On the transition from plastic deformation to crack initiation in the high- and very high-cycle fatigue regimes in plain carbon steels

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Abstract

It is well known that fatigue life of metallic materials involves processes at different stages. Two main regimes can be distinguished: The first is governed by plastic deformation and related dislocation processes like cyclic saturation and strain localization. The second regime is mainly dominated by crack initiation and propagation. Whether an infinite fatigue life is obtained or not is therefore ultimately determined by the complex interplay of plastic deformation processes, the formation of small crack nuclei and their subsequent interaction with the surrounding material’s microstructure. Thus, it is necessary to investigate the transition from plastic deformation to crack initiation in the high- and very high-cycle fatigue regime in more detail. Three plain carbon steels with different ferrite to pearlite ratios were investigated in order to determine the influence of different microstructures on the transition from cyclic deformation to crack initiation in the high and very high cycle fatigue (VHCF) regime. A new method was developed where the changes in the dissipated energy are used to account for irreversible plastic deformation during ultrasonic fatigue loading. At very small fatigue amplitudes, which still lead to VHCF-failure, the cyclic deformation regime covers the main part of the fatigue life. In this regime dislocation interactions lead to the accumulation of irreversible plastic deformation followed by small crack nuclei that initiate at phase or grain boundaries (GBs), marking the transition to the damage regime. In order to better understand the fundamental mechanisms at the transition between both regimes, idealized atomistic simulations were performed. To model fatigue-induced plastic deformation various defects, i.e. dislocations and vacancies, were placed in the vicinity of a GB. These defects generally decrease the globally applied critical stress for crack initiation whilst the local critical stress stays mainly unchanged in the same range as the theoretical GB strength. Based on the experimental results and on the general findings from the atomistic simulations it is concluded that an infinite fatigue life is obtained either when cyclic irreversible deformation is too small to build up the necessary stresses for crack initiation or when the formed crack nuclei cannot overcome the next microstructural barriers.

Introduction

“There is no infinite fatigue life in metallic materials” – with this provocative title Claude Bathias summarized his observations on many different alloys from high-strength steels over titanium and aluminum alloys to nickel base alloys, that fatigue failure occurs also in the range of more than 107 cycles [1]. He also concluded that the “very high-fatigue life regime, called the gigacycle regime, requires more attention with respect to choice of alloys and the techniques used in the prediction of endurance” [1]. Thus, one key ingredient necessary to explore this so-called very high-cycle fatigue (VHCF) regime was the availability of high frequency piezoelectric testing machines. Manson and Wick [2] as well as Kromp et al. [3], Wielke and Stanzl [4] and Puskar [5] contributed pioneering work in this respect. Bathias realized very early the advantage of such ultrasonic fatigue systems and developed testing systems focusing on the one hand on engineering aspects [6], [7] and on the other hand on the fundamental question whether there is a fatigue limit [1], [8] and the identification of the related fatigue damage mechanisms [9], [10].

Damage in the VHCF-regime is strongly localized and the number of crack initiation sites decreases with decreasing loading amplitudes [8], [11]. Therefore, detailed studies of the early stages of crack initiation and of fatigue damage mechanisms in the VHCF-regime are the key to answer the question whether an infinite fatigue life exists or not. In this context, advanced techniques have to be applied to monitor relevant changes of the deformation behavior during ultrasonic cyclic loading. Due to the very high loading frequencies this task is rather challenging and established techniques from fatigue experiments at intermediate frequencies are not suited. Starke et al. [12] showed that temperature and resistivity could be used to determine late fatigue failure and fatigue life. Infrared thermography methods were used by Wagner et al. [13] to detect crack initiation sites in an aluminum alloy and by Wang et al. [14] to detect the formation of PSBs. Through the use of advanced techniques to monitor fatigue experiments and their combination it is possible to obtain a deeper understanding of the different fatigue stages.

Mughrabi [15] pointed already in 1985 out that the obtained fatigue life is the result of a multistage process taking place during cyclic loading. He distinguished between two main regimes: The cyclic deformation regime where dislocation processes govern the internal processes in the material, and the fatigue damage regime where crack initiation and crack-propagation are dominant, see Fig. 1. At very low loading amplitudes, which result in fatigue lives in the very high cycle fatigue (VHCF) regime, the first stage (cyclic deformation and strain localization) covers most of the fatigue life of the specimen [16]. During the cyclic deformation stage, dislocation interactions lead to the formation of irreversible plastic deformation. This irreversible plastic deformation accumulates during the fatigue experiment and leads to localization of plastic deformation and finally to crack initiation [17]. In case the so developed crack nuclei can overcome the first microstructural barrier, like grain or phase boundaries, it will be able to grow further and can lead to macroscopic fatigue failure [18].

On the basis of this concept, the question whether an infinite fatigue life exists can only be answered by a thorough investigation of the processes shown in Fig. 1. The complexity of the mechanisms leading to irreversible deformation, damage accumulation, localization, crack initiation and propagation, as well as its influence on the microstructure are inherently difficult to study directly at the relevant scale of the defects. While the formation of dislocation structures can be studied theoretically using 3D discrete dislocation dynamics [19], [20], the interaction of dislocations with grain or interphase boundaries and the initiation of cracks is determined by the atomic structure of the defects and can therefore only be modeled using atomistic methods. However, only few studies on crack initiation, e.g. at grain boundaries [21] have been published. For a recent review of atomistic fracture simulations see also [22].

One focus of this work is to monitor the cyclic deformation behavior and the relevant damage mechanisms in the VHCF-regime. A new analysis method to investigate in more detail the role of irreversibility of cyclic deformation on late fatigue failure is presented and the interaction of cracks with the surrounding microstructure, which is critical for fatigue failure under small stress amplitudes in the VHCF-regime, is studied. The influence of different microstructures is examined by using three steels with varying ferrite/pearlite ratios as model materials. Furthermore, the critical conditions for crack initiation at interfaces are studied by atomistic simulations with the objective to assess the influence of defects, which are typically produced during fatigue loading (absorbed vacancies, dislocations, dislocation pile-ups), on the fracture strength of grain boundaries.

Section snippets

Materials and fatigue experiments

In this study three plain steels C15E, C45E and C60E, similar to SAE 1017, 1045 and 1064, were investigated. The microstructures of the three different steels mainly varied in their pearlite/ferrite ratio. The carbon contents lied between 0.12 wt.% for C15E, 0.42–0.5 wt.% for C45E and max. 0.65 wt.% for C60E. All specimens were annealed at 900 °C for 3 h in argon atmosphere prior to fatigue loading. After annealing the specimens were cooled down with a rate of 10 °C/min also in argon atmosphere. This

Fatigue data and damage monitoring using dissipated energy

The fatigue lives of the investigated steels, plotted in a Wöhler S–N plot (stress amplitude Δσ/2 versus log Nf), are shown in Fig. 4. Fatigue life curves are shifted to higher lives with increasing pearlite content. For the steel with the lowest pearlite content (C15E), fatigue failure was observed for stress amplitudes as low as 290 MPa and Nf = 1.54 × 107. C45E also showed late fatigue failure up to Nf = 3.58 × 107 for a stress amplitude of 315 MPa, below this stress amplitude only run-outs were

Atomistic simulations of crack initiation

To study the role of defects introduced by cyclic deformation for crack initiation at GBs, we performed atomistic simulations with the asymmetrical Σ7(1¯1¯1)1/(11,1¯,5¯)2135.6°/[112] tilt grain boundary as model GB. The subscripts 1 and 2 refer to the corresponding coordinate systems of grain 1 and 2, respectively. This special Σ7 GB was chosen because the experimental observations presented in Section 3.2 showed that crack initiation frequently takes place between two grains, of which one

Correlation of fatigue life and contiguity of ferrite grains

The formation and growth of cracks in bcc materials in the HCF- and VHCF-regimes are most often found at interfaces like grain- or phase boundaries [41]. The investigated steels also showed crack initiation at or, respectively, along interfaces, i.e. mainly at grain boundaries in C15E and C45E and at phase boundaries in C60E. Depending on the composition of the steel, crack nuclei face different obstacles which vary in strength. The investigated steels have different carbon and thus different

Summary

Fatigue experiments and atomistic simulations were performed to address the question whether an infinite fatigue life exists or not. Fatigue experiments on three different plain carbon steels show late fatigue failure in the HCF and VHCF regimes. The fatigue crack initiation sites change from ferrite-ferrite grain boundaries to ferrite-pearlite phase boundaries as the ferrite/pearlite ratio decreases. Atomistic simulations of crack initiation at a model grain boundary in iron show that grain

Acknowledgments

The authors gratefully acknowledge the funding by the German Research Council (DFG) through its priority program “1466∞ – Infinite life for cyclically loaded high performance materials” and the Cluster of Excellence “Engineering of Advanced Materials”. The authors thank Hael Mughrabi for fruitful discussion.

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