To simplify the analysis and characterisation of composite laminates, an invariant-based approach to stiffness that takes the trace of the plane stress stiffness matrix as a material property was recently proposed. In the present work, a study based on micro-mechanical models brings new insight to this invariant-based approach. The Rule of Mixtures and the Halpin-Tsai models are used to establish the relations between the fibre volume fraction, the fibre/matrix stiffness ratios, and the trace-normalised engineering constants of unidirectional laminae and multidirectional laminates. For sufficiently high longitudinal fibre/matrix stiffness ratios and for fibre volume fractions between 50% and 70%, typical of advanced CFRPs, the variation of the trace-normalised longitudinal Young's modulus is within 6% for unidirectional laminae and within 1% for multidirectional laminates, supporting the definition of an invariant-based approach to stiffness based on a Master Ply concept and laminate factors derived thereof, defining clearly a domain of applicability of the invariant theory and confirming the empirical observations of the past.

Single lap bonded joints with four different composite adherend stacking sequences were tested and numerically simulated. The aim was to evaluate the effect of the layups on the quasi-static tensile failure of the bonded joints. The study shows that increasing the adherends bending stiffness postpones the damage initiation in the joint. However, this is no longer valid for final failure. The ultimate load is influenced by how the damage progresses. For similar bending stiffness, a layup that leads to the crack propagating from the adhesive towards the inside layers of the composite increases the ultimate load. The failure mode is highly influenced by the orientation of the interface lamina in contact with the adhesive, such that, a 0° interface ply causes failure within the bond line, while a 90° interface ply causes failure inside the composite adherend. Finally, it is concluded that a quasi-isotropic layup may not be the best choice in terms of tensile joint strength. In order to improve tensile strength up to damage initiation, the layup should be optimized for bending stiffness, while up to final failure, a stacking sequence that yields to a complex crack path inside the composite can lead to higher ultimate loads.