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2016 | Buch

Recent Trends in Fracture and Damage Mechanics

herausgegeben von: Geralf Hütter, Lutz Zybell

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book covers a wide range of topics in fracture and damage mechanics. It presents historical perspectives as well as recent innovative developments, presented by peer reviewed contributions from internationally acknowledged authors.

The volume deals with the modeling of fracture and damage in smart materials, current industrial applications of fracture mechanics, and it explores advances in fracture testing methods. In addition, readers will discover trends in the field of local approach to fracture and approaches using analytical mechanics.

Scholars in the fields of materials science, engineering and computational science will value this volume which is dedicated to Meinhard Kuna on the occasion of his 65th birthday in 2015. This book incorporates the proceedings of an international symposium that was organized to honor Meinhard Kuna’s contributions to the field of theoretical and applied fracture and damage mechanics.

Inhaltsverzeichnis

Frontmatter

Historical Perspective

Frontmatter

Meinhard Kuna: Physics and Engineering at the Crack Tip—A Retrospective

Abstract

The present volume appeared on occasion of the 65th birthday of Prof. Meinhard Kuna. This section outlines the biography of Meinhard Kuna including main scientific projects and some personal anecdotes.

Geralf Hütter, Lutz Zybell

Experimental and Numerical Fracture Mechanics—An Individually Dyed History

Abstract

Almost half a century ago, fracture mechanics started in Germany with the foundation of the DVM Working Group Fracture Mechanics in 1969. The present authors have been partly involved in the further development of fracture and damage mechanics, one with particular interest in elastic-plastic fracture and modelling, the other in thin-walled structures, fatigue and assessment. They take the colloquium in honour of the 65th birthday of Professor Meinhard Kuna as occasion to highlight some significant achievements on the background of personal experience. In particular, they intend to show that both fracture and damage mechanics started with paradigm changes which were partly looked at with distrust in the beginning but turned out to be seminal.

Wolfgang Brocks, Karl-Heinz Schwalbe

Applications

Frontmatter

Fracture Mechanics Assessment of Welded Components at Static Loading

Abstract

Special aspects of welded components such as geometrical imperfections, inhomogeneity, strength mismatch and welding residual stresses have to be taken into account in a fracture mechanics analysis since they affect the crack driving force in the component as well as the fracture resistance of the material. The treatment of components subjected to static loading is based on methods such as the European SINTAP procedure, which has been validated in a number of case studies. In the present paper the influence of strength mismatch and residual stresses on the fracture resistance and the assessment of a component are discussed.

Peter Hübner, Uwe Zerbst

Application of Fracture Mechanics for the Life Prediction of Critical Rotating Parts for Aero Engines

Abstract

The application of fracture mechanics based methods forms an integral part in the prediction of safe life and damage tolerant behaviour of critical parts in aero engines. For compressor and turbine discs, this comprises the calculation of cyclic life to burst, integrity under extreme loading conditions and damage tolerant behaviour for different kinds of anomalies encountered in manufacturing and/or in-service application. Taking the example of the introduction of the new nickel-based disc alloy ATI 718Plus^®, the typical methods, the extent of material and component testing, and some limitations of current methods are presented. This project is a joint effort between Rolls-Royce Deutschland and several universities and research institutions.

M. Springmann, M. Schurig, D. Hünert, W. Rothkegel, H. Schlums

Consideration of Fatigue Crack Growth Aspects in the Design and Assessment of Railway Axles

Abstract

Current design rules for railway wheelsets do not directly address issues related to fatigue crack propagation. Nevertheless, the latter topic is a part of the revised safety concept for passenger trains recently adopted in German railway applications. Numerous research activities, including international cooperative projects, have been conducted in the past decade aiming at quantifying fatigue crack growth rates in railway axles and estimating their inspection intervals based on the fracture mechanics methodology. This paper summarizes some experience and findings obtained by the authors within several studies dealing with the assessment of fatigue crack propagation in railway steels. Particular aspects highlighted in the paper include material characterization, effects of the specimen geometry and crack tip constraint on fatigue crack growth rates, stress analyses of axles and wheelsets, the derivation of stress intensity factor solutions applicable to specific conditions achieved in railway axles, considerations of the variability and scatter of geometrical parameters and material data in fatigue crack growth calculations.

Igor Varfolomeev, Michael Luke

Fracture Testing

Frontmatter

Assessment of Material Properties by Means of the Small Punch Test

Abstract

In recent years the small punch test (SPT) method has become an attractive alternative compared to traditional material testing procedures, especially in cases where only small amounts of material are available. We provide a literature review with focus on the history and application of the method. The main difficulty using the SPT is the fact that relevant material parameters cannot be as simply obtained by SPTs as by standard test methods, because of its non-uniform stress and deformation state. However, this can be achieved by comparing the experimental SPT results with those obtained by finite element computations of SPTs using advanced material models. Then the task is to determine the parameters of the material models using special optimization techniques. This paper presents SPT techniques for a broad temperature range. Work done on both ductile and brittle materials is presented. The analysis will focus on different advanced methods for determining parameters of state of the art material models for elastic-plastic, ductile damage and brittle failure behaviour. Results are provided for a weld line of a pressure gas pipe and brittle ceramic refractory materials.

Martin Abendroth, Stefan Soltysiak

Determination of Fracture Mechanics Parameters for Cast Iron Materials Under Static, Dynamic and Cyclic Loading

Dedicated to Professor Meinhard Kuna on the Occasion of his 65th Birthday

Abstract

The results of extensive measurements of fracture mechanics parameters of cast iron materials under static, dynamic and cyclic loading at the Institute of Materials Engineering (IWT) at the TU Bergakademie Freiberg are shown. A special attention for this group of materials must be given to the microstructural influence on the crack resistance behavior and thus the component reliability. In collaboration with the Institute of Mechanics and Fluid Dynamics (IMFD) of the TU Bergakademie it was shown for castings, such as components of wind turbines made of ductile cast iron, railway wheels made of ADI or transport casks for spent nuclear fuel assemblies that the fracture mechanical strength analysis including possible casting defects extends the conventional strength analysis.

G. Pusch, S. Henkel, H. Biermann, P. Hübner, A. Ludwig, P. Trubitz, T. Mottitschka, L. Krüger

On the Development of Experimental Methods for the Determination of Fracture Mechanical Parameters of Ceramics

Abstract

Because of their high yield strength and hardness as well as their brittle fracture characteristics the behavior of cracks in ceramics can be described within the framework of linear elastic fracture mechanics. For fracture toughness (K _Ic) measurements the test techniques which were developed for metallic materials are unfavorable, as an economical preparation is impossible in the case of ceramic materials. Therefore simple geometries e.g. bend bars became a preferred specimen shape for K _Ic measurements. A major difficulty arises when sharp and well-defined pre-cracks for crack propagation studies have to be created. Several methods to overcome this problem are introduced. Additionally, methods to investigate small amounts of material are discussed.

Robert Danzer, Tanja Lube, Stefan Rasche

Transition from Flat to Slant Fracture in Ductile Materials

Abstract

We investigate ductile fracture in an aluminum alloy which exhibits an interesting switch in mode from flat fracture to slant fracture. While this transition is typically considered to be triggered by a change in crack tip constraint with specimen thickness, we explore this transition in rolled sheet material simply by controlling the strain hardening behavior of the material. Specifically, experiments are performed on two different heat-treatments of the same alloy, resulting in two materials that differ only in their strain-hardening behavior. Based on an examination of the microscopic and macroscopic strain evolution, we conclude that the transition arises because of strain localization that precedes fracture.

William F. Hickey, Krishnaswamy Ravi-Chandar

Smart Materials

Frontmatter

Interaction of Cracks and Domain Structures in Thin Ferroelectric Films

Abstract

The fracture behavior of ferroelectric materials is a complex problem that has been addressed in numerous experimental and theoretical studies. Several factors have been identified to play an important role, such as the applied electric field, the medium inside the crack, the electrical conditions on the crack faces, and polarization switching at or near the crack tip. In this investigation, a phase field model for ferroelectric domain evolution is used to calculate crack tip driving forces for mode-I cracks in barium titanate thin films. The driving forces are obtained by employing the theory of configurational forces, which is equivalent to considering the J-integral. Simulations are done for permeable, impermeable, semi-permeable, and energetically consistent crack face conditions with both air and water as crack medium. The finite element calculations are performed for films with thicknesses varying from 5 to 30 nm. The results show that the impermeable, semi-permeable and energetically consistent conditions lead to similar crack tip driving forces if air is used as crack medium. In the absence of mechanical loading, strong electric fields result in a closing crack tip driving force, while the use of water as crack medium leads to opposite driving forces. It can be confirmed that polarization switching at the crack tip has a significant effect on the driving force.

D. Schrade, R. Müller, D. Gross

Modeling Approaches to Predict Damage Evolution and Life Time of Brittle Ferroelectrics

Abstract

Reliability and life time of smart materials are crucial features for the development and design of actuator and sensor devices. Being widely used and exhibiting brittle failure characteristics, ceramic ferroelectrics are of particular interest in this field. Due to manifold interactions of the complex nonlinear constitutive behavior on the one hand and the damage evolution in terms of microcrack growth on the other, modeling and simulation are inevitable to investigate influence parameters on strength, reliability and life time. Two approaches are presented, both based on the same constitutive law and damage model. The one is going along with a discretisation scheme exploiting the finite element method (FEM). The so-called condensed approach, on the other hand, considers just one characteristic point in the material, nonetheless accounting for polycrystalline grain interactions. The focus of the simulations is two-fold. Life-time predictions in terms of high cycle fatigue under electromechanical loading conditions are presented based on the condensed approach. Second, the formation of macroscopic cracks at electrode tips in a stack actuator is investigated applying the FEM.

Andreas Ricoeur, Stephan Lange, Roman Gellmann

Numerical Analysis of Interface Cracks in Layered Piezoelectric Solids

Abstract

In this paper, transient dynamic crack analysis in two-dimensional, layered, anisotropic and linear piezoelectric solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed. The layered piezoelectric solids are modelled by the multi-domain BEM formulation. The time-domain dynamic fundamental solutions for homogeneous linear piezoelectric solids are applied in the present BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method, while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is obtained to compute the discrete boundary data including the generalized crack-opening-displacements (CODs). To show the effects of the interface, the material combinations and the dynamic loading on the intensity factors, several numerical examples are presented and discussed.

Michael Wünsche, Chuanzeng Zhang, Jan Sladek, Vladimir Sladek

Analytical Mechanics

Frontmatter

Crack-Tip Fields of a Crack Impinging upon the Yielding/Debonding Slippage in Anisotropic Body

Abstract

This paper presents a fundamental solution for a crack impinging normally upon the slippage in anisotropic materials under tensile loading. The slippage could occur in the form of yielding (e.g., a well-bonded ductile layer with plastic yielding) or debonding (e.g., a weak, sliding-free one). A superposition method is employed to explicitly solve the problem which combines the solution of a crack in an elastic homogeneous medium, the solution of a continuous distribution of dislocations which represent slippage, and an appendix solution which offsets the stress on the crack faces induced by the dislocations. This procedure reduces the problem to a singular integral equation which can be numerically solved by using Chebyshev polynomials. Numerical implementations are performed to analyze the influence of slippage on cracking and stress redistribution near the crack tip in anisotropic bodies. It is found that yielding or debonding slippage redistributes the stress ahead of the crack tip. The presence of yielding or debonding lowers the high stress concentration in the tensile stresses ahead of the crack tip. It is also concluded that debonding appears to be more effective in lowering the stress concentration than yielding.

Qun Li, Junling Hou, Guangyan Liu, Hong Zuo

On Conservation Laws and Reciprocity in Configurational Mechanics

Abstract

Material conservation laws and associated path-independent integrals play a prominent role in the assessment of defects in structures. Especially Rice’s J-integral is widely used in fracture mechanics. For systems governed by a Lagrangian, the usual tool for the derivation of material conservation laws is the application of Noether’s first theorem in combination with Bessel-Hagen’s extension. The so-called Neutral-Action (NA) method is a different approach. Its advantage in comparison with the classical Noether’s approach lies in the fact that it is applicable to field equations that are not necessarily the Euler-Lagrange equations of a variational principle, i.e., for systems not governed by a Lagrangian. After a short review of the NA method, a complete set of characteristics and the associated conserved currents are derived and interpreted in physical terms. As an example, path-independent integrals are evaluated around a crack tip and a defect-interaction problem is treated in terms of reciprocity. Finally, the application of conservation laws in defect mechanics and its potential are discussed.

R. Kienzler, S. Boettcher

Local Approach to Fracture

Frontmatter

A Model for Predicting Fracture Toughness and Scatter in Thermally Embrittled Steels

Abstract

Temper embrittlement in a thick plate of a Mn-Ni-Mo pressure vessel steel was investigated using fracture toughness tests on Charpy and CT type specimens. A shift of the ductile-to-brittle transition temperature (~30–40 °C) was measured when the material was aged at 450 °C for 5000 h. Moreover an unusual scatter in fracture toughness tests was determined on aged material, such as \(K_{IC} (P_{R} = 90\,\% )/K_{IC} (P_{R} = 10\,\% ) \sim 5\), where P _R is the probability of failure. Scanning electron micrographs (SEM) indicated that the fracture surface was partly intergranular along micro-segregated zones (MSZ). This observation was made both on the initial and the aged conditions. Intergranular facets were largely covered by phosphorus segregation. A fully predictive model involving a combination of a local approach to fracture based on Beremin theory and accounting for MSZ distribution, and on the modelling of segregation kinetics in ternary (Fe-C-P) systems is developed to analyze these results. This model predicts the scatter in fracture toughness measurements and the shift in DBT. Moreover the statistical distribution of MSZ leads to a size effect in fracture toughness measurements which is different from the \(K^{4} B\) law inferred from the Beremin model applied to a homogeneous material.

A. Pineau, A. Andrieu

Micromechanical-Based Models for Describing Damage of Ferritic Steels

Abstract

Usually the safety margin against failure for precracked components is calculated with fracture mechanics approaches. Due to several severe limitations of these approaches, it was searched for alternative calculation models. Starting with McClintock and Berg in the sixties, so-called damage models have been developed for describing ductile fracture on the basis of micromechanical processes. The development of such kind of models is in progress now for nearly 50 years, but until today no model is generally accepted and incorporated into the international standards. In an extended introduction, the micromechanical phases of ductile rupture of metal and alloys are presented. Against this background, a summary of the evolution and the different kinds of micromechanical-based model approaches is given. The theoretical background, the advantages/ disadvantages and the limitations of the models are discussed critically. Finally non-local formulations of damage models are presented. Combinations of ductile damage models and models for cleavage to describe fracture in the brittle-ductile transition region are discussed.

Michael Seidenfuss, Thomas Linse

Recent Trends in the Development of Gurson’s Model

Abstract

The original Gurson model for porous materials has undergone numerous modifications in order to improve its adequacy with experimental or numerical results. In this chapter various modifications of Gurson’s model and models created on the basis of the idea of Gurson’s model are presented. This chapter includes the following issues: (i) development of Gurson’s model, (ii) development of models for nucleation, growth and coalescence of voids and (iii) modification of Gurson’s model for failure prediction under shear deformation.

Jacek Jackiewicz

Titel: Recent Trends in Fracture and Damage Mechanics
herausgegeben von: Geralf Hütter
Lutz Zybell
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-21467-2
Print ISBN: 978-3-319-21466-5
DOI: https://doi.org/10.1007/978-3-319-21467-2

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