Fatigue Limit in Metals

Claude Bathias

• Publisher: Wiley-ISTE
• Year: 2013
• ISBN:
  9781118648728
• Edition: 1
• Topic: Tecnología e ingeniería
• Subtopic: Ingeniería minera

Is there a fatigue limit in metals? This question is the main focus of this book.
Written by a leading researcher in the field, Claude Bathias presents a thorough and authoritative examination of the coupling between plasticity, crack initiation and heat dissipation for lifetimes that exceed the billion cycle, leading us to question the concept of the fatigue limit, both theoretically and technologically.
This is a follow-up to the Fatigue of Materials and Structures series of books previously published in 2011.

Contents

1. Introduction on Very High Cycle Fatigue.
2. Plasticity and Initiation in Gigacycle Fatigue.
3. Heating Dissipation in the Gigacycle Regime.

About the Authors

Claude Bathias is Emeritus Professor at the University of Paris 10-La Defense in France. He started his career as a research engineer in the aerospace and military industry where he remained for 20 years before becoming director of the CNRS laboratory ERA 914 at the University of Compiègne in France. He has launched two international conferences about fatigue: International Conference on the Fatigue of Composite Materials (ICFC) and Very High Cycle Fatigue (VHCF).

This new, up-to-date text supplements the book Fatigue of Materials and Structures, which had been previously published by ISTE and John Wiley in 2011. A thorough review of coupling between plasticity, crack priming, and thermal dissipation for lifespans higher than a billion of cycle has led us to question the concept of fatigue limit, from both the theoretical and technological point of view. This book will address that and more.

1

Introduction on Very High Cycle Fatigue

This chapter is a summary of several decades of reasearch on gigacycle fatigue of metals. For more detail please see references [BAT 04] and [BAT 10].

1.1. Fatigue limit, endurance limit and fatigue strength

Fatigue limit, endurance limit and fatigue strength are all expressions used to describe a property of materials under cyclic loading: the amplitude (or range) of cyclic stress that can be applied to the material without causing fatigue failure. In these cases, a number of cycles (usually 10⁷) are chosen to represent the fatigue life of the material.

According to the American Society for Testing and Materials (ASTM) Standard E 1150, the definition of fatigue is summarized as follows: “The process of progressive localized permanent structural damage occurring in a material subjected to conditions that produce fluctuating stresses and strains at some point or points and that may culminate in cracks or complete fracture after a sufficient number of fluctuations”. The plastic strain resulting from cyclic stress initiates the crack; the tensile stress promotes crack growth propagation. Microscopic plastic strains also can be present at low levels of stress where the strain might otherwise appear to be totally elastic. The ASTM defines fatigue strength, S_Nf, as the value of stress at which failure occurs after N_f cycles, and fatigue limit, S_f, as the limiting value of stress at which failure occurs as N_f becomes very large. The ASTM does not define endurance limit, the stress value below which the material will withstand many load cycles, but implies that it is similar to fatigue limit.

Some authors use endurance limit for the stress below which failure never occurs, even for an indefinitely large number of loading cycles, as in the case of steel, and fatigue limit or fatigue strength for the stress at which failure occurs after a specified number of loading cycles, such as 500 million, as in the case of aluminum. Other authors do not differentiate between the expressions even if they do differentiate between the face center cubic (FCC) metals and the base center cubic (BCC) metals [BAT 10].

Since the word “fatigue” was used by Braithwaite, A. Wöhler established the first basic approach to the fatigue life of metals, in the mid-1800s, when the main industrial applications were railcar axles and steam engines for railways and boats [BAT 10]. The slow rotation of a steam engine was about 50 cycles per minute, more or less. Thus, the fatigue limit was defined by Wöhler to be between 10⁶ and 10⁷ cycles, but it seems that the quasi-hyperbolic stress number of cycle (SN) curve was suggested by Basquin [BAS 10]. Today, the fatigue life of a high-speed train ranges in the gigacycle, 10⁹, regime and for an aircraft turbine it is of the order of 10¹⁰ cycles, according to the rotation speed of several thousand turns per minute.

Figure 1.1. International standard for SN curve and fatigue limit

The fatigue curve or SN curve is usually defined in reference to carbon steel. The SN curve is generally limited to 10⁷ cycles and it is acknowledged, according to the standard, that a horizontal asymptote allows us to determine a fatigue limit value for an alternating stress between 10⁶ and 10⁷ cycles. Beyond 10⁷ cycles, the standard considers that the fatigue life is infinite. For other alloys, it is assumed that the asymptote of the SN curve is not horizontal.

A few results for fatigue limit based on 10⁹ cycles can be found in the literature [BAT 10]. Using standard practice, the shape of the SN curve beyond 10⁷ cycles is predicted using the probabilistic method, and this is also true for the fatigue limit. In principle, the fatigue limit is given for a number of cycles to failure (Figure 1.1). Using, for example, the staircase method, the fatigue limit is given by the average alternating stress σ_D and the probability of fracture is given by the standard deviation of the scatter (s). The classical way to determine the infinite fatigue life is to use a Gaussian function. Roughly speaking, it is said that σ_D minus 3s gives a probability of fracture close to zero. Assuming s is equal to 10 MPa, the true infinite fatigue limit should be σ_D – 30 MPa. However, experiments show that between σ_D for 10⁶ and σ_D for 10⁹, the difference is greater than 30 MPa for many alloys.

The so-called standard deviation (SD) approach to the average fatigue limit is certainly not the best way to reduce the risk of rupture in fatigue. When one is conscious that it is the last resort, only experience can remove this ambiguity by appealing to some tests of accelerated fatigue. Today some piezoelectric fatigue machines are very reliable, capable of producing 10¹⁰ cycles in less than one week, whereas the conventional systems require more than 3 years of tests for only one sample.

To summarize the present situation, it is acknowledged that the concept of a fatigue limit is bound to the hypothesis of the existence of a horizontal asymptote on the SN curve between 10⁶ and 10⁷ cycles (Figure 1.1). Thus, a sample that reaches 10⁷ cycles and is not broken is considered to have an infinite life; that is, in fact, a convenient and economical approximation but not a rigorous approach. It is important to understand that if the staircase method is popular today to determine the fatigue limit, this is because of the convenience of this approximation. A fatigue limit determined by this method to 10⁷ cycles requires 30 h of tests to get only one sample with a machine working at 100 Hz. To reach 10⁸ cycles, 300 h of tests would be required, which is expensive. Using a 20 kHz piezoelectric fatigue machine, it takes around 14 h to obtain 10⁹ cycles, 6 days for 10¹⁰ cycles and 58 days for 10¹¹ cycles. The basic design of the piezoelectric fatigue machine is the same at 30 kHz as a 20 kHz piezoelectric fatigue machine, where the vibration of the specimen is induced by a piezoceramic converter, which generates acoustic waves in the specimen through a power concentrator (horn) in order to obtain desired displacement and an amplification of the stress [WU 93]. The resonant specimen dimension and stress concentration factor were calculated by the Finite Element Method (FEM) subject to 20 and 30 kHz [WU 93]. Such computer-controlled piezoelectric fatigue machines are able to work in tension-compression, tension-tension-tension, bending and torsion loading (Figure 1.2). It is of importance to note that the temperature of the specimen and the amplitude of the stress must stay constant during a standard test at 20 kHz to keep the comparison with low-frequency testing. A complete description of the procedure is given in [BAT 04].

Figure 1.2. Experimental system for ultrasonic fatigue at 20 kHz

1.2. Absence of an asymptote on the SN curve

Generally speaking, it is assumed that the steel SN curves are different from the others. To get an overview of the gigacycle behavior, many alloys, including steel, are considered in this chapter. For results of fatigue SN curves based on 10⁹ cycles, a few results are available in the literature. Many of those results come from our laboratory [BAT 04]. The other results come from Japanese researchers such as Naito [NAI 84], Kanazawa [NIS 97], Murakami [MUR 99] and Sakai [SAK 07]. They are limited to 10⁸ cycles. Also, some SN curves for light alloys come from the laboratory of S. Stanzl-Tschegg and H.R. Mayer [STA 99]. They are limited to 10⁹ cycles.

Safe-life design based on the infinite life criteria was initially developed from the Wöhler approach, which is the stress-lif...

Table of contents

• Cover
• Contents
• Title
• Copyright
• Acknowledgments
• 1 Introduction on Very High Cycle Fatigue
• 2 Plasticity and Initiation in Gigacycle Fatigue
• 3 Heating Dissipation in the Gigacycle Regime
• Index