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A phenomenological approach is proposed to describe and predict the random behaviour of the total strain in plain and fiber concrete under compressive fatigue loading. Twofold viewpoints are considered in the assessment of the fatigue damage process. The first one, acknowledged as the stochastic cumulative damage evolution in terms of the number of applied cycles is represented by a sample function, physically identified with the total specimen strain caused by matrix microcracking. The second one is ascribed to the intrinsic scatter of the total lifetime referred to as the prefixed ultimate fatigue strain limit state (not necessarily failure). The sample function, once normalized to the total fatigue lifetime, is identified as a cumulative distribution function (cdf) of the generalized extreme value (GEV) family, particularly as Weibull distribution. Besides the reliable probabilistic lifetime prediction for the material under compressive fatigue, the approach allows fatigue tests to be prematurely interrupted while the remaining evolution of the ε-N curve up to failure is fully restored from the fragment recorded. In this way, a remarkable time and cost reduction of the experimental program is achieved without detriment of data reliability.
Fatigue models that accurately resolve the complex three-dimensional failure mechanisms of concrete are numerically expensive. Especially the calibration of fatigue parameters to existing Wöhler lines requires solving for thousands or millions of cycles and a naive cycle-by-cycle integration is not feasible.
The proposed adaptive cycle jump methods provide a remedy to this challenge.
They greatly reduce the numerical effort of fatigue simulations and provide the basis for a development of those models.
Accurate models for the long term behavior of concrete structures are important to ensure a durable and reliable design.
A variety of interacting phenomena, such as the loss of prestress, the degradation due to chemical reactions or creep and shrinkage, influence the fatigue resistance. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required.
The presented fatigue model is an extension of a static damage model to allow easy coupling in a multiphysics context. The evolution equation of the damage driving variable is enhanced to allow damage growth below the static limit. The model is defined in the time domain and does not include the number of cycles as a parameter.
Thus, it can capture both static and cyclic failure.
Additionally, this allows calibrating the majority of the model parameters static experiments. The model is integrated by resolving each loading cycle, requiring about ten time steps per cycle. The high computational costs are handled via a time scale separation.
The short time scale describes one cycle with marginal changes in the internal variables. These changes are integrated along the large time scale of material deterioration. Various high-order time integration schemes are compared.
Wöhler curves relate loading amplitudes to the number of cycles that the material endures. They are used to validate the model against experimental data.
The durability of concrete structures and its performance over the lifetime is strongly influenced by many interacting phenomena such as e.g. mechanical degradation due to fatigue loading, loss of prestress, degradation due to chemical reactions or creep and shrinkage. Failure due to cyclic loading is generally not instantaneous, but characterized by a steady damage accumulation.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales. A key limitation is that the models often 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.
The objective of this paper is the presentation of numerical methods for the simulation of concrete under fatigue loading using a temporal multiscale method.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. 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. 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. This evolution equation is then solved on the long time scale using different time integration schemes.
In structural parts under vibrational loading fatigue cracks can initiate and grow, which can lead to structural failure. Conventional non-destructive testing methods for crack detection provide just a snapshot of fatigue crack evolution, whereas crack luminescence coating realizes clear visibility of the entire crack formation. Fatigue causing cyclic tensile tests and examinations on special test bodies allowing control of the crack opening width demonstrate a high sensitivity of the coating.
Damage caused by stress concentrations in the complex mesoscopic geometry of concrete leads to continuous stress redistribution over the material’s life time. The presented fatigue damage model
captures this by resolving each load cycle in a cycle-by-cycle time integration. The model extends a static damage model to failure caused by the (time dependent) strain amplitudes and, thus, allows calibrating the majority of the material’s parameters in static experiments.
Conventional methods of crack detection only provide a snapshot of the fatigue evolution at a specific location and in the moment of examination. The crack luminescence method realizes a clear visibility of the occurring cracks in loaded components during ongoing operation. Several different experiments show that due to the sensitive coating even the early stage of the crack formation can be detected what makes the crack luminescence helpful to determine the incipient crack opening behavior depending on load alternation. Due to the emitting of light under UV-radiation the crack gets clearly visible what makes continuous monitoring and automated crack detection possible. This can reduce costs and time needed for maintenance and inspection.
Components in the Aerospace, Power and Automotive engineering sectors are frequently subjected to cyclic stresses induced by thermal fluctuations and mechanical loads. For the design of such components, reliable material property data are required which need to be acquired using well accepted and reproducible test procedures for thermo-mechanical fatigue (TMF) loading. There is limited availability of proven TMF data indicating there is need for further research and testing. The TMF behaviour of materials is often desired to be simulated in models which describe the cyclic stress-strain behaviour, the fatigue life and the cyclic crack growth behaviour. There is a continuous need for the development and amendment of such models. Models can be validated by using materials in industrial applications which are subjected to TMF loading.
The 3rd Workshop on Thermo-Mechanical Fatigue was held on 27–29 April 2016 at BAM, Berlin, Germany. The workshop was attended by 90 attendees coming from 17 countries in the world. 38 presentations including five poster presentations were held.
The following topics were covered by the workshop:
– TMF of materials coated with Thermal Barrier Coatings.
– Thermal Gradient Mechanical Fatigue.
– TMF crack growth.
– TMF + High Cycle Fatigue.
– TMF Modelling and Lifetime Prediction.
– TMF Properties of steels, cast iron, Al-, Mg- and Ni-alloys
– Advanced TMF Testing Techniques.
– Industrial Applications.
A panel discussion was held regarding the present state of TMF testing standards (ISO and ASTM) and their potential for improvement. The discussion and contributions were summarized and forwarded to the standard committees. The 3rd TMF-Workshop ensured the continuation of international exchange of knowledge providing a forum to present and discuss all recent developments in the field of thermo-mechanical fatigue.
The current special issue publishes eleven selected papers of the 3rd TMF-Workshop 2016. The papers were peer reviewed by a number of experts in the Thermo-Mechanical Fatigue sector. I hope you will enjoy reading papers of this special issue.
Components in the Aerospace, Power and Automotive engineering sectors are frequently subjected to cyclic stresses induced by thermal fluctuations and mechanical loads. For the design of such components, reliable material property data are required which need to be acquired using well accepted and reproducible test procedures for thermo-mechanical fatigue (TMF) loading. There is limited availability of proven TMF data indicating there is need for further research and testing. The TMF behaviour of materials is often desired to be simulated in models which describe the cyclic stress-strain behaviour, the fatigue life and the cyclic crack growth behaviour. There is a continuous need for the development and amendment of such models. Models can be validated by using materials in industrial applications which are subjected to TMF loading.
The 3rd Workshop on Thermo-Mechanical Fatigue was held on 27–29 April 2016 at BAM, Berlin, Germany. The workshop was attended by 90 attendees coming from 17 countries in the world. 38 presentations including five poster presentations were held.
The following topics were covered by the workshop:
– TMF of materials coated with Thermal Barrier Coatings.
– Thermal Gradient Mechanical Fatigue.
– TMF crack growth.
– TMF + High Cycle Fatigue.
– TMF Modelling and Lifetime Prediction.
– TMF Properties of steels, cast iron, Al-, Mg- and Ni-alloys
– Advanced TMF Testing Techniques.
– Industrial Applications.
A panel discussion was held regarding the present state of TMF testing standards (ISO and ASTM) and their potential for improvement. The discussion and contributions were summarized and forwarded to the standard committees. The 3rd TMF-Workshop ensured the continuation of international exchange of knowledge providing a forum to present and discuss all recent developments in the field of thermo-mechanical fatigue.
The current special issue publishes eleven selected papers of the 3rd TMF-Workshop 2016. The papers were peer reviewed by a number of experts in the Thermo-Mechanical Fatigue sector. I hope you will enjoy reading papers of this special issue.