Strain energy release rate and mode partitioning of moment-loaded elastically coupled laminated beams with hygrothermal stresses

Abstract

New closed-form, analytical solutions are derived for the strain energy release rate (SERR) and mode partitioning of uneven bending moments-loaded tests on layered beams with bending-extension coupling and residual hygrothermal stresses. The analytical modeling utilizes Timoshenko beam kinematics, a semi-rigid interface model, and the global method to perform mode partitioning. The proposed solutions are validated via the finite element method in two typical examples of metal-composite joints. In addition, experiments using the double cantilever beam with uneven bending moments test setup are performed in a titanium-carbon fiber reinforced plastic adhesive joint, and data reduction is performed utilizing the new analytical solutions. We demonstrate that the residual thermal stresses effect on the SERR and mode mixity of the metal/composite interfaces can be non-negligible and, thus, should be considered in the design and analysis of such structures. The proposed formulas serve as a data reduction scheme for the fracture toughness and mode mixity determination in the general case of layered beams with bending-extension coupling and hygrothermal stresses, when utilizing uneven bending moments for the characterization tests.