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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
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. 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. 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.
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. 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 statictests. 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. 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 implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
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. 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 statictests. 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. 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 implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Due to combined cyclic mechanical and thermal loading during operation, the material of exhaust gas conducting components of combustion engines is exposed to thermomechanical fatigue (TMF). This leads to formation and growth of cracks, especially at the most highly stressed points of these components. In order to better predict the service life of cracked components before failure, it is necessary to identify a crack propagation law for the material used. Isothermal crack propagation tests have been carried out at several temperatures with a typical cast iron to identify such a law. The crack length is measured by the potential drop method. The compliance method, fractography and thermographic camera measurements have been used to validate and calibrate the potential drop measurements. Each of the isothermal tests has been simulated using a specially developed FEM-algorithm based on remeshing and remapping. This algorithm has been implemented in python and ABAQUS. Thereby, the crack tip region is modeled by collapsed Quad8 elements. From the individual simulations, the cyclic crack tip opening displacement (ΔCTOD) is extracted and regarded as a potential fracture mechanics parameter which controls the crack growth rate. By combining the data from the experiments and the simulations, the crack propagation law has been identified. Finally, anisothermal crack propagation tests have been performed for validation of the crack growth law.
A key limitation of the most constitutive models that reproduce a Degradation of quasi-brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal Integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations.
The essential constituent of the fatigue model is an implicit gradient-enhanced formulation of the damage rate. The evolution of the field variables is computed as amultiscale Fourier series in time.On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration. The performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.
Systematic microstructure design requires reliable thermodynamic descriptions of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of microstructure defects is challenging because of their individualistic nature. In this paper, a model is devised for assessing grain boundary thermodynamics based on available bulk thermodynamic data. We propose a continuous relative atomic density field and its spatial gradients to describe the grain boundary region with reference to the homogeneous bulk and derive the grain boundary Gibbs free energy functional. The grain boundary segregation isotherm and phase diagram are computed for a regular binary solid solution, and qualitatively benchmarked for the Pt–Au system. The relationships between the grain boundary's atomic density, excess free volume, and misorientation angle are discussed. Combining the current density-based model with available bulk thermodynamic databases enables constructing databases, phase diagrams, and segregation isotherms for grain boundaries, opening possibilities for studying and designing heterogeneous microstructures.
Additive manufacturing (AM) offers significantly greater freedom of design compared to conventional manufacturing processes since the final parts are built layer by layer. This enables metal AM, also known as metal 3D printing, to be utilized for improving efficiency and functionality, for the production of parts with very complex geometries, and rapid prototyping. However, despite many technological advancements made in recent years, several challenges hinder the mass adoption of metal AM. One of these challenges is mechanical anisotropy which describes the dependency of material properties on the material orientation. Therefore, in this work, stainless steel 316L parts produced by laser-based powder bed fusion are used to isolate and understand the root cause of anisotropy in AM parts. Furthermore, an efficient and accurate multiscale numerical framework is presented for predicting the deformation behavior of actual AM parts on the macroscale undergoing large plastic deformations. Finally, a novel constitutive model for the plastic spin is formulated to capture the influence of the microstructure evolution on the material behavior on the macroscale.
The methods of computational damage mechanics are well-established for the description of degradation of materials under monotone loading. An extension to structural damage induced by cyclic loading is however significantly limited. This is due to enormous computational costs required to resolve each load cycle by conventional temporal incremental integration schemes while a typical fatigue loading history comprises between thousands and millions of cycles. Despite the permanent increase of computational resources and algorithmic performance, a successful approach is rather based on the development of novel multiscale in time integration schemes.
A Fourier transformation-based temporal integration (FTTI) is represented, which takes advantage of temporal scale separation incorporated into the cycle jump method. The response fields are approximated by a Fourier series whose coefficients undergo the evolution on a long-time scale. This is correlated with the evolution of the history variables, including damage, by means of the adaptive cycle jump method of various orders. The necessary extrapolation rates are obtained from the underlying solution of a short-time scale problem, which results from the oscillatory boundary condition and fulfills the global equilibrium of the Fourier coefficients. In this way, a remarkable speedup is achieved because the number of cycles to be fully integrated dramatically decreases.
The key idea behind the FTTI method is that the global in space equilibrium problem is linear since it is decoupled from the evolution equations. The latter are solved in the quadrature points under response fields prescribed throughout the whole load cycle. Consequently, integration of a single load cycle is much more efficient than the conventional single scale integration where the global equilibrium iteration and the local iteration of the evolution equations are coupled. This results in an additional speedup of the FTTI method.
The performance of the FTTI technique is demonstrated for two different constitutive behaviors: a viscoplastic model with a damage variable governed by the local equivalent viscoplastic strain; a quasi-brittle response where the damage variable is driven by a non-local equivalent strain. The latter is implicitly introduced as proposed by Peerlings. Both, the explicit and implicit extrapolation schemes are validated. The FTTI solutions agree very well with the reference cycle-by -cycle solutions, while significantly reducing the computational costs. The adaptive determination of the jump length can properly recognize the particular responses throughout the fatigue loading history (stationary fatigue, acceleration of fatigue damage when approaching failure) as well as stress redistribution phenomena.
A constitutive model for the mechanical behaviour of single crystal Ni-base superalloys under high temperature conditions has been developed in the framework of a Cooretec project in cooperation with Siemens AG, MTU Aero Engines AG and University Bayreuth. In addition to the conventional material properties e.g. elastic constants, the model requires the parameters of the initial microstructure as an input. Thus, the γ’-precipitate size and the channel width of the γ-matrix were obtained from SEM micrographs. The model uses the slip system theory and describes the movement, multiplication and annihilation of dislocations in the channels. Furthermore, the cutting of precipitates is another mechanism contributing to the plastic flow. The evolution of the morphology due to rafting and its effects on the deformation have been implemented according to. The kinematic hardening is introduced as a stress tensor to realistically represent the strain hardening of arbitrary oriented single crystals.
The mechanical behaviour of single crystal specimens has been experimentally investigated in tension tests at different strain rates and in creep tests under various loads. The constitutive model has been calibrated based on the experimental data for temperatures of 950°C and 850°C and the [001] and [111] crystallographic orientations.
Finally, a micromechanical model was created to simulate the creep response of additive manufactured polycrystalline structures. An EBSD image is taken to obtain the grain geometry and their respective orientation. The grain boundaries are discretised using cohesive elements, whereas the single crystal model was applied to each grain in the representative volume. The polycrystal model is generated using Dream3D, NetGen and other software previously developed at the BAM.
The amount of data generated worldwide is constantly increasing. These data come from a wide variety of sources and systems, are processed differently, have a multitude of formats, and are stored in an untraceable and unstructured manner, predominantly in natural language in data silos. This problem can be equally applied to the heterogeneous research data from materials science and engineering. In this domain, ways and solutions are increasingly being generated to smartly link material data together with their contextual information in a uniform and well-structured manner on platforms, thus making them discoverable, retrievable, and reusable for research and industry. Ontologies play a key role in this context. They enable the sustainable representation of expert knowledge and the semantically structured filling of databases with computer-processable data triples.
In this perspective article, we present the project initiative Materials-open-Laboratory (Mat-o-Lab) that aims to provide a collaborative environment for domain experts to digitize their research results and processes and make them fit for data-driven materials research and development. The overarching challenge is to generate connection points to further link data from other domains to harness the promised potential of big materials data and harvest new knowledge.
With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase-field approach is presented with an embrittlement-based coupling mechanism. The underlying functionals are expressed in terms of the displacement, mass concentration and crack phase-field. Within the phase-field approach the modelling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to an accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations by a multi-field finite-element method. A thermodynamically consistent coupling relation that accommodates the required mechanisms is presented.
An improved diffusion model is proposed for pore annihilation during HIP of single-crystal nickel-base superalloys. The model assumes the pore dissolution by emission of vacancies and their sink to the low angle boundaries. Calculation, considering distribution of the pore sizes, predicts the kinetics of pore annihilation similar to the experimental one.
Many metallic materials gain better mechanical properties through controlled heat treatments. For example, in age-hardenable aluminium alloys, the strengthening mechanism is based on the controlled formation of nanometre-sized precipitates, which represent obstacles to dislocation movement and consequently increase the strength. Precise tuning of the material microstructure is thus crucial for optimal mechanical behaviour under service condition of a component. Therefore, analysis of the microstructure, especially the precipitates, is essential to determine the optimum parameters for the interplay of material and heat treatment. Transmission electron microscopy (TEM) is utilized to identify precipitate types and orientations in the first step. Dark-field imaging (DF-TEM) is often used to image the precipitates and thereafter quantify their relevant dimensions. Often, these evaluations are still performed by manual image analysis, which is very time-consuming and to some extent also poses reproducibility problems.
Our work aims at a semantic representation of an automatable digital approach for this material specific characterization method under adaption of FAIR data practices. Based on DF-TEM images of different precipitation states of a wrought aluminium alloy, the modularizable, digital workflow of quantitative analysis of precipitate dimensions is described. The integration of this workflow into a data pipeline concept will also be discussed. Using ontologies, the raw image data, their respective contextual information, and the resulting output data of the quantitative image analysis can be linked in a triplestore. Publishing the digital workflow and the ontologies will ensure data reproducibility. In addition, the semantic structure enables data sharing and reuse for other applications and purposes, demonstrating interoperability.
Laser powder bed fusion (LPBF) is an additive manufacturing process for materials which inherently tends to yield various degrees of metastable hierarchical microstructures, defects and high residual stresses in the as-built condition depending on the process parameters. The understanding of the evolution of these typical features during heat treatment and subsequent thermal and mechanical ageing is crucial for the wider acceptance for safety critical structures. A multi-disciplinary research project at BAM studying the development of the microstructure, defects, residual stresses typical of LPBF 316L and their evolution during thermal and mechanical ageing has led to insights into the stability of these inherent features. This presentation aims to give a broad overview of the project with a few specific cases of investigation. Firstly, the formation of residual stresses, the nature of the initial microstructure, the tensile properties and a modelling approach to understand the anisotropy will be presented. This will be followed by examples of studies of their evolution during heat treatment, long term thermal exposure, and room temperature and high temperature mechanical testing compared to a baseline of conventional wrought variant of the same alloy.
An overview of the BAM funed Focus Area Materials Project "AGIL" will be presented. AGIL focussed on the stdiy of the ageing characteristics of additively manufactured austenitic stainless steel with a "powder to mechanical failure" Approach. Recent Highlights are presented and a perspective for future studies.
The mechanical strength of wrought high-strength aluminum alloys is essentially based on precipitation hardening, possibly in combination with prior forming, e. g. by stretching. Important parameters for achieving an optimum combination of hardness, strength, ductility, toughness, and further properties such as corrosion resistance are age-hardening temperature and time.
During thermal (mechanical) treatment, nucleation and growth of precipitates takes place, leading to the desired degree of hardening. In aluminum alloys, precipitation sequences are usually passed through, i. e. a sequence of metastable precipitates is formed before the stable phase can precipitate. The optimum combination of properties is therefore based on a certain (optimum) microstructure, which can, however, change during the use of a component, since the microstructure is not stable. This happens in particular when the operating temperatures are close to the aging temperature and/or the operating times are sufficiently long. An external mechanical load may accelerate the processes. The presentation gives some examples for this.
The studied aluminium alloy is EN AW-2618A (2618A). It is very widely used for exhaust gas turbo-charger compressor wheels. Due to long operating times, high cycle fatigue (HCF) and material aging under the influence of temperatures up to 230 °C is particularly relevant for the wheels. The wheels are typically milled from round wrought blanks. From such round blanks, different testpieces are extracted and a comprehensive series of HCF tests is conducted at room temperature. The tests investigate the materials fatigue performance in the T61 state for two load-ratios, namely R = -1 and R = 0.1. Additionally, two overaged material states are tested, accounting for the aging process the material undergoes during long operating times at high temperatures. The experimental results are evaluated and compared to each other.
Furthermore, the design process of notched specimens is presented. With the notched specimens, it is aimed to quantify the notch sensitivity of the material. Relating thereto, two potential model parameters for the fatigue lifetime model are introduced.