A quadratic elastic-limit criterion for adhesively bonded tubular joints under tension and torsion

A quadratic interaction criterion is analytically derived for the damage initiation of adhesively bonded tubular joints under combined tension and torsion: (Fs/Fspure)2 + (Ts/Tspure)2=1. The joint is modelled as a symmetric half-joint in which the axial force and torque are applied to the inner pipe at its loaded end, while the bond-wise loads transfer to the outer pipe through the adhesive interface. The criterion follows as an exact algebraic consequence of the boundary-value problem: the elastic slip components vanish at the symmetry plane and increase monotonically toward the loaded end, so the maximum equivalent slip is always attained at the loaded end. This eliminates any endpoint-switching mechanism and renders the interaction exactly quadratic for all stiffness ratios, bond lengths, and loading ratios. The criterion is exact within the stated symmetric half-joint elastic formulation (linear elastic adherends, thin shear-lag interface, isotropic Euclidean equivalent-slip initiation law); absolute initiation loads depend on the cohesive model parameters. Implementation consistency is assessed through parametric evaluation, 3D finite-element stress-field checks, and recovery of published single-mode limits. The criterion provides a normalised interaction relation—parameter-independent in its dimensionless form—for the elastic design limit of bonded tubular connections.