Failure of thin-walled structures under impact loading

Abstract: Increase in computational power during recent years contributed to a significant development in numerical methods in mechanics. There are many methods developed that address various complex problems, yet modelling of initiation and propagation of failure in thin-walled structures requires further development. Among numerous challenges involved, one main complexity is to capture the behaviour of the material at the failure process zone, where the underlying micro-structure governs the macroscopic process. Accounting for all details in a model will increase the computational cost, which thereby requires finding a balance between the level of details and the cost incurred. The research in the present thesis aims at developing a framework capable of analysing ductile fracture in terms of initiation and propagation of cracks, which is applicable to thin-walled steel structures subjected to high strain rates. Of particular importance is to address the application to large scale structures for which capturing the accurate response of the structure calls for an efficient numerical procedure. First, a method is developed to analyse and predict the crack propagation in thin-walled structures subjected to large plastic deformation under high strain rate loading. In order to represent crack propagation independent of the finite element discretisation, the extended finite element method (XFEM) based on a 7-parameter shell formulation with extensible directors is employed. For the temporal discretisation, as typically used in high speed events and high strain rates, an explicit time integration is used which is observed to be prone to generate unphysical oscillations upon crack propagation. To remedy this problem, two possible solutions are proposed. To verify and validate the proposed model, various numerical examples are presented. It is shown that the results correlate well with the experiments. Second, to capture the fine scale nature of the ductile fracture process, a new XFEM based enrichment of the displacement field is proposed that allows for a crack tip and/or kink to be represented within an element. It concerns refining the crack tip element locally yet retaining the macroscale node connectivity unchanged. This in turn results in a better representation of the discontinuous kinematics, however, unlike regular mesh refinement, this requires no change to the macroscale solution procedure. To show the accuracy of the proposed method, a number of examples are presented. It is shown that the proposed method enhances the analyses of the ductile fracture of the thin-walled large scale structures under high strain rates. Third, in line with the previous developments, a new Phantom node based approach for analyses of the ductile fracture of thin-walled large scale structures is proposed. It concerns subscale refinement of the elements through which the crack progresses. As compared to the XFEM approach, the Phantom node method is more efficient implementation-wise and computationally. It allows for a detailed representation of the crack tip and kink, which leads to a more smooth progression of the crack. The proposed approach is applicable to both low and high order elements of different types. In order to show the accuracy of the new approach a number of examples are presented and compared to the conventional approach. Finally, a new approach to analyse ductile failure of thin-walled structures based on the continuum damage theory is developed. For this, a Johnson-Cook visco-plasticity formulation coupled to continuum damage is developed, whereby the total response is obtained from a damage enhanced effective visco-plastic material model. Production of the fracture area is governed by a rate dependent damage evolution law, where the damage-visco-plasticity coupling is realised via the inelastic damage driving dissipation. In addition, a local damage enhanced model (without damage gradient terms) is used, which contributes to the computational efficiency. A number of examples are presented to investigate the accuracy of the proposed model and it is shown that the model provides good convergence properties.