Aligned fibre composites tensile modulus

A composite material consists of 40% (l volume) continuous, uniaxially aligned, glass fibres in a matrix of thermoset polyester. A tensile stress of 100 MPa is to be applied parallel to the fibres. Predict the strains which will result. Take the tensile modulus and Poisson s ratio of glass to be 76 GPa and 0.22, and of thermoset polyester to be 3 GPa and 0.38, respectively. 

A sheet of composite material consists of aligned continuous fibres in an isotropic matrix. A tensile specimen is cut from the sheet at angle 0 to the fibres. Show that the tensile modulus E of the specimen will vary with 6 as follows ... 

The reduction in tensile stress towards the ends of each fibre inevitably leads to a decrease in the tensile modulus compared with the continuous filament case. Consider a plane drawn perpendicular to the stress direction in an aligned discontinuous fibre composite (Figure 8.4), which must intercept individual filaments at random positions along their length. Hence the stress carried by the composite must be lower than that for the continuous filament case, and is dependent on the length of each fibre. Cox [9] predicted a correction factor rji for the tensile modulus in the axial direction that takes into account the finite length of the fibres so that Equation (8.3) is modified to... 

A polymer matrix composite is made from a duromer matrix containing continuous carbon fibres aligned in the loading direction. Young s modulus is 3 GPa in the matrix and 350 GPa in the carbon fibres, the tensile strengths are 60 MPa and 4900 MPa. The volume fraction of the carbon fibres is 55%. 

A composite material consists of 50% (by volume) continuous, uniaxially aligned, carbon fibres (high-strength form) in a matrix of epoiy. Predict the tensile strength parallel to the fibres. Take the axial tensile strength and modulus of these fibres to be 3200 MPa and 230 GPa, and of epoi to be 60 MPa and 2.4 GPa, respectively. 

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