Failure of thin-walled structures under impact loading

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

Explicit dynamics simulation of blade cutting of thin elastoplastic shells using "directional" cohesive elements in solid-shell finite element models

The intentional or accidental cutting of thin shell structures by means of a sharp object is of interest in many engineering applications. The process of cutting involves several types of nonlinearities, such as large deformations, contact, crack propagation and, in the case of laminated shells, delamination. In addition to these, a special difficulty is represented by the blade sharpness, whose accurate geometric resolution would require meshes with characteristic size of the order of the blade curvature radius. A computational finite element approach for the simulation of blade cutting of thin shells is proposed and discussed. The approach is developed in an explicit dynamics framework. Solid-shell elements are used for the discretization, in view of possible future inclusion in the model of delamination processes. Since a sharp blade can interfere with the transmission of cohesive forces between the crack flanks in the cohesive process zone, standard cohesive interface elements are not suited for the simulation of this type of problems unless extremely fine meshes, with characteristic size comparable to the blade curvature radius, are used. To circumvent the problem, the use of a new type of directional cohesive interface element, previously proposed for the simulation of crack propagation in elastic shells, is further developed and reformulated for application to the cutting of elastoplastic thin structures, discretized by solid-shell elements. The proposed approach is validated by means of application to several cutting problems of engineering interest

Mixed finite elements with independent strain interpolation for isotropic and orthotropic damage

Tesi per compendi de publicacionsThe numerical modelling of fracture has been an active topic of research for over five decades. Most of the approaches employed rely on the use of the Finite Element Method, which has shown to be an effective and cost-efficient tool for solving many physical phenomena. However, the issue of the spurious dependency of the computed solution with the mesh orientation in cracking problems has raised a great concern since its early reports in the 1980s. This matter has proved to be a major challenge in computational solid mechanics; it affects numerous methods employed to solve the problem, in which the computed crack trajectories are spuriously dependent on the arrangement of the finite element (FE) mesh employed. When performing a structural analysis and, in particular, when computing localized failure, it is fundamental to use a reliable and mesh objective method to be able to trust the results produced by the FE code in terms of the fracture paths, bearing capacity, collapse mechanism and nonlinear responses. In this doctoral thesis, the mixed e/u strain/displacement finite element method is used together with multiple isotropic and orthotropic damage constitutive laws for the numerical modelling of quasi-brittle fracture with mesh objectivity. The independent interpolation of the strains increases the accuracy of the computed solution, guaranteeing the local convergence of the stress and strain fields. This feature is a crucial improvement over the standard FE formulation in solid mechanics where the strains are computed as local derivatives of the displacements and the local convergence of the resulting stresses and strains is not ensured. The enhanced precision provided by the mixed formulation in the area near the crack tip is decisive for obtaining unbiased numerical results with regard to the orientation of the FE mesh. The strain-driven format of the mixed formulation enables to readily consider different constitutive laws defined in a stress-strain structure in the numerical simulations. The thesis includes the study of the effect of the material model employed in the resulting crack trajectories as well as the analysis of the relative performance of several isotropic and orthotropic damage behaviors in mode I, mode II, mode III and mixed mode fracture problems. In this work specific isotropic and orthotropic damage laws are proposed for the numerical modelling of fracture under cyclic loading, which include tensile and compressive damage, stiffness recovery due to crack closure and reopening, as well as irreversible strains. Also, the capacity of the proposed model in reproducing the structural size effect is examined, which is an essential requirement for models aiming at computing quasi-brittle behavior. In this thesis, a comprehensive comparison of the mixed FE formulation with other techniques employed for computing fracture, specifically the Extended Finite Element Method (XFEM) and the Phase-field model, is made, revealing the cost-efficiency of the proposed Mixed Finite Element Method for modelling quasi-brittle cracking with mesh objectivity. This allows to perform the analysis of real-scale structures, in 2D and 3D, with enhanced accuracy, demonstrating the applicability of this method in the engineering practice. The validation of the model is performed with an extensive comparison of computed results with existing experimental tests and numerical benchmarks. The capacity of the mixed formulation in reproducing force-displacement curves, crack trajectories and collapse mechanisms with enhanced accuracy is demonstrated in detail.En esta tesis doctoral, el método de los elementos finitos mixtos e/u deformación/desplazamiento es utilizado junto con varias leyes constitutivas de daño isótropo y ortótropo para la modelización numérica de la fractura cuasi-frágil de forma objetiva con respecto a la orientación de la malla. La interpolación independiente de las deformaciones aumenta la precisión de la solución calculada, garantizando la convergencia local de los campos de tensiones y deformaciones. Esta característica representa una mejora crucial con respecto a la formulación estándar de elementos finitos de la mecánica de sólidos, donde las deformaciones se calculan como derivadas locales de los desplazamientos y la convergencia local de las tensiones y deformaciones resultantes no está garantizada. La mayor precisión aportada por la formulación mixta en la zona cercana a la punta de la fisura es decisiva para obtener resultados numéricos que no presenten una dependencia espuria con la orientación de la malla de elementos finitos. El formato expresado en función de la deformación de la formulación mixta permite considerar directamente diferentes leyes constitutivas que siguen una estructura tensión-deformación para su uso en las simulaciones numéricas. La tesis incluye el estudio del efecto que tiene la ley constitutiva utilizada en la trayectoria de las fisuras resultantes, así como el análisis del desempeño relativo de varias leyes de daño isótropas y ortótropas en problemas de fractura en modo I, modo II, modo III y modo mixto. En este trabajo se proponen leyes de daño isótropo y ortótropo específicas para la modelización numérica de la fractura bajo carga cíclica, que incluyen daño a tracción y a compresión, recuperación de la rigidez por el cierre y reapertura de fisuras, así como deformaciones irreversibles. Además, se comprueba la capacidad del modelo propuesto para reproducir el efecto tamaño, que es un requisito esencial para los modelos que tengan como objetivo calcular el comportamiento cuasi-frágil de los materiales. En la tesis se realiza una comparación exhaustiva de la formulación mixta de elementos finitos con otras técnicas que se utilizan para calcular el problema, específicamente el Método de los Elementos Finitos Extendidos (XFEM) y el modelo Phase-field, revelando la eficiencia computacional del Método de los Elementos Finitos Mixtos propuesto para modelizar la rotura cuasi-frágil de forma objetiva con respecto a la malla. Ello permite realizar el análisis de estructuras de tamaño real, en 2D y 3D, con mayor precisión, demostrando la aplicabilidad del método a problemas reales de ingeniería. La validación del modelo se realiza con una comparación de resultados calculados con ensayos de laboratorio existentes y con simulaciones de casos teóricos de referencia. Se demuestra la capacidad de la formulación mixta para reproducir curvas fuerza-desplazamiento, trayectorias de fisuras y mecanismos de colapso con precisión mejorada.Postprint (published version

Strength prediction of notched thin ply laminates using finite fracture mechanics and the phase field approach

Thin ply laminates are a new class of composite materials with great potential for application in the design of thinner and highly optimized components, resulting in potential weight savings and improved mechanical performance. These new composites can stir the development of lighter structures, overcoming current design limitations as well as notably reducing the onset and development of matrix cracking and delamination events. This paper presents the application of two recent modeling methods for the failure analysis and strength prediction of open-hole thin ply laminates under tensile loading, which exhibit a brittle response upon failure: (i) the analytical coupled energy-stress Finite Fracture Mechanics (FFMs) technique, and (ii) the FE-based Phase Field (PF) approach for fracture that is incorporated into an enhanced assumed solid shell element. The predictions obtained using both strategies are compared with experimental data. These correlations exhibit a very satisfactory level of agreement, proving the robustness and reliability of both methods under consideration

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized. © 2022, The Author(s)

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized

Damage modelling in fibre-reinforced composite laminates using phase field approach

Thin unidirectional-tape and woven fabric-reinforced composites are widely utilized in the aerospace and automotive industries due to their enhanced fatigue life and impact damage resistance. The increasing industrial applications of such composites warrants a need for high-fidelity computational models to assess their structural integrity and ensure robust and reliable designs. Damage detection and modelling is an important aspect of overall design and manufacturing lifecycle of composite structures. In particular, in thin-ply composites, the damage evolves as a result of coupled in-plane (membrane) and out-of-plane (bending) deformations that often arise during critical events, e.g., bird strike/ hail impact or under in-flight service loads. Contrary to metallic structures, failure in composites involves complex and mutually interacting damage patterns, e.g., fibre breakage/ pullout/ bridging, matrix cracking, debonding and delamination. Providing high-fidelity simulations of intra-laminar damage is a challenging task both from a physics and a computational perspective, due to their complex and largely quasi-brittle fracture response. This is manifested by matrix cracking and fibre breakage, which result in a sudden loss of strength with minimum crack openings; subsequent fibre pull-outs result in a further, although gradual, strength loss. To effectively model this response, it is necessary to account for the cohesive forces evolving within the fracture process zone. Furthermore, the interaction of the failure mechanisms pertinent to both the fibres and the matrix necessitate the definition of anisotropic damage models. In addition, the failure in composites extends across multiple scales; it initiates at the fibre/ matrix-level (micro-scale) and accumulates into larger cracks at the component/ structural level (macro-scale). From a simulation standpoint, accurate prediction of the structure’s critical load bearing capacity and its associated damage thresholds becomes a challenging task; accuracy necessitates a fine level of resolution, which renders the corresponding numerical model computationally expensive. To this point, most damage models are applied at the meso-scale based on local stress-strain estimates, and considering material heterogeneity. Such damage models are often computationally expensive and practically inefficient to simulate the failure behaviour in real-life composite structures. Moreover at the macro-scale, the effect of local stresses is largely minimised, which necessitates definition of a homogenised failure criterion based on global macro-scale stresses. This thesis presents a phase field based MITC4+ (Mixed Interpolation of Tensorial Components) shell element formulation to simulate fracture propagation in thin shell structures under coupled membrane and bending deformations. The employed MITC4+ approach renders the element shear- and membrane- locking free, hence providing high-fidelity fracture simulations in planar and curved topologies. To capture the mechanical response under bending-dominated fracture, a crack-driving force description based on the maximum strain energy density through the shell-thickness is considered. Several numerical examples simulating fracture in flat and curved shell structures which display significant transverse shear and membrane locking are presented. The accuracy of the proposed formulation is examined by comparing the predicted critical fracture loads against analytical estimates. To simulate diverse intra-laminar fracture modes in fibre reinforced composites, an anisotropic cohesive phase field model is proposed. The damage anisotropy is captured via distinct energetic crack driving forces, which are defined for each pertinent composite damage mode together with a structural tensor that accounts for material orientation dependent fracture properties. Distinct 3-parameter quasi-quadratic degradation functions based on fracture properties pertinent to each failure mode are used, which result in delaying or suppressing pre-mature failure initiation in all modes simultaneously. The degradation functions can be calibrated to experimentally derived strain softening curves corresponding to relevant failure modes. The proposed damage model is implemented in Abaqus and is validated against experimental results for woven fabric-reinforced and unidirectional composite laminates. Furthermore, a dynamic explicit cohesive phase field model is proposed to capture the significantly nonlinear damage evolution behaviour pertinent to impact scenarios. A strategy is presented to combine the phase field and the cohesive zone models to perform full composite-laminate simulations involving both intra-laminar and inter-laminar damage modes. Finally, the developed phase field model is employed within the framework of a multiscale surrogate modelling technique. The latter is proposed to perform fast and efficient damage simulation involving different inherent scales in composites. The technique is based on a multiscale FE2 (Finite Element squared) homogenisation approach, however the computationally expensive procedure of solving the meso- and macro-scale models simultaneously is avoided by using a robust surrogate model. The meso-scale is defined as a unit-cell representative volume element (RVE) model, which is analysed under a large number of statistically randomised mixed-mode macro-strains, applied with periodic boundary conditions. The complex damage mechanisms occurring at the meso-scale are captured using the anisotropic cohesive phase field model, and the homogenised stress-strain responses post-damage evolution are obtained. These anisotropic meso-scale fracture responses are used to train the Polynomial Chaos Expansion (PCE) and Artificial Neural Network (ANN) based surrogate models, which are interrogated at the macro-scale using arbitrary macro-strain combinations. The accuracy of the surrogate model is validated against high-fidelity phase field simulations for a set of benchmarks

2nd International Workshop on Physics-Based Modelling of Material Properties and Experimental Observations with special focus on Fracture and Damage Mechanics: Book of Abstracts

This report covers the book of abstracts of the 2nd International Workshop on Physics Based Modelling of Material Properties and Experimental Observations, with special focus on Fracture and Damage Mechanics. The workshop is organized in the context of European Commission’s Enlargement and Integration Action, by the Joint Research Centre in collaboration with the TOBB University of Economics and Technology (TOBB ETU) on 15th-17th May 2013 in Antalya, Turkey. The abstracts of the keynote lectures and all the technical presentations are included in the book. This workshop will give an overview of different physics-based models for fracture and degradation of metallic materials and how they can be used for improved understanding and more reliable predictions. Models of interest include cohesive zones to simulate fracture processes, ductile-brittle transition for ferritic steels, ductile fracture mechanisms such as void growth or localized shear, fatigue crack initiation and short crack growth, environmental assisted cracking. Experimental studies that support such models and case studies that illustrate their use are also within the scope. The workshop is also an opportunity for scientists and engineers from EU Member States and target countries to discuss research activities that could be a basis for future collaborations.JRC.F.4-Nuclear Reactor Integrity Assessment and Knowledge Managemen

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells