A crack density analytical model for multidirectional composite laminates under biaxial stress at cryogenic temperature

Fiber-reinforced polymer composite tanks for cryogenic energy storage are subjected to biaxial loading at low temperatures, which leads to the formation of matrix cracks. The density of these cracks plays a critical role in determining both the load-bearing capacity and leakage resistance of the tank structure. Most previous theoretical studies have focused only on the crack density of cross-ply laminates under uniaxial loading, neglecting the complexities of multidirectional laminates. This study develops a crack density prediction model for multidirectional laminates, accounting for adjacent ply constraints, biaxial stress conditions, and thermal residual stresses, using two-dimensional shear lag theory and an equivalent constraint model. The crack density of various layers under uniaxial and biaxial stresses at different temperatures is predicted. The effects of lay-up configuration, ply thickness, and material properties on the evolution of crack density are examined. Results show that crack density increases with rising biaxiality ratios or decreasing temperatures. The in-plane transverse stress distribution within the ply governs crack formation. While the 45° ply shows a lower crack density than the 90° ply under identical stresses, it displays greater sensitivity to biaxial loading. At 1% axial strain, crack density rises 126% in the 45° layer and 38% in the 90° layer under 1:1 biaxial versus uniaxial loading. The theoretical predictions align closely with numerical simulations and experimental measurements across different laminate configurations and stress conditions. This work offers a theoretical foundation for improving the mechanical performance and leakage resistance of composite cryogenic storage systems.