Composite Structures. Indian Institute of Technology Kanpur
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1 Mechanics of Laminated Composite Structures Nachiketa Tiwari Indian Institute of Technology Kanpur
2 Lecture 21 Behavior of Ribbon Fiber Composites
3 Ribbon Reinforced Composites: Introduction Quite often, ribbons are used, instead of fibers, as the reinforcement material in composites. Ribbons, also known as tapes, are essentially filaments with rectangular cross sectional area, where width of the cross section is significantly larger than its thickness. A typical cross section for such a tape is shown below. The dimensions of the cross section are w t and t t, standing for tape width, and tape thickness, thickness, respectively. t t w t
4 Ribbon Reinforced Composites: Introduction Composites reinforced with ribbons offer following advantages over those reinforced with fibers having circular cross section. Higher stiffness and strength in longitudinal as well as in plane transverse direction: This is attributable to the fact that each ribbon s width is significant large vis à vis its thickness. This geometric feature enhances the strength as well as the stiffness of such composites. A direct advantage of this feature is that such composites may exhibit equal strength in all direction in the L T plane, where T direction corresponds to inplane transverse direction. This is a very significant advantage of such composites over unidirectional composites reinforced with fibers with circular cross section. Highly resistant to puncture when impinged by sharp objects Significantly reduced permeability to fluids, both gases and liquids: This feature is attributable to the factthatthat fluid particles or molecules have to undertake a rather long and circuitous route around the impermeable tape, to pass through the overall composite. Such composites can achieve higher volume fractions vis à vis those with circular fibers. This feature is attributable to their rectangular cross section.
5 Ribbon Volume Fraction Consider the following cross section of a ribbon fiber composite along the T T plane. Here, w t = width oftape t t = width of tape O = overlap between two ribbons g T = gap bt between two adjacent ribbons in T direction g T = gap between two adjacent ribbons in T direction
6 Ribbon Volume Fraction For the packing arrangement as shown in Fig. 21.1, the volume fraction for tape (or ribbon) can be expressed as: (Eq. 21.1) Equation 21.1 can also be expressed in terms of overlap, O, as: (Eq. 21.2) Equation 21.1 shows that tape s volume fraction can be increased significantly, if gaps between two adjacent tapes, and also between two adjacent layers of tapes, are made very small. Theoretically, ribbon volume fraction of 100% is achievable in such a configuration. However, there are some practical limitations, which prevent us from achieving such a mark.
7 Moduli of Ribbon Reinforced Composites The modulus of ribbon reinforced composites in fiber direction can be calculated by rule of mixtures. Thus, for such composites, their longitudinal modulus is: E L = V f E t + V m E m (Eq. 21.3) Here, E t, is the elastic modulus of tape in length direction. The in plane transverse tensile performance of these composites is similar to that of unidirectional short fiber composites in longitudinal direction. Thus, we can use following Halpin Tsai equation to calculate the in plane transverse modulus (E T ) for these composites. E T /E m =(1+2ξη t V t )/(1 η t V t ) (Eq. 21.4) where, η t = [(E t /E m ) 1] / [(E t /E m ) + ξ], and ξ = tape s aspect ratio = w t /t t
8 Moduli of Ribbon Reinforced Composites Equation 21.4 works well for tapes, with moderate aspect ratios. However, when aspect ratios are very large, then we may as well use rule of mixtures (Eq. 21.3) to calculate transverse modulus. In such a case, the modulus of the material in longitudinal (L) aswellasinplane transverse directions (T) is essentially the same, and the composite exhibits in plane isotropy in L T plane. Such a behavior of ribbon reinforced composites is markedly different than that of unidirectional composites with circular fibers, which exhibit transverse isotropy in T T pl Finally, it may be pointed out that the modulus of ribbon reinforced composite in T direction may be found by using Eq. 21.4, while using the reciprocal of (w t /t t ) as tapes aspect ratio, ξ.
9 Strength of Ribbon Reinforced Composites Ribbon reinforced composites longitudinal strength can be calculated using relations similar to those used for unidirectional composites with circular fibers. Their in plane transverse strength is approximately equal to that their longitudinal strength, provided: The aspect fiber for the tape is very high, and, Failure occurs due to fiber splitting in L direction, rather than by interlaminar shear effects. This once again requires the aspect ratio of the tape to be very large. Strong adhesion between matrix and tape is required to ensure high values of composite s ultimate strength. In presence of weak interfacial bonds, this strength gets reduced by significant fraction.
10 Rf References 1. Analysis and Performance of Fiber Composites, Agarwal, B.D.and Broutman, L. J., John Wiley & Sons. 2. Mechanics of Composite Materials, Jones, R. M., Mc Graw Hill. 3. Engineering Mechanics of Composite Materials, Daniel, I. M. and Ishai, O., Oxford University Press.
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