Fatigue of Materials and Structures

Application to Design and Damage

Claude Bathias, André Pineau, Claude Bathias, André Pineau

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781848212916
• eBook ISBN: 9781118617229
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

The design of mechanical structures with predictable and improved durability cannot be achieved without a thorough understanding of the mechanisms of fatigue damage and more specifically the relationships between the microstructure of materials and their fatigue properties.
Written by leading researchers in the field, this book, along with the complementary books Fatigue of Materials and Structures: Fundamentals and Application to Damage and Design (both also edited by Claude Bathias and André Pineau), provides an authoritative, comprehensive and unified treatment of the mechanics and micromechanisms of fatigue in metals, polymers and composites. Each chapter is devoted to one of the major classes of materials or to different types of fatigue damage, thereby providing overall coverage of the field.

This book deals with multiaxial fatigue, thermomechanical fatigue, fretting-fatigue, influence of defects on fatigue life, cumulative damage and damage tolerance, and will be an important and much used reference for students, practicing engineers and researchers studying fracture and fatigue in numerous areas of materials science and engineering, mechanical, nuclear and aerospace engineering.

Chapter 1

Multiaxial Fatigue ¹

1.1. Introduction

Nowadays, everybody agrees on the fact that good multiaxial constitutive equations are needed in order to study the stress-strain response of materials. After many studies, a number of models have been developed, and the “quality/cost” ratio of the different existing approaches is well defined in the literature. Things are very different in the case of the characterization of multiaxial fatigue. In this domain, as in others related to the study of damage and failure phenomena, the phase of “settling” which leads to the classification of the different approaches has not been carried out yet, which can explain why so many different models are available. These models are not only different because of the different types of equations they present, but also because of their critical criteria. The main reason is that fatigue phenomena involve some local mechanisms, which are thus controlled by some local physical variables, and which are thus much more sensitive to the microstructure of the material rather than to the behavior laws which only give a global response. It is then difficult to present in a single chapter the entire variety of the existing fatigue criteria for the endurance as well as for the low cycle fatigue domains.

Nevertheless, right at the design phase, the improvements of the methods and the tools of numerical simulation, along with the growth supported by any available calculation power, can provide some historical data stress and strain to the engineer in charge of the study. The multiaxiality of both stresses and strains is a fundamental aspect for a high number of safety components: rolling issues, contact—friction problems, anisothermal multiaxial fatigue issues, etc. Multiaxial fatigue can be observed within many structures which are used in every day life (suspension hooks, subway gates, automotive suspensions). In addition to these observations, researchers and engineers regularly pay much attention to some important and common applications: fatigue of railroads involving some complex phenomena, where the macroscopic analysis is not always sufficient due to metallurgical modifications within the contact layer. Friction can also be a critical phenomenon at any scale, from the industrial component to micromachines. The thermo-mechanical aspects are also fundamental within the hot parts of automotive engines, of nuclear power stations, of aeronautical engines, but also in any section of the hydrogen industry for instance. The effects of fatigue then have to be evaluated using adapted models, which consider some specific mechanisms. This chapter presents a general overview of the situation, stressing the necessity of defending some rough models which can be clearly applied to some random loadings rather than a simple smoothing effect related to a given experiment, which does not lead to any interesting general use.

Brown and Miller, in a classification released in 1979 [BRO 79], distinguish four different phases in the fatigue phenomenon: (i) nucleation — or microinitiation — of the crack; (ii) growth of the crack depending on a maximum shearing plane; (iii) propagation normal to the traction strain; (iv) failure of the specimen. The germination and growth steps usually occur within a grain located at the surface of the material. The growth of the crack begins with a step, which is called “short crack”, during which the geometry of the crack is not clearly defined. Its propagation direction is initially related to the geometry and to the crystalline orientations of the grains, and is sometimes called micropropagation. The microscopic initiation, from the engineer’s point of view, will also be the one which will get most attention from the mechanical engineer because of its volume element: it perfectly matches the moment where the size of the crack becomes large enough for it to impose its own stress field, which is then much more important than the microstructural aspects. At this scale (usually several times the size of the grains), it is possible to give a geometric sense to the crack, and to specifically treat the problem within the domain of failure mechanics, whereas the first ones are mainly due to the fatigue phenomenon itself. This chapter gathers the models which can be used by the engineer and which lead to the definition of microscopic initiation.

Section 1.2 of this chapter presents the different ingredients which are necessary to the modeling of multiaxial fatigue and introduces some techniques useful for the implementation of any calculation process in this domain, especially regarding the characterization of multiaxial fatigue cycles. Section 1.3 briefly deals with the main experimental results in the domain of endurance which will lead to the design of new models. Section 1.4 tries then to give a general idea of the endurance criteria under multiaxial loading, starting with the most common ones and presenting some more recent models. Finally, section 1.5 introduces the domain of low cycle multiaxial fatigue. Once again, some choices had to be made regarding the presented criteria, and we decided to focus on the diversity of the existing approaches, without pretending to be exhaustive.

1.1.1. Variables in a plane

Some of the fatigue criteria that will be presented below — which are of the critical plane type — can involve two different types of variables: the variables related to the stresses and the strains normal to a given plane, and the variables related to the strains or stresses that are tangential to this same plane.

From a geometric point of view, a plane can be observed from its normal line

. The criteria involving an integration in every plane us...

Table of contents

• Cover
• Title Page
• Copyright
• Foreword
• Chapter 1: Multiaxial Fatigue
• Chapter 2: Cumulative Damage
• Chapter 3: Damage Tolerance Design
• Chapter 4: Defect Influence on the Fatigue Behavior of Metallic Materials
• Chapter 5: Fretting Fatigue: Modeling and Applications
• Chapter 6: Contact Fatigue
• Chapter 7: Thermal Fatigue
• List of Authors
• Index