Nonlinear finite element simulation of non-local tension softening for high strength steel material.

The capability of current finite element softwares in simulating the stress-strain relation beyond the elastic-plastic region has been limited by the inability for non- positivity in the computational finite elements' stiffness matrixes. Although analysis up to the peak stress has been proved adequate for analysis and design, it provides no indication of the possible failure predicament that is to follow. Therefore an attempt was made to develop a modelling technique capable of capturing the complete stress-deformation response in an analysis beyond the limit point. This proposed model characterizes a cyclic loading and unloading procedure, as observed in a typical laboratory uniaxial cyclic test, along with a series of material properties updates. The Voce equation and a polynomial function were proposed to define the monotonic elastoplastic hardening and softening behaviour respectively. A modified form of the Voce equation was used to capture the reloading response in the softening region. To accommodate the reduced load capacity of the material at each subsequent softening point, an optimization macro was written to control this optimum load at which the material could withstand. This preliminary study has ignored geometrical effect and is thus incapable of capturing the localized necking phenomenon that accompanies many ductile materials. The current softening model is sufficient if a global measure is considered. Several validation cases were performed to investigate the feasibility of the modelling technique and the results have been proved satisfactory. The ANSYS finite element software is used as the platform at which the modelling technique operates

Multifield-based modeling of material failure in high performance reinforced cementitious composites

Cementitious materials such as mortar or concrete are brittle and have an inherent weakness in resisting tensile stresses. The addition of discontinuous fibers to such matrices leads to a dramatic improvement in their toughness and remedies their deficiencies. It is generally agreed that the fibers contribute primarily to the post-cracking response of the composite by bridging the cracks and providing resistance to crack opening. On the other hand, the multifield theory is a mathematical tool able to describe materials which contain a complex substructure. This substructure is endowed with its own properties and it interacts with the macrostructure and influences drastically its behavior. Under this mathematical framework, materials such as cement composites can be seen as a continuum with a microstructure. Therefore, the whole continuum damage mechanics theory, incorporating a new microstructure, is still applicable. A formulation, initially based on the theory of continua with microstructure Capriz, has been developed to model the mechanical behavior of the high perfor-mance fiber cement composites with arbitrarily oriented fibers. This formulation approaches a continuum with microstructure, in which the microstructure takes into account the fiber-matrix interface bond/slip processes, which have been recognized for several authors as the principal mechanism increasing the ductility of the quasi-brittle cement response. In fact, the interfaces between the fiber and the matrix become a limiting factor in improving mechanical properties such as the tensile strength. Particularly, in short fiber composites is desired to have a strong interface to transfer effectively load from the matrix to the fiber. However, a strong interface will make difficult to relieve fiber stress concentration in front of the approaching crack. According to Naaman, in order to develop a better mechanical bond between the fiber and the matrix, the fiber should be modified along its length by roughening its surface or by inducing mechanical defor-mations. Thus, the premise of the model is to take into account this process considering a micro field that represents the slipping fiber-cement displacement. The conjugate generalized stress to the gradient of this micro-field verifies a balance equation and has a physical meaning. This contribution includes the computational modeling aspects of the high fiber rein-forced cement composites (HFRCC) model. To simulate the composite material, a finite element discretization is used to solve the set of equations given by the multifield approach for this particular case. A two field discretization: the standard macroscopic and the micro-scopic displacements, is proposed through a mixed finite element methodology. Furthermore, a splitting procedure for uncoupling both fields is proposed, which provides a more convenient numerical treatment of the discrete equation system. The initiation of failure in HPFRCC at the constitutive level identified as the onset of strain localization depends on the mechanical properties of the all compounds and not only on the matrix ones. As localization criteria is considered the bifurcation analysis in combination with the localized strain injection technique presented by Oliver et al. It consists of injecting a specific localization mode during the localization stage, via mixed finite element formulations, to the path of elements that are going to capture the cracks, and, in this way, the spurious mesh orientation dependence is removed. Model validation was performed using a selected set of experiments that proves the via-bility of this approach. The numerical examples of the proposed formulation illustrated two relevant aspects, namely: 1) the role of the bonding mechanism in the strain hardening be-havior after cracking in the HPFRCC and 2) the role that plays the finite element formulation in capturing the displacement localization in the localization stage

Random lattice particle modeling of fracture processes in cementitious materials

The capability of representing fracture processes in non-homogeneous media is of great interest among the scientific community for at least two reasons: the first one stems from the fact that the use of composite materials is ubiquitous within structural applications, since the advantages of the constituents can be exploited to improve material performance; the second consists of the need to assess the non-linear post-peak behavior of such structures to properly determine margins of safety with respect to strong excitations (e.g. earthquakes, blast or impact loadings). Different kinds of theories and methodologies have been developed in the last century in order to model such phenomena, starting from linear elastic equivalent methods, then moving to plastic theories and fracture mechanics. Among the different modeling techniques available, in recent years lattice models have established themselves as a powerful tool for simulating failure modes and crack paths in heterogeneous materials. The basic idea dates back to the pioneeristic work of Hrennikoff: a continuum medium can be modeled through the interaction of unidimensional elements (e.g. springs or beams) spatially arranged in different ways. The set of nodes that interconnect the elements can be regularly or irregularly placed inside the domain, leading to regular or random lattices. It has been shown that lattices with regular geometry can strongly bias the direction of cracking, leading to incorrect results. A variety of lattice models have been developed. Such models have seen a wide field of applications, ranging from aerodynamics (using Lattice-Boltzman models) to heat transfer, crystallography and many others. Every material used in civil and infrastructure engineering is constituted of different phases. This is due to the fact that the different features of different elements are usually coupled in order to obtain greater advantages with respect to the original constituents. Even structural steel, which is usually thought of as a homogeneous continuum-type medium, includes carbon particles that can be seen as inhomogeneities at the microscopic level. The mechanical behavior of concrete, which is the main object of the present work, is strongly affected not only by the presence of inclusions (i.e. the aggregates pieces) but also by their arrangement. For this reason, the explicit, statistical representation of their presence is of great interest in the simulations of concrete behavior. Lattice models can directly account for the presence of different phases, and so are advantageous from this perspective. The definition of such models, their implementation in a computer program, together with validation on laboratory tests will be presented. The present work will briefly review the state of the art and the basic principles of these models, starting from the geometrical and computing tools needed to build the simulations. The implementation of this technique in the Matlab environment will be presented, highlighting the theoretical background. The numerical results will be validated based on two complementary experimental campaigns,which focused on the meso- and macro-scales of concrete. Whereas the aim of this work is the representation of the quasi-brittle fracture processes in cementitious materials such as concrete, the discussed approach is general, and therefore valid for the representation of damage and crack growth in a variety of different materials

Modelling of Interfacial Problems at Various Length Scales in Polycrystalline Materials

The goal of this research project was to develop a modelling technique making it possible to simulate grain boundaries and inclusion-matrix material interfaces using numerical techniques. This is particularly of interest when investigating the effects of grain boundary sliding and decohesion of the material interfaces under hot deformation conditions. This can then be used to predict damage nucleation and growth at the grain boundaries applicable to both creep type damage and plasticity induced damage. A novel scheme was developed based on the Controlled Voronoi Poisson’s Tessellation technique (CVPT) to generate statistically equivalent microstructures based on the physical parameters of the microstructure in free cutting steel under hot forming conditions. The generated microstructure was then used to study the effect of different parameters on the global response of the material. Furthermore, this model was utilised to calibrate the crystal plasticity material model using the experimental data available for high strain rate deformation of free cutting steel at elevated temperatures. A micro-scale Representative Volume Element (RVE) was developed in which the grain boundaries and material interfaces have been represented by cohesive elements. The RVE consisting of an MnS inclusion surrounded by four austenitic grains was used to study the effect of inclusion orientation, grain orientations and the relative strength of grain boundaries and the matrix/inclusion interfaces on overall failure of the RVE. Furthermore, in the endeavour of finding the right modelling technique an extension to the conventional finite element method called XFEM proved to be capable of modelling strong and weak discontinuities independent of the FE mesh. The crystal plasticity material model was implemented in the open-source FE package OOFEM and was used to simulate interface decohesion and grain boundary motion using the XFEM technique

Studies on strain localization, ductile fracture and damage in structural metals

One of the most important limit states in structural metals is ductile fracture, and the prediction of ductile fracture is of great importance in many engineering applications. The overall objective of the research reported in this dissertation is to advance the understanding and modeling of ductile fracture in metals. This research addresses three main issues: micromechanical modeling of ductile fracture, the development of a micromechanics-based ductile fracture model and its numerical implementation, and a numerical investigation of geometry and damage induced strain localization based on a nonlocal formulation. It has long been recognized that stress triaxiality is a key parameter affecting initiation of ductile fracture. More recently, shear stress has been identified as another important parameter, in addition to stress triaxiality, that influences the process of ductile fracture. In this research, a micromechanics-based model is proposed for predicting initiation of ductile fracture that couples both stress triaxiality and shear stress. The new model is based on a combination of the existing Rice-Tracey and modified maximum shear stress models. The new model is applied to construct the fracture locus of different types of metal alloys and is used to predict fracture initiation by numerical tools. The predicted results are in good agreement with experimental data reported in literature that covers a wide range of triaxialities and shear stress. Another portion of this research, within the framework of micromechanics, investigated the effect of combined normal and shear stress components on micro-void evolution and material behavior. This work involved finite element modeling of a cubic unit cell associated with a spherical void. The results show that the void growth process and macroscopic stress-strain response is highly dependent on the shear stress component. At different ranges of triaxialities, and with different void growth and coalescence mechanisms, shear stress has an important effect on the ductile fracture process. Numerical modeling of strain localization in ductile metals based on standard continuum mechanics exhibits non-convergent mesh sensitivity. This issue is addressed in the final portion of this research. A one-dimensional model based on the nonlocal theory is proposed to analyze geometry-induced strain localization, i.e., necking in structural metals. A nonlocal continuum damage model using the same enhanced continuum law is developed to deal with the damage induced strain localization in metals. Both models provide encouraging performance in eliminating the non-convergent mesh sensitivity problem. Such improved strain localization modeling techniques show potential to be useful for further exploration of ductile fracture phenomena.Civil, Architectural, and Environmental Engineerin

Multified-based modeling of material failure in high performance reinforced cementitious composites

Cementitious materials such as mortar or concrete are brittle and have an inherent weakness in resisting tensile stresses. The addition of discontinuous fibers to such matrices leads to a dramatic improvement in their toughness and remedies their deficiencies. It is generally agreed that the fibers contribute primarily to the post-cracking response of the composite by bridging the cracks and providing resistance to crack opening (Suwaka & Fukuyama 2006). On the other hand, the multifield theory is a mathematical tool able to describe materials which contain a complex substructure (Mariano & Stazi 2005). This substructure is endowed with its own properties and it interacts with the macrostructure and influences drastically its behavior. Under this mathematical framework, materials such as cement composites can be seen as a continuum with a microstructure. Therefore, the whole continuum damage mechanics theory, incorporating a new microstructure, is still applicable. A formulation, initially based on the theory of continua with microstructure Capriz (Capriz 1989), has been developed to model the mechanical behavior of the high performance fiber cement composites with arbitrarily oriented fibers. This formulation approaches a continuum with microstructure, in which the microstructure takes into account the fibermatrix interface bond/slip processes, which have been recognized for several authors (Li 2003, Naaman 2007b) as the principal mechanism increasing the ductility of the quasi-brittle cement response. In fact, the interfaces between the fiber and the matrix become a limiting factor in improving mechanical properties such as the tensile strength. Particularly, in short fiber composites is desired to have a strong interface to transfer effectively load from the matrix to the fiber. However, a strong interface will make difficult to relieve fiber stress concentration in front of the approaching crack. According to Naaman (Naaman 2003), in order to develop a better mechanical bond between the fiber and the matrix, the fiber should be modified along its length by roughening its surface or by inducing mechanical deformations. Thus, the premise of the model is to take into account this process considering a microfield that represents the slipping fiber-cement displacement. The conjugate generalized stress to the gradient of this micro-field verifies a balance equation and has a physical meaning. This contribution includes the computational modeling aspects of the high fiber reinforced cement composites (HFRCC) model. To simulate the composite material, a finite element discretization is used to solve the set of equations given by the multifield approach for this particular case. A two field discretization: the standard macroscopic and the microscopic displacements, is proposed through a mixed finite element methodology. Furthermore, a splitting procedure for uncoupling both fields is proposed, which provides a more convenient numerical treatment of the discrete equation system. The initiation of failure in HPFRCC at the constitutive level identified as the onset of strain localization depends on the mechanical properties of the all compounds and not only on the matrix ones. As localization criteria is considered the bifurcation analysis in combination with the localized strain injection technique presented by Oliver et al. (Oliver et al. 2010a). It consists of injecting a specific localization mode during the localization stage, via mixed finite element formulations, to the path of elements that are going to capture the cracks, and, in this way, the spurious mesh orientation dependence is removed. Model validation was performed using a selected set of experiments that proves the viability of this approach. The numerical examples of the proposed formulation illustrated two relevant aspects, namely: 1) the role of the bonding mechanism in the strain hardening behavior after cracking in the HPFRCC and 2) the role that plays the finite element formulation in capturing the displacement localization in the localization stage

Mechanical Instability of Thin Solid Film Structures

Instability of thin film structures as buckling and wrinkling are important issues in various fields such as skin aging, mechanics of scars, metrology of the material properties of thin layers, coating of the surfaces and etc. Similar to the buckling, highly ordered patterns of wrinkles may be developed on the film‒substrate due to compressive stresses. They may cause a failure of the system as structural damage or inappropriate operation, however once they are well understood, it is possible to control and even use them properly in various systems such as the gossamer structures in the space, stretchable electronics, eyelike digital cameras and wound healing in surgery. In this thesis, the mechanical instability of the thin film is considered analytically and numerically by solving the eigenvalue problem for the governing equation of the system, and the effects of the different factors on the instability parameters such as load, amplitude, wavenumber and length of the wrinkles are studied. Different problems such as wrinkling within an area on the film, and buckling and wrinkling of the non‒uniform systems with variable geometry and material properties for both of the film and substrate are investigated. It is shown that the effects of the non‒uniformity of the system are very significant in localization of the wrinkles on the film; however, such a factor has been ignored by many researchers to simplify the problems. In fact, for the non‒uniform systems, the wrinkles accumulate around the weakest locations of the system with lower stiffness and the wrinkling parameters are highly affected by the non‒uniformity effects. Such effects are important especially in thin film technology where the thickness of the film is in the order of Micro/Nano scale and the uniformity of the system is unreliable. The results of this dissertation are useful in the design and applications of thin films in science, technology and industry. They consider the relation of the loading and structural stiffness with the wrinkling parameters and provide more insight into the physics of the localization of the wrinkling on the thin structures, how and why wrinkles are accumulated at some positions. Therefore, deliberate application of these results provides appropriate tools to control and use the buckling and wrinkling of thin films effectively in different fields

Fracture mechanics of high strength concrete members

This study investigates the behavior of High Strength Concrete (HSC) under uniaxial state of stresses. Emphasis is placed on experimental evaluation of important mechanical and fracture properties. Owing to high brittleness of HSC, experimental results especially on tensile behavior have been largely limited and scarce. In this research, direct uniaxial tension tests are employed for determination of the post-peak tensile softening characteristics of HSC. The softening characteristics of high strength concrete is found to be considerably different than that of normal strength concrete (NSC). Fracture energies evaluated form the descending branch of the stress softening reveal significant drop in the post peak compliance of the high strength concretes. Such relationships of stress-crack separation are vital input for developing a model capable of accurately predicting behavior of HSC in tension. The obtained softening relationship is incorporated into an non-linear finite element model using ABAQUS program. The model is shown to be successful in predicting the test results of the present study as well as the ones of other researchers. The predictions are of equal degree in accuracy for both the load crack mouth opening displacement (CMOD) and load-Deflection (LPD) responses. Performing of a parametric study as well as development of a methodology that suggests the use of load-CMOD response in beam fracture tests as an alternative method of determining the fracture toughness (GF) from beam tests are undertaken. Important parameters such as flexural strength, size of process zone of normal and high strength concrete are also determined using the FEM model. It is found that for an increase of about 30% in the fracture toughness GF and the tensile strength f\u27t of HSC, the reduction in the difference between flexural strength and tensile strength is considerable and the size of process zone is also significantly smaller in HSC as compared to NSC. It is shown that to apply Linear Elastic Fracture Mechanics (LEFM) principles, a minimum size (depth) of beam of HSC is about 9.0 whereas for NSC the minimum depth of the beam is almost twice as much i.e. about 18.0 . An important recommendation for determining the fracture energy GF from load-CMOD curves instead from the conventional Load Deflection response is shown to produce lesser variation in GF values since CMOD measurements are less likely to be affected by experimental setups and errors. Errors that are known to generally affect the load-line deflection (LPD) measurements can cause significant inflated values of fracture energy GF to be reported. Finally based on the test results of beam bending tests, a recommendation is made regarding a suitable size of beam specimen that can be used as a standardized fracture test specimen. The beam specimen of span depth (S/D) ratio of 4 is found to be more suitable than the RILEM recommended beam size S/D = 8

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

Thermomechanical Characterization and Modeling of Superelastic Shape Memory Alloy Beams and Frames.

Of existing applications, the majority of shape memory alloy (SMA) devices consist of beam (orthodontic wire, eye glasses frames, catheter guide wires) and framed structures (cardiovascular stents, vena cava filters). Although uniaxial tension data is often sufficient to model basic beam behavior (which has been the main focus of the research community), the tension-compression asymmetry and complex phase transformation behavior of SMAs suggests more information is necessary to properly model higher complexity states of loading. In this work, SMA beams are experimentally characterized under general loading conditions (including tension, compression, pure bending, and buckling); furthermore, a model is developed with respect to general beam deformation based on the relevant phenomena observed in the experimental characterization. Stress induced phase transformation within superelastic SMA beams is shown to depend on not only the loading mode, but also kinematic constraints imposed by beam geometry (such as beam cross-section and length). In the cases of tension and pure bending, the structural behavior is unstable and corresponds to phase transformation localization and propagation. This unstable behavior is the result of a local level up-down-up stress/strain response in tension, which is measured here using a novel composite--based experimental technique. In addition to unstable phase transformation, intriguing post-buckling straightening is observed in short SMA columns during monotonic loading (termed unbuckling here). Based on this phenomenological understanding of SMA beam behavior, a trilinear based material law is developed in the context of a Shanley column model and is found to capture many of the relevant features of column buckling, including the experimentally observed unbuckling behavior. Due to the success of this model, it is generalized within the context of beam theory and, in conjunction with Bloch wave stability analysis, is used to model and design SMA honeycombs.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113455/1/watkinrt_1.pd