Closed-form solution for interfacially cracked layered beams with bending-extension coupling and hygrothermal stresses

Abstract

This paper investigates the problem of the mechanical behavior of an interfacially cracked layered beam with possible bending-extension coupling (BEC) and residual hygrothermal stresses (RHTS), as well as shear deformations and crack-root rotations. The paper presents a mechanical model of a beam that results by assembling two sublaminates by a semi-rigid interface. The beam is clamped at its one end and interfacially cracked and generally loaded at the other. First, the mathematical problem is formulated and analytically solved in terms of the internal forces, strains, displacements, and interfacial stresses. Novel closed-form expressions are derived regarding these quantities and thoroughly reported in tables. The proposed expressions stand out for their generality; they apply to beams with arbitrary layers of random thicknesses and materials and consider general loading, BEC, and RHTS. Next, we highlight some specific cases by appropriately reducing the general expressions. As an example, we investigate the mechanical responses of composite laminates with possible BEC and RHTS using the double cantilever beam configuration. Lastly, the paper discusses new ways to deepen our knowledge of additional aspects of the fracture response of interfacially cracked beams with BEC and RHTS.