment , =, [mm] k Fig. 6 FE analysis of a repaired opon. Sensitivity stdy. t, =, t, = 5 ; t, = 8, t, = ; t, =, t, = 5 MPa 8

9 EXPERMENTAL AND NUMERCAL STUDY OF DEBONDN reslts was exellent. Sensitivity stdies were performed to stdy the inflene of the parameters defining the interfae non-linear material degradation k,,. Agreement with the experimental reslts old be ahieved by several sets of parameters. Experimental reslts for varios mode ratios wold be reqired for a niqe determination of these parameters. 6. Referenes [] Tenhev R.T. and Falzon B.. Composite adhesive repairs - experimental and nmerial analysis of delamination failre. Report ELRPS-WP7a-CL- TREP-8, Dept Aeronatis, mperial College, London, 7. [] Shellekens J.C.J. and de Borst, R. Free edge delamination in arbon epoxy laminates: a novel nmerial/experimental approah. Compt. Strt. Vol. 8, pp 57-7, 99. [] William J.. On the allation of energy release rates for raked laminates. nt. J. Fratre. Vol. 6, pp -9, 988. [] Davies P., Blakman B.R.K. and Brnner A.J. Standard test methods for delamination resistane of omposite materials: Crrent stats. Applied Composite Materials Vol. 5, pp. 5 6, 998. [5] Blakman B.R.K., Hadavinia H., Kinloh A.J., Parashi M. and Williams J.. The allation of adhesive fratre energies in mode : revisiting the tapered doble antilever beam (TDCB) test. Engineering Fratre Mehanis, vol. 7, pp. 8,. [6] Mi Y., Crisfield M., Davies. and Hellweg H. Progressive delamination sing interfae elements. J. Compos. Mater. Vol., pp 6 7, 998. [7] Tenhev R.T. and Falzon B.. A psedo-transient soltion strategy for the analysis of delamination by means of interfae elements. Finite Element in Analysis and Design, Vol. pp , 6. [8] Tvergaard V. Effet of fibre debonding in a wiskerreinfored metal. Mater. Si. Eng., Vol. 5, pp -, 99. 9