THE OUT-OF-PLANE BEHAVIOUR OF SPREAD-TOW FABRICS

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Stanley Lynch
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1 ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Sevie, Spain, -6 June 04 THE OUT-OF-PLANE BEHAVIOUR OF SPREAD-TOW FABRICS M. Wysocki a,b*, M. Szpieg a, P. Heström a and F. Ohsson c a Swerea SICOMP AB, Box 04, SE-43 Mönda, Sweden b Chamers University of Technoogy, Dept. of Appied Mechanics, SE-4 96 Göteborg, Sweden c Oxeon AB, Företagsgatan 4, SE Borås, Sweden *maciej.wysocki@swerea.se Keywords: Preform mechanics, textie composites, Hertzian contact, experimenta characterisation. Abstract In this paper the constitutive compressive behaviour of neary parae spread-tow textie reinforcement is studied. The striking resut of our anaysis is that the spread-tow type of reinforcement shoud obey inear reation between force and deformation. This is in contrast to standard textie reinforcements that obey a power-aw type of behaviour. To support the theoretica investigation we have deveoped an test rig who's chief purpose is to achieve compression between neary perfecty parae surfaces. This is achieved using a mechanica arrangement consisting of a ba-joint.. Introduction Presenty, the aerospace industry is ooking into spread-tow textie reinforcement for use in primary structura composites. This is mainy due to their reativey ow price and improved mechanica performance, hand abiity and manufacturabiity. As introduction of new structura composite materias into aero structures requires a timey and costy certification process, there is presenty a arge effort towards characterisation, understanding and modeing various aspects of the spread-tow based composite materias. Since forming of reinforcements pays a key roe in terms of the subsequent composite manufacturing and the performance of the fina product, we focus in this contribution on the eastic compression of such a preform. Since, the mechanica properties of a fibre mass are important in many fieds of engineering, incuding composite manufacturing, a significant effort has been spent to describe and mode these properties. In particuar, Van Wyk [] pioneered the mechanistic anaysis of the compressibiity of 3D random fibre masses. Van Wyk regarded the fibre mass as a system of bending units consisting of fibre beam eements between adjacent fibre contacts and he ignored twisting, sip, and extension of the fibres. His key assumptions were that the mean contact spacing is proportiona to the reciproca of the fibre voume fraction and that the segments deform as in bending of straight sender beams. The resut of his anaysis is a simpe power aw for the compressive stress as P k E, () 3 3 0

2 ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Sevie, Spain, -6 June 04 where k is a structure dependent constant; E is the Young s moduus of the fibres; and 0 is the imiting fibre voume fraction beow which P=0. Most of the work foowing van Wyk has accepted the form Eq. and focused on finding an appropriate expression for k by extending the theories describing the structure deveopment during deformation. It was not unti 998 that To [] suggested a more genera expression for the packing of fibre masses n n P k E 0, () where the exponent, n, was shown anayticay to take the vaue of 3 for the 3D and 5 for the D random cases. The author aso succeeded to fit experimenta data for materias where the contacts between fibres are ines rather than points, e.g., fibre bundes, by adjusting the exponent in Eq.. Nevertheess, since the assumptions used in the anayses in [, ] proceeds from an assumption of point contact and bending of fibre segment, the fitting of Eq. to data for highy parae fibre architectures in [] is to be considered as painy phenomenoogica. Figure. Geometry of the contact between eiptic parobooids with principa axes of body (x, y, z ) and the principa axes of body (x, y, z ). The ange is the ange between the x, z and x z panes, i.e. the principa radii of curvatures R and R. A striking quaity of the spread tow technoogy is the possibiity to obtain extremey parae fibre assembies. This is in contrast to a typica reinforcement where the fibre architecture are usuay somehow irreguar. Therefore in the context of mechanica behaviour, the compressive response of the highy oriented spread-tow fabrics is expected to be significanty different from the standard reinforcement. The main difference between the two types of fabrics is the constitutive assumption of oad transfer mechanism between the fibres []. Namey, in standard fabric the oad transfer is assumed via bending of fibre segments, whie in spread tow fabric the main mechanism is assumed to be Hertzian contact between adjacent fibres. Therefore, in this paper we study the constitutive behaviour of highy parae fibre network governed by Hertzian contact. The theoretica study is aso supported by experimenta characterisation of the transverse compressibiity of the highy anisotropic and packed CF spread-tow fibre assembies. The resuting force-defection curve is anaysed against the Hertzian contact modeing effort to give effective transverse moduus.

3 ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Sevie, Spain, -6 June 04. Theoretica background The probem of contact between eastic bodies has ong been of considerabe interest. Assume that two eastic soids are brought into contact at a point 0, as shown in Fig.. If coinear forces are appied so as to press the two soids together, deformation occurs, and we expect a sma contact area to repace the point of the unoaded state. If we woud abe to determine the size and shape of this contact area and the distribution of norma pressure, then the interva stresses and deformation coud be cacuated. Figure. Geometry of deformed bodies. Dashed ines show the surface as they woud be in the absence of deformation. Continuous ines show the surfaces of the deformed bodies. In the anaysis of the contact probem by Hertz, as extended by Timoshenko and Goodier [3], the foowing is assumed: () the contacting surfaces are perfecty smooth so that the actua shape can be described by a second degree equation of the form z Dx Ey Fxy where D, E and F are arbitrary constants.; the eastic imit of the materias are not exceeded during the contact; (3) ony norma forces between the contacting surfaces are considered; and (4) the contacting surfaces are sma in comparison to the entire surfaces. Based on the above assumptions and by appying potentia theory it can be showed that: () the contact area is bounded by an eipse whose semi-axes can be cacuated from the geometric parameters of the contacting bodies; and () the norma pressure distribution over this area is x a x P p0 b, where p 0 is maximum pressure at centre, a is the major axis of eipse of contact and b is the minor axis of eipse. If the two bodies are pressed together by appied norma forces (cf. Figure 3), then a deformation occurs near the origina point of contact aong the Z-axis. Here again, we consider ony forces acting parae to the z-axis where the distance from the z-axis is sma. The dispacements at a point are w and w where w is the deformation of point P of body and w is the deformation of point P for body, pane C is the origina pane of tangency; z is the distance from P to the undeformed state, and z is the distance from P to the undeformed state. For points inside the contact area, we have z w z, where P w is the deformation function we seek. To sove the probem, consider the contact surfaces and define the foowing geometrica reations [4] A B R R R R (3) 3

4 ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Sevie, Spain, -6 June 04 and B A cos. (4) R R R R R R R R The constants A and B are expressions for the combinations of the principa curvatures of the surfaces and the ange between the panes of curvature. These are used to cacuate via the reation Ax By w w. (5) The probem is now to find a pressures distribution and potentia functions to satisfy the Eq. 5. The generic soution based on the use of eiptic integras is to found in numerous textbooks onto contact mechanics, see e.g. [4]. Therefore we wi here focus on the contact mechanics of fibres in contact with fibres and pane, i.e. the specia case of ine contact. To sove this probem we sha make use of the expressions aready deveoped [3] to sove for the "pressure distribution" and size of the area of contact by aowing one axis of the eipse of contact to become infinite. To determine the deformation, the contact area wi be taken as being a finite rectange with one side very much greater than the other. The derivation wi be for the case of a pair of cyinders with their axes parae and is based on the work presented in [3]. The soution for a cyinder to pane contact can easiy be obtained by aowing the radius of one of the cyinders to become infinite. Figure 3. Contact geometry between two parae cyinders. Line contact occurs when two cyinders rest on each other with their axes parae, cf. Fig. 3, and when a cyinder rests on a pane. As the two cyinders are pressed together aong their axes, the resuting pressure area is a narrow "rectange " of width b and ength L (assuming no taper in the cyinders). In other words, the area of contact is an eongated eipse with the major axis of the eipse equa to L and the eccentricity approaching unity. Without going into detais, due to imited space, the tota deformation of a pair of cyinders with their axes parae (after some engthy agebra) can be obtained as P n 4 n L n b, (6) L 4

5 ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Sevie, Spain, -6 June 04 where b is given by b 4 P RR L R R (7) and where i i. (8) E i The Eq. 6 (together with Eq. 7) is simpified to the foowing expression for a cyinder on a fat surface 3 P L n n 4. (9) L 4 PR Machine attachment Ba joint Testing area Machine attachment Figure 4. Sef-adjusting compaction rig. The main resut of the above derivations is the observation that the reation between the deformation and the appied force is neary inear for moderate oadings such as the expected for typica manufacturing processes of composite materia. This is evident when representative materia data for carbon fibres and stee pate are used in Eqs. 6 and 9: CFs 9 transverse stiffness of E 50 Pa and Poisons ratio of 0. 35, CFs diameter of T T 6 R fib 30 m, together with data for stee. This eads to a reation between deformation and force in terms of 7 8 P n P or P (0a) for contact between two fibres, and as 5

6 ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Sevie, Spain, -6 June P n P or P (0b) for contact between a fibre and stee surface. Of course, the above derivations are for a singe fibre ony and needs to be further revised for mutipe fibres and fibre assembies. However, one can sti concude that compressibiity of parae fibre assembies is (neary) inear with respect to the appied force (foowing from a simpe assumption of P in Eq. 0a,b being a sum of individua fibre forces). This is in contrast to the commony observed behaviour in standard reinforcement where the behaviour is expected to be power aw, cf. Eqs. and.. Experimenta method and resuts Since compressive testing of extremey thin fabric (in the case of the studied TeXtreme UD spread-tow band approximatey 0.05 mm) requires an terrific paraeism of the testing equipment, we decided to deveop an sef-adjusting test rig where the adjustment is performed using a ba-joint, cf. Fig. 4. The test rig was machined from a singe piece of stee and consist of machine attachment, testing area and a ba-joint used for the paraeism adjustment. Machine compiance was subtracted from the experimenta force-defection data by assuming a spring mode. The tested materia was TeXtreme UD spread-tow bands from Oxeon consisting of TR50S 5k CF fibres. A typica force-defection data for the TeXtreme UD spread-tow, after correcting for machine compiance, resuts in an amost inear reation between Force and Defection given as P Concuding remarks In this contribution we have studied the constitutive behaviour of neary parae fibre assembies in the form of TeXtreme UD spread-tow bands from Oxeon. The resuts indicate that the compressive behaviour of the neary parae fibres shoud obey a inear reation, see Eqs. 0a and b, which is in contrast to the standard textie reinforcements that obey power aw type of behaviour. This theoretica investigation is further supported by our initia experimenta data which shows amost inear behaviour. Compared to the theoretica investigation, the experimenta data shows however somehow higher compiance. This coud be due to various phenomena such as, amongst other; imited fibre paraeism resuting in partia or eiptica-type of contact, non-homogeneous fibre distribution and theoretica deveopment performed for a singe fibre ony. This needs to be further investigated into in the near future. References [] C.M. van Wyk, Note on the Compressibiity of Woo, Journa of the Textie Institute, 85-9, 946 [] S. To, Packing mechanics of fiber reinforcements, Poymer Engineering and Science, , 998 [3] S.P. Timoshenko and. L.N. Goodier, Axisymmetric stress and deformation in a soid of revoution, in: Theory of Easticity, 3rd ed., pp , McGraw Hi, NY, 95 [4] K.L. Johnson, Contact Mechanics, Oxford University Press, Oxford, 985 6

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