The mechanics of fibre reinforcement

Predicting accurately the mechanical properties of a composite material is not an ea task. Differences between the properties of reinforcing particles and the matrix cause complex distributions of stress and strain at the microscopic level, when load is applied. Reasonably accurate predictions can be made for fibre composites, however, by employing simplified assumptions about the stress and strain distributions. 

consider the case of fibres which are so long that the effects of their 

Fibres extend the entire length of the block, so that at any section the area fractions occupied by fibres and matrix equal their respective volume fractions. The total stress ctj must then equal the weighted sum of stresses in fibres and matrix and respectively  

Fibres and matrix are assumed to cany pure axial tension, with no stress in the 2-3 plane (6.N.4)  

11 Fibre matrix coupling in aligned fibre composite (a) coupling for tensile stress parallel to axis 1 and (b) coupling for tensile stress parallel to axis 2. 

consider the case of fibres which are so long that the effects of their ends can be ignored. A block of polymer reinforced with uniaxially aligned continuous fibres is sketched in Fig. 6.10. Three orthogonal axes 1, 2, and 3 are defined within it. When loads are applied to the block we can assume that it deforms as if the mechanical coupling between fibres and matrix took special 

If a stress acts parallel to axis 1, fibres and matrix are approximately coupled together in parallel, as shown in Fig. 6.11(a). Fibres and matrix elongate equally in the direction of a. Their axial strains and e ,, respectively, equal the strain Ci in the composite 

---

It has been demonstrated that polydiacetylene single crystal fibres are relatively perfect and have excellent molecular alignment. In consequence they display high values of stiffness and strength and are very resistant to creep. It has been shown that such fibres have considerable promise as reinforcing fibres in an epoxy resin matrix and the study of such composite systems has enabled considerable fundamental information to be obtained concerning the mechanisms of fibre reinforcement. 

Hull [21] discusses an expression by Nielsen and Chen [22] for the calculation of the modulus of laminae containing randomly oriented fibres. The issues involved in computing the mechanical properties of short, random fibre composites, and the mechanics of fibre reinforced plastics are also discussed. 

The mechanism of fibre reinforcement of the cementitious matrix in concrete has been extensively studied in terms of the resistance of the fibres, pullout from the matrix and as a result from the breakdown of the fibre-matrix interfacial bond. Undoubtedly, the knowledge of the individual phases as well as the interface between fibre and matrix is paramount in understanding the mechanical behaviour of FRC. There are a huge number of studies on the mechanical effect of fibres in concrete. The following sections will only... 

Recent investigations [61. 623 into the behaviour of polydiacetylene fibres In epoxy resin matrices have shown that not only such composites have good mechanical properties but that Important fundamental details of the mechanisms of fibre reinforcement can also be revealed from their study. 

Aveston, J., Mercer, R.A., Sillwood, J.M., The Mechanism of Fibre Reinforcement of Cement and Concrete (Part I), National Physical Laboratory, publ. n°SI 90/11/98, January 1975. 

Guan Liqiu and Zhao Guofan, A study on the mechanism of fibre reinforcement in short steel fibre concrete, RILEM Symposium FRC86... 

R.N. Swamy, PS. Mangatand C.V.S.K Rao, The mechanics of fibre reinforcement of cement matrices . Fiber ReinforedConcrete, ACI SP-44, American Concrete Institute, Detroit, Mi, 1974, pp. 1-28. 

The first part deals with the theoretical background underlying the behaviour of FRC, including an intensive treatment of the mechanics of fibre reinforced brittle matrices and its implications for cementitious systems, taking into account the special bulk and interfacial microstmcture of FRC. 

---