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 ap￾proach (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 The￾ory (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 configura￾tions 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 con￾sisted of two types of fibres, S-2 glass and T700S carbon. Their se￾lected 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 cer￾tain 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 cen￾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] 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 lam￾inate is modelled by applying symmetry boundary conditions, and the right end is simply supported by constraining the y-displace￾ment 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 Ha￾shin’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 experi￾mental results. Test specimens were manufactured in house utiliz￾ing the hand lay-up process as employed by Sudarisman and Davies [11]. Testing was conducted in a three point bend configu￾ration 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 low￾er experimental values are most likely due to process-related fibre misalignment. Since fibres are strongest in the longitudinal direc￾tion, 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