Numerical simulation of fatigue processes : application to steel and composite structures

The present thesis aims at advancing an innovative computational methodology that simulates steel and composite material fracture under cyclic loading following a phenomenological approach, with calibration from both small scale and large scale testing. This work addresses fatigue processes ranging from high cycle to ultra-low-cycle fatigue. An assessment of the current state of the art is done for all the different fatigue types. Following, for ultra-low cycle fatigue a new constitutive law is proposed and validated with experimental results obtained on small scale samples. Industrial applications are shown for a large diameter straight pipe under monotonic loading conditions and for a bent pipe under cyclic loading. Emphasis is made on the capacity of the model to represent different failure modes depending on the loading conditions. The research regarding this part has been used in the frame of the European Project: ¿Ultra low cycle fatigue of steel under cyclic high-strain loading conditions¿ (ULCF). Regarding high cycle fatigue, a classic damage model is presented in combination with an automatic load advancing strategy that saves computational time when dealing with load histories of millions of cycles. Numerical examples are shown in order to demonstrate the capabilities of the advancing strategy and a validation of the model is done on small scale samples. A new constitutive model is presented for Low Cycle Fatigue that uses the classic plasticity and damage theories and simultaneously integrates both processes in the softening regime. The capabilities of the model are shown in numerical examples. Finally, the high cycle fatigue damage model is applied to the constituents of a composite material and the structural behaviour is obtained by means of the serial/parallel rule of mixtures. Validation of the constitutive formulation is done on pultruded glass fiber reinforced polymer profiles.La presente tesis propone una metodología innovadora para la simulación numérica de la rotura de materiales metálicos y compuestos sometidos a cargas cíclicas. El enfoque es fenomenológico y la formulación se calibra con resultados experimentales obtenidos en especímenes a pequeña escala y con experimentos a gran escala. Este trabajo abarca procesos de fatiga desde alto número de ciclos hasta muy bajo número de ciclos. Una evaluación del estado del arte hasta el momento se ha llevado a cabo para los diferentes tipos de fatiga. A continuación, se propone una nueva ley constitutiva para la fatiga de muy bajo número de ciclos y se presenta la validación con resultados experimentales obtenidos en especímenes a escala pequeña. El modelo constitutivo se ha probado en dos aplicaciones industriales: una tubería de gran diámetro bajo condiciones de carga monótonas y una tubería doblada a un ángulo de 90 grados sometida a cargas cíclicas. Se ha enfatizado la capacidad del modelo de reproducir diferentes modos de rotura dependiendo de las condiciones de carga. El trabajo referente a este modelo se ha usado en el marco del proyecto europeo: ¿Fatiga de muy bajo número de ciclos del acero bajo grandes deformaciones cíclicas¿. Respecto a la fatiga de alto número de ciclos, se presenta un modelo clásico de daño combinado con una estrategia automatizada de avance en la carga por número de ciclos. La estrategia conduce a un ahorro en tiempo de computación cuando se aplican millones de ciclos de carga. Las capacidades y particularidades de la estrategia de avance en la carga se enseñan en una serie de ejemplos numéricos. El modelo se valida con resultados experimentales obtenidos en especímenes a pequeña escala. Un nuevo modelo constitutivo se presenta para la fatiga de bajo número de ciclos que se basa en las teorías básicas de plasticidad y daño y que integra simultáneamente las ecuaciones de ambos procesos en el régimen de ablandamiento. Las capacidades del modelo se enseñan a través de ejemplos numéricos. Finalmente, se estudia la aplicación del modelo de daño para fatiga de alto número de ciclos en los componentes de materiales compuestos. El comportamiento estructural del material compuesto se obtiene a través de la teoría de mezclas serie/paralelo. La formulación se valida con resultados experimentales obtenidos en perfiles de GFRP.Postprint (published version

Analysis of ultra low cycle fatigue problems with the barcelona plastic damage model

This paper presents a plastic formulation based on the Barcelona plastic damage model ([1], [2]) capable of predicting the material failure due to Ultra Low Cycle Fatigue. This is achieved taking into account the fracture energy dissipated during the cyclic process. This approach allows the simulation of ULCF in regular cyclic tests, but also in non-regular cases such as seismic loads

A rule of mixtures approach for delamination damage analysis in composite materials

The present study aims at investigating the delamination behavior of laminated composites in different loading modes within a homogenization theory of mixtures. The delamination damage phenomenon is introduced at the bulk level by eliminating the explicit representation of interfaces. Potential delamination planes are identified according to the developed interfacial stresses, and damage evolution is computed for each mode independently through a stress-based formulation. An arc-length strategy is employed to solve equilibrium equations owing to the snap-back effects. Reliability of the adopted mixing theory, as a framework for integrating the delamination theory into, is assessed by comparing the results with the ones obtained from micromechanical models in a fiber metal laminate structure. Considering delamination, a good agreement is observed in mode I, mode II and mixed mode configurations by evaluating the results against available numerical and experimental data in thermoset and thermoplastic composite systems. The present method has the capability to be used in the conventional finite element codes with the number of elements kinematically needed in the thickness, regardless of the number of layers, which dramatically reduces the computational cost in modeling composites with large number of layers. The proposed approach is not intended to replace other exact methods at the coupon scale, however, its main application would be in modeling delamination on large scale systems with minimum loss of accuracy.Peer ReviewedPostprint (published version

Stepwise advancing strategy for the simulation of fatigue problems

A time advance strategy for cyclic loading will be presented, applied to the fatigue formulation first proposed by [1]. The coupling of both formulations provides a comprehensive approach to simulate high cycle fatigue problems accurately and with an important computational cost reduction. The capabilities of the proposed procedure are shown in a numerical example

Analysis of ultra low cycle fatigue problems with the Barcelona plastic damage model

This paper presents a plastic formulation based on the Barcelona plastic damage model capable of predicting the material failure due to Ultra Low Cycle Fatigue. This is achieved taking into account the fracture energy dissipated during the cyclic process. This approach allows the simulation of ULCF in regular cyclic tests, but also in non-regular cases such as seismic loads.Postprint (published version

Stepwise advancing strategy for the simulation of fatigue problems

A time advance strategy for cyclic loading will be presented, applied to the fatigue formulation first proposed by [1].The coupling of both formulations provides a comprehensive approachto simulate high cycle fatigue problems accurately and with an important computational cost reduction. The capabilities of the proposed procedure are shown in a numerical examplePostprint (published version

High-cycle fatigue constitutive model and a load-advance strategy for the analysis of unidirectional fiber reinforced composites subjected to longitudinal loads

A fatigue constitutive model valid for the composite constituent will be presented in this paper. The composite behaviour will be obtained by means of the serial/parallel mixing theory that is also used as a constitutive equation manager. The constitutive formulation is coupled with a load advancing strategy in order to reduce the computational cost of the numerical simulations. Validation of the constitutive formulation is done on pultruded glass fiber reinforced polymer profiles. Special emphasis is made on the comparison between the experimental and the numerical failure mode.Peer ReviewedPostprint (author's final draft

Coupled plastic damage model for low and ultra-low cycle seismic fatigue

This paper presents the theoretical framework for a coupled plastic damage constitutive model valid for materials subjected to cyclic loads that lead to low and ultra-low cycle fatigue. Two numerical examples were presented in order to illustrate the behaviour of the model and its capabilities.Postprint (published version

Methodology for the analysis of post-tensioned structures using a constitutive serial-parallel rule of mixtures: large scale non-linear analysis

The main purpose of this paper is to develop a reliable method based on a three-dimensional (3D) finite-element (FE) model to simulate the constitutive behaviour of reinforced concrete structures strengthened with post-tensioned or pre-stressed tendons well beyond the elastic domain. The post-tensioned concrete is modelled as a composite material whose behaviour is described with the serial-parallel rule of mixtures (S-P RoM) (Rastellini et al., 2008; Martinez et al., 2008; Martinez et al., 2014 [3]) and the nonlinear behaviour of each component is accounted for by means of plasticity and damage models. 3D FE models were used, where the nonlinear material behaviour and geometrical analysis based on incremental-iterative load methods were adopted. Several examples are shown where the capabilities of the method on large scale structures are exhibited taking into account the self-weight, the post-tension load and different pressure loads. A new metric for computing the crack opening displacement inside a finite element is proposed.Peer ReviewedPostprint (author's final draft

A unified non-linear energy dissipation-based plastic-damage model for cyclic loading

A new energy-dissipation-based rate-independent constitutive law within the framework of elastoplasticity coupled with damage is proposed. With this methodology, the inelastic strains and the stiffness degradation exhibited by quasi-brittle materials under monotonic or cyclic loading conditions are taken into account. The proposed constitutive model is able to capture micro-cracks closure-reopening effects due to load reversal. A wide variety of hardening/softening laws on the stress–strain relationship are described and considered for the novel normalized plastic-damage energy dissipation internal variable. This normalized internal variable allows the model to be independent on the sign of the load and dissipate different fracture energies (tensile, compressive and potentially shear) in a natural way. Several numerical examples are presented in order to ensure the efficiency and validity of the proposed model for simulating the non-linear behaviour of quasi-brittle materials under monotonic and cyclic loading. Some numerical aspects of the implemented algorithm and the return mapping procedure are also described in detail and discussed.This work has been done within the framework of the Fatigue4Light (H2020-LC-GV-06-2020) project: “Fatigue modelling and fast testing methodologies to optimize part design and to boost lightweight materials deployment in chassis parts”. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 101006844. The work has been also supported by the Spanish Government program FPU17/04196. The authors gratefully acknowledge all the received support. Finally, acknowledge the support received by the Severo Ochoa Centre of Excellence (2019–2023) under the grant CEX2018-000797-S funded by MCIN/AEI /10.13039/501100011033.Peer ReviewedPostprint (published version