OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES

Transcription

1 ICAMS th Internatonal Conference on Advanced Materals and Systems OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES VLAD LUPĂŞTEANU, NICOLAE ŢĂRANU, RALUCA HOHAN, PAUL CIOBANU Gh. Asach Techncal Unversty of Ias, Faculty of Cvl Engneerng and Buldng Servces, 4 Dmtre Mangeron Blvd. Ias Romana, vlad.lupasteanu@gmal.com, taranu@ce.tuas.ro, hohan@ce.tuas.ro, paul.cobanu84@yahoo.com Composte structures made of fbre renforced polymer (FRP) compostes are usually bult-up of several ndvdual undrectonal lamnas whch may have ther natural materal axes at dfferent orentatons wth respect to the loadng drecton. Off-axs mechancal propertes of the undrectonal FRP lamna can be determned ether expermentally or predcted theoretcally. One way to theoretcally predct the off-axs stffness and strength propertes of a undrectonal orthotropc lamna s by applyng the macromechancal concepts. Ths paper presents the avalable macromechancal approaches utlzed to calculate the off-axs stffness and strength propertes of a undrectonal orthotropc lamna for whch the loadng drectons are dfferent from the prncpal materal axes. In addton, a case study s presented, n order to apply the macromechancal tools to a FRP lamna made of glass fbres and epoxy matrx. Keywords: FRP composte lamna, off-axs strength propertes, off-axs stffness propertes. INTRODUCTION From macromechancal pont of vew, the off-axs mechancal propertes of the undrectonal FRP compostes are ansotropc, due to ther varaton wth respect to the orentaton of the reference plane. The am of the macromechancal approach s to correlate the stffness and strength propertes along an arbtrary drecton wth the basc propertes of the undrectonal FRP composte referred to ts prncpal materal drectons (Danel and Isha, 2006). FRP composte lamnates consst of two or more lamnas, bonded together so that they can act as ntegral structural elements (Agarwal et al., 2006). For ths reason the understandng of the ndvdual lamna characterstcs should precede the analyss of the lamnated structures theory. Orthotropc Lamnas A lamna or a ply conssts of a flat or curved arrangement of undrectonal fbers embedded n a support matrx and t represents the basc element of a composte materal. For the orthotropc lamna, the materal axes are perpendcular and stand as symmetry planes. Generally Orthotropc Lamna The generally orthotropc lamna s that for whch the materal axes (, 2) do not concde wth the global coordnates axes (x,y), that may be the axes of the loadng drectons (Barbero, 20). The materal axes are rotated wth respect to the reference system by angle Ɵ, as presented n Fgure.

2 Off-axs Mechancal Propertes of FRP Compostes Fgure. Generally orthotropc lamna The consttutve equatons for the generally orthotropc lamna are presented n Equatons and 2. { } { } Q j () { } S j { } where, { } and { } The matrces are the components of the stress and stran matrces, respectvely. Q j and S j are the reduced transformed stffness and complance matrces, respectvely. The elements Q j and S j are functons of the elastc propertes of the lamna along ts prncple axes (,2) and of the fbre orentaton angle, Ɵ. Stffness Propertes (2) Axal Modulus of Elastcty, E x Assumng that the only nonzero stress component actng on the lamna s σ x, the axal modulus of elastcty (E x ) can be expressed n terms of the engneerng constants n the prncpal materal coordnates and of the fbre orentaton Ɵ. E x c + 2 s c + s E G2 E E where, E, E 2 and G 2 are the axal and shear modul of elastcty n the prncpal materal axes, ν 2 s the frst Posson s coeffcent and the trgonometrc functons snɵ and cosɵ are denoted wth s and c, respectvely. The varaton of the axal modulus of elastcty s presented n Fgure 2. It can be seen that the values of E x decrease as the angle between the materal axes and the global coordnates axes ncreases, between E and E 2. (3)

3 ICAMS th Internatonal Conference on Advanced Materals and Systems Fgure 2. Varaton of E x wth respect to Ɵ Axal Modulus of Elastcty, E y Imposng that the only stress component dfferent from zero s σ y, the axal modulus of elastcty E y can be also expressed wth respect to the fbre nclnaton angle Ɵ and to the elastc propertes of the lamna along ts prncpal axs. E y s + 2 s c + c E G2 E E Fgure 3 presents the varaton of E y wth respect to angle Ɵ. Unlke the case of the longtudnal modulus of elastcty n x drecton, the nterval between 0 and 60 s characterzed by a smaller rate of ncrease whle n the nterval, E y has the hghest rate of ncrease. Applng Equaton 4 for Ɵ 0 and Ɵ 90, E y equals E 2 and E, respectvely. (4) Fgure 3. Varaton of E y wth respect to Ɵ

4 Off-axs Mechancal Propertes of FRP Compostes Shear Modulus of Elastcty, G xy The shear modulus of elastcty can be calculated under the assumpton of pure shear state of stress. In ths case, the only non-zero stress component s τ xy ; the shear modulus of elastcty, G xy can be also expressed as a functon and of the elastc propertes of the lamna n ts prncpal drectons and of the fbres nclnaton angle. G xy () E E E G G s c + s + c The varaton of the shear modulus of elastcty s presented n Fgure 4. It can be seen that G xy has the hghest values when Ɵ s 45 whle G xy equals G 2 when Ɵ s 0 or 90. (5) Fgure 4. Varaton of G xy wth respect to Ɵ Posson s Ratos, ν xy, ν yx The frst Posson s rato ν xy, can be calculated consderng that the only nonzero stress component s σ x (Equaton 6), whle the second Posson s rato ν yx, can be obtaned when σ y s dfferent from zero, (Herakovch, 998), (Equaton 7). 2 2 E E 4 4 c s () + c + s 2 E2 G2 xy E 4 E c + c s s G2 E2 2 2 E E 4 4 c s () + c + s 2 E2 G2 yx E 4 E s + c s c G2 E2 (6) (7) Fgure 5 presents the varaton of ν xy and ν yx wth respect to the nclnaton angle of the fbres, Ɵ. The frst Posson s rato has the hghest values when Ɵ s 29 and equals ν 2 or ν 2 when Ɵ s 0 or 90, respectvely. Smlarly, the second Posson s rato has the same values as ν 2 or ν 2 when the nclnaton angle of the fbres s 0 or 90 but ν yx reaches ts maxmum value when Ɵ s 6.

5 ICAMS th Internatonal Conference on Advanced Materals and Systems Strength Propertes Off-axs Tensle Strength Fgure 5. Varaton of ν xy and ν yx wth respect to Ɵ The maxmum tensle strength along any drecton can be calculated wth Equaton 8 whch s derved from the Tsa-Hll falure crteron (Kaw, 2005). f x() Θ t 4 4 c s c s flt ftt flts flt where, f Lt and f Tt are the longtudnal and transverse tensle strength of the lamna along ts prncple drectons and f LTs s the n-plane shear strength of the lamna. (8) CASE STUDY Determne the mechancal propertes n the global coordnates system (x,y) of the followng 45 angle undrectonal E glass / Epoxy composte (Taranu et. al., 203). The propertes of the lamna along ts prncpal axes are: f Lt 900 MPa, f Tt 9.5 MPa, f LTs 25.9 MPa, E GPa, E GPa, G GPa, ν and ν Fgure angled undrectonal E glass / Epoxy composte lamna

6 Off-axs Mechancal Propertes of FRP Compostes Because Ɵ 45 (s c) t results that E x E y and ν xy ν yx. Ex MPa E c + 2 s c + s E G2 E E2 Gxy MPa () + + s c + s + c E E2 E G2 G2 2 2 E E 4 4 c s () + c + s 2 E2 G2 xy yx E 4 E c + c s s G2 E2 f x() Θ t 3.5MPa 4 4 c s c s flt ftt flts flt y (3) (5) (6) (8) CONCLUSION Ths paper presents the macromechancal approach that can be appled to determne the off-axs stffness and strength propertes of FRP composte lamnas. These theoretcal methods of predctng the propertes of an FRP product subjected to a certan state of stress havng reference drectons dfferent from the materals prncpal ones, can turn to be effectve not only from the economcal pont of vew but also from the tme consumng one. Expermental determnatons for varous nclnaton angles ( Ɵ) of the fbers orentaton are prohbtve and dffcult to be carred out. Moreover, the off-axs propertes of an FRP composte lamna should be prevously determned by theoretcal approaches followed by selectve expermental tests amng to valdate these results. REFERENCES Agarwal, B.D., Broutman, L.J., Chandrashekhara, K. (2006), Analyss and Performance of Fber Compostes, 3 rd Ed., John Wley & Sons, New Jersey. Barbero, E.J. ( 20), Introducton to Composte Materal Desgn, 2 nd Ed., CRC Taylor & Francs, Boca Raton. Danel, I. and Isha, O. ( 2006), Engneerng Mechancs of Composte Materals, Oxford Unversty Press, New York. Herakovch, C.T. (998), Mechancs of Fbrous Compostes, John Wley & Sons, New York. Kaw, A. (2005), Mechancs of Composte Materals, 2 nd Ed., CRC Taylor & Francs, Boca Raton. Taranu, N., Bejan, L., Cozmancuc, R. and Hohan, R. ( 203), Composte Materals and Elements I (n Romanan), Poltehnum Press, Ias.