EFFECT OF SHEAR STRESS ON FATIGUE LIFE OF COMPOSITE LAMINATES

18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS Abstract EFFECT OF SHEAR STRESS ON FATIGUE LIFE OF COMPOSITE LAMINATES G. Mustafa 1 *, S.K. Ha 2, Y. Haung 2, K. Jin 2 1 Design Departent, AE Design, Pakistan, 2 Departent of Mechanical Engineering, Hanyang University, Ansan, Korea *Corresponding author(enginer315@gail.co) Keywords: Coposite lainates, icroechanics of failure (MMF), fatigue life, constituents, stress ratio, daage paraeter The effect of coplex stress state is not properly taken into account for deterining the fatigue life of thin-walled structures ade of coposite aterials like wind turbine blade. Fatigue life predictions, as per state-of-the-art design codes like IEC 61400-1 and GERMANISCHER LlOYD (Part 1), account only for noral stresses, neglecting the contribution of shear stresses. This is due to either isconception or lack of experiental data and theoretical odels. Many echanical tests are required to fully characterize the coposite lainates ade of various aterials and having different layup sequences under any load cobinations of inplane stress tensor coponents. A icroechanics based fatigue life prediction of coposite lainates under ulti-axial loading was developed that can take care of coplex stress state. In order to reduce nuber of tests, a ethodology was presented in this paper to predict fatigue life of coposite lainates based on fatigue life of constituents, i.e. the fiber, atrix and interface, using icroechanics of failure (MMF). For atrix, the equivalent stress odel which is generally used for isotropic aterials was eployed to take care of ulti-axial fatigue loading. For fiber, a axiu stress odel considering only stress along fiber direction was used. Critical plane odel was introduced for the interface of the fiber and atrix. The odified Goodan approach was utilized to take into account the ean stress effect. In order to validate the proposed ethodology, the fatigue life of three different GFRP lainates, UDT [90 ], BX [±45 ]S and TX [0 2/±45 ]S, was exained experientally. The predictions are copared with the experiental data, and are shown in good agreeent. A coprehensive ipleentation exaple is also presented for the case of wind turbine rotor blade coposite lainates. An initial estiate on the effect of neglecting shear stresses in fatigue life calculations is provided based on predictions. It is concluded that in wind turbine blade GFRP lainates, shear stresses have an iportant contribution in reducing fatigue life. 1 Introduction Fiber reinforced lainated coposites have been used in any structural applications because of their superior specific properties copared with etals. Typical odern coposite structures include aeronautical vehicles, ships, wind turbine blades, flywheels, pressure vessels, helipads, Clock Tower in KSA, and sporting goods. Fiber reinforced coposites consist of fibers and visoelastic atrix. With the increase of loads and changes in environental conditions, the daage grows and progresses until ultiate failure of structures. The stress state in coposite structural eleents, either in the for of thin or oderately thick shell construction, can be assued plane, i.e. coposed of two noral coponents and an in-plane shear coponent of the stress tensor. The coposite structures should be stiff enough to resist deforations and strong enough for long ter operation in service under particular stress state. Fatigue failure of coposite aterials has been widely discussed in the literature by the researchers during the past two decades [1-5]. Hashin and Rote [3] presented a siple fatigue failure criterion expressed in ters of S-N curves obtained by uniaxial cyclic testing of unidirectional speciens. Energy-based criteria incorporate both stresses and strains. In this approach, the daage is related to

input energy which cannot give any inforation about failure echanis [6, 7]. Several researchers [8, 9] have investigated fatigue daage response of polyer coposites based on reduction of coposite stiffness as the nuber of fatigue cycles increased. Mayes and Hansen [10] proposed a uti-continuu theory (MCT) in which phases averaging of icro-level stresses is applied to each constituent. This icroechanical approach effectively includes changes in constituent level properties. However, since they used volue averaged icro stresses, it is difficult to distinguish failure location either in fiber or atrix or interface and, also, incorporating daage degradation in fatigue analysis. Due to the large variety of lainates resulting fro nuerous aterials, lay-ups and stacking sequences, and loading conditions, it is uneconoic to deterine fatigue life curves for any degree of generality by experients only. Most of fatigue life assessent ethods used to estiate the experiental results was epirically approxiated by phenoenological theories which cannot prove its absolute validity and universal generality. In this paper, a general ethodology based on icroechanics of failure (MMF) approach is presented for fatigue life prediction of coposite lainates. The ethodology is based on fatigue life of constituents, i.e. the fiber, atrix and interface. A wide range of experiental fatigue data of coposite lainates are used to validate the proposed ethodology. The predictions based on the MMF based fatigue odel agree very well with the experiental results. 2 Theory and Methodology 2.1 Microechanics of Failure (MMF) Approach The coposite structures are ade fro coposite lainates. The Fig. 1 shows the Microechanical approach to evaluate fatigue life of coposite structure. This approach is divided into two parts, naely Macro Stress Analysis and Micro Fatigue Analysis. In Macro Stress Analysis, acroscopic stresses are calculated on the coposite lainates under varying external echanical and theral loads using finite eleent ethod (FEM). In addition, onaxis acro ply stresses are calculated using Classical Lainate Theory (CLT) or FEM. In Micro Fatigue Analysis, icro odel is eployed to calculate stresses in fiber, atrix, and interface. These six coponents of stresses, varying with, depend on icro odel. Fro these stress coponents, effective stress is calculated which, also, is a function of. The Modified Goodan diagra is used to take care of ean stress effects. For particular ean and aplitude of effective stress cycles, daage index is calculated. Finally, Linear Daage Accuulation rule, i.e., Miner's Rule is used to give fatigue daage for all varying stresses with different eans and aplitudes. 2.2 Macro and Micro Stresses Coposite lainates are subjected to vary ing load. These causes in-plane loads and in-plane oents, expressed also as function of, in laina tes. Then using FEM or CLT, on-axis acro stresses are calculated on each ply. Micro stresses in fiber, atrix, and interface are calculated fro on-axis ply acro stresses using Micro-echanics. For this, diff erent icro unit cell odels are available. Unidirecti onal (UD) coposite ply icro odel depends on fi ber arrangeent. It consists of square array (SQR) or hexagonal array (HEX). These unit cell odels can siulate the behavior of entire UD [11, 12]. There is another choice for icro odel based on Multi-Con tinuu Theory (MCT) that defines stress and strain s iply as average over unit cell odel [13]. Micro str esses at any arbitrary point within fiber and atrix c an be obtained using these odels which vary over f M ij ( f, i,) iber and atrix., stress aplification factor ( SAF) gives relation between acro-icro stresses. ( f, i,) A j Loads & Teperatures, stress aplification factor for teperature in Macro Stress Analysis Coposite Lainate structures F T FEM Micro Fatigue Analysis Micro odel Micro stresses Matrix τ Interface n Fiber f i eff, a eff N M Multi-axial Rando Fatigue loading ia, i, eff, CLT S-N curve of each constituent Ply Predict life ni D N Fig. 1 MMF based fatigue life prediction procedure for coposite lainates S N i

creent. A direct finite eleent analysis was perfor ed to deterine stress aplification factors. 2.3 Fatigue Life Prediction Models Three different odels were eployed for each constituent. Figure 2 shows all these odels. For Fiber, Maxiu Stress Model is used. Critical Plane Model is incorporated for fiber/atrix interface. For atrix, Equivalent Stress Model is used. Originally, this odel is for isotropic aterial and atrix in coposites has also isotropic characteristics. This odel is also take care of ultiaxial fatigue. This forulation depends on isotropic atrix tensile and copressive strength characteristics. Various ultiaxial fatigue life prediction odels have been proposed in the past decades. But, Equivalent Stress Model sees to perfor better than the von Misses criteria and others [14]. Therefore, in this paper, Equivalent Stress Model is adopted. Figure 5 shows scheatically Equivalent Stress Model. The six coponents of the varying stress is converted into, aplitude eq a, and ean eq values of equivalent stress as expressed in Equation (1). Here, β is the ratio of the uniaxial copressive yield stress (C) to the uniaxial tensile yield stress (T), i.e., ( β C/ T ). 2 2 2 1, a I1, a VM, a I a 2 2 2 1, I1, VM, I β 1 + β 1 + 4β 2β β 1 + β 1 + 4β 2β (1) Although, fiber is anisotropic aterial and fatigue behavior is very uch dependent on direction. But in analysis, only axiu stress in fiber direction is considered. Equivalent stress odel for the atrix ( ) 2 ( ) 2 ( ) 2 β 1 I1 ± ( β 1) I1 + 4β v eq 2β Matrix i i τ n τ t Interface Fiber Maxiu stress odel for fiber z f n xx ( f ) ( f ) eq xx y x Critical plane odel f xx for interface ( i) (, τ) 2 + ( τ) 2 eq sign n n k Fig. 2. MMF based fatigue life prediction odels For fiber/atrix interface, Critical Plane Model is used. The interface failure is governed by noral and shear stress coponents. Figure 6 shows deterination of equivalent stress at interface. Fro this, aplitude and ean stress as a function of is calculated. Modified Goodan equation is used to include ean stress effect. This equation includes aplitude, ean, tensile and copressive stress of the aterial, as expressed in Equation (2). eff a TC T + C T C 2 2 (2) Fatigue life prediction needs to odel daage accuulation in the general case of external variable aplitude loading. The coon approach for such a odel is a cycle-by-cycle suation of a daage paraeter, D, where fatigue failure is defined as a critical value of the daage su. A linear fatigue daage accuulation rule proposed by Palgren and Miner is given by the relation. The cuulative daage factor is equal to or greater than 1 is considered as fatigue failure. This relation is ost popular because of its siplicity. Daage index is calculated for each constituent, i.e., fiber, atrix and interface, based on their respective fatigue failure criterion. The daage will be the one that has axiu value. Generally, atrix fails first. Then, using progressive failure to find final fatigue failure of ply, and hence lainates. Thus, icroechanics approach used to predict fatigue failure of coposite lainates fro constituent failure. Also, failure ode can easily be distinguish, either atrix or fiber or interface failure. 3 Experients and Results The resin syste used in this study is Hexion MGS RIM 135 (L135i) epoxy and Hexion MGS RI MH 134 hardener with the ixing ratio of 10:03. Re sin Speciens were fabricated by curing resin for 18 hours at 60 C. For epoxy tensile and copressive c haracterization, ASTM D 638 and ASTM D 695, res pectively, guidelines were followed. Three different Woven Coposite Lainates of E-glass with the sa e epoxy as above were used. The E-glass/Epoxy la inates were UDT [90 ], BX [±45 ]s and TX [0 2/± 45 ]s. Siilarly, lainates tensile and fatigue proper 3

ties were characterized by ASTM D 3039 and AST M D 3479, respectively. In order to reduce uncertain ty in test results, all tests (tensile and fatigue) were c onducted on the sae test achine. The static speci ens were loaded to failure with a speed of 1 / in. All fatigue tests were perfored at stress ratio of 0.1. The load levels for fatigue tests were fro 50-8 0% of static strength. The results of static tests are shown in Table 1. observed is atrix, which is exactly the real behavior of this lainate. In case of TX, the initial fatigue failure is [±45 ] which is atrix doinant. The final fatigue failure is [0 ], i.e., fiber breakage. The test results of TX also atch well with the predictions. This shows that the icroechanics of failure approach predict not only atrix doinant lainate failure but also catches well fiber doinant lainate behavior. Table 1 Material properties of epoxy and lainates; Mean value (Standard Deviation) Young s odulus (GPa) Tensile strength (MPa) Copressive strength (MPa) Epoxy 3.35(0.41) 67.7(1.1) 73.8(1.2) UDT 13.07(0.26) 35.1(2.8) - BX 22.3(5.12) 111.6(5.2) - TX 26.55(0.82) 464.2(39.6) - The suary of fatigue test results is given in Table 2. Table 2 Suary of fatigue test results Maxiu stress (MPa) Nuber of cycles to failure Epoxy 54.6 1008, 1476, 1237 47.8 8713, 3981, 5012 41.0 39811, 50119, 25119 UDT 28.1 32232, 45516, 39406 24.6 98597, 63433, 46923 21.1 225647, 229270, 225957 BX 78.1 3138, 3227, 2364 67.0 17702, 20398, 24428 55.8 262711, 292423, 315449 TX 325.0 2475, 1389, 1487 278.5 5595, 5152, 6027 232.1 13361, 18918, 14619 4 Verification of Life Prediction Methodology Fig. 3 shows test results of UDT, BX, and TX along with the predictions fro icroechanics of failure. This shows that predictions ade by HEX and SQR unit cell odels are in good agreeent with test results. UDT [90 ] prediction is based on atrix failure ode. Also, in BX [±45 ]s, the failure ode x,ax (MPa) x,ax (MPa) x,ax (MPa) UDT[90 ] BX[±45 ] s TX[0 2 /±45 ] s SQR(FEM) HEX(FEM) MCT Volue Average 5 Structural Applications: Wind Turbine Blade Lainates A case study was carried out to highlight iplication of MMF based fatigue life prediction ethodology for a realistic application of coposite wind turbine blade structure. Wind turbine blade can be analyzed as typical bea-like structure as described by stateof-the-art design codes [15, 16]. The reason to ake this assuption about the blade as bea-like structure is that blade behaves like a bea in whole. Also, the equivalent bea can produce results with reasonable accuracy and with an ease which design engineers prefer. The coputation is also greatly reduced coparing to the 3D shell- Multi- Continuu Theory Fig. 3. Fatigue life prediction of the UDT, BX and TX

constructed FEM odel. The investigated blade has shell and spar/web type structure. There exist flanges and stiffeners as well. Shell and spars are assued to carry only shear stresses, and flanges and stiffeners are assued to carry only axial stresses. A 35 GRP wind turbine rotor blade, for which detailed finite-eleent odels, aterial properties and design load case (power production at rated wind speed) definitions were available [17, 18], was analyzed for this case study. The investigated blade consists of different types of E-glass/Epoxy coposites: BX [±45 ]s, and TX [0 2/±45 ]s. The TX is used in the shell structure along with PVC core. BX and PVC core is used in shear webs. The reason of using PVC core is to avoid local buckling. Fro FEM analysis, it is found that the in-plane shear load N6 is varying fro 0.5% to 65% of inplane noral load N1at different locations of wind turbine blade like on outer skin and shear webs. The shear stress is of coparable agnitude to the axial stress in areas such as the shear webs and leading/trailing edges of the rotor blade, as shown in Figure 12. An exaple is given in Fig. 4 where the resulting stresses in the transition section of a 35 wind turbine blade under typical loading during power production are presented [18]. but it has an effect on the strength and life of the coposite structures. The life prediction ethodology as described earlier is used in this section to show the effect of in-plane shear stress resultant in defining service fatigue life of wind turbine rotor blade lainates. For the purpose of coparison, stress ratio R is kept constant which is -1. Also, with R -1, there is no ean stress effect that will ake the conclusion straightforward. Also, for ease of calculations, sinusoidal cycling is considered. Assuing that the stacking sequence of ultilayer eleent is sae as considered in this study, i.e., TX [0 2/±45 ]s. The MMF based life prediction with and without contribution of in-plane shear stress coponent yields ipressive results in reducing fatigue life. The results are presented in Fig. 5. In this layup considered, nuber of cycles is drastically reduced when in-plane shear stress resultant is considered. This shows that life is over estiated when only axial stress coponent N1 is taken in the life analysis. Interesting to note that for these calculations, as shown in Fig. 5, shear stress coponent N6 has agnitude say about 60% of the axial (longitudinal) noral stress coponent N1 (this value is at shear web) but life is over estiated by a factor of 19 at soe load level like 250 MPa. Stress (MPa) 100 80 60 40 20 0-20 0 2 4 6 8 10 12 14 16 18 20 22 24 26-40 -60-80 Sig_x Sig_xy xy -100 x ax (MPa) 350 300 250 200 150 100 R -1 N6 0% N1 N6 30% N1 N6 50% N1 N6 60% N1 Eleent # 50 N 6 N 1 Fig. 4. Typical stress state at the transition section for a 35 blade As these eleents of blade are placed in the confined region, edge effect will not occur and, therefore, Classical Lainate Theory (CLT) is appropriate to calculate on-axis acro ply stresses. The fatigue life calculations by the state-of-the-art design codes [15, 16] are liited by the considering only in-plane noral stress resultant coponent in the blade axis direction. Although, shear stress levels in thin walled structures are often negligibly sall, Lainate [0 2 /+45] s 0 1 1.5 2 2.5 3 3.5 4 4.5 5 Nuber of Cycles to Failure, Log N f Fig. 5. Fatigue Life Curves with and without Shear Coponent 5

6 Conclusion In this study, a new ethodology for fatigue life prediction of coposite lainates based on Microechanics of Failure is presented. This ethodology is based upon behavior of the constituents, i.e., fiber, atrix, and interface. The odel deterines the fatigue failure of coposites by considering failure of constituents in Microechanical analysis. This unified fatigue prediction odel has been successfully applied to predict fatigue lives of different lainates under cyclic tension considering various cobinations of fiber angles. For this, various test perfored on three different lainates, UDT, BX, and TX. The current approach predicts very well the test data. In addition, the ain data needed for fatigue analysis of coposite lainates is aterial properties of atrix, fiber and interface. Once such constituents properties is established, then by using Microechanics of Failure odel the nuber of experients to characterize the aterial properties of a coposite lainates of any layup and under any stress ratio can be iniized. Therefore, the Microechanics of Failure odel is potentially a valuable tool for fatigue design. Finally, a case study of fatigue life prediction of coposite wind turbine rotor blade is considered to deonstrate application of MMF based life prediction approach to the real structural application. A paraetric study of life prediction with and without considering in-plane shear stress resultant was perfored. Results indicate that the in-plane shear stress has an effect on life and it reduces life drastically. It was concluded that the life is reduced by 19 s with respect to situation where only the in-plane axial noral stress coponent was used in calculations. References [1] Caprino, G. and G. Giorleo, Fatigue life of glass fabric/epoxy coposites. Coposites Part A: Applied Science and Manufacturing, 1999. 30(3): p. 299-304. [2] Ellyin, F. and H. El-Kadi, A fatigue failure criterion for fiber reinforced coposite lainae. Coposite Structures, 1990. 15(1): p. 61-74. [3] Hashin, Z. and A. Rote, A fatigue failure criterion for fiber reinforced aterials. Journal of Coposite Materials, 1973. 7(4): p. 448. [4] Kassapoglou, C., Fatigue life prediction of coposite structures under constant aplitude loading. Journal of Coposite Materials, 2007. 41(22): p. 2737. [5] Sihn, S., MAE: An Integrated Design Tool for Failure and Life Prediction of Coposites. Journal of Coposite Materials, 2008. 42(18): p. 1967. [6] Shokrieh, M. and F. Taheri-Behrooz, A unified fatigue life odel based on energy ethod. Coposite Structures, 2006. 75(1-4): p. 444-450. [7] Varvani-Farahani, A., H. Haftchenari, and M. Panbechi, An energy-based fatigue daage paraeter for off-axis unidirectional FRP coposites. Coposite Structures, 2007. 79(3): p. 381-389. [8] Highsith, A. and K. Reifsnider, Stiffness reduction echaniss in coposite lainates. Daage in coposite aterials, 1982. 775: p. 103 117. [9] Philippidis, T. and A. Vassilopoulos, Fatigue design allowables for GRP lainates based on stiffness degradation easureents. Coposites Science and Technology, 2000. 60(15): p. 2819-2828. [10] Mayes, J.S.a.H., A. C., A Coparison of Multicontinuu Theory based failure siulation with experiental results. Coposites Science & Technology, 2004. 64(3-4): p. 517-527. [11] Huang, Y., K. Jin, and S. Ha, Effects of Fiber Arrangeent on Mechanical Behavior of Unidirectional Coposites. Journal of Coposite Materials, 2008. 42(18): p. 1851. [12] Jin, K., Distribution of Micro Stresses and Interfacial Tractions in Unidirectional Coposites. Journal of Coposite Materials, 2008. 42(18): p. 1825. [13] Garnich, M. and A. Hansen, A ulticontinuu theory for theral-elastic finite eleent analysis of coposite aterials. Journal of Coposite Materials, 1997. 31(1): p. 71. [14] Tao, G. and Z. Xia, Biaxial fatigue behavior of an epoxy polyer with ean stress effect. International Journal of Fatigue, 2009. 31(4): p. 678-685. [15] DRAFT, IEC 61400-1: Wind turbine generator systes Part 1: Safety Requireents. 1998. 2. [16] DRAFT, GERMANISCHER LlOYD: Rules and regulations, IV-Non-arine technology, Part 1-Wind Energy. 1993. [17] Harris, B., Fatigue in coposites: science and technology of the fatigue response of fibre-reinforced plastics. 2003: Woodhead Publishing. [18] Wedel-Hei, J., Reliable Optial Use of Materials for Wind Turbine Rotor Blades. OPTIMAT BLADES, 2006.