Autoclave Cure Simulation of Composite Structures Applying Implicit and Explicit FE

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1 Autoclave Cure Simulation o Composite Structures Applying Implicit and Explicit FE Abdelal, G. F., Robotham, A., & Cantwell, W. (2013). Autoclave Cure Simulation o Composite Structures Applying Implicit and Explicit FE. International Journal o Mechanics and Materials in Design, 9(1), DOI: /s Published in: International Journal o Mechanics and Materials in Design Document Version: Peer reviewed version Queen's University Belast - Research Portal: Link to publication record in Queen's University Belast Research Portal Publisher rights Springer Science+Business Media Dordrecht 2012 The inal publication is available at Springer via General rights Copyright or the publications made accessible via the Queen's University Belast Research Portal is retained by the author(s) and / or other copyright owners and it is a condition o accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The Research Portal is Queen's institutional repository that provides access to Queen's research output. Every eort has been made to ensure that content in the Research Portal does not inringe any person's rights, or applicable UK laws. I you discover content in the Research Portal that you believe breaches copyright or violates any law, please contact openaccess@qub.ac.uk. Download date:02. Feb. 2018

2 Virtual Manuacturing o Composite Structures Applying Implicit and Explicit FE Techniques Gasser F. Abdelal 1 *, Antony Robotham 2, Wesley Cantwell 3 1 The Virtual Engineering Centre, University o Liverpool, Warrington, UK, WA44AD ( G.Abdelal@liverpool.ac.uk) 2 The Virtual Engineering Centre, University o Liverpool, Warrington, UK, WA44AD ( Ajr@liverpool.ac.uk) 3 Centre or Materials and Structures, University o Liverpool, Liverpool, UK, L69 3GH ( Cantwell@liverpool.ac.uk ) *Corresponding Author Abstract Simulation o the autoclave manuacturing technique o composites can yield a preliminary estimation o induced residual thermal stresses and deormations that aect component atigue lie, and required tolerances or assembly. In this paper, an approach is proposed to simulate the autoclave manuacturing technique or unidirectional composites. The proposed approach consists o three modules. The irst module is a Thermo-chemical model to estimate the temperature and the degree o cure distributions in the composite part during the cure cycle. The second and third modules are a sequential stress analysis using FE-Implicit and FE-Explicit respectively. Usermaterial subroutine is used to model the Viscoelastic properties o the material based on theory o micromechanics. Keywords Autoclave, chemical reaction, composites, cure, exthothermic, explicit, inite element, implicit, micromechanics, thermal stress. 1

3 1 Introduction The main objective o our approach is the early estimation o composite part deormations during autoclave manuacturing. These early estimated deormations can be used to modiy autoclave-tool design to achieve better part design within speciied tolerances (customer requirements). Numerical autoclave simulation will reduce the cost o the iterative manuacturing process to ind the optimized autoclave-tool design. Autoclave simulation consists o three steps. The irst step is a Thermo-Chemical model to simulate the curing cycle and determine the temperature and degree o cure distributions as a unction o the cure-cycle time. The second and third components are stress-thermal models based on implicit and explicit techniques, to calculate residual stresses (that can aect part atigue lie) and deormations (that can aect assembly process)[1]. The chemical reaction which occurs during the curing o thermoset composites plays an important role in the process modelling o thermoset composites. The exothermic heat released during the curing process can possibly cause excessive temperatures in the interior o composites. Cure kinetics that provides inormation on the curing rate and the amount o exothermic heat release during the chemical reaction are important in the process simulation o composite materials with thermoset polymers. A number o dierent models have been proposed to describe the cure kinetics o various resin systems [2-5]. To characterize the exothermic cross-linking o a thermosetting polymer matrix, a thermal cure monitor technique such as isothermal Dierential Scanning Calorimetry (DSC) is commonly used. Capehart, Kia and Abujoudeh [6] discussed the procedure required to it a selected cure kinetic model to the experimentally-determined cure rates. A number o dierent actors lead to the development o residual stresses and deormations, during autoclave process. These actors can be summarized in the ollowing; thermal strains, resin cure shrinkage, and tooling mechanical constraints. Thermal strains are due to the mismatch o thermal properties o the laminate layers, gradient o temperature and resin degree o cure, and the mismatch o thermal expansion coeicients between the part and the tool. Cure shrinkage is reduction in volume due to an increase in resin density during polymerization. Shrinkage strains are higher in the transverse to the ibre direction than in the ibre direction in which they will be largely constrained. The role o cure shrinkage in generating residual stresses was studied by many researchers [7-8]. Process tooling aects part stress development by disturbing the component internal temperature, and via mechanical loads and constraints applied at tool/part interaces. Disturbing the part internal temperature occurs as a result o the dierence in component tool-side and vacuum bag-side temperatures. This actor is signiicant only or thick composite part. Boundary loads to the part, both in shear and 2

4 normal to the tool/part interace plays a major role in induced residual stresses. The resin mechanical behaviour during curing cycle can be divided to three steps; First stage is a purely viscous behaviour with no internal stresses, second stage is a viscoelastic behaviour as the resin starts to polymerize, and third stage is a elastic behaviour as the resin is ully cured. The resin is modelled as a cure-hardening instantaneously linear elastic material (CHILE) [1], with an isotropic resin modulus. The ibers are modelled as transverse isotropic material which is independent o the temperature and degree o cure (E 11, E 33, G 13,ν 13,ν 23). Instantaneous composite material elastic constants are determined using a micromechanics model rom Bogetti and Gillespie [8]. The aim o this paper is to propose a 3-D numerical method using inite element to estimate the induced residual stresses and deormations o thermoset polymer unidirectional composites during autoclave curing cycle. These deormations are used to change the autoclave-tool shape design to minimize part deormations. This module will be integrated within an optimization routine in a virtual engineering environment to reduce costs and time o the composite manuacturing process. 2 Thermo-Chemical Model Thermo-chemical module simulation requires the determination o the reaction kinetics o each resin and thermal transport o the heat o reaction across the laminate panel to calculate changes in the laminate temperature that aects thermal strains, and degree o cure that aects resin modulus. The ollowing mathematical equation is modeled applying transient thermal analysis (ABAQUS). T T c c k H Q t x i x j t i, j 1, 2,3 p ij R v (1) where denotes the composite density, c p the speciic heat, T the temperature, t the time, x i the coordinates, k ij the components o the thermal conductivity tensor, c the degree o cure, which is deined as the ratio o the heat released by the reaction to the ultimate heat o reaction H R, and Q v is the heat convection to the surrounding air in the autoclave. Orthotropic conductivity is assumed or all materials so that values o k 11, k 22, and k 33 are required. Assuming isotropic resin conductivity and transversely isotropic ibre conductivities, the rule o mixture is used Twardowski [9] to evaluate lamina thermal conductivity, 3

5 K V. K 1 V. K K r 22 K r B 2. 1 K22 V B Kr. V 2 1 B. 4. a tan V 2 V 1 B. 1 B. (2) where K 11, K 22 are the longitudinal and transverse conductivities o the ibers, K r is the isotropic conductivity o the resin. These values are assumed as a unction o temperature. Laminate global conductivity is calculated applying Kulkarni and Brady [12] methodology (Appendix A). The lamina speciic heat capacity is calculated using the ollowing equation [1], C p 1 V Cp 1V Cpr r V V C pr r (3) where C p, C pr are the speciic heat o the ibers and resin respectively, and modelled as a unction o temperature. The internal heat generated due to the exothermic cure reaction is described as in White and Hahan [10], dc K dt K Ae m E RT 1 n (4) where K is the Arrhenius rate, R=8.31 J/Mol.K is the universe gas constant, A the requency actor, and ΔE the activation energy. Heat transer coeicient or an autoclave o size (1.8 m x 1.5 m) is measured and can be expressed as [1], (9.3 5). ( / ) (5) h E P W m K 2 Stress-Thermal Model The temperature and degree o cure distribution as a unction o cure cycle time that is evaluated using the thermo-chemical. Then a sequential transient stress-thermal analysis is used to evaluate residual stresses and deormations. This analysis step involves two 4

6 main issues; Viscoelastic material model to simulate the resin behavior with temperature and degree o cure, and Micromechanical model to predict the composite part Elasticity tensor with time as a unction o the iber and resin material properties. Modeling the Viscoelastic behavior o a composite material is a complex problem, and is mostly diicult or a curing composite. The most serious diiculties arise rom the need to measure material behavior over a wide range o temperatures and degrees o cure and the act that curing o the resin changes its material response even as it is being tested. The isotropic matrix resin in composite materials is modeled as curehardening/instantaneously linear elastic (CHILE) material. This designation indicates that the modulus o the instantaneously linear elastic resin increases monotonically with the progression o cure. The model or prediction o resin modulus development is that used by Bogetti and Gillespie [8]. The estimation o the CHILE model parameters, requires searching the literature or stress-relaxation test data o the speciied epoxy (Hexcel material 914), or perorming a set o tests deined by Anderson [1]. 0 r 1 mod. r mod. r E E E mod 0 mod Er Er.. 1. (6) mod C1 C2 C1 (7) E 0 r, E are the ully uncured and ully cured temperature dependent resin modulus. The r α C1, α C2 represent the bounds on degree o cure between which resin modulus is assumed to develop. term γ is introduced to account or the competing mechanisms between stress relaxation and chemical hardening [8]. Increasing γ physically corresponds to a more rapid increase in modulus at lower degree o cure beore asymptotically approaching the ully cured modulus. The ibers are modelled as a transverse isotropic material which is independent on temperature (E 11, E 33, G 13,ν 13,ν 23). The micromechanical model to evaluate the transversely isotropic engineering constants is discussed in Appendix A. User material subroutine (UMAT) is used in ABAQUS to model the material behaviour. Resin chemical shrinkage only occurs during the curing process. Chemical resin shrinkage induces signiicant macroscopic strains in the composite, representing an important source o internal loading in thick-section laminates in addition to the traditionally recognized thermal expansion strains. The model developed by Bogetti and Gillespie [8] is applied to model the resin chemical shrinkage. The lamina cure shrinkage coeicients are calculated using a micromechanical model (Appendix A) and modeled in user subroutine (UEXPAN). 5

7 s s r r s V V. C1 s C2 C1 (8) The α C1, α C2 represent the bounds on degree o cure between which resin shrinkage is s assumed to develop. V r is the total volumetric resin shrinkage. Measurements o resin shrinkage during cure is discussed in Anderson [1]. 3 Case Study L-shaped angle laminates o AS4/8552 were layed up ply-by-ply on a pair o solid convex aluminium tool as shown in Figure 1 and Figure 2. The autoclave process cycle is shown in Figure o 0 o Figure 1. Angle laminate. Figure 2. Autoclave tool. 6

8 177 C o - 2 Autoclave Autoclave 107 C o - 1 Autoclave 375 KPa 170 KPa Vacuum 101 KPa Figure 3. Autoclave process cycle. Cycle time composite part is modelled with 3dierent lay-up; [90/+45/-45/0] 6, [0] 24, and [90] 24. The angle is meshed with 3-D composite solid elements (C3D8R) [3876 elements], with 6 elements along the depth direction to model bending eect. The autoclave tool is meshed with solid elements (C3D8R) [6955 elements]. Meshed assembly is shown in Figure 4. Figure 4. Meshed assembly. Autoclave process pressure is applied on the outer surace o the angle. Contact surace is deined between the inner surace and the autoclave tool. Mechanical contact properties are deined as rough along the tangential direction and no separation along the normal 7

9 direction o the contact surace. Thermal contact conductance is deined to be 10 5 W/m 2 K. Autoclave tool is ixed at the bottom let corner and let to slide along the longitudinal and transverse directions o the composite part. Thermal and mechanical material properties used or angle are listed in Table 1 and Table 2 respectively. Table 1. Thermal material properties. Speciic heat C p = 904 +(T-75)(2.05) capacity C pr = (T-20)(3.75) (J/Kg.K) Thermal k l = T(1.5E-2) conductivity k t = 2.4+T(5.07E-3) (W/m.K) k r = T(3.43E-4) Fibre volume V = raction Cure kinetic H R = 590E+3, ΔE = model 66.9KJ/gmole, A =5.333E+5 /s, m=0.79, n=2.16, α 0=0.01 Table 2. Mechanical material properties. Resin modulus E r = 4.67GPa 0 development E r = E r /10 2 α C1 = 0.608; α C2 = 0.75 s Cure shrinkage V r = 0.099, α C1 = model 0.055, α C2 = Fibre volume V = raction Thermal CTE1=0.6E-6, expansion CTE2=CTE3=28E-6 coeicient 8

10 Temp. with imperect bond Temp.B.C Temperature, C Degree o Cure Temp. with perect bond degree o cure perect bond degree o cure imperect bond x 10 4 Time (seconds) Figure 5. Temperature and degree o cure. The predicted temperature and degree o cure or two types o thermal bonding between composite part and tool are shown in ig. 5. The exothermic heat could only be simulated only or the low contact conductivity between part and tool. High contact conductivity between part and tool leads to less apparent exothermic heat, which is similar to 2-D results in Anderson [1]. This is due to the high heat transer rate at the part/tool interace, so the extra heat generated by the resin is rapidly transerred to the tool. Low contact conductivity leads to aster curing rate, due to the higher temperature distribution. Next, these thermal results will be used in the stress-thermal analysis applying the implicit and explicit techniques to calculate part deormations. The implicit inite element method is an iterative approach and can encounter numerical diiculties when solving non-linear quasi-static problems. The iterative approach employed may have trouble achieving convergence in analyses with a non-linear material behavior and contact analysis. In the case o the explicit FE method the solver equations can be solved directly to determine the solution without iteration, thus providing an alternative, more robust method. Assuming rough tangential contact between part and tool reduces the convergence diiculties, and matches the applied physical boundary condition. On the other side, composite section can be deined in implicit FE and not an option in explicit FE. To overcome this modeling diiculty, an average o the elasticity tensor is calculated and used in the user subroutine (VMAT) to update stress or each integration point. Following the simulation o the cure cycle, the composite part is removed rom tool (remove contact suraces) in a steady-state analysis step to calculate the inal part 9

11 deormations due to residual stresses. Boundary conditions or the tool-removal phase is allowing the plane o symmetry o the part to slide and ix one node on the same plane in all directions. Deormation in the composite part is measured in terms o the contraction o its 90 degrees angle (Fig. 6). Numerical results are shown in Table 3. Figure 6. Springback o composite part ater being released rom tool. Table 3. Numerical and experimental results. Simulation [90/- [0] 24 [90] 24 45/45/0] 6 3D Implicit high cond. 3D Implicitlow cond. 3D Explicithigh cond. 3D Explicitlow cond. Experimental D Implicit [1]

12 The higher springback evaluated applying implicit 3-D FE is mostly due to the composite section modeling available in the implicit solver, and on the other hand, averaging methods are used in explicit FE. Another actor is the contact stresses generated by the implicit FE is higher which induces higher deormations. Applying slippery layer between part and tool may reduces contact stresses, which leads to less deormations, but diicult to apply due to the high autoclave temperatures that leads to dryness o the applied layer. The high conductivity contact between the composite part and tool produced more accurate results, which relects the true nature o contact in the physical process. And it shows that applying a low conducting layer between the composite part and the tool surace or using low conducting tool can reduce springback. The 2-D implicit FE analysis by Anderson [1] over estimated the springback o the [90/+45/-45/0] 6 laminate and did not generate good results or the[90] 24 laminate. It can be concluded that 2D FE analysis is not recommended or cure simulation. 3 Conclusions An approach has been proposed to evaluate the springback deormations during the cure cycle o unidirectional composite materials. The approach was divided into three steps that are integrated together and to be applied in a virtual engineering environment to improve manuacturing and design phases. Numerical results shows the impact o the contact stresses and thermal conductivity on composite part springback. Reducing contact stresses and lowering conductivity between the composite part and tool leads to less deormations. The proposed approach ignored the eect o resin low which is sometimes used or compacting o laminate and voids removal. Variation o resin distribution may aect springback and it will be the ocus o the uture work. The same approach will be applied to study springback o 2-D woven composites. A dierent micromechanical model will be applied to simulate the woven lamina mechanical perormance. Acknowledgments The Virtual Engineering Centre is a University o Liverpool project partially unded by NWDA and ERDF. 11

13 Appendix A A.1 Global conductivity o laminate composite Global lamina conductivity tensor, k k cos k x sin k k sin k cos, K K y z 22 (9) where θ is the iber orientation angle with respect to the global x-axis. Global laminate conductivity tensor, K K K 1 x x i N i1 1 y y N i i1 z N i1 1 N N N k k k z i (10) where i denotes each individual lamina, N is the total number o lamina. A.2 Engineering constants In-Plane moduli, r E E E V r k krgr 1 V V k Gr kr k kr GrV Er E Gr ; k r (11) E E k 4G E T (12) Shear moduli, G G G G V r G12 G13 G r G G r G G V (13) 12

14 G 23 r r r r r 23 r G k G G G G k G G V k G G G G k G G G V r r r r r r (14) Poisson's ratios, V r 1V 13 1 k Gr kr k kr GrV k k G V V r r r (15) T T 22 2E k E E 4 k E (16) 2E k 11 T k T k G k k k G V r r r r k G k k V r r (17) Cure shrinkage coeicients, CSC Cure shrinkage strains, 1 Er1 V E11 V Er 1V r r 1V 1 CSC2 1 1V 13 V 1 V. (18) Er E11 V Er V CSC CSC 3 2 s ( ) ( 1). s k s k i CSCi i i (19) εr s(k), εr s(k-1) are the total cure shrinkage strains at the start and end o the time step respectively. s V 13 r s 1 1 (20) r A.3 Elasticity tensor calculations (VMAT) 3-D stress/strain transormation matrix, or the calculations o the average elasticity tensor in VMAT subroutine, 13

15 2 2 cos sin 0 2*sin *cos sin cos 0-2*sin *cos T 2 2 -sin *cos sin *cos 0 cos sin cos -sin sin cos (21) Transormed elasticity tensor or lamina, Average elasticity tensor, T G 1 1 [ C] i T C T (22) C A N C N G i (23) 1 E11 12 E11 13 E E11 1 E22 23 E E11 23 E22 1 E C (2. G12) (2. G23) (2. G31) (24) Reerences [1] Johnston, A. A. (1997), An Integrated Model o the Development o Process-Induced Deormation in Autoclave Processing o Composite Structures. PhD dissertation, University o British Columbia. [2] W.I. Lee, A.C. Loos, and G.S. Springer (1997), Heat o Reaction, Degree o Cure, and Viscosity o Hercules Resin, Journal o Composite Materials 16, [3] S.N. Lee, M.T. Chiu, and H.S. Lin (1992), Kinetic Model or the Curing Reaction o a Tetraglycidyl Diamino-Diphenyl Methane/Diamino Diphenyl Sulone (TGDDM/DDS) Epoxy Resin System, Polymer Engineering and Science 32 (15), [4] E.P. Scott (1991), Determination o Kinetic Parameters Associated with the Curing o Thermoset Resins Using Dielectric and DSC Data, Composites: Design, Manuacture, and Application, ICCM/VIII, Honolulu, [5] A. Johnston and P. Hubert (1994), Eect o Processing Variables on Springback o Composite Angles. A Report to the Boeing Company. 14

16 [6] Capehart T. W., Kia H. G. and Abujoudeh T. (2007), Cure Simulation o Thermoset Composite Panels, J. o Composite Materials, 41, [7] A.M. Boriek, J.E. Akin, and C.D. Armeniades (1988), Setting Stress Distribution in Particle Reinorced Polymer Composites, J. o Composite Materials 22, [8] T.A. Bogetti and J.W. Gillespie Jr. (1992), Process-Induced Stress and Deormation in Thick-Section Thermoset Composite Laminates, Journal o Composite Materials 26 (5), [9] M. R. Kulkarni and R. P. Brady (1996), A Model o Global Thermal Conductivity in Laminated Carbon/Carbon Composites, J. o composite Science and Technology 57, [10] S.R. White and H.T. Hahn (1992), Process Modeling o Composite Materials: Residual Stress Development during Cure. Part I. Model Formulation, J. o Composite Materials 26 (16),