Composite angle ply laminates and netting analysis

Abstract

This paper relates to the ‘netting–analysis’ approach, often used in calculations of the behaviour of helically wound reinforced pressure vessels and tubes. Numerical calculation of the stress–strain relations for angle ply composite laminates often gives the impression of unexpected instability in the underlying equations. For instance, when the in–plane principal stresses are in the ratio 2:1 and the fibres are inclined at an angle close to θ ± arctan 2, the stress–strain relations are very sensitive to the value of θ and to the relative stiffness of the fibres and matrix. There is a simple explanation for this, which is most clearly understood by developing analytical approximations for the stress–strain relations. It is shown that the stable angle of inclination of the fibres, where no strain–induced fibre rotations occur, deviates from the so–called ‘ideal’ fibre angle predicted by netting analysis by an amount that depends on the matrix–to–reinforcement–stiffness ratio. When the initial angle of inclination of the fibres deviates from the stable angle, the application of strain produces fibre rotation and nonlinear stress–strain relations result. Analytical expressions for the stress–strain relations have been obtained; they show the interaction of the parameters that control the shape of the stress–strain curves.