MODELING OF MECHANICAL RESPONSE IN CFRP ANGLE-PLY LAMINATES

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1 HE 9 H INERNAIONAL ONFERENE ON OMPOIE MAERIAL Introduction It is known that the failure rocess in angle-ly laminate involves matrix cracking and delamination and that they exhibit nonlinear stress-strain relation. here may be a significant effect of the constituent blocked ly thickness on the mechanical behavior of angle-ly laminates. hese days, thin reregs whose thickness is, for examle micron, are develoed and commercially available. herefore, we can design wide variety of laminates with various constituent ly thicknesses. In this study, effects of constituent ly thickness on the nonlinear mechanical behavior and the damage behavior of FRP angle-ly laminates are investigated exerimentally. Based on the exerimental results, the mechanical resonse in FRP angle-ly laminates is modeled by using the finite strain viscolasticity model. Exeriment MODELING OF MEHANIAL REPONE IN FRP ANGLE-PL LAMINAE. Ogihara *, H.Nakatani Deartment of Mechanical Engineering, okyo University of cience, Noda, hiba, Jaan * orresonding author (ogihara@rs.noda.tus.ac.j) Keywords: FRP angle-ly laminates, nonlinear mechanical resonse, finite deformation, viscolasticity arbon/eoxy laminates with stacking sequences of [((+4) m /(-4) m ) n ] s (where (m, n)=(4, ), (, ) and (, 4)) (laminates with 6.mm-thick reregs (conventional rereg)) and [(±4) ] s, (a laminate with 48.mm-thick reregs (thin-ly rereg)) are used as secimens. It should be noted that the laminate thickness is almost the same (about.4mm), but the constituent (blocked) 4 or -4 ly thicknesses are quite different. his situation is shown in Fig. schematically. In the 6.mmthick rereg laminates (Fig.(a)-(c)), the constituent ly thickness ranges from.6mm to.mm regarding the blocked lies as a continuous constituent ly. In the 48.mm-thick rereg laminate (Fig.(d)), the constituent ly thickness is.mm. Monotonic tensile s at different strain rates, loading-unloading and stress-relaxation s are conducted. (a) t=.6mm (b) t=.3mm (c) t=.mm (d) t=.mm Figure. chematics of laminate configurations used in this study (t: thickness of constituent (blocked) ly). (a)[(+4) 4 /(-4) 4 ] s, (b)[((+4) /(- 4) ) ] s, (c) [((+4) /(-4)) 4 ] s and (d) [(±4) ] s 3 Results and discussion Figure shows the stress-stress curves obtained by the monotonic tensile. It was found that the laminate strength and the ultimate strain are higher for the laminates with thinner constituent lies. here is little effect of constituent ly thickness on mechanical resonse within small strain regime. It also seems that laminates with relatively thin constituent lies exhibit aarent nonlinear mechanical resonse. hey exhibit softeninghardening behavior, which may be due to the fiber angle rotation. herefore, we made an attemt to estimate the fiber angle and resulting current laminate oung s modulus. We estimated the current fiber angle by using the strain data and the following equation. () x tan where x and y are longitudinal and transverse strains, resectively. We estimated current laminate oung s modulus by using the classical lamination y

2 ly angle (degree) oung's modulus (GPa) ly angle (degree) oung's modulus (GPa) theory. Figure 3 shows the estimated ly angle and oung s modulus s of FRP (+4/-4) anglely laminates as a function of (a) longitudinal strain and (b) stress (strain rate=9.3 - ). We found that as the longitudinal strain increases the fiber angle decreases and the resulting oung s modulus increases extensively. o we confirm that we have to consider the effect of fiber angle rotation when modeling the mechanical behavior of these laminates. transverse strain constituent ly thickness.mm.mm.3mm longitudinal strain.6mm - - Figure. tress-strain curves of laminates with different constituent ly thicknesses. (b) mm.3mm.mm mm 3 Figure 3. Estimated ly angle and oung s modulus s of FRP (+4/-4) angle-ly laminates as a function of (a) longitudinal strain and (b) stress (strain rate=9.3 - ) Figure 4 shows the effect of strain rate on the stressstrain relation for the laminate with different constituent ly thicknesses. It can be seen that as the strain rate increases the stress increases. he stress relaxation behavior and loading-unloading curves are also shown. onsidering that we see both the strain rate effect and stress-relaxation behavior, we need a viscolasticity model to describe the material mechanical behavior mm 38.3mm mm.mm longitudinal transverse strain (/s) (/s) (/s) longitudinal strain tress relaxation Loading-unloading (a) (a).6mm

3 MODELING OF MEHANIAL REPONE IN FRP ANGLE-PL LAMINAE transverse strain longitudinal strain (/s) (/s) (/s) 3 transverse strain longitudinal strain (/s) (/s) (/s) tress relaxation Loading-unloading tress relaxation Loading-unloading (b).3mm transverse strain longitudinal strain (/s) (/s) (/s) (d).mm Figure 4. tress-strain curves of (+4/-4) angle-ly FRP laminates with different ly thicknesses at various strain rates. tress relaxation and loadingunloading curves are also shown. onstituent ly thicknesses are (a).6mm, (b).3mm, (c).mm and (d).mm. (c).mm tress relaxation Loading-unloading Figure shows the aearance of the fractured laminates, which indicates that extensive matrix cracks and delaminations occur in the laminates with thinner constituent lies. We also observe necking in the transverse direction and swelling henomena in the thickness direction. Figure 6 shows damage rogress in FRP angle-ly laminates (constituent ly thickness t=.mm, strain rate=9.3 - (/s)) observed by the edge relica technique. Based on this observation, we evaluated the matrix crack density as a function of loading. Figure 7 shows the crack density in FRP angle-ly laminates with various constituent ly thicknesses as a function of alied strain (strain rate=9.3 - (/s)). 3

4 crack density (/mm) (a) t=.6mm (b) t=.3mm.mm constituent ly thickness (c) t=.mm (d) t=.mm.mm.3mm Figure. Aearance of fractured secimens..mm.mm.mm.mm (a) strain=.% (b) strain=.% (c) strain=.8% (d) strain=3.% Figure 6. Damage rogress in FRP angle-ly laminates (constituent ly thickness t=.mm, strain rate=9.3 - (/s)). Edge relica observation..6mm Figure 7. rack density in FRP angle-ly laminates with various constituent ly thicknesses as a function of alied strain (strain rate=9.3 - (/s)). By using the data obtained by the loadingunloading, we can evaluate the modulus. We can estimate also the damage arameter. We can also evaluate the ermanent strain. In this study, we consider the effect of fiber angle rotation on the initial oung s modulus. We looked at two kinds of modulus, one is the aarent one where we used the initial oung s modulus throughout, and the other is the modified one where we used the current oung s modulus considering the fiber rotation. Figure 8 shows crack density and modulus ratio of (+4/-4) angle-ly FRP laminates with different ly thicknesses as a function of alied strain (the constituent ly thicknesses are (a).6mm, (b).3mm, (c).mm and (d).mm).when we look at the data from the laminates with relatively thin constituent lies, the aarent modulus increases which may be unrealistic. However, when we look at the modified modulus, it decreases, which imlies the significance of the consideration of the effect of fiber rotation. Figure 9 shows the ermanent strain in FRP angle-ly laminates with various constituent ly thicknesses as a function of (a) alied maximum strain and (b) alied maximum stress.

5 crack density (/mm) crack density (/mm) crack density (/mm) modulus ratio modulus ratio modulus ratio ermanent transverse strain longitudinal strain crack density (/mm) modulus ratio MODELING OF MEHANIAL REPONE IN FRP ANGLE-PL LAMINAE. aarent modulus.9.9. modified modulus.8.. (a).6mm (b).3mm aarent modulus modified modulus aarent modulus modified modulus (d).mm Figure 8. rack density and modulus ratio of (+4/- 4) angle-ly FRP laminates with different ly thicknesses as a function of alied strain. he constituent ly thicknesses are (a).6mm, (b).3mm, (c).mm and (d).mm. - constituent ly thickness.6mm.mm.3mm.mm aarent modulus modified modulus (a) - alied maximum.7.7 (c).mm

6 ermanent transverse strain longitudinal strain material lastic sin. - - constituent ly thickness.6mm.mm.3mm.mm Kontou and athis roosed an elastic-viscolastic constitutive relation for unidirectional olymeric fiber comosites as follows. (6) D s m m s m m n n (b) - alied maximum W s m m s (7) Figure 9. Permanent strain in FRP angle-ly laminates with various constituent ly thicknesses as a function of (a) alied maximum strain and (b) alied maximum stress. In this study, an attemt is made to aly the finite strain viscolasticity model of unidirectional comosites to multidirectional laminated comosites. We use Kontou and athis finite strain viscolasticity model for unidirectional olymeric fiber comosites []. In the theory, multilicative decomosition of deformation gradient is used. F F e F () where F e and F are elastic and lastic arts of deformation gradient tensor F. he velocity gradient tensor L is defined by the following equation who is divided into its symmetric art D, rate of deformation tensor, and antisymmetric art W, the material sin tensor. - (3) L FF D W he tensor D can be additively decomosed into its elastic and lastic arts as D e D D (4) and W can be decomosed as follows W ω W () where is the substructural sin and W is the where s, m and n denote unit vectors in fiber, inlane transverse and thickness directions and where r c Ar h c Ar h (8) A is a function of imosed strain rate r, h is the hardening modulus and c is a constant. hey emloyed hyoelasticity constitutive relation, : D e (9) where is the objective rate of stress and is the elasticity tensor which is assumed to be linear. In this study, the theory is alied to a multidirectional laminated comosite assuming that the rate of deformation tensor is uniform in the laminate and the stress resultants N xy and N yy is zero. he relation between x and x is obtained. Figure shows the reliminary results. he arameters used are also shown. If we do not consider the effect of fiber angle rotation the stress-strain curve exhibits no hardening behavior, but if we consider the fiber angle rotation, we see the softening-hardening behavior which is observed in the exeriment. Because the rediction does not consider the effect

7 MODELING OF MEHANIAL REPONE IN FRP ANGLE-PL LAMINAE of damages, the rediction goes to high stress level in the high strain regime. 4 3 h= (MPa), =.7, =., c= = (Fiber angle rotation considered) = (No fiber angle rotation) longitudinal 4 3 constituent ly thickness.mm.mm he associated forces are D D D G D E he damage develoment is assumed as D D where,, / / / / b / / : materialconstants, b, / /, () () Hyoealasticity constitutive relation is modified to include the damage effect which is exressed by d e : D (3).6mm.3mm Figure. omarison between the analytical rediction and exerimental results of stress-strain relation of angle-ly (4/-4) laminates. Next, the imlementation of the damage model into the finite strain viscolasticity model is considered. We use Ladeveze and Le Dantec s damage mechanics model []. In the model, the thermomechanical otential for damaged ly is assumed to be σ,d, D E E D E D G () d d E E E D E D G (4) In Figs.-4, comarison between the exerimental results and the analytical redictions are shown for stress-strain curves, fiber angle as a function of alied strain, aarent modulus as a function of alied maximum strain and the ermanent strain as a function of the alied maximum strain, resectively. A qualitative agreement is obtained. 7

8 fiber angle (degree) ermanent Aarent modulus transverse strain longitudinal strain constituent ly thickness.mm.mm.3mm.6mm Analysis mm.9.3 mm. mm.8. mm Analysis.8 Alied maximum Figure tress-strain curves for angle-ly laminates. omarison between the exerimental results and analytical rediction. Figure 3 Aarent modulus as the function of alied maximum strain for angle-ly laminates. omarison between the exerimental results and analytical rediction mm constituent ly thickness.3mm Analysis.mm constituent ly thickness.6mm.mm.3mm.mm 3.mm - Analysis 3 longitudinal Figure Fiber angle as a function of longitudinal alied strain for angle-ly laminates. omarison between the estimated exerimental results and analytical rediction. - - alied maximum Figure 4 Permanent strain as a function of alied maximum strain for angle-ly laminates. omarison between exerimental results and analytical rediction.

9 MODELING OF MEHANIAL REPONE IN FRP ANGLE-PL LAMINAE UMMAR We evaluated the mechanical behavior and damage behavior in FRP angle-ly laminates with different constituent ly thickness under tensile loading exerimentally. It was found that as the constituent ly thickness decreases, the strength and failure strain increases. We also observed difference in damage behavior. he reliminary results of finite strain viscolasticity model considering the damage effect for laminated comosites are shown. A qualitative agreement is obtained. References [] E.Kontou and G.athis, Alication of finite strain viscolasticity to olymeric fiber comosites, International Journal of Plasticity,, 87-33, 6. [] P.Ladeveze and E.Le Dantec, Damage Modeling of Elementary Ply for Laminated omosites, omosites cience and echnology, 43, 7-67, 99 9