H. Riesch-Oppermann

Automatic finite element meshing of planar Voronoi tessellations

Abstract The concept of Voronoi tessellation has recently been extensively used in materials science, especially to model the geometrical features of random microstructures like aggregates of grains in polycrystals, patterns of intergranular cracks and composites. Solution of the underlying field equations usually requires use of numerical methods such as finite elements. The framework for automatic generation of quadrilateral finite element meshing of planar Voronoi tessellation is proposed in the paper, resulting in a powerful set of tools to be used in the rather wide field of micromechanics. As far as feasible, the implementation of features built in commercially available mesh generators was pursued. Additionally, the minimum geometric requirements for a “meshable” tessellation are outlined. Special attention is given to the meshes, which enable explicit modelling of grain boundary processes, such as for example contact (closure of cracks) or friction between grains. This is inline with numerical examples, which are oriented towards the fracture mechanics, in particular to the development of intergranular microcracks and/or their impact on the effective behaviour of the polycrystal. The examples were evaluated using the commercially available general-purpose finite element code abaqus . The usual continuum mechanics based numerical methods and boundary conditions were safely applied to aggregates of randomly oriented polycrystals with anisotropic elastic material behaviour as computational domains.

Application of first and second order reliability methods in the safety assessment of cracked steam generator tubing

Abstract The First- and Second Order Reliability Methods (FORM and SORM) have been applied in the safety assessment of steam generator tubes with through-wall axial stress corrosion cracks. The underlying probabilistic fracture mechanics model takes into account the scatter in tube geometry, material properties and stable crack propagation. Also, the effect of the maintenance strategy has been considered. A realistic numerical example has been given to compare the failure probabilities calculated by FORM and SORM to those obtained by different versions of Monte Carlo simulations. The relative errors of the numerical methods employed have been analysed, which has shown that FORM performs in an acceptable and SORM in an excellent manner. Some changes in failure surface properties, caused by different maintenance strategies, are indicated and a sensitivity analysis of influencing parameters is made. The results obtained demonstrate the applicability of FORM and SORM in the safety assessment of stress corrosion cracked steam generator tubing.

Propagation of stress corrosion cracks in steam generator tubes

Abstract A model suitable to describe the propagation of stress corrosion cracks in steam generator tubes made of Inconel-600 is proposed in this paper. It concentrates on axial cracks located in the tube expansion transition zones which are assumed to be through-wall. The residual stress field is therefore considered as the major contributing factor driving short cracks while operational stresses dominate the growth of longer cracks. An estimate of residual hoop stresses is obtained using a non-linear finite element simulation of the tube to tube-sheet rolling process. Scatter of the residual stresses due to the stochastic variations of the dominant influencing parameters was studied. The crack propagation model utilizes linear-elastic fracture mechanics theory. In particular, both crack tips are modelled to propagate with different velocities due to the highly asymmetric stress field. Provisions are also made to account for the reactor coolant temperature and chemical composition effects. The model performance is demonstrated by a numerical example considering the crack propagation data from D4 steam generators during a 15 month operational cycle as recorded by subsequent non-destructive tube examinations.

Modelling the early development of secondary side stress corrosion cracks in steam generator tubes using incomplete random tessellation

Abstract A thorough understanding of the secondary side stress corrosion cracking of Inconel 600 in steam generator (SG) tubes seems to be still somewhat in the future. Especially the early phase of the development of cracks, also called the initiation phase, is beyond the present state-of-the-art explanations. An effort was, therefore, made to propose modelling and visualisation of the kinetics of secondary side stress corrosion crack initiation and growth on the grain-size scale: • An incomplete random tessellation is used to approximate the random planar grain structure. • The crack initiation is modelled by random processes, taking into account the most important factors such as proximity of the aggressive medium and the orientation of the grain boundaries relative to the stress field. • The stochastic process describing crack growth accounts for crack branching, coalescence and interference between neighbouring cracks. Several numerical examples are provided to demonstrate the versatility of the proposed method. Reasonable qualitative agreement with metallographic results is shown.

Probabilistic fracture mechanics applied to high temperature reliability

Abstract An example is used to demonstrate the applicability of Probabilistic Fracture Mechanics (PFM) methods in high temperature reliability assessment. The failure probability of a pipe under pure bending at a temperature of 973 K is calculated using both Monte Carlo simulation and the First Order Reliability Method. The advantages and the accuracy of approximative methods for calculating failure probabilities are demonstrated. Additionally, probabilistic and deterministic methods for reliability assessment are compared with each other. It is shown that a deterministic reliability assessment becomes inadequate in cases where the failure probability is determined by equally significant contributions of several random variables.

Limitations of the Weibull Theory in Stress Fields With Pronounced Stress Gradients

The Weibull theory for brittle fracture of ceramic materials has to be modified for stress fields with pronounced spatial inhomogeneities, e.g. for severe thermal shock or for material joints. This is due to the fact that the stress intensity factor determining the failure behavior of the natural flaws is affected by the stress gradients. This leads to a rather involved relationship between critical flaw size and applied stress and affects the strength.Copyright

Modelling of scattering material properties with stochastic finite element methods

Abstract The method of stochastic finite elements is used to analyse the failure behaviour of a single crystal turbine blade. The failure probability is calculated using different numerical procedures, namely the first order reliability method together with the adjoint method and the response surface method. It is shown how the spatial fluctuations of the orientations of the single crystal influence the failure behaviour of the turbine blade.

In situ Observations and Quantitative Analysis of Short Circuit Probability Due to Ultrahigh Frequency Fatigue

Ultrahigh frequency fatigue (GHz) can lead to the formation of extrusions in aluminum thin film metallizations. Protruding from the surface, such extrusions can connect adjacent electrodes leading to the formation of short circuits. In situ observations presented in this paper verify this belief. Based on measurements from ex situ experiments, we present a defect-based probabilistic model to predict the failure probability, allowing to estimate the lifetime of test devices undergoing such load conditions.

Short Intergranular Cracks in Elasto-Plastic Polycrystalline Aggregate

Computational algorithms aiming at modeling and visualization of the initiation and growth of intergranular stress corrosion cracks (e.g., in the steam generator tubes) on the grain-size scale have already been proposed. Main focus of the paper addresses the influence of randomly oriented anisotropic elasto-plastic grains on the microscopic stress fields at crack tips. The limited number of calculations indicate that the incompatibility strains, which develop along the boundaries of randomly oriented grains, influence the local stress fields (J-integrals) at crack tips significantly.Copyright

Stresses in the First Wall of a Dual-Coolant Liquid-Metal Breeder Blanket during Electron-Beam Welding

Electron-beam (EB) welding is an important joining technique for fabricating and assembling blanket and first-wall components in fusion reactors. A numerical modeling of the EB procedure of a selected part of a DEMO fusion reactor blanket is presented. Stress and temperature distributions during and after EB welding are analyzed with the help of nonlinear finite element calculations, including phase transformations of MANET stainless steel. Residual stresses are discussed. Their magnitude and distribution may stimulate the initiation and growth of surface cracks parallel to the weld. Analysis of postweld heat treatment shows that the residual stresses can be neglected if appropriate postweld heat treatment is performed. The main drawback of this analysis seems to be the lack of appropriate material data for high temperatures close to the melting point. Despite this, qualitative statements on the feasibility of joints are possible, and improved analyses of welding stresses are expected to make a valuable contribution to future studies that address the safety and reliability of blanket structures.