INTEGRATED NUMERICAL ANALYSIS FOR COMPOSITE DAMAGE TOLERANCE

Transcription

1 ICAS CONGRESS INTEGRATED NUMERICAL ANALSIS FOR COMPOSITE DAMAGE TOLERANCE Guinar Stéphane, Thévenet Pascal, Vinet Alain, Maison-Le Poëc Serge EADS-CCR Keywors: impact, amage tolerance, laminate composites Abstract From initial amage to ultimate failure, there is a range of loas that structures can unergo while still keeping within the safety requirements. Mastering this amage tolerance woul enable to operate an aircraft with amage structures, proviing the remaining capabilities coul be certifie. When compare with metals, composite materials improve the structural amage tolerance, since their constitutive heterogeneity enforces amage to istribute over lengths wier than in homogeneous meia. Characterizing composite amage tolerance asks for expensive an time consuming experimental campaigns. In orer to integrate amage tolerance in the esign an the maintenance in a cost-effective way, numerical tools shoul enable the calculation of amage initiation an propagation: a thorough mastering of the moeling, the computation, an the experimental characterization of amage evolution has to be achieve. This paper summarizes the EADS s global approach to hit this target. 1 Introuction Aeronautical esign an maintenance engineers are face to pragmatic situations when ealing with amage tolerance: When esigning an aircraft, from cosmetic to structural elements, one has to assess the integrity of structures that will be subjecte to amage events. Moels shoul characterize the structural properties from the initial state to the amage initiation, propagation, an ultimate failure. When operating an aircraft, one has to ecie either to repair or replace in-service amage parts. Moels shoul characterize the structural properties from measure amage sizing to propagation an ruure. Low velocity impacts on laminate composites are of primary interest when ealing with amage tolerance, since both situations are encountere. The lecture will focus on preliminary tools CRC is eveloping, aiming at an integrate numerical analysis of amage tolerance. Characterization of the inuce amage.1 US C-Scan The numerous low-velocity impact-testing campaigns conucte at EADS-CCR resulte in a thorough unerstaning of the elementary amage events occurring in the laminate [1]. A cinematic scheme was built on the basis of ultrasonic scanning an istance-magnitue analysis. Fig. 1 - US C-Scan of a (45,,- 45,9 ) S,,7.1 J impacte T3/914 laminate 49.1

2 Guinar Stéphane During the loaing, transverse cracks evelop along the fibres in each UD ply, with symmetry with the central contact area. A release strip in each ply is free of moving in the thir irection, normally to the mi-plane (Fig. ). If epicte from the interfacial plane between two of these amage plies, the release planes are to be consiere as: an interfacial traction area, above the bottom release strip; an interfacial compression area, uner the top release strip. structures. In-situ investigation means are far less sophisticate than US C-Scan performe in laboratory conitions. Nevertheless, a prospective scheme is to operate these portable investigation means to characterize the outerskin amage inuce geometry. In a long-term, when effective calculation moels will be operational, an oimization computation woul help getting the actual elaminate configuration associate to this external amage inuce geometry. Then classical fracture mechanics woul give the resiual loa-carrying capabilities (cf. 4). Fig. 3 - measure impact external inuce amage area on a sanwich panel 3 Calculation of the impact inuce amage Fig. - cinematic scheme extracte from [1] Delamination evelo in the traction area, with the compression area acting as an antielaminating agent (Fig. ). Pairs of twintriangles evelop at each interface []. With the regular rotation of fibres from one ply to the other in quasi-isotropic laminates commonly use in aeronautical structures, this scheme epict a typical ouble-helix when repeate through all the thickness. Increasing from the impacte sie to the free sie of the impacte plate, elaminations are wrappe in a conical shape envelope. This conical shape makes it possible to visualise the whole periphery of the ouble helix through ultrasonic scanning.. In-service inspections During service life, aircraft are regularly inspecte to etect any efect on the composite 3.1 Empiric moel Before exploring sophisticate FE moels, pragmatic analytical moels have been eveloppe in orer to reuce experimental campaigns. Empiric laws were extracte from these campaigns. Two parameters were consiere, the inentation eh an the total elaminate area. The results of existing tests permitte to obtain master curves of these parameters [3]. This moel was implemente in a software, LAMKIT. 3. FE amage moel Experimental evience was given to the equivalence between low-velocity impacts an quasi-static inentation loaing for the same incient energy. For an impact, the quasi-static iso-energy is consiere, which enables a timeinepenent numerical treatment. A moifie Hertz istribution uner the impactor is consiere [4], [5], [6]. 49.

3 INTEGRATED NUMERICAL ANALSIS CONCEPT FOR COMPOSITE DAMAGE TOLERANCE Damage meso-moels esigne at LMT (Fig. 4) [7] were eicate to plane-stress loaing at first. Though some specifies with regars to plane-stresses loaing have been raise up, experimental observations showe that the elementary amage events are the same as those consiere in original LMT amage mesomoels: fibre ruure, fibre-matrix eboning, transverse cracks an elamination. Specifies are inherent to a strong coupling between these elementary events, relate to highly localise stress transfers, especially out-of-plane stress transfers: elaminations seem to be controlle by the neighbouring transverse cracks. variables, an are use to represent respectively fibre-matrix eboning an transverse cracks effects on elastic mouli G 1, G 13 an E. Energies are split into their compressive an tensile parts (respectively nonactive an active with regars to amage growth). A γ coefficient is associate to the nonlinear compressive behaviour in the fibre irection. At least, the strain energy E D is written as follows: ED σ11 γ σ σ σ E1 (1 f ) E1 E (1 ) E 1 σ σ σ G1(1 ) G13(1 ) G 3 ν σ σ ν σ σ ν σ σ E1 E E σ 33 E3 Damage forces: Conjugate thermoynamic forces an, relate to amage variables an respectively, are expresse by eriving the strain energy with respect to an : Fig. 4 amage mesomoel - At the mesoscopic scale, a laminate is consiere as a stacking of homogenise plies an interfaces. In opposition to macro- an micro-scale stuies, meso-scale enables a balance between numerical weight an physical reliability. Fibre-matrix eboning an transverse cracks will be escribe through their effects on the elastic mouli of the plies, elaminations through their effects on the elastic mouli of the interfaces. E E D D << σ G 1 1(1 >> ) << σ >> + E (1 ) Coupling between amage moes: << σ + G 13 13(1 >> To epict the interactions between transverse cracks an fibre-matrix eboning, two coefficients b an b are introuce. Two new amage forces are expresse as follows: ) Ply moelling Strain energy: The amage effects of out-of-plane stresses are integrate in the original moel. The expression of the strain energy is upate. Though new stresses are introuce, the same internal c c if if, else f <, else

4 Guinar Stéphane Damage evolution laws: amage initiation threshols, critical amage threshols c an a brittle threshol y f are introuce in a simple amage evolution law: Sup Sup t t { + b } { + b } Experimental ientification Though out-of-plane amage activity was introuce in the moel, no new material constant is neee. Experimental ientification proceure use for the original moel [8] is therefore still useful for the moifie moel. The strategy relies on tests conucte on specimens with characteristic layouts, which activate only the amage moe to be ientifie. The material use in this stuy has alreay been ientifie through this proceure at LMT [8]. Numerical implementation A software with the original moel integrate has been evelope at LMT for the analysis of in-plane stresses problems like laminate plates with a hole uner in-plane tension: DSDM (Delamination Simulation by Damage Mechanics) [9]. The numerical strategy procees in two ste: a first D elastic computation is performe on the whole structure with stanar finite element software (Fig. 5). Then the isplacements along a central circular line surrouning the impact area are extracte from the elastic solution. The 3D nonlinear analysis is performe insie this line with DSDM. A fast Fourier Transform enables to treat the 3D non-linear problem on the volume as series of D non-linear problems on orthoraial planes. Fig. 5 - numerical strategy in DSDM Each D non-linear problem is solve with a Large TIme Increment Metho (LATIN Metho) [1]. Calculation results show goo correlation with experimental observations. Intralaminar amage results Damage areas in the plies are to be compare with the release stri in the plies: accoring to the cinematic scheme, the elamination configuration woul result from these release stri. These stri an their orientations are simulate (Fig. 6); the size of the stri is increasing from the impacte sie to the free sie of the plate, as expecte when analysing experimental results. The funamentals of the ouble-helix shape are simulate. The size of the bottom basis of the amage area was compare to the measure maximal with of ultrasonic C-Scan: goo correlation was foun with experimental results. 49.4

5 INTEGRATED NUMERICAL ANALSIS CONCEPT FOR COMPOSITE DAMAGE TOLERANCE Remaining ifficulties This phenomenological moel breaks with classical interfacial moel use at LMT [9]. These classical moels were also teste but faile into catching the coupling between intraan interlaminar amage. This coupling has an intrinsic iscrete nature: intralaminar cracks concentrate stresses at their ti an promote interfacial amage. The numerical tests performe showe that such a iscrete phenomenon coul not be catche by a iscrete moel. Fig. 6 - amage calculation results in the plies Interfacial amage results In the cinematic scheme propose for explaining the ouble helix, intralaminar amage is the precursor of elamination. Therefore, a phenomenological interfacial moel was built on this cinematic scheme to valiate interlaminar amage results an the cinematic scheme: this scheme is a proposal for interpreting couplings between intra- an interlaminar amage. In this moel, interfacial amage is irectly connecte to the amage in the neighbouring plies: + + { ; } i Sup where i is the interfacial amage at an interfacial M Gauss point, X + an X - are intralaminar quantities at the associate M + an M - Gauss points in the plies above an uner the interface uner consieration. Results show a goo correlation with the observe ouble helix, which valiate both the intralaminar results an the cinematic scheme (Fig. 7). Fig. 7 - amage calculation results at interfaces In the framework of a DGA (French MoD) grante project, two stuies were initiate recently, emphasizing this iscrete aspect. Exploratory works have alreay been publishe [11]. Regaring the numerical implementation in inustrialize softwares, EADS-CCR alreay trie to export this kin of moels from university mocku to actual esign office software. Classical algorithms reveale ifficulties for integrating high material non linearities. 49.5

6 Guinar Stéphane 4 Calculation of elamination propagation Since the initial post-impact amage configuration was calculate from the impact parameters, the next calculation aims at simulating the propagation of the impact inuce elaminations. Classical fracture mechanics moels are use [1]. These calculations are still performe with a han-mae meshing of the elaminate geometry. The numeric link between the initiation calculation, performe with a FE amage moel, an the propagation calculation, performe with a fracture mechanics moel, is still not establishe. The feasibility of the full integrate calculation will be emonstrate within a GARTEUR action group (AG8: impact amage an repair of composite structures ). Fig. 8 - propagating elamination uner inplane compression of the laminate 5 Conclusion There still remains great efforts before performing fully software-integrate amage tolerant esigns for composite structures. But through both experimental an numerical progresses, some first ste towars this ultimate goal were built. Remaining ifficulties have been ientifie an keep uner research exploration. References [1] Guéra-Degeorges D., Maison-Le Poëc S., Renault M., Numerical simulation of the behaviour after impact of a carbon epoxy laminate plate, ICCM8, [] Clark G., Moelling of impact amage in composite laminates, Composites, (3), pp. 9-14, [3] Vinet A., Guéra-Degeorges D., établissement e courbes maîtresses pour la prévision es ommages impact sur CMO, Comes renus es JNC1, pp ,. [4] Greszuk B., Damage in composite materials ue to low velocity impact. In Zukas an al. eitors, Impact Dynamics, pp.55-95, John Wiley an Sons. [5] Tan T. an Sun C., Use of statical inentation laws in the impact analysis of laminate composite plates. Transactions of the ASME, 5, pp. 6-1, [6] Guéra-Degeorges D., Maison-Le Poëc S., Trallero D., Petitniot J.L., Analyse et simulation es mécanismes e égraation une plaque composite impactée, CNCS, Giens, [7] Laevèze P., Sur la mécanique e l enommagement es composites. In Bathias c. an Menkès D. eitors, Comesrenus es JNC5, pp , Paris, Pluralis, [8] Laevèze P. an Le Dantec E., Damage moelling of the elementary ply for laminate composites. Composite Science an Technology, 43(3), pp , [9] Allix O., Damage analysis of elamination aroun a hole. In Zienkiewicz O., eitor, New Avances in Computational Mechanics, pp , Elsevier Science, 199. [1] Laevèze P., Sur une famille algorithmes en mécanique es structures. Comesrenus e l Acaémie es Sciences, [11] Laevèze P., Lubineau G., An enhance moel on the micro- an mesoscale for laminate composites, Mechanics of materials, Elsevier, to be publishe. 49.6

7 INTEGRATED NUMERICAL ANALSIS CONCEPT FOR COMPOSITE DAMAGE TOLERANCE [1] Thévenet P., Impact sur matériau composite monolithique moélisation et simulation par éléments finis e la compression après impact -, rapport EADS-CCR,. 49.7