MESO-STRUCTURAL BEHAVIOUR OF COMPOSITE FABRIC FOR THE SIMULATION OF MANUFACTURING OF THIN COMPOSITE BY SHAPING PROCESS

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1 MESO-STRUCTURA BEHAVIOUR OF COMPOSITE FABRIC FOR THE SIMUATION OF MANUFACTURING OF THIN COMPOSITE BY SHAPING PROCESS J.. BIOËT 1 and A. CHEROUAT 1,2 1 M2S secteur ENSAM o Paris 151 Boulevard de l'hôpital Paris, France 2 ASMIS - GSM University o Technology o Troyes BP Troyes, France KEYWORDS: Preimpregnated abric, Finite deormation, Mesostructural approach, Corotational ormulation, Truss and membrane inite elements, Viscoelatic behaviour, Shaping process. SUMMARY The present study concerns the modelling o the behaviour o preimpregnated woven abric during the orming process. A new numerical model in inite strains has been developed. It make into account the various dominating mechanics in the physics o the mechanical transormation o composite material during the shaping process, namely large angular variations o yarns, viscoelasticity o resin and evolution o possible damages in yarns. Shear and tensile tests o composite abric specimens are presented to validate the mesostructural approach. Some numerical simulation o shaping process by deep-drawing are proposed and compared with the experimental results. These results examined the importance o understanding the inluence o prepreg shaping deormation and manuacturing conditions on the inal properties and resulting structure, which in turn can strongly aect the utilization o these material or the manuacturing o high perormance composites parts. INTRODUCTION Continuous ibre reinorced composites are now irmly established engineering materials or manuacturing o components in automotive and aerospace industries. The oer design engineers enormous opportunities or introducing new concept into their design whilst reducing costs. In this respect, preimpregnated composite abric gives lexibility in the design manuacture and is already playing an important role in increasing the use o advanced composites. The ability to deine, in advance, the ply shapes and material orientation allowed

2 the engineers to optimize the composite structural properties o the part or maximum strength, maximum material utilization and maximum lay-up eiciency. The ormulation o the new eiciency numerical models or the simulation o the shaping composite processes must permit to improve the delay o the realisation o complex pieces and to optimize costs in an integrated design approach. Indeed, the preimpregnated composite abric corresponds to a structure composed o the combination o the yarn network and resin membrane. So, it is diicult to globally characterize, by homogeneous methods, the behaviour o this preimpregnated abric without lose mechanical inormations. The new numerical inite element model Belhous 1998 [2] and Cherouat 1998 [8], developed an a mesostructural level permits to take into account the various dominating mechanics in the physics o the mechanical transormation o prepreg abrics during the shaping process, namely large angular variations o yarns, viscoelasticity o resin and evolution o possible damages in yarns. The dierent advantages o this modelling is irst to give the ability to obtain a very good material orientation o yarns and consequently to introduce good data in the preprocessing o the calculation o the inal piece ater polymerization, secondly to give the mechanical limits o the abric during the orming process and to limit the alls o the abric by an better deinition o the lat orm. The orming process o impregnated reinorcements usually includes important mechanisms which can have a signiicant eect on mechanical properties o the inished product 1. large angular variation due to in-plane shear strain, 2. straightening and elongation o ibres due to in-plane tension, 3. buckling o ibres due to large in-plane compression, 4. inter-ibre sliding due to relative local stretching o yarns. The ormability o preimpregnated reinorcements is strongly aected by the abric architecture, the rheological properties o resin and ibres, the size and the geometry o tools. The heterogeneous behaviour must take into account geometrical undulation o yarns, ibre properties, resin behaviour and contact with riction between composite and tools. The proposed model is described by continuum approach or inite strains and geometrical non linearities. Elastic and viscoelastic properties o material are investigated and homogenized on a mesostructural level. Bi-component inite elements is obtained by association o viscoelastic membrane inite elements representative o resin behaviour and truss inite elements representative o warp and wet ibres behaviour. MESOSTRUCTURA MODE OF PREIMPREGNATED COMPOSITE BEHAVIOUR The woven abrics impregnated with resin have complex internal microstructures and present an anisotropic behaviour due to the privileged directions o ibres. Some models are proposed to homogenize elastic properties o a composite material and to simulate the deormation o these materials by orming process. Geometrical approach is proposed in the literature to simulate the transormation o abrics during the draping process. This approach is based on geometrical aspects o the warping where the deormation is restricted to interibre shear mode and the abric can be approximated by trellis mechanism, Kawabata 1973

3 [12], Bergsma 1988 [3], Baser 1989 [1], Van de Ween 1991 [18], ong 1995 [14] and Chen 1998 [6]. Micro-macro structural approach is developed in order to take account all weave architecture and mechanical properties associated to the impregnated material and to the resin behaviour, Real 1993 [15] and Blanlot 1995 [4]. An updated lagrangian ormulation in inite deormations was used to simulate the deormation o dry abric by sheet orming process. The abric behaviour is obtained by discrete summation o tensile curve o a single yarn and the current o the yarns during the deormation, Sabhi 1993 [16], Cherouat 1995 [7] and Gelin 1995 [9]. So, it is diicult to globally characterise, by homegeneous methods, the behaviour o this abric without lose mechanical inormations. In order to predict structural behaviour o impregnated woven abric a new inite element model, developed an a mesostructural level is carried out. This approach makes it possible to model the deormation o composite abrics by taking account o the various dominating mechanisms in the physics o the mechanical transormation o abrics and geometrical non linearity, Belhous 1998 [2] and Cherouat 1998 [8]. arge angular variations o yarns, viscoelasticity o resin and evolution o damage in yarns are the principal mechanics mechanisms which control the shaping process o impregnated abric. The kinematic transormation o impregnated material in large displacements and inite strains is based on the ollowing assumptions : A1 : Non-sliding inter-ibre o impregnated composite abrics during the shaping process can be experimentally observed by the ollowing transormation o aligned straight lines drawn on the abric. For each point o continuum material the actual position is deined in actual coniguration by!!!! ibres resin ibres resin x = x = FX = FX (1) F describes the deormation gradient o composite abric. A2 : The current longitudinal orientation o each ibre n ( F ) geometrical transormation deined by the linear application! 1! n F FN λ (,θ ) ( θ )! 0 0,θ 0 is calculated rom the = (2) A3 : The shear angles deormation o ibres can be associated to the rotation o the rigid body o the ibre. We can note this assumption by the ollowing kinematic relation!!!!!! N ( θ ). N ( θ ) = 0 n ( F, θ ). n ( F, θ ) = 0 (3) 0 T 0 0 T 0 Using the above assumption, the right stretch tensor or heterogeneous material is deined in reerence coniguration as!! T λ i = Ni F FNi ibres (4) m T U = F F resin

4 The non linearity o the shaping problem imposes the use o incremental ormulation. The spatial velocity gradient in the current coniguration, expressed in the rigid body rotation rame by R λ" i = n n n n ibres i i i + " i i λ 1 3 mr m m i m = U" λ" U = e e re i i m 0i 0i sin = 1λ The rate constitutive equations or inite-strains use objective derivatives. In above equation the rotation rate o the local rame in which a simple derivative would give objective derivative deined by Green-Naghdi s (co-rotational ormulation). To characterise the objective behaviour o abric, the stretching tensor are written in the rigid body rotation rame as D = ibres λ" λ mr λ" i m D = e e re i i m i R R j sin = 13, λ For shaping deormation rate constitutive equations must be written in terms o objectives rates in order to maintain correct rotational transormation properties. Using Kirchho s and Green-Naghdi s tensor stress, the stress rate in the ibre and the resin can be written at each time as tn+ 1 λ" R R () τ ( σ ) = ( σ ) + E ( λ ) dτ ibres n n + 1 tn λ () τ tn+ 1 mr mr m mr ( σ ) = ( σ ) + C () τ D dτ resin n+ n 1 tn The constitutive law o ibres is non linear and is written in terms o longitudinal modulus o stretching E unction o principal elongation o ibre λ, elastic modulus o ibre E and undulation actor ε emb. The viscoelasticity behaviour law o resin is ormulated in the time domain by the hereditary integral and using the relaxation time τ k and the ourth order m relaxation tensor, which are material parameters C k ij. Approximating the creep unctions by a Prony series we have (5) (6) (7)

5 λ" λ E ( ) E e ε em λ = 1 ibres Cij m () t Cij m k Cij m k t τ = e k + resin 1 (8) FINITE EEMENT MODEING The continuum movement o each material point, ensured by the non-sliding inter ibre due to abric weaving and resin behaviour, means that a nodal approximation or the displacement can be used. A inite element method is used to modelling the equilibrium o abric during the shaping deormation. The deormation o prepreg woven abric is described with membrane assumptions. The global equilibrium o the abric is obtained by minimization o deormation energy mr mr R R Π( u) = σ δd dv + σ δd ds udv " uds " (9) V resin ibre The equilibrium equation on the actual coniguration (9) is non-linear (viscoelasticity behaviour o resin, elastic non linear o ibres, inite transormation and contact with riction between abric and tools) it is linearized by an iterative Newton method. According to the dierent modes o deormation occurring in the material, bi-component inite elements are developed to characterize mechanical behaviour o thin woven composite structures. The bicomponent element is based on an association o 2D membrane inite elements combined with a complementary truss inite elements. The resin is modelling by isotropic viscoelastic three or our nodes membrane inite elements and the warp and wet ibres are modelling with linear truss inite elements. Sσ v S u s APPICATIONS TO SOME PROCESS The present section relates experiments and models developed or the validation o the numerical model o impregnated composite abric. First experimental investigation is carried out a shear test on a dry woven abric specimens. Then tensile tests carried out on a impregnated woven abrics specimens in non polymerized phase consisting. To illustrated how the developed model can be used to predict the deormation o the composite abric during the orming process, some examples are treated and discussed. 1. Shear test o dry woven abric The validation o the mesostructural behaviour o impregnated reinorcements is carried out on shear tests. As the experimental tests are carried out with Serge 3x4 dry abrics Sabhi 1993 [16] and Gelin 1996 [9]. A glass ibres abric specimen is clamped on rigid shear rig. The shear rig was used to measure shear stiness and the locking angle o the abric reinorcement. Applying a vertical load (120 N), the specimen is subjected to a shear strain state. The equilibrium o the parallelogram rigid bars gives a relationship between the loads o the yarns in tension to the vertical load at crosshead mounting point. The experimental load

6 measured or a given displacement and or dierent orientation o ibres is compared to the numerical value obtained by using the numerical model. The numerical simulation is carried out with Abaqus sotware, where the abric is modelled by 300 linear truss inite elements representative o warp and wet ibres behaviour. For this test, the computation is irst made neglecting the inluence o the resin eect and the undulation on the abric behaviour. Numerical results, obtained by bi-component inite elements, are compared with the experimental elongation eort imposed by the machine. These results are illustrated in Figures 1 or dierent orientations o ibres 0 and 10. The agreement between numerical and experiment values is good and prove the validity o the mesostructural approach to modelling the behaviour o preimpregnated woven abric. %!!!! $"!!! oad (N) $!!!! #"!!! #!!!! oad (N) "!!! 5000! Displacement (mm) Displacement (mm) Fig. 1 : Variation o load orce or 0 and 10 ibre orientations 2. Tensile test o preimpregnated woven abric The impregnated abric developed in this study was a satin 5 woven abric in non polymerized phase consisting o carbon ibres Blanlot [4,5]. The behaviour o composite abrics subjected to shearing can be measure experimentally to determine the eective shear compliance on the shaping process. The locking angle is considered to be the shear angle at the commencement o out-o plane movement leading to wrinkling o the abric. At processing, the impregnated abric is idealised as a viscous material subject to the kinematic constraints o incompressibility and inextensibility in the ibre direction. Application o tensile strain caused a membrane stress within the abric. The eect o the membrane stress upon the locking angle has also been investigated. A vertical displacement is imposed at the moving extremity o the rectangular impregnated woven abric specimen. Four phases o transormation are identiied in the global behaviour : visco-elastic phase results rom resin shearing behaviour (relaxation modulus), a pseudokinematic phase results rom geometrical rotation o ibre and geometrical undulation o yarns, a hardening phase results rom locking ibre, rictional resistance and rom increasing density o ibres and linear phase results rom ibre tensile behaviour. The experimental eort imposed by the tensile machine is compared to the numerical values or dierent orientation o ibres 30 and 45. Figures 2 describe, at the beginning o the curves, the viscoelastic phase ollowed by a kinematic stage which increases with the angle o loading. The end part o this curves represents the hardening phase with a very high stiness du to ibre elongation. The

7 agreement between numerical and experiment values prove the validity o the proposed model and show clearly the strong non linearity o impregnated composite behaviour epage 1998 [13]. All the calculated are worked out using the ollowing values o material constants : mechanical characteristics o ibres are : E (MPa) ε emb ρ (g/cm 3 ) ,76 and mechanical characteristics o non polymerized resin are : time (s) Shear mk C %! oad (N) Without undulation With undulation./01)234 &'()!* $" $! #" Without undulation With undulation &'()#"* 10 #! 5 " Displacement (mm)! $! +!,! -! #!! 567(809:;:<=)2;;4 Fig. 2 : Variation o load orce or 30 and 45 ibre orientations 3. Deep-drawing process by hemispherical tools Deep-drawing is a common process used to manuacture composite structure by stamping impregnated abric into complex inal geometric orm. Coniguring a new deep-drawing process is highly empirical with many parameters determined by trial and error. The lange o the abric is held against the die with a blank holder, preventing the lange rom olding upward and to avoid the ormation o the olds in abric. As the punch is lowered, the material is drawn into the die, orming the hemispherical shape. The ability to perorm a successul deep draw operation depends on many parameters. These include the mechanical behaviour o abric material, initial direction o ibre, the hold down orce on the blank holder, the velocity o the punch, the riction between the abric and tools, the corner radius o tools. The eects o some o these parameters on a simple cup are explored using numerical analysis. In this study o shaping process, we are interested in the shear angular variation between the ibre wet and warp along symmetrical and diagonal directions o inal parts, contour o the inal shape, the strain and the distribution o ibre surace density in certain zones.

8 An experimental shaping test o dry glass ibre abric by deep drawing process with a hemispherical tools have been simulate in the laboratory or dierent orientation o ibres Cherouat 1995 [7]. The initial shape o the glass ibre abric is a square (360 x 360mm). Its edges are ree but a pressure equal 2 MPa is applied on the blank-holder and riction coeicient between the glass abric and the tools is 0.1. The numerical analysis o woven abric shaping is developed in the ABAQUS explicit sotware. The impregnated composite is modelling with 400 membrane inite elements representative o resin behaviour and 1600 truss inite elements representative o warp and wet ibres behaviour. The hemispherical die and punch rigid are modelling with 1600 Bezier patches. The parameter study was perormed on the eect o the ibre direction actor on the shear angles o abric. Figures 3 and 4 give the inal results in terms o angular distorsion within the abric along the diagonal and median lines. The experimental and the numerical values indicate a good agreement or (0,90 ) and (-45,+45 ) along the diagonal and median directions o the inal shaped part. We notice that these angular distorsion values are very large along the diagonal line or (0,90 ) abrics and along the median line or (-45,+45 ) abrics Angular distorsion ( ) Fabric Angular distorsion ( ) Distance to the center (mm) Distance to the center (mm) Fabric Fig. 3 : Shear strain or (0,90 ) abric along diagonal and median lines

9 Fabric Distance to the center (mm) Angular distorsion ( ) Fabric Distance to the center (mm) Fig. 4 : Shear strain or (-45,+45 ) abric along diagonal and median lines CONCUSIONS Numerical analysis are an eicient mean o evaluating actors related to manuacturing process, such as deep-drawing and laying-up. It is possible to obtain good, quantitative inormation on the orming process. A proposed manuacturing process, or a modiication to an existing process, can be easily investigated prior to investment in tooling. There are usually several problems that are identiied in an initial highly non linear numerical analysis, such as the behaviour o the material, the geometrical non linearities o the process and the contact with riction. A numerical mesostructural approach is proposed to modelling the behaviour o the impregnated composite and implemented in Abaqus sotware. The mechanical ormulation take account the speciic deormations o ibre, the eects structural o the abric weaving and the viscosity eects behaviour o the resin. The bi-component inite elements o the heterogeneous material is obtained by 2D membrane isotropic viscoelastic inite elements representative o resin behaviour added to the isotropic elastic rod inite elements representative o warp and wet ibres behaviour. al test has been carried out in order to validate the proposed computational method o the orming processes. Numerical orming results are in good agreement and prove the validity and the pertinence o the numerical ormulation. REFERENCES 1 Baser, J. Text. Inst, 1989, Vol 80 N 4, (1989). 2 Belhous S, Cherouat. A & Billoet J., 2 nd International Conerence on Integrated Design and Manuacturing in Mechanical Engineering, Compiègne France, Vol 2, pp (1998). 3 O.K. Bergsma & J. Huisman, Proceeding o the 2 nd In. Con On Computer Aided design in Composite Material Technology, pp (1988). 4 R. Blanlot & J.. Billoët, ICCM 10 Canada, pp (1995). 5 R. Blanlot & J.. Billoët, ICCE/3 New Orleans USA, pp (1996).

10 6 J. Chen and T. McBride, ICCE/5, as Vegas USA, pp41-42 (1998). 7 A. Cherouat, Simulation numérique de l emboutissage des tissus de ibres de verre par la méthode des éléments inis, PhD thesis, University o Franche-Comté Besançon France (1994). 8 Cherouat. A, Billoët J. & Belhous S, ICCE 5, as Vegas USA, pp (1998). 9] J.C Gelin, A. Cherouat, P. Boisse & H. Sabhi, Composites Science and Technology, 56, pp (1996). 10 P. Gilormini & P. Roudier, ABAQUS and Finite Strain, Intern report MT Cachan N 140 France, (1993). 11 A. Hoger, Int J. Solids Structures Vol 23, N 12, pp , (1987). 12 S. Kawabata, M. Niwa And H. Kawai, J. Text. Inst, 1973, Vol 64, (1973). 13 A. epage, Simulation numérique du comportement des tissus composites à résine non polymérisée, Intern report, ASMIS, UTT, (1998). 14 A.C. ong, C.D. Rudd, M Blagdon, K.N Kendall & M.Y. Demeri, ICCM-10, Canada, Vol III, pp (1995). 15 M. Reale, C. Marcy and S. Backer, Vol 46, Use o Plastic and Plastic Composites: Material and Mechanics Issues ASME, 1993, 64, H. Sabhi, Etude expérimentale et modélisation mécanique et numérique du comportement des tissus de ibres de verre lors de leur préormage, PhD thesis, University o Franche-Comté Besançon France (1993). 17 Sowerby R.& Chu E., Int J. Solids Structures, Vol 20, N 11/12, p (1987). 18 F. Van Der Ween, Int. J. Num. Meth. Engng, 31, pp (1991).