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Computational methods for lifetime prediction of metallic components under high-temperature fatigue
(2019)

The issue of service life prediction of hot metallic components subjected to cyclic loadings is addressed. Two classes of lifetime models are considered, namely, the incremental lifetime rules and the parametric models governed by the fracture mechanics concept. Examples of application to an austenitic cast iron are presented. In addition, computational techniques to accelerate the time integration of the incremental models throughout the fatigue loading history are discussed. They efficiently solve problems where a stabilized response of a component is not observed, for example due to the plastic strain which is no longer completely reversed and accumulates throughout the fatigue history. The performance of such an accelerated Integration technique is demonstrated for a finite element simulation of a viscoplastic solid under repeating loading–unloading cycles.

Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses [1]. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach [2]. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
[1] Vitaliy Kindrachuk, Marc Thiele, Jörg F. Unger. Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression, International Journal of Fatigue, 78:81-94, 2015
[2] Vitaliy Kindrachuk, Jörg F. Unger. A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration, International Journal of Fatigue, 100:215-228, 2017

Using continuum damage mechanics (CDM) 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 103–107 cycles. As a consequence, most approaches circumvent this problem and use empirical methods such as Wöhler curves. They are well suited for approximating the lifetime, but they are not capable to capture a realistic degradation of the material including redistribution of stresses. The main objective of the paper is to provide a technique for finite element (FE) simulations of structures under fatigue loading while reducing computational costs.
A Fourier transformation-based temporal integration (FTTI) scheme is proposed, which adapts the conventional FE method for modeling the viscoplastic deterioration in a structure subjected to cyclic loading. The response fields are represented by a Fourier series which assumes a temporal scale separation: a microchronological (short time) scale arises from the oscillatory loading and a macrochronological (long time) scale is due to the slow material relaxation resulting from yielding and damage evolution. The original dynamic boundary value problem (BVP) is approximated by the stationary BVP on the microchronological scale. Alternation of the displacement field on the macrochronological scale is correlated with evolution of the history variables by means of a high order adaptive cycle jump method. Performance and significant acceleration of the FE simulations is demonstrated at different loading scenarios for a constitutive damage model where the progressive damage accumulation is driven by viscoplastic yielding.

The fatigue behaviour of cast iron is usually investigated on machined specimens. Components of cast iron, however, have a casting skin; therefore the investigation of the influence of the casting skin on the lifetime is of interest. To study this influence isothermal fatigue tests were carried out on heat-resisting spheroidal graphite cast iron EN GJS SiMo 4.05 in 4–point-bending set-up at 400 °C. Specimens with and without casting skin were investigated comparatively. The number of cycles to failure was significantly lower for specimens with casting skin. Metallographic investigations underline the reduction of lifetime caused by casting skin.

Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression
(2015)

Conventional approaches to model fatigue failure are based on a characterization of the lifetime as a function of the loading amplitude. The Wöhler diagram in combination with a linear damage accumulation assumption predicts the lifetime for different loading regimes. Using this phenomenological approach, the evolution of damage and inelastic strains and a redistribution of stresses cannot be modeled. The gradual degration of the material is assumed to not alter the stress state. Using the Palmgren–Miner rule for damage accumulation, order effects resulting from the non-linear response are generally neglected.
In this work, a constitutive model for concrete using continuum damage mechanics is developed. The model includes rate-dependent effects and realistically reproduces gradual performance degradation of normal strength concrete under compressive static, creep and cyclic loading in a unified framework. The damage evolution is driven by inelastic deformations and captures strain rate effects observed experimentally. Implementation details are discussed. Finally, the model is validated by comparing simulation and experimental data for creep, fatigue and triaxial compression.

The following paper focuses on the evolution of micro damage in short fibre reinforced polyamide. Therefore, tube samples are subjected to uni- and biaxial fatigue loadings. The evolution of micro damage is analysed by the non-destructive method of X-ray refraction analysis with consideration of the fibre orientation distribution. For validation of the applied micro damage models, fractographic analyses are performed.
Concluding some general results, it has been observed that the load ratio influences the quantitative dominance of micro damage, whereas occuring damage phenomena depend on the type of loading (i.e. tension and torsion). Thus, zones in the Haigh-diagram are detected, where the occurence of damage mechanisms qualitatively and quantitatively changes. This is a basis for further research regarding anisotropic damage criteria.

Investigations on the breakdown of a heat recovery steam generator during the initial operation run
(2014)

Several years ago, in 2003, an industrial heat recovery steam generator in charge of generating process steam in a petrochemical refinery was installed and prepared for initial operation. The steam generator enclosed an evaporator section and a superheater section consisting mainly of bundles of tubes with the longest up to several metres in length. During initial operation test runs severe leakages in the evaporator and superheater modules became noticeable. The test runs were stopped and after disassembly, through-wall cracks in several tube bends were found. BAM was commissioned to carry out the investigations in order to find out the reasons for the failure of the tubes. During on-site inspection a number of relevant damaged components and parts were selected and taken away to the laboratories for detailed inspection. Planned analyses were to comprise metallographic as well as fractographic investigations, mechanical fatigue testing and experimental as well as finite element vibration analyses on specimens and components. Soon, the fracture mechanism was found to be mechanical fatigue due to the fact that the examined fracture surfaces showed the very characteristic beachmarks and colouring patterns. To identify the particular loading and time at which crack initiation and crack propagation took place, experimental and numerical vibration analyses of specific tubes as well as mechanical fatigue tests on tube bends were carried out. Thus it was possible to identify the eigenfrequencies of individual tubes, to estimate the dynamic response as well as the nominal stresses and, hence, experimentally characterise the in-service fatigue strength of the components. Mechanical and thermal comparative tests on tube bends were performed simulating the conditions during the initial test run in order to get crack surfaces comparable to that of the originally damaged components. Thereby it became obvious that the fatigue cracks were initiated by vibrations the tube bundles were exposed to during rail transport from the manufacturers site to the place of installation. Based on these results, the damaged components could be repaired or exchanged without modification of the construction, but the rules relating packaging and securing for shipping had to be revised.

Under cyclic thermomechanical loading conditions, various effects such as strain accumulation, creep damage, ageing, fatigue etc. may occur in the material of a gas turbine blade. Depending on the loading conditions, all these effects contribute to reduce the lifetime of the component. Subject of the present work is the development of a lifetime model able to discriminate between the different damage mechanisms, as well as the development of a material model to describe the mentioned effects and thus providing the input data for lifetime prediction.