Elsevier

Acta Materialia

Volume 61, Issue 4, February 2013, Pages 1197-1203
Acta Materialia

Cyclic slip irreversibility and fatigue life: A microstructure-based analysis

https://doi.org/10.1016/j.actamat.2012.10.029Get rights and content

Abstract

The evolution of fatigue damage is intimately related to different types of more or less pronounced irreversible cyclic slip, associated with gradual permanent microstructural and topological changes which ultimately can cause fatigue failure. Only in a few cases has it been possible to assess quantitatively the cyclic slip irreversibility. Based on a limited amount of available experimental data amenable to analysis, an attempt is made in this work to explore whether there exists an explicit relationship between the cyclic slip irreversibility and fatigue life. The existence of such a relationship is suggested by a microstructure-based reformulation of the Coffin–Manson fatigue life law, which involves the cyclic slip irreversibility. The analysis of the experimental data in two adequately documented cases indicates that the cyclic slip irreversibility is related very satisfactorily to fatigue life via a power law which contains two constants. These two constants can be expressed in terms of the fatigue ductility coefficient and the fatigue ductility exponent of the Coffin–Manson fatigue life law.

Introduction

The primary cause of fatigue damage in ductile metals and alloys usually lies in some form of cyclic slip irreversibility in the sense that reverse slip during a cycle differs locally in a microstructural sense from slip in the forward direction. As a consequence, permanent microstructural and topological changes, caused by repeated, partially irreversible cyclic microstrains, are left behind, and these accumulate with increasing numbers of cycles and ultimately lead to fatigue damage. The first evidence of irreversible fatigue-induced microstructural changes dates back to the pioneering work of Ewing and Humfrey. who observed slip bands on the surface of a steel that had been fatigued at low loading amplitudes that were then considered “safe” [1]. Cyclic slip irreversibilities may have many different causes and can manifest themselves – in most cases at the surface – in different ways [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]. As reviewed recently [15], these irreversibilities are usually difficult to analyze quantitatively. A necessary prerequisite is to identify the main or dominant type of life-governing cyclic slip irreversibility and to define it by a pertinent parameter. In the literature, different forms of characterizing the cyclic slip irreversibility are found [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. Here, as detailed in earlier work [2], [3], [4], [5], [6], [15], [16], [17], [18], the cyclic slip irreversibility p will be defined as the fraction of microstructurally irreversible cyclic plastic strain with respect to the total cyclic plastic strain (0 < p < 1). Thus, p = 1 would imply that slip is completely irreversible, whereas p = 0 would refer to completely reversible slip. In this sense, the cyclic slip irreversibility p is an important microstructural parameter of cyclic slip.

In order to assess quantitatively the value of the cyclic slip irreversibility p, it is generally necessary to have access to specific experimental data which can be evaluated in terms of simple theoretical concepts of dislocation glide. It has been shown that the important parameter p can be extracted from (and for quite different) dislocation mechanisms occurring at the surface and/or in the bulk such as

  • (a)

    mutual annihilation of dislocations (edge and/or screw) of opposite sign [2], [3], [4], [15];

  • (b)

    emergence and loss of dislocations at the surface [8], [9], [10], [11], [12], [13];

  • (c)

    cross-slip of screw dislocations [2], [3], [4], [5], [6], [15];

  • (d)

    irreversible dislocation displacements derived from cutting of precipitates [6], [7], [8], [9], [13],

  • (e)

    surface roughening caused by (random) to-and-fro glide of dislocations [3], [4], [5], [6], [15], [16], [17], [18],

  • (f)

    asymmetry of slip planes in tension and compression (typical of body-centred cubic (bcc) metals), leading to incompatible shape changes of neighbouring grains and intergranular cracking [19], [20], [21].

To give an impression of the various ways in which cyclic slip irreversibilities can manifest themselves, two examples, for cases (d) and (e), are presented. Fig. 1 shows the fatigue-induced surface roughness observed on a copper polycrystal that had been fatigued ultrasonically for more than 1010 cycles in the ultrahigh cycle fatigue (UHCF) regime at a rather low loading amplitude that lay below the traditional high cycle fatigue (HCF) threshold for PSB formation [18]. The analysis of the surface roughness yielded a very low value of p  0.000036, which, however, corresponds to an exceptionally large cumulative irreversible plastic shear strain of more than 30 because of the very large numbers of cycles. The second quite different example is presented in Fig. 2. The transmission electron microscopy (TEM) micrograph, from the work of Clavel and Pineau [22], of the nickel-base superalloy Waspaloy, fatigued at 600 °C in symmetric strain control, illustrates that slip offsets have accumulated as a result of repeated irreversible cutting of the coherent γ′ particles during cyclic deformation. In this case, a rather high value p  0.05 is deduced from the slip offsets [15], [16] observed in the bulk. Corresponding slip offsets observed at the surface act as sites of fatigue crack initiation. The two examples, shown in Fig. 1, Fig. 2, although quite different, provide valid evidence of cyclic slip irreversibilities and document that cyclic slip irreversibilities can manifest themselves in substantially different ways from case to case. In addition to the examples of cyclic slip irreversibilities discussed in the present work, cyclic slip irreversibilities also play an important role in the processes at the crack tip during crack growth. This aspect has been discussed quite recently in some detail by Sangid et al. in an experimental and theoretical study of the fatigue crack growth resistance of nanocrystalline metals [23].

An intriguing question is whether the cyclic slip irreversibility parameter p can be related explicitly to the fatigue life Nf (numbers of cycles to failure). Since cyclic slip irreversibilities can arise from quite different mechanisms, as exemplified above, and since fatigue damage can spread by different modes, it appears improbable that a universal relationship for different materials exists between p and Nf. Nonetheless, it is conceivable that such relations do exist for a particular material with specified cyclic slip irreversibilities and damage propagation modes. Even in such cases, it would not be adequate to identify the origin and mechanism of cyclic slip irreversibility but, at the same time, it would be necessary to ascertain that this particular type of irreversibility is responsible for causing life-determining fatigue damage. The situation can be additionally complicated by the simultaneous occurrence of different cyclically irreversible damaging dislocation mechanisms.

The earlier work of the author and his group focused on identifying the mechanisms responsible for cyclic slip irreversibility and to quantify them, where possible, compare [3], [5], [6], [15], [16], [17], [18], but did not address the question of fatigue life. In a different context, namely in a discussion of ultrahigh cycle fatigue mechanisms, a microstructure-based reformulation of the Coffin–Manson fatigue life law, in which the cyclic slip irreversibility p was introduced explicitly, was proposed [17]. Only very recently has it been shown, based on double-logarihmic plots of limited available data of p vs. fatigue life Nf [24], that empirical power law relationships seem to exist between the cyclic slip irreversibility p and the fatigue life Nf. In the present work, it will be shown that these preliminary indications of a relationship between fatigue life and cyclic slip irreversibility are in good consonance with the earlier microstructure-based version of the Coffin–Manson fatigue life law in which the cyclic slip irreversibility was taken into account [17]. More specifically, it will be shown that the available data seem to confirm that the cyclic slip irreversibility p is related in very good approximation quantitatively with fatigue life Nf through a power law which contains two constants that are readily interpreted in terms of the fatigue ductility coefficient and the fatigue ductility exponent of the Coffin–Manson relationship.

Section snippets

Microstructure-based reformulation of Coffin–Manson fatigue life law

The considerations in Ref. [17] start from the well-known Coffin–Manson fatigue life law, which is commonly written in the form [25]:Δεpl2=εf(2Nf)cwhere Δɛpl/2 is the plastic strain amplitude (Δɛpl: plastic strain range) and εf and c are the fatigue ductility coefficient and exponent, respectively. The fatigue ductility coefficient is typically c  −0.5 to −0.6 [25]. In the earlier study, an attempt was made to take into account explicitly that fatigue damage results from the irreversible

Specific cases of cyclic slip irreversibility p and fatigue lives Nf

In order to explore whether and how fatigue life Nf depends on the cyclic slip irreversibility p, at least two sets of values of Nf and p are needed, and Δɛpl should be known in addition, if one wished to evaluate εpl,cum,firr. Unfortunately, to the author’s knowledge, only very few cases are known which meet these requirements. Referring to the data assessed in Ref. [15], and as detailed in a preliminary report [24], three sets of data (Nf, Δɛpl, p) are available for polycrystalline α-iron

Interpretation of power-law relationship

The data plotted in Fig. 5 and the relationships, expressed in Eqs. (5), (6), suggest that the cyclic slip irreversibility p and the fatigue life Nf are related in an empirical way by a power law of the form:pα·Nf-β

Eq. (7) bears an obvious relationship to Eq. (4). After rearranging and resolving for p, Eq. (4) readsp(Δεpl)=εpl,cum,firr4εf·2cNf-c-1=const.·Nf-c-1

Of course, pɛpl) can also be regarded as p(Nf). From a comparison of Eqs. (7), (8) follows that:εpl,cum,firr4εf·2c=α=const.andβ=c+1

Summary and conclusions

The present work is based on an evaluation of some limited quantitative data of experimentally determined cyclic slip irreversibilities that were considered suitable for a more detailed analysis. The results suggest that an explicit power-law relation exists between the cyclic slip irreversibility p and the number of cycles to failure Nf. The constants of this relationship were found to be closely related to the fatigue ductility coefficient and the fatigue ductility exponent of the

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