An improved piecewise shear-lag model considering stiffness degradation for the fracture behavior of adhesively bonded tubular CFRP/steel joints

Abstract

This paper presents an improved piecewise shear-lag model that enhances the understanding of deformation and fracture behavior in adhesively bonded tubular CFRP/steel joints, incorporating adhesive stiffness degradation. The model employs a bilinear traction-separation law to accurately represent the non-linear load-displacement behavior of the adhesive layer. Experiments and simulations validate the analytical results, providing insights into the joint's fracture modes. Our findings highlight the crucial role of adhesive length in determining both initial pulling stiffness and peak pulling force. Specifically, the critical length $\pi {\lambda }_2/2$ serves as a key reference for structural design, as the load-bearing capacity remains stable with an increased adhesive layer length. Similarly, the characteristic length scale ${\lambda }_1$ indicates that the initial pulling stiffness remains constant for adhesive layers longer than approximately 2.5 ${\lambda }_1$. For shorter adhesive layers, both load-bearing capacity and initial stiffness vary quasi-linearly with adhesive length. The maximum length of the damaged adhesive layer does not exceed the threshold $\pi {\lambda }_2/2$ due to the interplay between damaged and undamaged regions. Additionally, two straightforward formulas are proposed for determining key adhesive parameters (e.g., damage displacement, shear stiffness, fracture toughness) from measurable quantities in standard experiments.