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Eingeladener Vortrag
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An extension of the constitutive viscoplastic model of Meric and Cailletaud is presented. The new model
accounts for coupling of plasticity and viscoplasticity to describe the rate dependence at low and moderate
temperatures. The model contains two boundaries: an elastic one and a viscoplastic one. Between the
boundaries, the only contribution to yielding is the rate dependent viscoplastic mechanism. Once the viscoplastic
boundary is reached, an additional rate independent flow mechanism becomes active. However, the extended
model is not able to predict properly both creep and long-term relaxation tests simultaneously. Therefore, a
deformation-induced softening is assumed, which is supposed to mainly affect static recovery.
The model has been calibrated with the mechanical tests on a single crystal nickel-basis superalloy. The uniaxial
tests have been carried out in the temperature interval 600°C – 1100°C in [001], [011] and [111] specimens.
The predicted creep, relaxation and non-isothermal cyclic tests exhibit reasonable agreement with the
experimental observations.
A computationally efficient solution scheme is presented for the mechanical problems whose formulations include the Kuhn–Tucker or Signorini–Fichera conditions. It is proposed to reformulate these problems replacing inequalities in these conditions by equations with respect to new unknowns. The solutions of the modified problems have simple physical meanings and determine uniquely the unknowns of the original problems. The approach avoids application of multi-valued operators (inclusions or inequalities) in formulation of the problems. Hence, the modified formulations are suitable for numerical analysis using established powerful mathematical methods and corresponding solvers developed for solving systems of non-linear equations.
To demonstrate the advantages of the proposed approach, it is applied for solving problems in two different areas: constitutive modeling of single-crystal plasticity and mixed boundary value problems of elastic contact mechanics with free boundaries. The original formulations of these problems contain respectively the Kuhn–Tucker and Signorini–Fichera conditions. A problem of the former area is integrated using an implicit integration scheme based on the return-mapping algorithm. The derived integration scheme is free of any update procedure for identification of active slip systems. A problem of the latter area is reduced to solution of non-linear integral boundary equations (NBIEs). Numerical examples demonstrate stability and efficiency of the solution procedures and reflect the mathematical similarities between the both non-linear problems.
A phase field model of brittle fracture has been developed to simulate the Hertzian crack induced by penetration of a rigid sphere to an isotropic linear-elastic half-space. The fracture formation is regarded as a diffusive field variable, which is zero for the intact material and unity if there is a crack. Crack growth is assumed to be driven by a strain invariant. The numerical implementation is performed with the finite element method and an implicit time integration scheme. The mechanical equilibrium and the phase field equations are solved in a staggered manner, sequentially updating the displacement field and the phase field variable. Numerical examples demonstrate the capability of the model to reproduce the nucleation and growth of the Hertzian cone crack.
A crystallographic constitutive model is developed, which accounts for both rate-sensitive and rate-insensitive flow. Single-crystal plasticity and viscoplasticity are the limiting cases of the model, so that it properly reflects the material response over a wide temperature range. A non-linear dynamic recovery is included to properly describe ratchetting. We provide a robust integration scheme based on generalization of the return-mapping algorithm and of the procedure for active set search.
The implicit integration and consistent tangent are implemented through the UMAT subroutine in the ABAQUS finite element program. The capability of the model to account for both high and low strain rates is demonstrated in numerical examples. Finally, the stability of integration scheme and quadratic convergence of the global NewtonRaphson equilibrium iterations are demonstrated on the example of a notched bar under tension.
Simulation of Mechanical Behaviour in a Single-Crystal Nickel-Basis Superalloy at High Temperature
(2010)
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.
Concrete is a complex material. Its properties evolve over time, especially at early age, and are dependent on environmental conditions, i.e. temperature and moisture conditions, as well as the composition of the material.
This leads to a variety of macroscopic phenomena such as hydration/solidification/hardening, creep and shrinkage, thermal strains, damage and inelastic deformations. Most of these phenomena are characterized by specific set of model assumptions and often an additive decomposition of strains into elastic, plastic, shrinkage and creep components is performed. Each of these phenomena are investigated separately and a number of respective independent models have been designed. The interactions are then accounted for by adding appropriate correction factors or additional models for the particular interaction. This paper discusses the importance of reconsider even in the experimental phase the model assumptions required to generalize the experimental data into models used in design codes. It is especially underlined that the complex macroscopic behaviour of concrete is strongly influenced by its multiscale and multiphyscis nature and two examples (shrinkage and fatigue) of interacting phenomena are discussed.
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.
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.
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.
In diesem Forschungsvorhaben erfolgte eine Überprüfung der Übertragbarkeit der Werkstoff- und Rechenmodelle für die Lebensdauervorhersage von ATL-Heißteilen unter TMF-Beanspruchung auf eine andere Werkstoffklasse, d. h. auf eine austenitische Gusseisenlegierung mit Kugelgraphit. Dafür wurde die Legierung EN-GJSA-XNiSiCr35-5-2 (Ni-Resist D-5S) ausgewählt. Zunächst wurde für diesen Werkstoff eine experimentelle Datenbasis geschaffen, da diese vor Beginn des Vorhabens nicht ausreichend war. Dazu wurden Zug-, Kriech-, LCF- und TMF-Versuche durchgeführt, die der Kalibrierung der Modelle dienten. Unter TMF-Belastung zeigte der untersuchte Werkstoff ein stark abweichendes Verhalten von den im vorangegangenen Vorhaben untersuchten ferritischen SiMo-Legierungen: Der Werkstoff Ni-Resist zeigte insgesamt eine vergleichbare Festigkeit unter OP- und IP-Bedingungen, während die ferritischen Legierungen unter IP-Beanspruchung eine deutlich höhere Festigkeit aufweisen. Mit zunehmenden Temperaturen und Haltezeiten unter Zugspannungen wurden dagegen beim Werkstoff Ni-Resist Hinweise auf Kriechschädigung gefunden, die schädigungsrelevant sind. Auch dies ist ein deutlicher Unterschied zu den SiMo-Legierungen. Das Spannungs-Verformungs-Verhalten in den LCF- und TMF-Versuchen wird durch das Modell auch für den neuen Werkstoff überwiegend gut beschrieben. Das Gleiche gilt für die Lebensdauervorhersage, die mit Ausnahme der Prüftemperatur 900 °C innerhalb eines Fak-tors zwei liegt. Eine Verifikation des Modells erfolgte mit Hilfe eines Bauteilversuchs an einem Abgassammler, der abwechselnd mit heißem und kaltem Gas durchströmt wurde. Ziel der Bauteilsimulation war insbesondere die Vorhersage der Rissbildungsorte. Eine Vorhersage der exakten Lebensdauer wurde nicht erwartet, da das Bauteil mit einer Gusshaut behaftet war, während die für die Kalibrierung des Lebensdauermodells verwendeten Versuche an bearbeiteten, glatten Proben ohne Gusshaut durchgeführt wurden. Die überwiegende Anzahl der experimentell ermittelten Rissorte wurden vorhergesagt. Schließlich war ein wesentliches Ziel des Vorhabens, den Einfluss von HCF-Schwingungen auf die TMF-Lebensdauer vertieft experimentell zu untersuchen und das bereits bestehende Lebensdauermodell auf HCF-Überlagerung zu erweitern. Dazu wurde zunächst die Daten-basis aus dem Vorgängervorhaben am Bespiel von SiMo 4.05 deutlich ausgebaut, um die verschiedenen Einflussparameter zu erfassen. Es wurde ein Ansatz entwickelt, in dem die Lebensdauerminderung durch die überlagerten HCF-Schwingungen abgebildet wird. Dabei wird davon ausgegangen, dass ab einer bestimmten Risstiefe die Überlagerung der HCF-Schwingungen die Rissausbreitung stark beschleunigt. Der Zeitpunkt, wann diese Beschleunigung eintritt, wird als maßgeblich für die Lebensdauerminderung angesehen. Mit diesem Ansatz lassen sich die Lebensdauern für beide Werkstoffe in guter Übereinstimmung mit dem Experiment vorhersagen.
In diesem Forschungsvorhaben erfolgte eine Überprüfung der Übertragbarkeit der Werkstoff- und Rechenmodelle für die Lebensdauervorhersage von ATL-Heißteilen unter TMF-Beanspruchung auf eine andere Werkstoffklasse als im Vorgängervorhaben, d.h. auf das austenitische Gusseisen EN-GJSA-XNiSiCr35-5-2 (Ni-Resist D-5S). Zunächst wurde dafür eine experimentelle Datenbasis geschaffen, da diese vor Beginn des Vorhabens nicht ausreichend war. Dazu wurden Zug-, Kriech-, LCF- und TMF-Versuche durchgeführt, die der Kalibrierung der Modelle dienten. Das Spannungs-Verformungs-Verhalten und die Lebensdauer in den LCF- und TMF-Versuchen werden durch das Modell auch für den neuen Werkstoff überwiegend gut beschrieben. LCF-Versuche mit Haltezeit bei 900 °C sowie IP-TMFVersuche mit einer Obertemperatur von 900 °C werden weniger gut vorhergesagt, da sich der Schädigungsmechanismus ändert. Eine Verifikation des Modells erfolgte mit Hilfe eines Bauteilversuchs an einem Abgassammler. Die überwiegende Anzahl der experimentell ermittelten Rissorte wurden von dem Modell vorhergesagt.
Ein wesentliches Ziel des Vorhabens war, den Einfluss von HCF-Schwingungen auf die TMF-Lebensdauer vertieft experimentell zu untersuchen und das bereits bestehende Lebensdauermodell auf HCF-Überlagerung zu erweitern. Es wurde ein bruchmechanisch motivierter Ansatz entwickelt, in dem die Lebensdauerminderung durch die im TMF-Zyklus überlagerten HCF-Schwingungen abgebildet wird. Mit diesem Ansatz lassen sich die Lebensdauern sowohl für den Werkstoff SiMo 4.05 als auch für den Ni-Resist in guter Übereinstimmung mit dem Experiment Vorhersagen.
Das Ziel des Forschungsvorhabens ist erreicht worden.
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.
The onset of plasticity in a single crystal C60 fullerite was investigated by nanoindentation on the (111) crystallographic plane. The transition from elastic to plastic deformation in a contact was observed as pop-in events on loading curves. The respective resolved shear stresses were computed for the octahedral slip systems ⟨011¯¯¯⟩{111}, supposing that their activation resulted in the onset of plasticity. A finite element analysis was applied, which reproduced the elastic loading until the first pop-in, using a realistic geometry of the Berkovich indenter blunt tip. The obtained estimate of the C60 theoretical shear strength was about 1/11 of the shear modulus on {111} planes.
Die Analyse der Lebensdauer von Bauteilen unter thermomechanischer Ermüdung (TMF) erfordert ein geeignetes Stoffgesetz, welches in der Lage ist, zyklische Plastizität die Abhängigkeit der Spannungsantwort nach der Dehnrate, Kriechen und Spannungsrelaxation temperaturabhängig zu beschreiben und ein Lebensdauermodell, welches in Abhängigkeit von der örtlich aufgelösten Spannungs- und Verformungsgeschichten eine Schätzung der Anzahl der Zyklen bis zum Anriss liefern kann.