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A Multi-scale temporal integration scheme for viscoplatic solids subjected to fatigue deterioration
(2016)
Using a continuum mechanics framework for lifetime prediction requires numerical integration of evolving damage until the onset of failure. The primary challenge for the simulation of structural fatigue failure is caused by the enormous computational costs due to cycle by cycle temporal integration throughout the whole loading history, which is in the order of 10^3 - 10^7 cycles. As a consequence, most approaches circumvent this problem and use an empirical method such as Wöhler curves. They are well suited for approximation of the lifetime, but they are not capable to capture a realistic degradation of the material with a redistribution of the stresses. The main objective of the paper is to provide a technique for the long time response of a finite element (FE) model while reducing computational costs.
A multi-scale temporal integration scheme is proposed, which adapts the conventional FE method for realistic modeling of deterioration in a structure subjected to cyclic loading. For a particular case of two-scale temporal homogenization, the displacement field is assumed to satisfy scale separation: a short time scale arises from the oscillatory loading and a long time scale is due to the slow response relating to yielding and damage evolution. The original boundary value Problem (BVP) is approximated by the time-Independent BVPs on the short time scale. Alternation of the displacement field on the long time scale is correlated with the damage evolution by means of the adaptive cycle jump method. The significant acceleration of FE simulations is demonstrated for a constitutive damage model where the progressive damage accumulation under fatigue loading is driven by viscoplastic deformation.
As subcritical crack growth (SCCG) can reduce tensile strength of glasses by many orders of magni-tude, the potential for improvement of fatigue behaviour is most intriguing in developing ultra-strong glasses. An essential bottleneck is the basic understanding of the numerous interplaying pressure-, temperature- and water-affected relaxation phenomena at the crack tip and related toughening strat-egies. Therefore, the present project aims to advance the basic understanding of structural relaxa-tion effects and local properties caused by increased water concentration and tensile stresses at the crack tip as they are a key for structural toughening designs to develop SCCG-free glasses and glass surfaces.
Our first studies give clear evidence that glass structure and dynamics is strongly modified upon hy-dration of glasses. These changes are highly related to the nature of network formers but are affect-ed as well by the counter ions (network modifier). Results of the 1st project part suggest that struc-tural relaxation below glass transition temperature, i.e. overlapping of short-range (beta) and long-range (alpha) interactions can contribute to SCCG in water-free environments and that structurally dissolved water in the glasses can have decisive impact on this effect.
In the 2nd project stage specific glasses compositions will be investigated to gain an improved un-derstanding on the relation of sub-Tg relaxation and inert SCCG as well as to shed light to the relat-ed effects of dissolved water and its speciation. These glasses cover a broader range of different glass topologies and binding partners, whereby the coupling of alpha and beta relaxations is varied systematically by alkali-, alkaline earth ions and water species concentrations. Preparation of hy-drous glasses (up to 8 wt% water) will be performed by high pressure syntheses. Structure will be resolved by NMR, Raman and IR spectroscopy while structural relaxation is accessed in the temper-ature and frequency domain using dynamic mechanical spectroscopy and ultrasonic damping. We will focus on measurements of inert SCCG (region III) conducting experiments in vacuum and dry gas atmospheres using indentation techniques and stressing of glass specimens in DCB geometry.
Experimental data on SCCG will be provided to SPP groups, which deals with fatigue in metallic glasses and vice versa we will test theoretical predictions of ab-initio simulations of partner within SPP 1594 in order to quantify the effect of water on the crack tip. In summa topological factors con-trolling the subcritical crack growth with respect to water will be identified from which structural toughening designs for highly fatigue resistant-glasses can be derived.
As subcritical crack growth (SCCG) can reduce tensile strength of glasses by many orders of magnitude, the potential for improvement of fatigue behaviour is most intriguing in developing ultra-strong glasses. An essential bottleneck is the basic understanding of the numerous interplaying pressure-, temperature- and water-affected relaxation phenomena at the crack tip and related toughening strategies. Therefore, the present project aims to advance the basic understanding of structural relaxation effects and local properties caused by increased water concentration and tensile stresses at the crack tip as they are a key for structural toughening designs to develop SCCG-free glasses and glass surfaces.
Our first studies give clear evidence that glass structure and dynamics is strongly modified upon hydration of glasses. These changes are highly related to the nature of network formers but are affected as well by the counter ions (network modifier). Results of the 1st project part suggest that structural relaxation below glass transition temperature, i.e. overlapping of short-range (beta) and long-range (alpha) interactions can contribute to SCCG in water-free environments and that structurally dissolved water in the glasses can have decisive impact on this effect.
In the 2nd project stage specific glasses compositions will be investigated to gain an improved understanding on the relation of sub-Tg relaxation and inert SCCG as well as to shed light to the related effects of dissolved water and its speciation. These glasses cover a broader range of different glass topologies and binding partners, whereby the coupling of alpha and beta relaxations is varied systematically by alkali-, alkaline earth ions and water species concentrations. Preparation of hydrous glasses (up to 8 wt% water) will be performed by high pressure syntheses. Structure will be resolved by NMR, Raman and IR spectroscopy while structural relaxation is accessed in the temperature and frequency domain using dynamic mechanical spectroscopy and ultrasonic damping. We will focus on measurements of inert SCCG (region III) conducting experiments in vacuum and dry gas atmospheres using indentation techniques and stressing of glass specimens in DCB geometry.
Experimental data on SCCG will be provided to SPP groups, which deals with fatigue in metallic glasses and vice versa we will test theoretical predictions of ab-initio simulations of partner within SPP 1594 in order to quantify the effect of water on the crack tip. In summa topological factors controlling the subcritical crack growth with respect to water will be identified from which structural toughening designs for highly fatigue resistant-glasses can be derived.
The current knowledge about fatigue behavior of concrete is still incomplete. This concerns especially the progress of fatigue which precedes the fatigue failure. Therefore, the process of fatigue itself under cyclic compressive loading was investigated in a systematic and comprehensive way. The aim of this investigation was to obtain a deeper insight and to provide a better understanding of the damage process occurring within the material during fatigue loading. Concrete cylinders were tested with a number of cycles to failure between 106 and 107. To investigate macroscopic and microscopic changes in the material, various methods of non-destructive and destructive testing were used. One main result was, in contrast to other authors, that the investigated changes in macroscopic material behavior could not be explained only by a development of micro-cracks. The results indicated rather, that the related changes in the fatigue behavior are mainly a result of viscous processes in the hardened cement paste, similar to the processes of creep. Based on the experimental results a description of the possible processes was derived which take place in the material structure during fatigue loading and also leads to the observed macroscopic changes in the material behavior. In this context, the results have shown that in case of isotropic material behavior a stiffness reduction related to a scalar value could not capture the damage effect on the stress-strain-relationship caused by fatigue.
Carbon Fibre Reinforced Plastics (CFRP) are more and more used in modern civil aircrafts. These days the whole fuselage is made of this material (B787; A350). Due to strict certification standards the normal in-service loading gives a low stress level compared to the static and even the fatigue strength of the material. Hence CFRP are assumed to have an infinite life. To evaluate this assumption, fatigue tests on CFRP-specimens were performed up to 108 load cycles and the first inter-fibre failure was evaluated non-destructively by accompanying X-ray-refraction topography.
A tensile testing machine was integrated in a small angle X-ray scattering (SAXS) setup. X-ray refraction topography was performed while the CFRP-samples were tensile loaded. This non-destructive technique enables the detection of micro-cracking and inter-fibre failure especially for CFRP. For Glass Fibre Reinforced Plastic (GFRP) X-ray refraction and in-situ loading has already been successfully used. The increase of inner surfaces due to inter fibre failure was measured as a function of the stress state. Fatigue tests were performed at and below the limit of inter-fibre failure strength.
State of the art is to assume the failure of the samples under cyclic loading as the fatigue life. Accompanying non-destructive X-ray refraction measurements reflects the damage state and enables to trace its evolution even if the total failure of the specimens does not occur. This investigation technique is of high interest to give the engineer a design value of infinite life which is practically often reached due to knock down factors of certification standards. Finally the infinite life was found for cyclic fatigue loaded CFRP-samples even under high inter fibre transverse and shear loading investigated up to 108 load cycles.
Carbon Fibre Reinforced Plastics (CFRP) are more and more used in modern civil aircrafts. These days the whole fuselage is made of this material (B787; A350). Due to strict certification standards the normal in-service loading gives a low stress level compared to the static and even the fatigue strength of the material. Hence CFRP are assumed to have an infinite life. To evaluate this assumption, fatigue tests on CFRP-specimens were performed up to 108 load cycles and the first inter-fibre failure was evaluated non-destructively by accompanying Xray-refraction topography. A tensile testing machine was integrated in a small angle X-ray scattering (SAXS) setup. X-ray refraction topography was performed while the CFRP samples were tensile loaded. This non-destructive technique enables the detection of micro-cracking and inter-fibre failure especially for CFRP. For Glass Fibre Reinforced Plastic (GFRP) X-ray refraction and in-situ loading has already been successfully used. The increase of inner surfaces due to inter fibre failure was measured as a function of the stress state. Fatigue tests were performed at and below the limit of inter-fibre failure strength. State of the art is to assume the failure of the samples under cyclic loading as the fatigue life. Accompanying non-destructive X-ray refraction measurements reflects the damage state and enables to trace its evolution even if the total failure of the specimens does not occur. This investigation technique is of high interest to give the engineer a design value of infinite life which is practically often reached due to knock down factors of certification standards. Finally the infinite life was found for cyclic fatigue loaded CFRP-samples even under high inter fibre transverse and shear loading investigated up to 108 load cycles.
In recent years the German highway network has seen an increase in the occurrence of damage in concrete road surfaces which can be attributed to the alkali-silica reaction (ASR). In view of the often drastic reduction in life expectancy experienced by concrete pavements due to ASR, research activity in this field has notably increased. Until now the main research focus has been, alongside preventative measures in concrete technology, the development of performance-oriented testing procedures for ASR prevention. This included more specifically the accelerated simulation of climatic effects and external alkali supply on concrete pavements. The effects of pre-damage from the additionally interacting cyclic traffic loading had previously not been taken into consideration.
Since 2011, a five-partner research group from the German Research Foundation has been pursuing research on the effects of simultaneous cyclic loading and external alkali supply on the destructive ASR in concrete pavements. The depiction of the myriad degradation and transport processes necessary for an understanding of these effects requires a close interaction between experiments and their multi-scale modelling. This contribution aims to focus on the aforementioned experiments by means of innovative testing techniques. The research is founded on a series of cyclic fatigue tests performed on large-format beams, both with and without previous application of a NaCl solution, with simultaneous tracking of crack development. Thereafter, smaller test specimens were extracted from the pre-damaged beams for further experiments. These included the spatial visualization and quantification of fatigue-induced cracks with X-ray 3D-computed tomography. Additionally, the effects of fatigue-induced cracks on moisture and alkali transport were investigated using 3D-CT and Laser-Induced Breakdown Spectroscopy (LIBS). Subsequent storage of the small-format test specimens, with and without cyclic pre-damage, in an ASR-conducive environment was then able to shed light on the influence of fatigue-induced pre-damage on the ASR.
Im Mittelpunkt der vorliegenden Arbeit steht das Ermüdungsverhalten von Beton unter hochzyklischen Druckschwellbeanspruchungen. Der aktuelle Wissensstand bezüglich des Ermüdungsverhaltens ist nach wie vor sehr lückenhaft. Ganz besonders trifft das auf den eigentlichen Ermüdungsprozess zu, der dem abschließenden Ermüdungsversagen vorausgeht. Dem Defizit im Wissen um das Ermüdungsverhalten steht allerdings eine zunehmende Bedeutung der Thematik in der Baupraxis gegenüber. Daher wurde im Rahmen dieser Arbeit eine systematische Untersuchung des Ermüdungsprozesses vorgenommen. Damit wird ein Beitrag geleistet, um einen tieferen Einblick und ein besseres Verständnis für den Schädigungsprozess und die damit verbundenen Vorgänge innerhalb des Betons zu gewinnen.
Die experimentellen Untersuchungen bestehen im Wesentlichen aus einstufigen Dauerschwingversuchen im Druckschwellbereich an zylindrischen Probekörpern aus Normalbeton. Verwendet wurden zwei verschiedene Ermüdungslastniveaus, die Bruchlastzyklen zwischen 10⁶ und 10⁷ sowie zwischen 10³ und 10⁴ erzeugten. Die Untersuchung des Ermüdungsvorgangs erfolgte durch den Einsatz verschiedener ZfP- und ZP-Methoden, wie der Dehnungsmessung, der Messung flächiger Oberflächenverformungen, der Ultraschallmessung, der Schallemissionsmessung, der Lichtmikroskopie und des Rasterelektonenmikroskops. Zur Bewertung einiger Einflussgrößen im Zusammenhang mit dem Ermüdungsverhalten fanden zudem ergänzende Versuche zum Kriecheinfluss sowie zum Einfluss der Probengröße statt.
Es konnte festgestellt werden, dass es sich bei dem Ermüdungsvorgang um eine von Beginn an einsetzende Schädigungsevolution innerhalb des Betons handelt. Diese beeinflusst die verschiedenen Materialeigenschaften des Betons in vielfältiger und sehr unterschiedlicher Weise. Die wesentlichste Feststellung in diesem Zusammenhang ist, dass die ermüdungsbedingte Materialschädigung zu einer Veränderung der gesamten Spannungs-Dehnungs-Beziehung führt, die sich ebenfalls in einem fortlaufenden Evolutionsprozess äußert.
Aus den Untersuchungen konnten als entscheidende Ursache für die beobachteten Veränderungen im makroskopischen Materialverhalten Veränderungen in der Mikrorissstruktur nicht festgestellt werden. Vielmehr weisen die Ergebnisse der Untersuchungen darauf hin, dass die ermüdungsbedingten Veränderungen speziell in den Phasen I und II vorrangig das Resultat von viskosen Prozessen innerhalb des Zementsteins sind. Darüber hinaus geht aus den Versuchen hervor, dass auch das Kriechen zu relativ ähnlichen, aber weniger stark ausgeprägten Veränderungen im Material führt. Ein Einfluss der Probengröße auf das resultierende Verhalten konnte sowohl im statischen als auch im zyklischen Fall beobachtet werden.
Aus den gewonnenen experimentellen Erkenntnissen wird eine Beschreibung der Vorgänge abgeleitet, die während des Ermüdungsprozesses im Materialgefüge ablaufen und zu den beobachteten makroskopischen Veränderungen führen. In diesem Zusammenhang hat sich herausgestellt, dass eine Erfassung der ermüdungsbedingten Schädigung anhand einer skalaren Größe über die Steifigkeit der tatsächlichen Veränderung der Spannungs-Dehnungs-Beziehung nicht gerecht wird. Eine Betrachtung im Hinblick auf einen zuverlässigen Schädigungsindikator im Zusammenhang mit den gemessenen Größen liefert zudem einen Überblick über die Eignung verschiedener Größen zur Erfassung des Ermüdungsschädigungsgrades im Beton. Abschließend wird ein Ansatz vorgestellt, der die beobachteten Entwicklungen entscheidender Größen im Ermüdungsvorgang abzubilden vermag.