Modeling of high-temperature creep for structural analysis applications

Für zahlreiche Bauteile für Hochtemperaturanwendungen ist die Lebensdauerabschätzung im Kriechbereich die wichtigste Aufgabe bei der Vorbereitung von Einsatzentscheidungen. Ziel dieser Arbeit ist es, einen umfassenden Überblick über die theoretische Modellierung und die Analyse des Kriechens und der Langzeitfestigkeit von Bauteilen zu geben. Dabei stehen folgende Schwerpunkte im Mittelpunkt: Konstitutivgleichungen für das Kriechen von Ingenieurwerkstoffen unter mehrachsigen Beanspruchungen, strukturmechanische Modelle für Balken, Platten, Schalen und dreidimensionale Körper sowie numerische Verfahren für die Lösung nichtlinearer Anfangs-Randwertaufgaben der Kriechmechanik. Im Rahmen der konstitutiven Modellierung werden zahlreiche Erweiterungen der Mises-Odqvist-Kriechtheorie wie die Einbeziehung der Art des Spannungszustandes, der Anisotropie sowie der Verfestigungs- und Schädigungsvorgänge diskutiert. Für Sonderfälle der Materialsymmetrien werden geeignete Invarianten des Spannungstensors, Ansätze für Vergleichsspannungen und -dehnungen sowie Konstitutivgleichungen zum anisotropen Kriechen formuliert. Das Primärkriechen und transiente Kriechvorgänge können durch die Einführung von Verfestigungsvariablen beschrieben werden. Die Modelle der Zeit- und Deformations- sowie der kinematischen Verfestigung werden bezüglich der Vorhersagbarkeit des mehrachsigen Kriechens untersucht. Danach erfolgen ein systematischer Überblick und die Bewertung der Konstitutivgleichungen mit Schädigungsvariablen, die bisher auf die Beschreibung des Tertiärkriechens und der Langzeitfestigkeit angewandt wurden. Für einige Ingenieurwerkstoffe werden Kriechkurven, Konstitutivgleichungen, konstitutive Funktionen und Werkstoffkennwerte anhand der in der Literatur publizierten Daten zusammengefasst. Ferner wird ein neues Modell zur Beschreibung des anisotropen Kriechens in einem mehrlagigen Schweißgut vorgestellt. Die Grundgleichungen für das Kriechen in dreidimensionalen Körpern werden zum Zweck der Formulierung von Anfangs-Randwertproblemen, Variationsverfahren und Zeitschrittalgorithmen zusammengefasst. Zahlreiche Modelle der Strukturmechanik für Balken, Platten und Schalen werden bezüglich ihrer Anwendbarkeit auf Kriechprobleme diskutiert. Hier wird auf Effekte wie Querschubverzerrung, Randschichten und geometrische Nichtlineatitäten aufmerksam gemacht. Modelle mit Schädigungsvariablen werden mit Hilfe einer benutzerdefinierten subroutine in das Programmsystem ANSYS eingebunden. Für deren Verifikation werden Testaufgaben entwickelt und mit Hilfe spezieller numerischer Verfahren gelöst. Berechnungen der selben Aufgaben mit der Methode der finiten Elemente illustrieren die Anwendbarkeit der entwickelten subroutine für verschiedene Typen von finiten Elementen. Weiterhin zeigen sie den Einfluss der Netzdichte auf die Lösungsgenauigkeit. Abschließend wird die Langzeitfestigkeitsanalyse einer räumlichen Rohrleitung vorgestellt. Die Ergebnisse zeigen, dass das entwickelte Verfahren in der Lage ist, die wesentlichen Kriech- und Schädigungsvorgänge in Ingenieurkonstruktionen darzustellen.For many structures designed for high temperature applications, e.g. piping systems and pressure vessels, an important problem is the life time assessment in the creep range. The objective of this work is to present an extensive overview about the theoretical modeling and numerical analysis of creep and long-term strength of structures. The study deals with three principal topics including constitutive equations for creep in structural materials under multi- axial stress states, structural mechanics models of beams, plates, shells and three-dimensional solids, and numerical procedures for the solution of initial-boundary value problems of creep mechanics. Within the framework of the constitutive modeling we discuss various extensions of the von Mises-Odqvist type creep theory to take into account stress state effects, anisotropy as well as hardening and damage processes. For several cases of material symmetries appropriate invariants of the stress tensor, equivalent stress and strain expressions as well as creep constitutive equations are derived. Primary creep and transient creep effects can be described by the introduction of hardening state variables. Models of time, strain and kinematic hardening are examined as they characterize multi-axial creep behavior under simple and non-proportional loading conditions. A systematic review and evaluation of constitutive equations with damage variables and corresponding evolution equations recently applied to describe tertiary creep and long term strength is presented. Stress state effects of tertiary creep and the damage induced anisotropy are discussed in detail. For several structural materials creep curves, constitutive equations, response functions and material constants are summarized according to recently published data. Furthermore, a new model describing anisotropic creep in a multi-pass weld metal is presented. Governing equations for creep in three-dimensional solids are introduced to formulate initial-boundary value problems, variational procedures and time step algorithms. Various structural mechanics models of beams, plates and shells are discussed in context of their applicability to creep problems. Emphasis is placed on effects of transverse shear deformations, boundary layers and geometrical nonlinearities. A model with a scalar damage variable is incorporated into the ANSYS finite element code by means of a user defined material subroutine. To verify the subroutine several benchmark problems are developed and solved by special numerical methods. Results of finite element analysis for the same problems illustrate the applicability of the developed subroutine over a wide range of element types including shell and solid elements. Furthermore, they show the influence of the mesh size on the accuracy of solutions. Finally an example for long term strength analysis of a spatial steam pipeline is presented. The results show that the developed approach is capable to reproduce basic features of creep and damage processes in engineering structures.von Konstantin Naumenk

Power plant component design using creep and fatigue damage analysis

Structural analysis and design of power plant components requires us to take into account inelastic deformation and material damage processes under constant and variable loading and temperature conditions. The aim of this presentation is to introduce the constitutive models of creep and damage for advanced heat resistant steels. An emphasis is placed on the description of ductilebrittle transition of the damage mode depending on the applied stress level and the duration of the creep process. The model is applied to the lifetime prediction of a real power plant component. For this purpose a user-defined material subroutine is developed inside a general finite element code. The results of computations illustrate basic features of the stress redistribution and the damage evolution during isothermal loading cycle. Based on the obtained stress, strain and damage fields, we discuss the extensions of the proposed method to non-isothermal variable loading

Extreme acoustic anisotropy in crystals visualized by diffraction tensor

Acoustic wave propagation in single crystals, metamaterials and composite structures is a basic mechanism in acoustic, acousto-electronic and acousto-optic devices. Acoustic anisotropy of crystals provides a variety of device performances and application fields, but its role in pre-estimation of achievable device characteristics and location of crystal orientations with desired properties is often underestimated. A geometrical image of acoustic anisotropy can be an important tool in design of devices based on wave propagation in single crystals or combinations of anisotropic materials. We propose a fast and robust method for survey and visualization of acoustic anisotropy based on calculation of the eigenvalues of bulk acoustic wave (BAW) diffraction tensor (curvature of the slowness surface). The stereographic projection of these eigenvalues clearly reveals singular directions of BAW propagation (acoustic axes) in anisotropic media and areas of fast or slow variation of wave velocities. The method is illustrated by application to three crystals of different symmetry used in different types of acoustic devices: paratellurite, lithium niobate, and potassium gadolinium tungstate. The specific features of acoustic anisotropy are discussed for each crystal in terms of their potential application in devices. In addition, we demonstrate that visualization of acoustic anisotropy of lithium niobate helps to find orientations supporting propagation of high-velocity surface acoustic waves.Comment: 12 pages, preprint submitted to EPJ Plu

Inelastic Deformation of Conductive Bodies in Electromagnetic Fields

Inelastic deformation of conductive bodies under the action of electromagnetic fields is analyzed. Governing equations for non-stationary electromagnetic field propagation and elastic-plastic deformation are presented. The variational principle of minimum of the total energy is applied to formulate the numerical solution procedure by the finite element method. With the proposed method, distributions of vector characteristics of the electromagnetic field and tensor characteristics of the deformation process are illustrated for the inductor-workpiece system within a realistic electro-magnetic forming process

Thermo‐mechanical analysis of a steam turbine rotor

In power plants, high temperatures prevail during long holding times. Furthermore, power plants are often started and shut-down in order to account for gaps or oversupplies in energy production. These loading conditions induce both creep and fatigue loads. Due to their excellent thermo-mechanical properties, such as high tensile strength and elevated corrosion resistance, heat-resistant steels are established materials for power plant components. Nevertheless, these steels tend to soften under deformation, which should be accounted for by a constitutive model. The contribution at hand analyses the thermo-mechanical behavior of a steam turbine rotor. For this purpose, a unified phase mixture model is introduced. This constitutive model accounts for rate-dependent inelasticity, hardening, as well as softening by employing an iso-strain approach with a soft and a hard constituent. While the soft constituent represents areas with a low dislocation density, such as the interior of subgrains, the hard constituent refers to regions with a high dislocation density, i.e. the subgrain boundaries. Furthermore, two internal variables are introduced: a backstress tensor of Armstrong-Frederick type and a scalar softening variable. The model results in a coupled system of three evolution equations with respect to the inelastic strain, the backstress, and the softening variable. To allow for the analysis of real power plant components, the model is implemented into the finite element method such that the evolution equations are integrated based on the backward EULER method. The applicability of the model is demonstrated by conducting a thermo-mechanical analysis of a steam turbine rotor with complex geometry under realistic boundary conditions. In a first step, the instationary temperature field in the rotor is computed in a heat transfer analysis. Thereby, typical steam temperatures in power plants and the corresponding heat transfer coefficients are prescribed. As a next step, the structural analysis is conducted based on the phase mixture model and the obtained temperature field as input. In addition, the time-dependent rotational frequency and steam pressure are taken into account. Note that the influence of different start-up procedures such as a cold or a hot start is examined in detail. As a result, the structural analysis provides the stress-strain hystereses, which constitute the basis for further fatigue and damage assessment.Projekt DEAL 201

A generalized framework towards structural mechanics of three-layered composite structures

Three-layered composite structures find a broad application. Increasingly, composites are being used whose layer thicknesses and material properties diverge strongly. In the perspective of structural mechanics, classical approaches to analys is fail at such extraordinary composites. Therefore, emphasis of the present approach is on arbitrary transverse shear rigidities and structural thicknesses of the individual layers. Therewith we employ a layer-wise approach for multiple (quasi-)homogeneous layers. Every layer is considered separately whereby this disquisition is based on the direct approach for deformable directed surfaces. We limit our considerations to geometrical and physical linearity. In this simple and familiar setting we furnish a layer-wise theory by introducing constraints at interfaces to couple the layers. Hereby we restrict our concern to surfaces where all material points per surface are coplanar and all surfaces are plane parallel. Closed-form solutions of the governing equations enforce an arrow frame since they are strongly restrictive in the context of available boundary conditions. Thusacomputational solution approach is introduced using the finite element method. In order to determine the required spatially approximated equation of motion, the principle of virtual work is exploited. The discretization is realized via quadrilateral elements with quadratic shape functions. Here by we introduce an approach where nine degrees of freedom per node are used. In combination with the numerical solution approach, this layer-wise theory has emerged as a powerful tool to analyze omposite tructures. In present reatise, e ould ike o arify he road cope f his pproach

Modelling of Creep and Oscillations in Material Described by Armstrong-Frederick Equations

Different structural elements at high temperatures and cyclic loading demonstrate essential creep behavior. Due to variety of materials which are used in modern industrial applications the different forms of creep response have to be analyzed. The one of them presents in materials are characterized by creep processes with essential recovery, which is expressed by strain decreasing after the unloading. Such material behavior is described by well-known Armstrong-Frederick model. The case of cyclic loading leading to forced oscillations at high temperature is studied. The Armstrong- Frederick creep model contains two equations: first for creep strain rate function as well as the second for socalled backstress evolution. The problem is solved by two time scales methods with subsequent averaging in a period of oscillations. The solution was performed for the hyperbolic creep strain rate function which satisfactory describes the high-temperature behavior of advanced steel with primary creep conditions. The stress function is presented by expansion in Fourier series. Asymptotic solution of creep equations was obtained and by use of the procedure of averaging in the period the new model describing ‘slow’ creep motion has been derived. The analytical forms of influence functions for both equations of the model expressing the role of cyclical loading were obtained. Numerical examples which demonstrate the cyclic creep behavior in advanced steel X20CrMoV12-l are presented and discussed

Kontaktwechselwirkung einer Rohrleitung mit der Reparaturbandage aus einem Kompositwerkstoff

In der vorliegenden Arbeit wird die Kontaktaufgabe über die Wechselwirkung einer langen Zylinderschale mit einer koaxialen zylindrischen Bandage aus einem Verbundwerkstoff untersucht. Der Verbundwerkstoff wird als ein homogenes orthotropes Material mit bekannten effektiven elastischen Eigenschaften modelliert. Basierend auf der klassischen Schalentheorie werden die Grundgleichungen für die Kontaktaufgabe sowie allgemeine Lösungen für die Durchbiegungen und Schnittgrößen formuliert. Die unbekannten Integrationskonstanten sowie die Kontaktfläche werden numerisch mit Hilfe des Programmpakets Maple ermittelt. Drei charakteristische Längen der Bandage, bei denen der Übergang von einemKontaktschema der Wechselwirkung zu einem anderen erfolgt, wurden ermittelt. Es wurde festgestellt, dass die Änderung des Innendrucks nicht zum Übergang von einem Kontaktschema zu einem anderen führt. Der Charakter der Kontaktwechselwirkung wird durch geometrische Parameter derVerbindung und elastische Materialeigenschaften der Schale und der Bandage bestimmt.In the present work the contact interaction of a long cylindrical shell with a coaxial cylindrical wrap made of a composite material is investigated. The composite material is modeled as a homogeneous orthotropic medium with known effective elastic properties. Based on the classical shell theory governing equations for the contact problems and general solutions to the deflections and internal forces are formulated. The unknown integration constants and the contact surface area are determined numerically using the software package Maple. Three characteristic lengths of the wrap, for which the transition from one contact mode to another takes place, have been determined. It was found that the change in the internal pressure does not affect the transition between the contact modes. The nature of the contact interaction is determined by the geometric parameters of the contact pair and elastic material properties of the shell and the repair wra