Characterization of Crack Kinking Behavior in Sandwich Structures: Experiments and Modelling

Sandwich structures, marked by their superior stiffness-to-weight and strength-to-weight ratios, are increasingly used in the aeronautical and naval sectors. Impact events, such as bird or hail strikes, are very frequent in aviation, and due to climate change, ships are required to navigate new routes in the Arctic, where collisions with floating ice are common. These impacts can cause significant undetectable damage, potentially leading to catastrophic failure under operational conditions. The most common damage mechanism is face/core debonding. Depending on the loading conditions, this damage can either propagate along the interface or kink into the core. Knowledge of the crack propagation path can facilitate the design of new damage mitigation concepts that extend the lifespan of structural components. However, how does the crack propagate? How can predictions be made regarding the kinking direction? Answers to these questions have been addressed in the literature through the formulation of a complex mathematical model describing crack kinking out of an interface. This model is based on three complex coefficients that depend on the mechanical properties of the two materials forming the interface. By employing these coefficients and applying the maximum energy release rate criterion, it is possible to predict whether the crack will kink out of the interface and the direction it will follow. However, solutions of this model have so far been limited to isotropic bimaterial interfaces with moderate elastic mismatches, which do not reflect the modern orthotropic systems now commonly adopted.

The semi-analytical method available in the literature to derive the complex coefficients with the help of finite element simulation had been verified only for isotropic bimaterial interfaces. In this work, the method was critically investigated, raising awareness of potential numerical issues arising from an ill-conditioned matrix and limitations related to the approximation of the T-stress. Subsequently, the semi-analytical method was extended to orthotropic bimaterial interfaces, and the resulting coefficients were validated against the only data available in the literature. The coefficients were derived for new interfaces, including both isotropic bimaterials with high elastic mismatch and orthotropic bimaterial interfaces commonly found in sandwich structures for naval and aeronautical applications.

The semi-analytical method was then applied to iteratively solve the kinking problem for thousands of different bimaterial interfaces, covering most of the sandwich structures commonly used in the naval and aeronautical sectors. The results were embedded in a novel stand-alone Matlab application, which can provide the solution coefficients without the need to perform finite element simulations. An optimized eight-dimensional curve fitting of the embedded results enables straightforward and accurate computation of the coefficients. The coefficients obtained with the Matlab application for selected interfaces were successfully verified by comparison with those available in the literature or those directly derived using the semi-analytical method. Furthermore, they were also used to predict kink angles, and these predictions were compared with expected kink angles derived from the maximum J-integral values calculated via finite element simulations. The results were very promising, as the observed absolute errors remained approximately 4◦.

An experimental campaign was conducted to verify the applicability of the kink angle predictions obtained using the Matlab application to real structures. Sandwich structures with carbon fiber laminates as facesheets and a PMI foam core were tested using a Double Cantilever Beam loaded with Uneven Bending Moment (DCB-UBM) test rig at different interface phase angles. Tests aimed at accurately characterizing the mechanical properties of the carbon fiber laminate, essential for precise kink angle prediction, were also performed. With the DCB-UBM tests, the interface pre-crack was driven to kink, and the kink angle was measured and compared with the predicted values. The results showed an average absolute error of approximately 3.5◦, demonstrating the predictive capability of the tool for sandwich structures. The mode I fracture toughness of the PMI foam core was obtained experimentally, along with an investigation of the interface phase angle at which the transition occurs between interface crack propagation and kinking. Based on these results and observations of the resulting three-dimensional kinking plane, the energetic kinking criterion was validated. It was shown that the energy release rate at the tip of the branched cracks increases compared to that at the interface crack tip as the interface phase angle increases, demonstrating a stronger tendency for the crack to kink.