A layerwise spectral finite element method for the prediction of stresses and delamination crack growth in composite structures subjected to static and impact loading

• Κύριος συγγραφέας: Σιορίκης, Δημήτριος
• Άλλοι συγγραφείς: Siorikis, Dimitris
• Γλώσσα: English
• Έκδοση: 2022
• Θέματα: Spectral finite element; Layerwise mechanics; Laminated composite plates; Fracture mechanics; Delamination; Impact loading; Φασματικό πεπερασμένο στοιχείο; Θεωρία διακριτών στρώσεων; Πολύστρωτες πλάκες; Θραυστομηχανική; Διαστρωματική αποκόλληση; Κρουστική απόκριση

A sophisticated numerical tool is developed for the prediction of delamination crack onset and propagation in sandwich and laminated composite structures under static and impact loading, which is capable of reducing numerical complexities involved in classical fracture mechanics approaches with substantially improved efficiency and computational savings. The proposed method incorporates: i) novel layerwise mechanics for the accurate prediction of the complex displacement and stress fields through the thickness of the laminate and across ply interfaces of highly heterogeneous composite structures in conjunction with ii) a multi-node spectral finite element model (SFE) with high-order spatial approximation in the plane of the structure and with integration points collocated with the nodes, leading to improved prediction of interlaminar stresses and fracture energy at the nodes, and at the same time yielding a consistent diagonal or nearly diagonal mass matrix, and (iii) inherent capability for the simulation of impact events through the combination of a fast explicit time-integration scheme and contact laws Initially, a newly developed cubic spline layerwise theory (CSLT) combined with a spectral finite element is presented for the fast and precise prediction of through the thickness stress fields at free edges, ply interfaces, resin-rich layers and artificial delaminations. The conducted validations revealed the capabilities and advantages of the present method over other competitive solid FEA based models in critical and highly demanding computational problems, establishing the present model as an attractive candidate for the analysis of delamination propagation problems. Within the framework of the finite element method in conjunction with fracture mechanics theory, the virtual crack closure technique (VCCT) and a cohesive zone model (CZM), the two most famous methods of delamination modelling, are implemented and elaborated. The previously established CSLT is further enriched with additional degrees of freedom (DoFs), representing the resultant discontinuities in the displacement field induced by the presence of delamination cracks, which allows the modelling of delamination crack onset and growth by simply activating the delamination degrees of freedom without FE remeshing. Strain energy release rate is predicted by adapting the VCCT method to rely exclusively on the damage DoFs. Finally, an iterative solution method is developed that takes advantage of the damaged DoFs to quickly predict the crack propagation without remeshing and the proposed numerical scheme is applied to mode I, II and mixed-mode static delamination fracture problems and is validated vs. reference literature solutions, experimental results and standard 2D plane-strain FE models. When a pre-crack exists and the fracture process zone is negligible compared to the specimen size, the VCCT is still a favorable candidate to predict delamination. However, the VCCT scheme suffers from several limitations, such as a-priori knowledge of the crack path, which is very restrictive for the modelling of impact-induced delamination in healthy structures, and the inability to model material softening present in ductile adherents and finite-thickness adhesive joints. In order to address the previous shortcomings of the VCCT approach a cohesive zone approach is also formulated. In this context, a variable kinematic layerwise theory is developed to reduce the numerical complexities involved in classical cohesive approaches, which employs cubic Hermite splines for the composite laminates and the core and linear interpolation functions for the thin resin-rich layers in connection with continuum damage mechanics for predicting and tracking the debonding propagation. The layerwise mechanics and continuum damage mechanics are integrated into a SFE for laminated composite strips, termed thereafter as cohesive-layerwise spectral finite element (CLW-SFE) and the developed computational model is applied to analyze global mode I, mode II, and mixed-mode fracture problems and is correlated with experimental results and reference high-fidelity finite element models for composite sandwich and laminated composite structures. Finally, the previous CLW-SFE is extended to enable the modelling of delamination growth in laminated and sandwich plates under impact loading. The variable kinematic layerwise strip theory is extended in three dimensions to address and explore the three-dimensional generated delamination footprints in laminated and sandwich plates and is subsequently integrated into a time-domain SFE combined with an explicit time integration scheme to model impact loading responses. Admissible contact laws for both rigid and deformable (hailstone) impactors are investigated numerically and experimentally to provide realistic and representative impact loads for laminated composite and sandwich plates. Green Lagrange non-linear strain terms are incorporated into the non-linear explicit impact dynamics to account for large displacements and rotations. The convergence, stability and accuracy of the proposed numerical framework are verified for the entire spectrum of the impact characterization diagram. Obtained results of the developed numerical code are correlated with experimental data and reported high-fidelity finite element models, demonstrating crucial enhancements in computational speed and meshing process due to elimination of cohesive layer parameter calibration, alleviation of finite element aspect ratio constraints, block-diagonal mass matrix and high-convergence rates.