MODE I FATIGUE DELAMINATION GROWTH ONSET IN FIBRE REINFORCED COMPOSITES: EXPERIMENTAL AND NUMERICAL ANALYSIS

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1 21 st International Conferene on Composite Materials Xi an, th August 2017 MODE I FATIUE DELAMINATION ROWTH ONSET IN FIBRE REINFORCED COMPOSITES: EXPERIMENTAL AND NUMERICAL ANALYSIS Man Zhu 1,3, Larissa orbatikh 1,3, Sander Fonteyn 2,3, Liny Pyl 2, Danny Van Hemelrijk 2, and Stepan V. Lomov 1,3 1 Department of Materials Engineering, KU Leuven, Kasteelpark Arenberg 44 bus 2450, 3001 Leuven, Belgium, man.zhu@kuleuven.be, larissa.gorbatikh@kuleuven, stepan.lomov@kuleuven.be, 2 Department Mehanis of Materials and Construtions, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium, liny.pyl@vub.be, danny.van.hemelrijk@vub.be, 3 SIM M3 program, Tehnologiepark 935, 9052 Zwijnaarde, Belgium, Keywords: Fatigue delamination growth, Mode I, Cohesive zone models, Digital image orrelation ABSTRACT Mode I fatigue delamination growth in fibre reinfored omposite laminates is studied here by experimental and modelling tools. Mode I fatigue growth tests were onduted on Double Cantilever Beam speimens at various load levels. Digital image orrelation (DIC) was used to detet movement of the inter-laminar rak tip position during the tests and then to determine the fatigue delamination life whih is the yle to of delamination growth. The fatigue life obtained using the DIC approah is signifiantly lower than that determined by the ompliane monitoring method that is reommended in the ASTM standard. A ohesive zone model was developed to predit the fatigue delamination growth in omposites. The progressive degradation law developed in the ohesive zone model desribes the derease of the ritial strain energy release rate of the interfae based on the -N urve from fatigue delamination growth test. The proposed model ould suessfully reprodue the fatigue delamination life of omposite laminates. 1 INTRODUCTION Modelling and haraterization of fatigue delamination behaviour of fibre reinfored plastis (FRP) are important for understanding and prediting durability and damage tolerane of omposite strutures. The fatigue delamination growth test is ommonly used to haraterize the interlaminar fatigue behaviour of FRP omposites under yli loading. This test measures the number of yles (N) before an existing delamination rak starts growing under a ertain loading level (), and this is desribed by a -N urve [1]. The growth test desribes the fatigue damage of a material at the rak tip and gives an important referene for the fatigue no-growth design of FRP omposite strutures. At present, the -N urve is ommonly obtained by performing a Mode I fatigue growth test aording to ASTM D6115 standard [2]. Three different ways are introdued in the standard to determine the rak growth. These are: (1) visual observation; (2) detetion of 1% inrease in system s ompliane; (3) detetion of 5% inrease in system s ompliane. Beause of the diffiulties in visual monitoring of the rak tip, ompliane-monitoring-based methods are reommended in the standard. As the ompliane haraterises the full sample deformation resistane rather than preisely the rak growth, the ompliane-based method is prone to errors [1]. To overome this diffiulty, several methods have been developed in reent years to improve the auray of the delamination growth detetion in omposites, inluding the eletri potential-based method [3], wavebased methods [4] and aousti emission tehniques [5]. However, these studies have been limited to

2 Man Zhu, Larissa orbatikh, Sander Fonteyn, Liny Pyl, Danny Van Hemelrijk and Stepan V. Lomov either quasi- loading onditions or/and small-size speimens. Few studies foused on the in-situ detetion of delamination development under fatigue loads. Apart from experimental studies, the fatigue delamination of omposites has also been studied numerially using finite-element (FE) models. In these modelling works, ohesive zone models (CZMs) have been used due to their suess in the simulation of quasi- delamination. In most CZMs, the damage evolution at the interfae during fatigue loading is alulated based on Paris law obtained from fatigue delamination propagation tests [6-9]. One may question validity of suh an approah, as Paris law is a marosopi desription of the rak growth, while the CZMs rely on loal pointwise evaluation of fatigue damage. Consequently, some theoretial assumptions are further required to physially math Paris law with CZMs, for example, the definition of a ohesive zone [6, 8]. The physial meaning and validity of these assumptions are still an open topi of disussion. Compared to the Paris law, the test for fatigue delamination growth fouses on the delamination behaviour ahead of a rak tip, whih diretly reflets the loal onept of CZMs. In this work a new method based on DIC is proposed to detet the delamination growth under fatigue loading. The auray of the rak tip position obtained from the new method is verified by mirosope observations. A CZM based on the measured -N urve is also developed for modelling the Mode I fatigue delamination growth. 2 MODE I FATIUE DELAMINATION ROWTH ONSET EXPERIMENT To haraterize the mode I fatigue delamination growth, fatigue tests were performed using DCB speimens. In this setion experimental details about the speimens, test proedure and data proessing method are presented. 2.1 Material and speimen onfiguration The omposite laminates used in this work have 18 layers of 0 o unidiretional PYROFIL TM arbon/epoxy from Mitsubishi Rayon Co., Ltd. A 12.5 μm PTFE film was plaed in the middle plane to at as an initial delamination. The speimens were nominally 150 mm long, 25 mm wide and 4.2 mm thik with a 50 mm PTFE insert at one end of the speimen. The spekle patterns were applied at the edge of the speimens for the following DIC proessing. Two aluminium load-bloks were adhesively bonded onto the speimen s end for load introdution. 2.2 Fatigue delamination growth test proedure In the fatigue tests, speimens were loaded under a onstant displaement amplitude proess with the ratio of minimum/maximum displaement R = 0.1. The frequeny of the fatigue test was 10 Hz. Images of the fatigue rak extension on one side of the speimen were automatially reorded at a maximum displaement during the fatigue tests with two digital ameras whih were synhronized with the testing mahine. A photograph of the test set-up is shown in Figure 1.

3 21 st International Conferene on Composite Materials Xi an, th August Crak tip detetion with DIC Figure 1: Test set-up. With a ommerial software Vi-3D TM, the vertial displaement field, V, at the edge of the DCB speimens was obtained with the resolution of 1 pixel = 37 μm. An example of the vertial displaement field lose to the rak path is shown in Figure 2 for yle 20 (the displaement of the speimen due to its small rotation was eliminated). The vertial displaement varies along the thikness diretion beause of the opening of the rak and this variation gradually dereases to zero as the analysis point approahes the rak tip. The rak tip position ould be deteted through finding a zero variation of the vertial displaement (seen as green zone of displaement field V). Figure 2: The vertial displaement field V for yle 20. Crak tip position is shown with arrows. 2.4 Determination of fatigue life The new rak tip detetion method was used to determine the progression of the rak tip with yles (i.e. rak growth urve). Fatigue life N (defined as the yle number at whih the rak starts growing) ould be determined by deteting movement of the rak tip position. The rak growth urve expression is desribed as x f N a, N N N N a, N N 0 0, (1) 2 i i min, (2) 2 R f N x i where a0 and N stand for the initial rak length and fatigue life, and represents the rate of rak growth. N i and x i are the number of yles and rak tip position obtained from DIC detetion, respetively. Before the fatigue life, N, is reahed, the rak doesn t grow and its tip stays at the initial position a 0. Therefore a onstant funtion was adopted when N N. A

4 Man Zhu, Larissa orbatikh, Sander Fonteyn, Liny Pyl, Danny Van Hemelrijk and Stepan V. Lomov simple linear fitting funtion was used to desribe the rak growth when N N. The fitting parameters were determined aording to the least square method R 2 (Eq.(2)). A representative example of the usage of the fitting is shown in Figure 3, in whih a 95% onfidene band of the fatigue life, N, is also given to evaluate the error of the N identifiation. 2.5 Results and disussion Figure 3: An example of N identifiation. The proposed rak tip detetion method was applied to nine different tests, and the measured initial rak tip position, a 0, are listed in Table 1. Here both raw data at yle 20 and fitted data with Eq. (1) are given. To verify the new rak tip detetion method, the initial rak lengths obtained from mirosope observation are provided for omparison. It indiates that the fitted initial rak length from Eq. (1) exhibits a high auray, whih differs from mirosope observation by less than 0.32 mm. The fitted initial rak tip position and raw data are also of the same magnitude, whih implies that the expression Eq. (1) doesn t introdue extra errors. Speimen number Mirosope observation before the tests (mm) DIC detetion at yle 20 (mm) value Differene from mirosope Fitted initial rak length a (mm) value 0 Differene from mirosope ± Table 1: Comparison of the initial rak tip positions determined with different tehniques. It is interesting to ompare the differene of fatigue life obtained by the DIC and onventional ompliane monitoring. Figure 4(a) shows a variation of the ompliane of the beam arm with a number of yles for a given speimen. The ompliane inrease detetion yielded a fatigue life N = 5500 by deteting 5% inrease of ompliane. With the use of the mathematial model developed in setion 2.4, the present DIC measurement gave N =2600 yles. Thus, the fatigue life obtained from the DIC method is signifiantly lower than that from the ompliane inrease detetion method. The same proedure was applied to all speimens, and -N urves were obtained for the two methods (see Figure 4(b)), respetively. At all loading levels, the DIC method gave shorter fatigue life than the onventional ompliane inrease detetion

5 21 st International Conferene on Composite Materials Xi an, th August 2017 method. In onlusion, the present DIC method is linked to the real rak opening displaement, and gives more onservative results for fatigue life than the ompliane monitoring method reommended in ASTM D6115 standard. Figure 4: (a) Comparison of fatigue life from DIC measurement and ompliane method for one speimen; (b) Comparison of -N urves from DIC method and ompliane method. 3 FEM SIMULATION ON MODE I FATIUE DELAMINATION ROWTH ONSET This setion introdues a new CZM that is apable of modelling the fatigue delamination growth in FRP omposites. In this model, the progressive damage aused by yli loading was simulated as degradation of the ritial strain energy release rate (SERR) with yli number. 3.1 Cohesive zone model A bilinear onstitutive law was adopted to desribe the interfaial behaviour under quasi- loading as shown in Figure 5(a). and stand for the displaement orresponding to 0 damage initiation and full failure, respetively. The ritial SERR, f, is the area under the quasi stress-strain urve, whih represents the strain energy dissipated during formation of a unit of a new surfae. One the externally applied SERR equals to, the ohesive element fails ompletely and a new rak surfae is formed. Figure 5: (a) Bilinear onstitutive law for loading; (b) Failure of ohesive element at yle N. As yli loading inreases damage aumulation ahead of the rak tip relative to the quasi- ase, the rak under fatigue loading starts growing even if the maximum applied SERR,, is lower than, that is, max. enerally, fatigue life ( N ) inreases as max max

6 Man Zhu, Larissa orbatikh, Sander Fonteyn, Liny Pyl, Danny Van Hemelrijk and Stepan V. Lomov dereases, whih is desribed by the -N urve. Therefore, the degradation law of from the -N urve, as: an be obtained d max d max, (3) dlnn ln N dn N ln N where ( N, max ) orresponds to a point on the -N urve. The degradation of an be desribed as a derease of the area under the onstitutive ohesive law urve. Figure 5(b) shows that the total area under the stress-displaement urve dereases to the applied SERR max when the element has failed after N yles. 3.2 Simulation of Mode-I delamination The developed CZM was implemented as a user-written finite element material program in FE software. The FE model of DCB is shown in Figure 7. The arms are omposed of 8-node solid elements, whih are onneted by 8-node ohesive elements. Only one element was built along the width diretion and a generalised plane strain boundary ondition was applied to the FE model. The quasi- tests were onduted to get the elasti properties of the used arbon/epoxy UD laminates and the interlaminar properties of 0 o //0 o interfae, whih are shown in Table 2. The -N urve in Figure 4(b) obtained from the new DIC-based method was used as input of the material properties as Equation (4) where C and n are fitting parameters. n max CN, (4) Cohesive Elements Solid Elements Figure 7: Finite element model of the DCB speimen Elasti properties Interlaminar ohesive properties E11 [Pa] E22=E33 [Pa] ν12=ν13 [-] ν23 [-] 12=13 [Pa] 23 [Pa] C n 0 [N/mm] [-] [N/mm] [MPa] Table 2: Material properties for UD laminates The simulation was performed under the Mode I ondition. The DCB model was firstly loaded to the maximum displaement ally, and the ohesive elements follow the bilinear onstitutive law in this stage. After the maximum displaement was reahed, the fatigue damage law was triggered. The maximum load in yles is maintained, and the pseudo-time inrement in FE analysis

7 21 st International Conferene on Composite Materials Xi an, th August 2017 was assumed to be proportional to the number of loading yles. On this basis, the fatigue damage aumulation was taken into aount in the CZM. The fatigue delamination growth was determined by omplete failure of the ohesive element ahead of the rak tip. In Figure 8, the simulated fatigue life under different loading levels are ompared with the measured -N urve, whih indiates a good agreement between simulation and experimental results. Figure 8: FEM simulation results of Mode I fatigue growth based on the experimental -N urve 4 CONCLUSIONS A DIC-based rak tip detetion method is proposed to determine Mode I fatigue life of omposite laminates. The fatigue life obtained from the DIC measurement is signifiantly lower than that based on 5% of the ompliane inrease. A CZM was developed based on a -N urve from the experimental growth test. The model suessfully reprodues the input experimental data by modelling the rak growth as the failure of the ohesive element at the rak tip, and the next step of the work is to validate the model on independent test ases. ACKNOWLEDEMENTS The work has been funded by the SBO projet M3Strength, whih fits in the MaroModelMat (M3) researh program funded by SIM (Strategi Initiative Materials in Flanders) and VLAIO (Flanders Innovation & Entrepreneurship). REFERENCES [1] B.L.V. Bak, C. Sarrado, A. Turon and J. Costa, Delamination under fatigue loads in omposite laminates: a review on the observed phenomenology and omputational methods, Applied Mehanis Reviews, 66, 2014, pp [2] ASTM D , Standard test method for mode I fatigue delamination growth of unidiretional fibre reinfored polymer matrix omposites, ASTM International, 2011 [3] M. Zappalorto, F. Panozzo, P.A. Carraro and M. Quaresimin, Eletrial response of a laminate with a delamination: modelling and experiments, Composites Siene and Tehnology, 143, 2017, pp [4] D. Wang, L. Ye, Y. Tang and Y. Lu, Monitoring of delamination and growth during Mode I and Mode II interlaminar frature tests using guided waves, Composites Siene and Tehnology, 72, 2012, pp [5] M. Saeedifar, M. Fotouhi, M.A. Najafabadi, H.H. Toudeshky and. Minak, Predition of quasi- delamination and growth in laminated omposites by aousti emission, Composites Part B: Engineering, 85, 2016, pp

8 Man Zhu, Larissa orbatikh, Sander Fonteyn, Liny Pyl, Danny Van Hemelrijk and Stepan V. Lomov [6] A. Turon, J. Costa, P. Camanho and C. Davila, Simulation of delamination in omposites under high-yle fatigue, Composites Part A: Applied Siene and Manufaturing, 38, 2007, pp [7] B.L. Bak, A. Turon, E. Lindgaard and E. Lund, A simulation method for high-yle fatiguedriven delamination using a ohesive zone model, International Journal for Numerial Methods in Engineering, 106, 2016, pp [8] P.W. Harper and S.R. Hallett, A fatigue degradation law for ohesive interfae elements development and appliation to omposite materials, International Journal of Fatigue, 32, 2010, pp [9] L.F. Kawashita and S.R. Hallett, A rak tip traking algorithm for ohesive interfae element analysis of fatigue delamination propagation in omposite materials, International Journal of Solids and Strutures, 49, 2012, pp