Modelling stiffness degradation due to matrix cracking in angleply composite laminates

Abstract

When a multidirectional composite laminate is subjected to in plane static or fatigue tensile loading, matrix cracks parallel to the fibres appear in the off axis plies long before catastrophic failure. Matrix cracking significantly reduces the laminate stiffness properties and triggers development of other harmful resin dominated damage modes such as delaminations. Concurrent matrix cracking in the adjacent off axis plies is an extremely complex problem to model analytically and has been analysed mostly using finite element methods.

The present paper is concerned with the theoretical modelling of stiffness reduction in cracked angleply [θ₁ /θ₂ ]_s laminates subjected to multiaxial in plane loading. A new approach based on the equivalent constraint model of the damaged ply and an improved two-dimensional shear lag method has been applied to model matrix cracking in angleply [θ₁ /θ₂ ]_s laminates. Stresses in the cracked ply are determined from a system of two coupled ordinary differential equations and used to calculate the in situ damage effective functions, which describe the stiffness loss. For angleply [±θ ]_s laminates with a cracked midlayer, it is found that the reduction due to matrix cracking of the laminate axial and transverse moduli is more significant than in crossply laminates, while for the shear modulus, the opposite is true. Matrix cracking in such laminates can result in an increase in the Poisson's ratio – a phenomenon not observed in crossply [0/90]_s laminates. In addition, matrix cracking in angleply [±θ ]_s laminates introduces coupling between extension and shear.