Meaning
Theoretical calculations for stress transfer between a resin matrix and a reinforcing fibre are often based on a specific micromechanical model. Cox shear lag theory assumes that the matrix and fibre behave elastically and that the bond between them is perfect. This analysis defines how the stress in a short fibre increases from zero at the ends to a maximum in the middle.
It identifies the critical fibre length required for efficient reinforcement in composite materials.
Interface Efficiency
Shear stress concentration at the fibre tips is a primary result of this calculation. The theory shows that if the fibre is too short, the full tensile strength of the reinforcement cannot be utilised. Excessive shear at the interface may lead to debonding or matrix cracking before the fibre reaches its breaking point.
Reinforcement Geometry
Aspect ratio of the filler particles determines the effectiveness of the load transfer. Long, thin glass fibres offer more surface area for shear lag to operate compared to spherical beads. Processing steps like extrusion or high-pressure injection often break these fibres, which reduces the mechanical performance of the final part by moving away from the optimal geometry.
Modulus Prediction
Composite stiffness is calculated by averaging the stress distributions across the entire volume. The model links the individual properties of the resin and the fibre to the macroscopic behaviour of the moulded component.
