《复合材料 Composites》课程教学资源（学习资料）第二章增强体_glass fiber-3 Flexural and tensile moduli of unidirectional hybrid epoxy composites reinforced by S-2 glass and T700S carbon fibres.pdf_大学文库

Materials and Design 54(2014)893-899 Contents lists available at ScienceDirect Materials and design ELSEVIER journalhomepagewww.elsevier.com/locate/matdes Flexural and tensile moduli of unidirectional hybrid epoxy composites () cosMark reinforced by s-2 glass and T700S carbon fibres Chensong Dong, lan J Davies Department of Mechanical Engineering, Curtin University, GPO Box U1987, Perth, WA 6845, Australia A INFO ABSTRACT A study on the flexural and tensile moduli of S-2 glass and T700S carbon fibre reinforced hybrid epoxy Received 18 April 2013 nent analysis(FEA)ar Accepted 24 August 2013 Lamination Theory(CLt) were employed to model the flexural behaviour of hybrid composites, which line 30 August 201 was obtained from the three point bend test in accordance with ASTM: D790-10 at various span-to-depth ratios. The flexural moduli were obtained from the load-dis rves. Th against the experimental results from a previous study. with the aid of the developed models, the effects of fibre volume fractions, hybrid ratio and span-to-depth ratio were studied. The results show that flex ral modulus increases when the span-to-depth ratio is increased from 16 to 32 and becomes stable as ne span-to-depth ratio further increases. Since the modulus of glass fibres is much lower than that of exural modulus arbon fibres, both flexural and tensile moduli decrease with increasing hybrid ratio From the full car Tensile modulus bon/epoxy laminate, when a carbon/epoxy lamina close to the outermost surface of the laminate is eplaced by a glass/epoxy lamina, the flexural modulus decreases rapidly. This is due to the maximum ensile and compressive stresses occur at the two faces of the laminate in bending, and the stresses round the mid-plane are close to zero Tensile modulus decreases with increasing hybrid ratio Under nsion, the stress distribution is determined by the relative difference in the tensile moduli of the car- bon/epoxy and glass/epoxy laminas. If the difference is small, tensile modulus versus the hybrid ratio resembles a linear relationship and no significant hybrid effects exist; if rence is large, a strong non-linear relationship is present and large hybrid effects exist. Simple hemat tical formulas are pre- sented for calculation of the flexural and tensile moduli of hybrid composi the moduli of the car- bon/epoxy and glass/epoxy composites, and the hybrid ratio. o 2013 Elsevier Ltd. All rights reserved. 1 Introduction High elongation fibres enhance the strain levels required to propagate cracks through the composites and hence behave like Many types of fibres, e. g. glass, carbon, have been used to make crack arrestors on a micromechanical level [4]. fibre reinforced polymer composites. Each fibre type has its advan- According to the layup hybrid composites can be categorized tages and disadvantages. If two or more different types of fibres are into intimately mixed, intra-ply, inter-ply and sandwich types 5]. sed to reinforce a polymer, it is possible to obtain a composite A convenient way to estimate the stiffness or strength of a hy- with balanced properties. Such composite is called hybrid brid composite is using the rule of i es(roM)approach from composite. the individual properties and the volume concentration of its con- In a fibre reinforced composite, fibres are the main load carrying stituents. However, it has been found that the rom predictions component. In general, carbon fibres have high strength and stiff- fer to the actual properties. a positive or negative hybrid effect is ness while glass fibres have moderate strength and low stiffness defined as a positive or negative deviation of a certain mechanical [1, 2]. In other words, carbon fibres are low elongation fibres while property from the roM behaviour, respectively [6. glass fibres are high elongation fibres. Thus, it is possible to incor The mechanical properties of glass and carbon fibre reinforced porate glass fibres into carbon fibres to improve the failure strain hybrid epoxy composites have been studied extensively [4,5.7 to modify the failure strain 3. 14. Most studies were focused on the strength,9-14. Fu et al [10 showed that no hybrid effects for the tensile modulus, while a positive hybrid effect for the flexural modulus. Sudarisman and Davies 11 showed no significant effects of hybridisation to the Corresponding author. Tel. +61(8)92669204: fax: +61(8)92662681 flexural modulus of unidirectional glass and carbon reinforced hy- brid epoxy composites. Fu et al. [15 studied the elastic modulus of 069/S- see front matter o 2013 Elsevier Ltd. All rights reserved Lx. doiorg/10. 1016/j mates. 2013.08.086

Flexural and tensile moduli of unidirectional hybrid epoxy composites reinforced by S-2 glass and T700S carbon fibres Chensong Dong ⇑ , Ian J. Davies Department of Mechanical Engineering, Curtin University, GPO Box U1987, Perth, WA 6845, Australia article info Article history: Received 18 April 2013 Accepted 24 August 2013 Available online 30 August 2013 Keywords: Polymer–matrix composites Carbon fibre Glass fibre Hybrid Flexural modulus Tensile modulus abstract A study on the flexural and tensile moduli of S-2 glass and T700S carbon fibre reinforced hybrid epoxy composites in intra-ply configurations is presented in this paper. Finite element analysis (FEA) and Classic Lamination Theory (CLT) were employed to model the flexural behaviour of hybrid composites, which was obtained from the three point bend test in accordance with ASTM: D790-10 at various span-to-depth ratios. The flexural moduli were obtained from the load–displacement curves. The models were validated against the experimental results from a previous study. With the aid of the developed models, the effects of fibre volume fractions, hybrid ratio and span-to-depth ratio were studied. The results show that flexural modulus increases when the span-to-depth ratio is increased from 16 to 32 and becomes stable as the span-to-depth ratio further increases. Since the modulus of glass fibres is much lower than that of carbon fibres, both flexural and tensile moduli decrease with increasing hybrid ratio. From the full carbon/epoxy laminate, when a carbon/epoxy lamina close to the outermost surface of the laminate is replaced by a glass/epoxy lamina, the flexural modulus decreases rapidly. This is due to the maximum tensile and compressive stresses occur at the two faces of the laminate in bending, and the stresses around the mid-plane are close to zero. Tensile modulus decreases with increasing hybrid ratio. Under tension, the stress distribution is determined by the relative difference in the tensile moduli of the carbon/epoxy and glass/epoxy laminas. If the difference is small, tensile modulus versus the hybrid ratio resembles a linear relationship and no significant hybrid effects exist; if the difference is large, a strong non-linear relationship is present and large hybrid effects exist. Simple mathematical formulas are presented for calculation of the flexural and tensile moduli of hybrid composites from the moduli of the carbon/epoxy and glass/epoxy composites, and the hybrid ratio. 2013 Elsevier Ltd. All rights reserved. 1. Introduction Many types of fibres, e.g. glass, carbon, have been used to make fibre reinforced polymer composites. Each fibre type has its advantages and disadvantages. If two or more different types of fibres are used to reinforce a polymer, it is possible to obtain a composite with balanced properties. Such composite is called hybrid composite. In a fibre reinforced composite, fibres are the main load carrying component. In general, carbon fibres have high strength and stiffness while glass fibres have moderate strength and low stiffness [1,2]. In other words, carbon fibres are low elongation fibres while glass fibres are high elongation fibres. Thus, it is possible to incorporate glass fibres into carbon fibres to improve the failure strain to modify the failure strain [3]. High elongation fibres enhance the strain levels required to propagate cracks through the composites and hence behave like crack arrestors on a micromechanical level [4]. According to the layup, hybrid composites can be categorized into intimately mixed, intra-ply, inter-ply and sandwich types [5]. A convenient way to estimate the stiffness or strength of a hybrid composite is using the rule of mixtures (RoM) approach from the individual properties and the volume concentration of its constituents. However, it has been found that the RoM predictions differ to the actual properties. A positive or negative hybrid effect is defined as a positive or negative deviation of a certain mechanical property from the RoM behaviour, respectively [6]. The mechanical properties of glass and carbon fibre reinforced hybrid epoxy composites have been studied extensively [4,5,7– 14]. Most studies were focused on the strength [7,9–14]. Fu et al. [10] showed that no hybrid effects for the tensile modulus, while a positive hybrid effect for the flexural modulus. Sudarisman and Davies [11] showed no significant effects of hybridisation to the flexural modulus of unidirectional glass and carbon reinforced hybrid epoxy composites. Fu et al. [15] studied the elastic modulus of 0261-3069/$ - see front matter 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.08.086 ⇑ Corresponding author. Tel.: +61 (8) 92669204; fax: +61 (8) 92662681. E-mail address: c.dong@curtin.edu.au (C. Dong). Materials and Design 54 (2014) 893–899 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes

C Dong, L Davies/Materials and Design 54 (2014)893-899 Nomenclature extensional stiffness matrix for the laminate lope of the tangent to the initial straight-line portion of upling stiffness matrix for the laminate stiffness matrix for the laminat width of the specimen(mI lulus of the full carbon/epoxy composite(GPa) odulus of the full glass/epoxy composite(gPa) flexural modulus of hybrid composites(GPa) mMNnsv the load-deflection curve(N/ ml hybrid ratio span of the specimen(distance between to supporting pins)(mm) Efc modulus of the carbon fibres(GPa) fibre volume fraction of the carbon/epoxy laminas modulus of the glass fibres(GPa) fibre volume fraction of the glass/epoxy laminas modulus of the matrix(GPa) u,t,w displacements(mm) Er tensile modulus of hybrid col x, y, z depth of the specimen(total thickness of the laminate) zo membrane strains(strains of the mid-plane h e hickness of the carbon/epoxy laminas(mm) hickness of the glass/epoxy laminas(mm hybrid particle/ short-fiber/polymer composites using the rule of Based on the constituent properties, the lamina properties hybrid mixtures(RoHM)equation and the laminate analogy ap- including the longitudinal modulus Ell, the transverse moduli e roach(LAA), and found that the modulus of hybrid particle/ and E33, and the shear moduli G12, G13 and G3, are derived by Ha short-fiber/polymer composites showed a positive hybrid effect. shins model 16. Thus. it is shown from the literature that various results for the The diameter of the loading nose is 10 mm. In FEA, the load tensile and flexural moduli have been presented. defined by applying 1 MPa along 1 mm at the mid-span(0.5 mm In this study, the flexural and tensile moduli of unidirectional s- when symmetric boundary conditions are applied). with this load 2 glass and T700S carbon fibre reinforced epoxy hybrid composites definition, singularity is eliminated. The deflections from the FEA ere studied using two methods: FEA and Classic Lamination The- for the [02G/03C configuration are shown in Fig. 2. It is seen that ory(CLT). The hybrid composites consisted of two sections: glass/ the maximum deflection under this 1 MPa load is 0. 134 mm. Using epoxy and carbon/epoxy and three fibre volume fractions, 30%, 50% the deflection dy and s/h ratio, the flexural modulus can b and 70%, were chosen for each section. Nine stacking configura- calculated. tions of various hybrid ratios were studied For flexural modulus, The developed FEA approach was validated against the experi- four span-to-depth ratios, 16, 32, 48 and 64, were chosen mental results Test specimens were manufactured in house utiliz- ing the hand lay-up process as employed by Sudarisman and 2. Methodology Davies 11]. Testing was conducted in a three point bend configu- ration in accordance to procedure A of ASTM: D790-10, using an 2.1. Finite element analysis of 32, as shown in Fig 3. The average loading rate for this analysis The hybrid composites being investigated in this study con- was in the order of 3 mm/ min sisted of two types of fibres, S-2 glass and T700S carbon. Their se- The flexural moduli from the experiments and FEa are shown in lected properties are shown in Table 1 ig. 4. It is seen in general, good agreement is found. The slight low- In this study, flexural properties were obtained from three point er experimental values are most likely due to process-related fibre bend test in accordance to procedure A of ASTM: D790-10 at a cer- misalignment. Since fibres are strongest in the longitudinal direc tain span-to-depth ratio. For a test specimen, the flexural modulus ion, slight misalignment will reduce the stiffness of composites. (Er) is given by 2. 2. Classic Lamination Theory(CLT) As shown in Fig. 5, the geometric mid-plane of the laminate contains the xy axes, and the z-axis defines the thickness direction. S/h in eq. (1)is called the span-to-depth ratio, which is the ratio of According to the Classical Laminate Theory(CLT)[17. the the distance between two supporting pins and the thickness of the strains in a laminate can be written in the form In this study, the flexural behaviour of hybrid composites was &=8+ZK studied using commercial FEA software package ANSYS. Because the loading nose is across the width of the test specimens, the cen- where tre load is uniformly distributed and unidirectional. Thus, the cross-section of each specimen was modelled by assuming plane strain condition. The FEA model for the [02G/03C configuratio is shown in Fig. 1, where the top and bottom layers are S-2 glass/ 80 avo 1 awo a2 epoxy and T700S carbon/epoxy, respectively. Only half of the lam- inate is modelled by applying symmetry boundary conditions, and the right end is simply supported by constraining the y-displace duo avo dwo awo ment of one node. For this plane strain problem, this will not cause singularity. Eight-node PLAnE183 elements are used for goo ccording to the clt, the laminate consecutive equations are onvergence ressed as

hybrid particle/short-fiber/polymer composites using the rule of hybrid mixtures (RoHM) equation and the laminate analogy approach (LAA), and found that the modulus of hybrid particle/ short-fiber/polymer composites showed a positive hybrid effect. Thus, it is shown from the literature that various results for the tensile and flexural moduli have been presented. In this study, the flexural and tensile moduli of unidirectional S- 2 glass and T700S carbon fibre reinforced epoxy hybrid composites were studied using two methods: FEA and Classic Lamination Theory (CLT). The hybrid composites consisted of two sections: glass/ epoxy and carbon/epoxy and three fibre volume fractions, 30%, 50% and 70%, were chosen for each section. Nine stacking configurations of various hybrid ratios were studied. For flexural modulus, four span-to-depth ratios, 16, 32, 48 and 64, were chosen. 2. Methodology 2.1. Finite element analysis The hybrid composites being investigated in this study consisted of two types of fibres, S-2 glass and T700S carbon. Their selected properties are shown in Table 1. In this study, flexural properties were obtained from three point bend test in accordance to procedure A of ASTM: D790-10 at a certain span-to-depth ratio. For a test specimen, the flexural modulus (EF) is given by: EF ¼ mS3 4bh3 ð1Þ S/h in Eq. (1) is called the span-to-depth ratio, which is the ratio of the distance between two supporting pins and the thickness of the specimen. In this study, the flexural behaviour of hybrid composites was studied using commercial FEA software package ANSYS. Because the loading nose is across the width of the test specimens, the centre load is uniformly distributed and unidirectional. Thus, the cross-section of each specimen was modelled by assuming plane strain condition. The FEA model for the [02G/03C] configuration is shown in Fig. 1, where the top and bottom layers are S-2 glass/ epoxy and T700S carbon/epoxy, respectively. Only half of the laminate is modelled by applying symmetry boundary conditions, and the right end is simply supported by constraining the y-displacement of one node. For this plane strain problem, this will not cause singularity. Eight-node PLANE183 elements are used for good convergence. Based on the constituent properties, the lamina properties, including the longitudinal modulus E11, the transverse moduli E22 and E33, and the shear moduli G12, G13 and G23, are derived by Hashin’s model [16]. The diameter of the loading nose is 10 mm. In FEA, the load is defined by applying 1 MPa along 1 mm at the mid-span (0.5 mm when symmetric boundary conditions are applied). With this load definition, singularity is eliminated. The deflections from the FEA for the [02G/03C] configuration are shown in Fig. 2. It is seen that the maximum deflection under this 1 MPa load is 0.134 mm. Using the deflection dy and S/h ratio, the flexural modulus can be calculated. The developed FEA approach was validated against the experimental results. Test specimens were manufactured in house utilizing the hand lay-up process as employed by Sudarisman and Davies [11]. Testing was conducted in a three point bend configuration in accordance to procedure A of ASTM: D790-10, using an Instron 550R universal testing machine at a span-to-depth ratio of 32, as shown in Fig. 3. The average loading rate for this analysis was in the order of 3 mm/min. The flexural moduli from the experiments and FEA are shown in Fig. 4. It is seen in general, good agreement is found. The slight lower experimental values are most likely due to process-related fibre misalignment. Since fibres are strongest in the longitudinal direction, slight misalignment will reduce the stiffness of composites. 2.2. Classic Lamination Theory (CLT) As shown in Fig. 5, the geometric mid-plane of the laminate contains the xy axes, and the z-axis defines the thickness direction. According to the Classical Laminate Theory (CLT) [17], the strains in a laminate can be written in the form: e ¼ e0 þ zj ð2Þ where e0 ¼ @u0 @x þ 1 2 @w0 @x 2 @v0 @y þ 1 2 @w0 @y 2 @u0 @y þ @v0 @x þ @w0 @x @w0 @y 8 >>>>>>>>>>>>>>>>>: 9 >>>>>>>>>= >>>>>>>>>; ; j ¼ @2 w0 @x2 @2 w0 @y2 2 @2 w0 @x@y 8 >>>>>>>>>>>>>>>>>: 9 >>>>>>>>>= >>>>>>>>>; According to the CLT, the laminate consecutive equations are expressed as: Nomenclature A extensional stiffness matrix for the laminate B coupling stiffness matrix for the laminate D bending stiffness matrix for the laminate b width of the specimen (mm) Ecc modulus of the full carbon/epoxy composite (GPa) Ecg modulus of the full glass/epoxy composite (GPa) EF flexural modulus of hybrid composites (GPa) Efc modulus of the carbon fibres (GPa) Efg modulus of the glass fibres (GPa) Em modulus of the matrix (GPa) ET tensile modulus of hybrid composites (GPa) h depth of the specimen (total thickness of the laminate) (mm) hc thickness of the carbon/epoxy laminas (mm) hg thickness of the glass/epoxy laminas (mm) m slope of the tangent to the initial straight-line portion of the load–deflection curve (N/mm) M moments (Nm) N external forces (N) rh hybrid ratio S span of the specimen (distance between to supporting pins) (mm) Vc fibre volume fraction of the carbon/epoxy laminas Vg fibre volume fraction of the glass/epoxy laminas u, v, w displacements (mm) x, y, z coordinates (mm) e strains e 0 membrane strains (strains of the mid-plane) j flexural strains (curvatures) 894 C. Dong, I.J. Davies / Materials and Design 54 (2014) 893–899

C Dong I Davies/ Materials and Design 54(2014) 893-899 Constituent materials and selected properties. Tensile strength Tensile modulus S-2 glass unidirectional Unitex plain wave UT-S500 fibre mat (SP System, Newport, Isle of wight, UK) 4890 Toray T700S 12 K carbon fibre(Toray Industries Inc. Tokyo, Japan 230 Kinetix R240 high performance epoxy resin with H160 hardener at a ratio of 4: 1 by weight, as recommended by manufacturer 69.6 3.1 (ATL Composites Pty Ltd, Australia) Experiment FEA 叫 Fig. 1. FEA model for [O2c/Ocl configuration. 10 ,134293119371 -,10445 08952-,074607 ,044764 Fig. 2. Deflections from FEA Fig 4. Flexural moduli from experiments and FEA. B (3)D1 It is seen from Fig. 5 that Mo is not constant, which is zero at two For a test specimen under three point bending, the only non- ends and reaches the maximum,-FS4, at the mid-span. From Eq zero element of N and M is Mxx. Thus, Eq ( 3)becomes bend- D ing, the deflection at the mid-span is the resultant of the curvatures loped along the beam, i.e where The strain [Mx puted as: A6后6kxmx(1-3dx Eo=B,M K= D,M The flexural modulus can be calculated using Eq (1) where 2.3. Parametric study B1=-A B(D-BA B In this study, the effects of two variables, the fibre volu me irac tions of carbon/e nd glass/epoxy laminas, Vfc and Vig. were studied using Response Surface Methodology(RSM). For each var- iable. three levels were chosen as shown in table 2. in order to construct a 32 factorial design. A three-level factorial design was used to model possible curvature in the response function and to handle the case of nominal factors at 3 levels[18. For each fibre volume fraction combination, nine stacking con- ed. All the laminates were 2 mm thick and consist of 8 laminas of equal thickness, i.e. the thickness of each lamina is 0.25 mm. The stacking configurations are shown in Fig. 6. From the full carbon/epoxy laminate to the full glass/epoxy minate, the topmost lamina of the carbon/epoxy section is re- placed by a glass/epoxy lamina each time. or the purpose of characterising the degree of hybridisation the hybrid ratio is intre Th Fig 3. Flexural testing being conducted

N M ¼ A B B D e0 j ( ) ð3Þ For a test specimen under three point bending, the only nonzero element of N and M is Mxx. Thus, Eq. (3) becomes: 0 M ¼ A B B D e0 j ( ) ð4Þ where ½M ¼ ½ Mxx 0 0 T : The strains are computed as: e0 ¼ B1M ð5aÞ j ¼ D1M ð5bÞ where, B1 ¼ A1 BðD BA1 BÞ 1 D1 ¼ ðD BA1 BÞ 1 : It is seen from Fig. 5 that Mxx is not constant, which is zero at two ends and reaches the maximum, FS/4, at the mid-span. From Eq (5b), the resulting curvature, jxx, is proportional to the moment Mxx. Since jxx ¼ @2w0 @x2 , for a test specimen under three point bending, the deflection at the mid-span is the resultant of the curvatures developed along the beam, i.e. w0 ¼ R S 0 R S 0 jxx max 1 x S dx ¼ jxx maxS2 3 ð6Þ The flexural modulus can be calculated using Eq. (1). 2.3. Parametric study In this study, the effects of two variables, the fibre volume fractions of carbon/epoxy and glass/epoxy laminas, Vfc and Vfg, were studied using Response Surface Methodology (RSM). For each variable, three levels were chosen, as shown in Table 2, in order to construct a 32 factorial design. A three-level factorial design was used to model possible curvature in the response function and to handle the case of nominal factors at 3 levels [18]. For each fibre volume fraction combination, nine stacking con- figurations were studied. All the laminates were 2 mm thick and consist of 8 laminas of equal thickness, i.e. the thickness of each lamina is 0.25 mm. The stacking configurations are shown in Fig. 6. From the full carbon/epoxy laminate to the full glass/epoxy laminate, the topmost lamina of the carbon/epoxy section is replaced by a glass/epoxy lamina each time. For the purpose of characterising the degree of hybridisation, the hybrid ratio is introduced, which is defined as: rh ¼ 1 1 þ hfcVfc hfgVfg ð7Þ Table 1 Constituent materials and selected properties. Material Tensile strength (MPa) Tensile modulus (GPa) S-2 glass unidirectional Unitex plain wave UT-S500 fibre mat (SP System, Newport, Isle of Wight, UK) 4890 86.9 Toray T700S 12 K carbon fibre (Toray Industries Inc., Tokyo, Japan) 4900 230 Kinetix R240 high performance epoxy resin with H160 hardener at a ratio of 4:1 by weight, as recommended by manufacturer (ATL Composites Pty Ltd., Australia) 69.6 3.1 Fig. 1. FEA model for [02G/03C] configuration. Fig. 2. Deflections from FEA. Fig. 3. Flexural testing being conducted. Fig. 4. Flexural moduli from experiments and FEA. C. Dong, I.J. Davies / Materials and Design 54 (2014) 893–899 895

C Dong, L Davies/Materials and Design 54 (2014)893-899 Flexura At low hybrid ratios, the flexural modulus is lower than the ten- sile one with the largest difference occurring at [02G/06C]. As more glass epoxy laminas are introduced, flexural modulus tends to ex- ceed tensile modulus The results from this study show that both flexural and tensile moduli, which is greement with previously found 9-11. The occurrence of positive or negative hy- brid effects is dependent on the stacking configuration 3. 4. Regression models It is shown from a previous study [12 that the flexural modulus of glass and carbon fibre reinforced hybrid epoxy composites can be described by a regression model: E=Ecc-[crn+(1-2. 1c)rn+1.1cral(Ecc-Ec where c is given by c=1.981+0.5224 Eacll Fig. 16. Flexural modulus at S/h=64 and tensile modulus versus hybrid ratio for The tensile modulus of hybrid composites is then given by a similar functional relationship Et=Ecc -(Ecc-Ecg)g(rn) 180 ere g(rn)is a function of Ih to be determined and it satisfies g(rn)=0 when rh=0 and g(rn)=l when h=1. a power function was used to describe the relationship between g(rn)and of h 140 100 ch, The following model was fitted to the data being presented in Er=E-0.9(E/Ec)2rh 5(a/Egl(Ea -Ec (12) The flexural and tensile moduli of the s-2 glass and T700S ca 0.8 bon fibre reinforced hybrid epoxy composites were studied using Hybrid FEa and clt. the results show that flexural modulus increases Fig. 17. Flexural modulus at S/h=64 and tensile modulus hybrid ratio for when the span-to-depth ratio increases from 16 to 32 and becomes stable as the span-to-depth ratio further increases. Since the mod- ulus of glass fibres is much lower than that of carbon fibres, both flexural and tensile moduli decrease with increasing hybrid ratio. The results confirm the existence of hybrid effects. From the full the hybrid effect becomes positive. When the laminate approaches carbon/epoxy laminate, flexural modulus decreases rapidly when the full glass/epoxy, a rapid decrease occurs. In other words, when the carbon/epoxy laminas on the compressive side start to be a carbon/epoxy lamina close to the outermost surface of the replaced by glass/epoxy laminas and negative hybrid effects occur. laminate is replaced by a glass/epoxy lamina, flexural modulus As more glass/epoxy laminas are introduced, flexural modulu decreases rapidly. This is due to under bending, the maximu ecomes stable, and the hybrid effect becomes positive. When ensile and compressive stresses occur at the two faces of the the laminate approaches full glass/epoxy flexural modulus sees a laminate and the stresses around the mid-plane are close to zero. rapid decrease. This is due to the maximum tensile and The hybrid effect is dependent on the difference in the moduli of compressive stresses occur at the two faces of the laminate in the carbon/epoxy and glass epoxy laminas. If the difference is bending, and the stresses around the mid-plane are close to zero. small,e.g. Vfc=30% and Vig-70%, little hybrid effects exist. On Tensile modulus decreases with increasing hybrid ratio Under the contrary, when the difference is large, e.g. Vfc=70% an nsion, the stress distribution is determined by the difference in Vig=30%, strong non-linear relationships exist for the flexural the tensile moduli of the carbon/epoxy and glass/epoxy laminas. modulus versus hybrid ratio and large hybrid effects exist If the difference is small, tensile modulus versus hybrid ratio Tensile modulus decreases with increasing hybrid ratio Under resembles a linear relationship and no significant hybrid effects tension, the stress distribution is determined by the difference in exist; if the difference is large, a strong non-linear relationship is e tensile moduli of the carbon/epoxy and glass/epoxy laminas. present, and large hybrid effects exist Similar to flexural modulus, if the difference is small, e. g It is also noted at low hybrid ratios, flexural modulus is lower Vf=30% and Vig=70%, the tensile modulus versus hybrid ratio than tensile modulus with the largest difference occurring at resembles a linear relationship, and no significant hybrid effects 02c/06c. As more glass/epoxy laminas are introduced, flexural xist:if the difference is large, e.g. Vfe=70% and VEg-30%, a strong modulus tends to exceed tensile modulus non-linear relationship is present, and large hybrid effects exist. Simple mathematical formulas are presented to calculate the This is in contrast to the literature 10, 15 flexural and tensile moduli of the hybrid composites from the

the hybrid effect becomes positive. When the laminate approaches the full glass/epoxy, a rapid decrease occurs. In other words, when a carbon/epoxy lamina close to the outermost surface of the laminate is replaced by a glass/epoxy lamina, flexural modulus decreases rapidly. This is due to under bending, the maximum tensile and compressive stresses occur at the two faces of the laminate and the stresses around the mid-plane are close to zero. The hybrid effect is dependent on the difference in the moduli of the carbon/epoxy and glass/epoxy laminas. If the difference is small, e.g. Vfc = 30% and Vfg = 70%, little hybrid effects exist. On the contrary, when the difference is large, e.g. Vfc = 70% and Vfg = 30%, strong non-linear relationships exist for the flexural modulus versus hybrid ratio and large hybrid effects exist. Tensile modulus decreases with increasing hybrid ratio. Under tension, the stress distribution is determined by the difference in the tensile moduli of the carbon/epoxy and glass/epoxy laminas. Similar to flexural modulus, if the difference is small, e.g. Vfc = 30% and Vfg = 70%, the tensile modulus versus hybrid ratio resembles a linear relationship, and no significant hybrid effects exist; if the difference is large, e.g. Vfc = 70% and Vfg = 30%, a strong non-linear relationship is present, and large hybrid effects exist. This is in contrast to the literature [10,15]. At low hybrid ratios, the flexural modulus is lower than the tensile one with the largest difference occurring at [02G/06C]. As more glass/epoxy laminas are introduced, flexural modulus tends to exceed tensile modulus. The results from this study show that hybrid effects exist for both flexural and tensile moduli, which is in disagreement with previously found [9–11]. The occurrence of positive or negative hybrid effects is dependent on the stacking configuration. 3.4. Regression models It is shown from a previous study [12] that the flexural modulus of glass and carbon fibre reinforced hybrid epoxy composites can be described by a regression model: EF ¼ Ecc ½crh þ ð1 2:1cÞr2 h þ 1:1cr3 hðEcc Ecg Þ ð9Þ where c is given by c = 1.981 + 0.5224 Ecc/Ecg. The tensile modulus of hybrid composites is then given by a similar functional relationship. EL ¼ Ecc ðEcc Ecg Þ gðrhÞ ð10Þ where g(rh) is a function of rh to be determined and it satisfies g(rh) = 0 when rh = 0 and g(rh) = 1 when rh = 1. A power function was used to describe the relationship between g(rh) and of rh. gðrhÞ ¼ a0r a1 h ð11Þ The following model was fitted to the data being presented in this paper. ET ¼ Ecc 0:9ðEcc=Ecg Þ 0:27r 1:5ðEcc=Ecg Þ 0:5 h ðEcc Ecg Þ ð12Þ 4. Conclusions The flexural and tensile moduli of the S-2 glass and T700S carbon fibre reinforced hybrid epoxy composites were studied using FEA and CLT. The results show that flexural modulus increases when the span-to-depth ratio increases from 16 to 32 and becomes stable as the span-to-depth ratio further increases. Since the modulus of glass fibres is much lower than that of carbon fibres, both flexural and tensile moduli decrease with increasing hybrid ratio. The results confirm the existence of hybrid effects. From the full carbon/epoxy laminate, flexural modulus decreases rapidly when the carbon/epoxy laminas on the compressive side start to be replaced by glass/epoxy laminas and negative hybrid effects occur. As more glass/epoxy laminas are introduced, flexural modulus becomes stable, and the hybrid effect becomes positive. When the laminate approaches full glass/epoxy, flexural modulus sees a rapid decrease. This is due to the maximum tensile and compressive stresses occur at the two faces of the laminate in bending, and the stresses around the mid-plane are close to zero. Tensile modulus decreases with increasing hybrid ratio. Under tension, the stress distribution is determined by the difference in the tensile moduli of the carbon/epoxy and glass/epoxy laminas. If the difference is small, tensile modulus versus hybrid ratio resembles a linear relationship, and no significant hybrid effects exist; if the difference is large, a strong non-linear relationship is present, and large hybrid effects exist. It is also noted at low hybrid ratios, flexural modulus is lower than tensile modulus with the largest difference occurring at [02G/06C]. As more glass/epoxy laminas are introduced, flexural modulus tends to exceed tensile modulus. Simple mathematical formulas are presented to calculate the flexural and tensile moduli of the hybrid composites from the Fig. 16. Flexural modulus at S/h = 64 and tensile modulus versus hybrid ratio for Vfc = 70% and Vfg = 50%. Fig. 17. Flexural modulus at S/h = 64 and tensile modulus versus hybrid ratio for Vfc = 70% and Vfg = 70%. 898 C. Dong, I.J. Davies / Materials and Design 54 (2014) 893–899

moduli of the carbon/epoxy and glass/epoxy laminas and the hybrid ratio. References [1] Sudarisman, Davies IJ. Flexural failure of unidirectional hybrid fibre-reinforced polymer (FRP) composites containing different grades of glass fibre. Adv Mater Res 2008;41-42:357–62. [2] Sudarisman, Davies IJ. Influence of compressive pressure, vacuum pressure, and holding temperature applied during autoclave curing on the microstructure of unidirectional CFRP composites. Adv Mater Res 2008;41- 42:323–8. [3] Manders PW, Bader MG. The strength of hybrid glass/carbon fibre composites. J Mater Sci 1981;16:2233–45. [4] Zweben C. Tensile strength of hybrid composites. J Mater Sci 1977;12:1325–37. [5] Kretsis G. A review on the tensile, compressive, flexural and shear properties of hybrid fibre-reinforced plastics. Composites 1987;18:13–23. [6] Fischer S, Marom G. The flexural behaviour of aramid fibre hybrid composite materials. Compos Sci Technol 1987;28:291–314. [7] Kalnin IL. Evaluation of unidirectional glass-graphite fibre/epoxy resin composites. Composite materials: testing and design. Baltimore (MD USA): American Society for Testing and Materials; 1972. p. 551-63. [8] Bunsell AR, Harris B. Hybrid carbon and glass fibre composites. Composites 1974;5:157–64. [9] Marom G, Fischer S, Tuler FR, Wagner HD. Hybrid effects in composites: conditions for positive or negative effects versus rule-of-mixtures behaviour. J Mater Sci 1978;13:1419–26. [10] Fu SY, Lauke B, Mäder E, Yue CY, Hu X. Tensile properties of short-glass-fiberand short-carbon-fiber-reinforced polypropylene composites. Compos Part A: Appl Sci Manuf 2000;31:1117–25. [11] Sudarisman, Davies IJ. The effects of processing parameters on the flexural properties of unidirectional carbon fibre-reinforced polymer (CFRP) composites. Mater Sci Eng A 2008;498:498 65–8. [12] Dong C, Davies IJ. Optimal design for the flexural behaviour of glass and carbon fibre reinforced polymer hybrid composites. Mater Des 2012;37:450–7. [13] Dong C, Ranaweera-Jayawardena HA, Davies IJ. Flexural properties of hybrid composites reinforced by S-2 glass and T700S carbon fibres. Compos Part B: Eng 2012;43:573–81. [14] Pandya KS, Veerraju C, Naik NK. Hybrid composites made of carbon and glass woven fabrics under quasi-static loading. Mater Des 2011;32:4094–9. [15] Fu S-Y, Xu G, Mai Y-W. On the elastic modulus of hybrid particle/short-fiber/ polymer composites. Compos Part B Eng 2002;33:291–9. [16] Chou T-W. Microstructure Design Fiber Composites. Cambridge (UK): Cambridge University Press; 1992. [17] Mallick PK. Fiber-reinforced composites: materials, manufacturing, and design. 2nd ed. New York: Marcel Dekker; 1993. [18] Montgomery DC. Design and analysis of experiments. 5th ed. New York: John Wiley & Sons, Inc.; 2000. C. Dong, I.J. Davies / Materials and Design 54 (2014) 893–899 899

《复合材料 Composites》课程教学资源（学习资料）第二章 增强体_glass fiber-3 Flexural and tensile moduli of unidirectional hybrid epoxy composites reinforced by S-2 glass and T700S carbon fibres

《复合材料 Composites》课程教学资源（学习资料）第二章增强体_glass fiber-3 Flexural and tensile moduli of unidirectional hybrid epoxy composites reinforced by S-2 glass and T700S carbon fibres