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

Validation on large scale tests of a new hardening–softening law for the Barcelona plastic damage model

This paper presents the results of finite element simulations made on a bent pipe subjected to an in-plane variable cyclic displacement combined with internal pressure. Special emphasis is put on the capacity of the model to illustrate different failure modes depending on the internal pressure applied on the pipe. The results of the numerical analyses will be compared to experimental ones. The constitutive model used for the simulation of Ultra Low Cycle Fatigue (ULCF) loading and the hardening–softening law used are only briefly touched upon. The monotonic behavior of a large diameter pipe, as obtained from the constitutive model proposed, is also shown and compared to experimental results under two different loading conditions. The total axial load at failure for this case resulted in less than 10% error as compared to the experiments. Regarding the ULCF in-plane bending simulations conducted on a 16-in. 90º elbow, the results were in good agreement with the experimental test in terms of force–displacement hysteresis loops and total fatigue life of the specimen. An analysis of the dependence of the failure mode to the internal pressure applied has been conducted, showing that the formulation is capable of obtaining both habitual failure types

High cycle fatigue simulation: A new stepwise load-advancing strategy

A stepwise load-advancing strategy for cyclic loading will be presented in this paper that yields convergence in reasonable computational time for highly nonlinear behaviour occurring past the S–N curve. The algorithm is also effective when dealing with combinations of cyclical loads. The strategy is coupled to a continuum damage model for mechanical fatigue analysis. A brief overview of the constitutive model is also presented although it is not the main focus of this work. The capabilities of the proposed procedure are shown in two numerical examples. The model is validated by comparison to experimental results

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

Numerical Simulation of Fatigue in Composites

For the past several years, composite marine structures have been designed but without having a complete characterization the composite materials. The main reason is due to the large quantity of variables that affect the behavior of said materials. One of the tasks that has not been properly characterized is the behavior of composite structures under fatigue loads that appear in marine structures that are subjected to cyclic loads. Therefore, numerical tools that characterize fatigue performance are required in order to design more reliable structures. The formulation proposed in this work is based on the Serial/Parallel Rule of Mixtures [1] and a fatigue damage model [2]. The Serial/Parallel Rule of Mixtures can be understood as a constitutive law manager that provides the response of the composite from the constitutive performance of its constituents. Therefore, the constitutive laws chosen to represent the behavior of each constituent material have to fit with their real performance. Also, the fatigue damage model is based on the use of a reduction function which takes into account the cyclic degradation of the materials, both strength and stiffness degradation, in function of the number of cycles, maximum stress and stress amplitude. Current work presents a numerical tool developed to characterize fatigue in composites. The fatigue behavior of constituent materials is defined using mechanic parameters taken from literature. Afterwards, a reproduction of the tests will be done in order to validate the fatigue formulation proposed. [1] Car, E., Oller, S., Oñate, E. "Estudio del comportamiento no lineal en materiales compuestos", Techincal Report 264,CIMNE, 1997. [2] Oller, Salomon, O., Oñate, E. “A continuum mechanics model for mechanical fatigue analysis", Composite Materials Science, Vol 32, Issue 2, pp 175-195, 2005

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

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

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

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