Efficient cohesive zone modelling of flexible adhesive joints across extreme environmental conditions

Accurate prediction of the fracture behavior of highly flexible adhesive joints, such as those employing ductile polyurethane (PU) systems, under varying thermal and loading conditions remains a major challenge, owing to complex fracture mechanisms and multiple crack paths that are not well captured by conventional cohesive zone models (CZMs). Building on a previously established calibrated cohesive zone modelling (CZM) concept, the present study extends the framework to mixed-mode behaviour using a bilinear traction–separation law (TSL) and a reduced set of calibration conditions. Instead of relying directly on dedicated pure Mode II tests, the shear-related cohesive parameters are identified from single lap joint (SLJ) response at three temperatures ( $$-30$$ , 23, and 60\,∘C ) and three loading rates (1, 200, 6000 mm/min), spanning a broad temperature–rate range relevant to service conditions. The bilinear CZM, implemented in a standard finite element framework, successfully replicates joint initial stiffness and peak failure loads across all conditions with an average error below 10%, although peak load is slightly overpredicted and displacement at failure is not accurately captured. Compared to a full-scale calibration approach, the proposed methodology reduces both the number of required calibration conditions and the number of test configurations by 50%, yet delivers robust predictions over the studied service envelope. These results demonstrate that simplified CZM schemes, when carefully calibrated, can serve as a practical engineering-level framework for the design and reliability assessment of highly flexible adhesive joints.