Non-deterministic damage analysis of DCB bonded composite joints using a surrogate model

Composite bonded joints are increasingly used in structural applications due to their high strength-to-weight ratio and design flexibility. However, understanding and predicting their fracture behaviour, especially in Mode I, is important for ensuring structural integrity and reliability. This study focuses on evaluating two-dimensional numerical models of the Double Cantilever Beam (DCB) manufactured of composite laminates. It builds upon previous experimental studies related to bonding while considering the manufacturing process and associated uncertainties, using the Finite Element Method (FEM). Deterministic analyses were carried out to assess the advantages and disadvantages of the models. Based on these assessments, a numerical model was selected to perform non-deterministic studies and apply metamodeling to estimate fracture strength of Mode I DCB bonded composite joints. This involved generating numerical models using Python® scripts linked with Abaqus® software. A Design of Experiments (DoE) strategy was developed to reduce the number of experiments while evaluating the effect of various design parameters. The design variable space was defined in terms of the geometrical characteristics of the specimen and their material properties, encompassing a total of 11 parameters. In other words, this evaluation aims to determine how much each variable influences the energy release rate $\left(G_{\text{Ic}}\right)$. The Compliance-Based Beam Method (CBBM) was applied to determine the critical fracture energy in Mode I of the DCB bonded composite joint. From the DoE ranking, the five most influential variables were selected as design variables for the development of the surrogate model. It was noted that most of the variables exhibited epistemic uncertainty, particularly among the geometric variables. Subsequently, the training of the metamodel was conducted using Latin Hypercube Sampling (LHS) in conjunction with Efficient Global Optimization (EGO) defined by the optimized model. Overall, the proposed methodology effectively combines deterministic modelling, uncertainty quantification, and surrogate modelling to provide information into the fracture behaviour of bonded composite joints. The results indicate that the mechanical strength of the joint in Mode I, as predicted by the surrogate model, is strongly influenced by variables such as the energy release rate, adhesive and adherent thicknesses, fibre orientation, and initial crack length. Thus, this methodology helps the development of more robust design strategies for bonded composite structures subjected to out-of-plane stress components.