Interfacial fracture analysis of layered beams with elastic couplings and hygrothermal stresses using an elastic-interface model

This work presents our progress in studying the problem of an interfacial crack in a layered beam with bending-extension coupling (BEC) and residual hygrothermal stresses (RHTS). These effects have occupied us in our recent work [1–3]. Here, we consider a beam element that is an assemblage of two sublaminates connected by a linearly elastic (until fracture) interface of negligible thickness. Both sublaminates may have arbitrary stacking sequences (which introduces BEC) and are modeled as shear-deformable laminated beams. In addition, we assume that the beam element is affected by RHTS. The mathematical problem is formulated and then reduced to two differential equations in the interfacial stresses. To formulate and solve this mathematical problem, we rely heavily on our recent work in [3], which, in turn, extended the so-called enhanced beam theory model proposed in [4]. In simpler words, the present work updates the model of [3] to account for RHTS, while it also discusses some issues not mentioned there (e.g., on the boundary conditions). The aim of the work is twofold. First, we intend to explore the mechanical behavior of the beam element. Thus, we derive explicit analytical expressions for various mechanical quantities: internal forces and moments, strain measures, and generalized displacements in both sublaminates. The effect of the RHTS on these expressions is highlighted through comparison with the respective solutions in [3] that ignore this effect. The second aim of the work is to determine the energy release rate (ERR) and its mode I and mode II contributions. For this purpose, we adopt the J-integral method, also using the so-called interface potential energy. For the beam element under consideration that is affected by residual stresses, J-integral ceases to be path independent [5]. We address this issue using a recently proposed approach [5], which, in a nutshell, splits the loading into two steps. Thus, we compose a valid J-integral solution that allows computing the ERR. Mode partitioning is achieved by assuming, as in [3], that the compressive normal stresses at the crack tip do not promote the crack opening. Ongoing work on validating the proposed analytical solutions using finite element analysis will be presented in a subsequent publication. Lastly, future extensions for the calculations of other essential mechanical quantities (e.g., compliance) are possible.