Dealing with multiaxial non-proportional fatigue with varying mean stress: Invariant and critical plane approaches for component-like structural adhesive joints

A comparative investigation between an invariant-based approach using the signed Beltrami-stress and critical-plane approach using the Findley-stress is carried out for the fatigue lifetime prediction of an epoxy structural adhesive under multiaxial non-proportional loading with varying mean stress. Fatigue experiments with uniaxial and multiaxial loading (proportional and non-proportional) are done at stress ratios of $-1$ and $0.1$. Two adhesive joints are evaluated: a hollow-cylinder butt-joint (HCBJ, sample with homogeneous stresses distribution), and a flange-rod-joint (FRJ, component-like specimen with complex stress state). For both geometries, multiaxial loading and an increasing mean stress lead to fatigue strength reduction, whereas the phase-shift effect is less pronounced. A systematic procedure for parameter determination is implemented for both approaches. For predictions of the HCBJ-sample, stresses are analytically obtained. For validation with the FRJ-sample, FEA-based stress calculation is used. For both joints, the critical plane approach results in more accurate predictions than the invariant-based approach. In comparative terms, the invariant-based approach is experimentally more complex, by requiring a mean stress correction, but its numerically simpler with lower calculation time. The critical-plane approach requires fewer experiments for parameter determination and provides more accurate results for non-proportional loading. However, it is more numerically demanding with larger computing time.