Chen, J., Ravey, E., Hallett, S. R., Wisnom, M. R., & Grassi, M. (2009). Predition of delamination in braided omposite T-piee speimens. Composites Siene and Tehnology, 69(14), 2363-2367. 10.1016/j.ompsiteh.2009.01.027 Early version, also known as pre-print Link to published version (if available): 10.1016/j.ompsiteh.2009.01.027 Link to publiation reord in Explore Bristol Researh PDF-doument University of Bristol - Explore Bristol Researh General rights This doument is made available in aordane with publisher poliies. Please ite only the published version using the referene above. Full terms of use are available: http://www.bristol.a.uk/pure/about/ebr-terms.html Take down poliy Explore Bristol Researh is a digital arhive and the intention is that deposited ontent should not be removed. However, if you believe that this version of the work breahes opyright law please ontat open-aess@bristol.a.uk and inlude the following information in your message: Your ontat details Bibliographi details for the item, inluding a URL An outline of the nature of the omplaint On reeipt of your message the Open Aess Team will immediately investigate your laim, make an initial judgement of the validity of the laim and, where appropriate, withdraw the item in question from publi view.
PREDICTION OF DELAMINATION IN BRAIDED COMPOSITE T-PIECE SPECIMENS Jiye Chen*, Eri Ravey**, Stephen Hallett***, Mihael Wisnom*** and Marello Grassi **** *University of Portsmouth, Portsmouth PO1 3AH, UK **Rolls-Roye Ltd, Derby DE24 8BJ, UK ***University of Bristol, Bristol BS8 1TR, UK ****QinetiQ, Farnborough, Hants GU14 0LX, UK Keywords: A. Polymer-matrix omposites (PMCs); B. Modelling; C. Delamination; E. Braiding; T-piee ohesive models Abstrat: This paper presents an approah to predit the delamination of braided omposite T- piee speimen using ohesive models. As part of an investigation on simulation of delamination in T-piee speimens, ohesive elements from ABAQUS were employed in forming a ohesive model to study the progressive delamination. Preditions given by the model of single delamination together with experimental results are presented. These results suggest that predition of progressive delamination using ohesive models is feasible. Finally this paper proposes future work for preise predition of delamination of braided omposite T-piee speimens. 1
1. Introdution T-piee speimens have been paid a high degree of attention in the study of behavior of aerospae omposite strutures beause they are representative of features in key aerospae strutures suh as omposite vanes in aero engines and T and I stiffeners and beams suh as stringers [1, 2]. Study of the failure mehanisms in T-piee speimens and predition of their damage resistant apability is fundamental for the design of suh omposite omponents. This paper aims to investigate the failure of T- piee speimens by simulating delamination propagation under a mehanial pull-off load ase. The T-piee speimen investigated in this publiation is a arbon fibre based braided omposite speimen, whih onsists of a vertial blade, radius transition region, a horizontal base and a uniform unidiretional deltoid also alled gap filler. Experimental test work at quasi-stati strain rates was investigated [3]. This showed the main failure mode to be delamination. Figure 1 shows the loal delamination pattern in the area of the deltoid of one failed speimen. The failure mode is multiple delaminations progressing from the point of initiation. The dominant delamination is along the interfae between the deltoid and braid ply in the radius area. This starts at the loation of higher interlaminar stresses whih is in the upper half of the urved interfae in the radius region as indiated in Figures 1 and 4. This loation is reognised as the initial failure point. From this loation delamination not only grows down along the urved interfae but also grows up to the end of laminate blade. It should be noted that the test failure loads given refer to initial failure loads and ultimate failure loads [3]. These values relate to the point of initiation and the point of maximum load, one delamination has propagated signifiantly. 2
Upper raking Initial failure point Lower raking Initial thermal shrinkage rak Fig. 1 Failure modes of T-piee speimen Delamination rossing through deltoid an also be seen in Figure 1. This is onsidered to be due to thermal effets from the uring proess. This paper presents the numerial simulation of progressive delamination, the main failure mode of the T-piee speimens, using finite element ohesive interfae models. This modelling work fouses on the simulation of a single dominant delamination between the deltoid and braid ply in the radius area, whih develops down to the base from the initial failure point. This work aims to determine the failure load at this single delamination by simulation. 2. Geometry, materials properties and loading Figure 2 shows the 2D finite element model with the definition of geometry of T- piee speimens, boundary onditions. 3
1 and 2kN fore applied over lamp length for T-pull analysis Normal restraints over full lamp length for T-pull analysis Outer lamp 52mm Normal restraints over 4 mm lamp length on upper and lower surfaes Wide lamps - 76 mm Fig. 2 A 2D finite element model Figure 3 shows the defleted shape of the T-Piee speimen under the pulling fore whih defines the loading ase onsidered in this study. Fig. 3 T-Piee under pulling fore The width of speimen is 20mm, the thikness of the upper arm is 4.4mm and the total thikness of the base is 6.87mm. The material is a braided arbon fibre omposite. A shemati onfiguration of the laminates an be seen in Figure 2 with details of layup. Material properties of eah layer are given in Table 1. 4
Table 1 Materials properties E 11 (GPa) E 22 (GPa) E 33 (GPa) G 12 (GPa) G 13 (GPa) G 23 (GPa) ν12 ν13 ν23 Outer Braided Wrap 59.7 60.1 9.7 21.95 4.7 4.7 0.279 0.28 0.28 Braided UD layer 160 9.7 9.7 5.9 5.9 4.7 0.33 0.33 0.28 [0 ] layer 152 9.7 9.7 5.9 5.9 4.7 0.33 0.33 0.28 [90 ] layer and Deltoid 9.7 152.0 9.7 5.9 4.7 5.9 0.021 0.28 0.33 Platform Braids 65.8 46.1 9.7 25.8 4.7 4.7 0.421 0.28 0.28 It should be noted that so far there are no reported fundamental frature tests for suh material. The frature energy and interlaminar material strength given in Table 2 are trial ones based on literature for other omposites [4, 5, 6, 7]. This affets the auray of omparison between modelling predition and test results sine only approximate values were assumed. For this reason the investigation of effets of varying frature energy by ± 50% and varying interlaminar material strength by ±50% on predition are given in this paper. Table 2 Interlaminar material strength and frature energy σ33 σ13 σ23 G I G II G III (MPa) (MPa) (MPa) J/m 2 J/m 2 J/m 2 45 35 35 300 1000 1000 5
3. Modelling Delamination A half plane strain model has been set up due to its symmetri features, as shown in Figure 4. N Symmetri ondition Initial failure point Potential rak Fig. 4 Half 2D model definition It should be noted that the initial failure point indiated in Figure 4 was determined by onsidering failed test samples shown in Figure 1 and interlaminar stresses supplied by a stati stress analysis [8]. The potential rak path shown in Figure 5 was determined from experimental observations suh as in Figure 1, whih shows the most dominant delamination. Figure 5 also shows a loal mesh of the radius and deltoid regions. The interfae between the laminate radius and deltoid is the potential raking path into whih ohesive interfae elements were inserted. 6
Initial failure point Potential raking interfae Fig. 5 The mesh around raking interfae Basi plane strain elements CPE4 and 2-D ohesive elements COH2D4 from ABAQUS were employed in this investigation [9]. Plane strain elements were used for the plies and the deltoid of T-piee. Cohesive elements were applied along the potential raking interfae. The ritial rak length a m is about 0.36mm as alulated from the linear frature mehanis based formula in Eq. 1. GE a m = (1) ψ σ 2 π 2 where, frature energy G is taken as G I, material property E is taken as E 33 of UD ply and interlaminar strength σ is taken as σ 33. ψ is raking shape parameter [10] and was taken to be 1.12 in this model. The atual modelled rak length should be less than this value, and 0.125mm was therefore used as element length along potential rak path in this model, whih determines the length of eah ohesive element and hene ensures 7
that modelling of the rak an be aptured below its ritial length. It should be noted however that no pre-rak was inserted. This analysis has been run using ABAQUS/standard ode with displaement ontrol. From the initial failure point delamination developed down to the bottom of deltoid. This proess ours relatively quikly. It should be noted that a sliding restraint at the lamp position was applied in this model to onsider any possible slight moving at lamp position. 4. Formulations of ohesive elements in ABAQUS Cohesive elements an simulate several types of behaviours at interfaes when the interfae load arrying apability is lost. They have been the subjet of signifiant investigation in the open literature and are beoming widely used for the predition of omposites delamination failure [4, 6, 7,11,12]. A review by Hallett [13] desribes more fully many of the different formulations that have been investigated and their appliations to omposite materials and strutures. Appliation of ohesive elements in this simulation of delamination is the key issue. Firstly, the relative displaement at damage initiation ε needs to be defined, whih an be determined by Eq. 2. σ ε = k (2) Where, σ and k is interlaminar strength and initial stiffness respetively for eah single rak mode. The damage initiation an be aounted by the quadrati formula of Eq. 3. σ I σ IC 2 σ II + σ IIC 2 σ + σ III IIIC 2 = 1 (3) 8
model. The linear softening damage law as shown in Figure 6 [9] was employed in this Fig. 6 Linear softening damage law This linear softening law was used together with the mixed mode frature energy riteria based on Benzeggagh-Kenane (BK) [14] law (Eq. 4) or the power law (Eq.5). G S ( G G ) G G I + II I = G T α (4) Where, G is the total mixed-mode frature energy, G I is the normal strain energy release rate, G II and G III are shear strain energy release rates in two diretions respetively, G S =G II +G III. G is the normal frature energy, I G is shear frature energy, II the total strain energy release rate G T =G I +G S. Equation (4) is suitable for the ase when G = II G III, the mode III frature energy. G G I I α G + G II II α G + G III III α = 1 (5) The ohesive elements with zero-thikness are usually hosen for simulation of interfaial delamination in omposites. These elements require the oordinates of the 9
node pairs on the raking path to be heked when it is a urved interfae. All nominally oinident nodes with a small differene in position (10-5 ) in the T-piee fillet have to be orreted to be exatly oinident. The visosity parameter is required to be defined for stability in solving the nonlinear equations. As this slightly affets the CPU time but not the results, values from 10-3 to 10-5 were reommended and an optimum value of 10-4 was hosen in this model. It is noted that it would be diffiult to ahieve the nonlinear iteration onvergene without this parameter. 5. Results using the power and BK failure riteria All preditions in this setion were obtained using the linear softening damage law plus BK energy riteria where α=1 or 2, and power law where α=1 or 2. The loal deformation after delamination is shown in Figure 7, whih shows the delamination is mixed mode I and mode II raking. Figure 8 gives predited failure loads together with experimental results, where it an be seen that there is an overall good agreement between predition and the tested ultimate failure results. Delaminated interfae Fig. 7 Deformation after delamination 10
Power(2) Power(1) BK(2) BK(1) Test - Max Ultimate Failure Load Test-Mean Ultimate Failure Load Test - Min Ultimate Failure Load 0 10 20 30 40 50 60 70 80 Delamination Load(N/mm) Fig. 8 Comparison between predition and tests Figure 9 shows the effets of different energy based failure riteria laws on the predited load-displaement urves. When using BK(2), the predited failure load redued by 16% ompared to BK(1), and was very lose to the maximum ultimate test failure load. When using power law, the predited failure load from the ase α=1 is 8% lower than that from the ase α=2, also very lose to the maximum ultimate test failure load. Unlike the BK riteria the first order power law predited better failure load then the seond order power law. This implies that the linear power law presents a better frature energy relationship in this mixed mode delamination ase, and supplies a simple alulation in determination of delamination propagation. A similar ase that a higher order power law predits higher failure loads for mixed mode delamination was disussed in referene 6. It should be noted that all these investigations used the frature properties and interlaminar material strengths given in Table 2. 11
Fig. 9 Failure response with different energy riteria laws Assuming materials data in Table 2 as the most representative frature properties and interlaminar material strengths, the modelling predition using the linear softening damage law plus energy riteria power law (α=1) and BK law (α = 2) with approximated frature energy data adequately agrees with the tested ultimate failure load. 6. Investigation of effets of varying frature properties on predition Beause the frature energies given in Table 2 are trial ones, it is neessary to investigate the effets of varying frature energy on the failure predition. Figure 10 shows suh effets by giving predited-to-mean test failure load ratios together with tested ultimate failure loads, where original materials given in Table 2 is onsidered to produe the mean predition, inreasing and dereasing by 50% frature energy are referred to produe the maximum and minimum predition respetively. Both G I and 12
G II affet the predition in this mixed mode delamination, with G II having a slightly greater effet than G I. Fig. 10 Predited-to-mean test failure load ratios for ABAQUS ohesive model with BK(α= 1) An investigation of the effets of varying the interlaminar strength (normal strength σ 33 and shear strength σ 13 ) by ±50% an be seen respetively in Figure 11 and Figure 12. 13
Load (N/mm) 90 80 70 60 50 40 30 20 10 0 σ 33 Effet σ33 = 67.5MPa σ33 = 45MPa σ33 = 22.5MPa 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Displaement u2 (mm) Fig. 11 Failure response with varied σ 33, linear softening law + BK(α=1) Load (N/mm) 90 80 70 60 50 40 30 20 10 0 σ 13 Effet σ13 =52.5MPa σ13 = 35MPa σ13 = 17.5MPa 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Displaement u2 (mm) Fig. 12 Failure response with varied σ 13, linear softening law + BK(α=1) Inrease of interlaminar strength by 50% slightly hanges the global model stiffness, but the inrease in failure load is less than 5%. In addition, a redution of interlaminar strength by 50% also slightly hanges the global model stiffness, and the apparent failure point (the drop in the load-displaement urve) is lost. 14
7. Comments and Future work This paper investigated the failure predition of T-piee speimens by simulating a single delamination. It shows generally the possibility of prediting failure loads using ohesive models. The modelling predition using the linear softening damage law plus energy riteria power law (α=1) and Benzeggagh-Kenane law (α=2), normal frature properties and the sliding lamp ondition adequately agrees to the tested ultimate failure load without any variations of the frature energy data. It should however be noted that these were only approximated from literature values and were not measured for the urrent material. The effets of varying frature energy and interlaminar strength on predition therefore were given as referene. This would indiate that the failure is dominated by the propagation of the rak rather than its initiation. This is onsistent with many results from literature that have given rise to strategies suh as that proposed by Turon et al [15] for artifiially reduing the initiation stress used for interfae elements to allow use of a oarser mesh. The variation in results with hoie of mixed mode failure riterion used indiates the need for areful onsideration in this area. Referring to the deformed shape in Figure 7, the initial failure point appears over restrained. This means delamination would quite possibly grow up to the end of laminate blade as well as down to the base. This an be investigated by reating a model with multiple delamination sites to study their effets on failure predition [16] The following is suggested in future work in order to be able to ahieve preise predition: a. frature tests to obtain G I and G II. b. analysis with thermal effets on failure predition. 15
. simulation of multiple delamination (raks whih an potentially propagate up, down and aross the deltoid from the initial failure point). 8. Aknowledgements The authors would like to aknowledge the MoD for their support of this programme. The authors would also like to aknowledge the MoD, Rolls-Roye and QinetiQ for their permission to publish. 16
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10 Benham P P, Crawford R J and Armstrong C G, Mehanis of engineering materials, Pearson Eduation, 1987 11 Goyal VK, Johnson ER, and Davila CG., Irrevesible onstitutive law for modeling the delamination proess using interfae surfae disontinuities, Composite Strutures, 65, p289-305, 2004 12 Camanho PP, Davila CG, De Moura MF. Numerial simulation of mixed-mode progressive delamination in omposite materials. J Composite Materials 2003;37:1415 24 13 Hallett SR, Prediting progressive delamination via interfae elements, in Delamination behaviour of omposites, S. Sridharan, Editor. Woodhead. 2008 14 Benzeggagh ML and Kenane M, Measurement of Mixed-Mode Delamination Frature Toughness of Unidiretional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus, Composites Siene and Tehnology, 56, pp. 439 449, 1996. 15 Turon A, Davila CG, Camanho PP, Costa J. An engineering solution for mesh size effets in the simulation of delamination using ohesive zone models.eng Frat Meh 2007;74:1665 82 16 Ravey EP, Investigation of omposite damage tolerane and frature assessment: delamination predition in T-piee, Rolls-Roye internal report, June 2006 18