Improved description of low-cycle fatigue behaviour of 316L steel under axial, torsional and combined loading using plastic J-integral

Highlights

• Axial, torsional and in-phase combined loading of tubular samples made of 316L steel.

• Fatigue lives much longer in torsion than in tension for equal ε_eq,p,a.

• Extensive non-linear finite element modelling with locally deflected cracks.

• Plastic part of J-integral unified crack growth data for all test types and amplitudes.

• New proposed equivalent strain function for better multiaxial fatigue live prediction.

Abstract

Low-cycle fatigue behaviour and fatigue crack kinetics of the 316L austenitic stainless steel were studied under cyclic axial, torsional and in-phase combined loading using hollow cylindrical (tubular) specimens with a small hole for crack initiation. The concept of plastic.

J-integral was used, which was shown in previous studies to unify the crack growth rate data for several different materials. Dependencies of J_p on crack length were determined by extensive finite element modelling considering non-linear material behaviour according to the cyclic stress–strain curve. Locally deflected cracks were modelled in accordance with amplitudes of the axial and torsional components of combined loading. The measured crack growth rate diagrams for all types of loading and for various loading amplitudes were unified using amplitude of J_p. Fatigue lives under torsional loading were much longer than under axial loading for the same equivalent plastic strain amplitude, which was explained by higher crack driving forces in terms of J_p under axial loading than under torsional loading. Fatigue lives estimated by crack propagation based on a master curve in terms of J_p,a were in a good agreement with those obtained experimentally under all types of loading. The used concept can reduce the experimental program to obtaining of material data only for axial loading, which can then be used for prediction of behaviour under in-phase multiaxial loading. The von Mises formula for multiaxial low-cycle fatigue loading ε_eq,p² = ε_p² + γ_p² / 3 was modified so that the fatigue lives under axial, torsional and combined loading were characterized in a matching way. Using the formula ε_p,Nf² = ε_p² + γ_p² / 25, the fatigue life data fell on a single Coffin-Manson curve.

Introduction

In high-cycle fatigue (HCF), the cyclic plastic deformation is restricted to a very small volume of material comparable with the grain size [1]. The amount of cyclic plastic deformation is dictated by elastic deformation in the remaining part of the body, which has much larger volume (i.e. the small-scale yielding case). Therefore, description of HCF behaviour using linear elastic continuum mechanics usually correlates well with experiments. Since the linearity between deformation and stress is valid, stress-like quantities can be used, which is more convenient in applications. In particular, stress amplitude is used to describe the fatigue limit, while the stress intensity factor is used for fatigue crack propagation [2]. Under low-cycle fatigue (LCF), the volume of plastically deformed material is initially stretched throughout the whole cross section of the specimen, while later the cyclic plastic deformation localises into the slip bands within individual grains. Therefore, strain quantities need to be used for the description of fatigue behaviour. It is common to express loading of the body using the strain amplitude or the plastic strain amplitude [3]. Under HCF loading, the stage of crack initiation is by far longer than the stage of stable crack propagation. In LCF, these two phases have comparable duration and in the case of crack initiation at a defect, the crack propagation period can be predominant [1], [2]. In some approaches, even the whole LCF live is described by a crack propagation law, which can be mathematically related to the Coffin-Manson law, as proposed by Polak et al. [4], [5]. Therefore, it is reasonable to consider a crack propagation parameter for description of behaviour under LCF, which was also done in the presented study.

An overview of development of various crack driving force parameters can be found e.g. in [6], [7]. The most relevant parameter from the point of view of crack growth mechanism (cyclic plastic deformation) would be the range of crack tip opening displacement ΔCTOD [8]. Some researchers have used plastic component of ΔCTOD to reach good correlation with crack growth rates [9], [10]. These attempts show reasonability in using of the plastic component as a physically justified crack driving force parameter even under small-scale yielding. However, this parameter is very difficult to determine both experimentally and numerically. Under large-scale yielding (LSY), the J-integral has probably been the most widely used parameter. Its use for cyclic loading was extended in later works, e.g. [11], [12]. Tchankov et al. [13] analysed LCF in four materials using a crack opening displacement approach, where a special parameter based on the range of J-integral and parallel stress applied to a mode I crack was derived. A good correlation of the experimental data was shown.

In the present work, a simple parameter was used, the plastic part of J-integral, which can be obtained by finite elements for arbitrary material, geometry and loading scenarios. Recent works [14], [15], [16], [17], [18], [19], [20] showed that the use of amplitude of the plastic part of J-integral (J_p,a) led to better description of crack growth kinetics under LSY than using total J-integral. Experimental data for various applied strain amplitudes as well as for various materials were described well by a single curve [20]. The aim of the presented research was to characterize low-cycle fatigue lives of the 316L austenitic stainless steel under cyclic axial, torsional and combined in-phase axial/torsional loading based on crack propagation modelling. Multiaxial or mixed-mode loading scenarios have attracted a lot of attention in fatigue research [21]. One of the problems associated with these studies is that it is very difficult to reach stable crack growth under shear-mode loading. Several experimental setups were suggested in the past for mixed-mode loading [22], [23]. However, not all of them are suitable for large-scale yielding. One possibility is to load a hollow cylindrical (tubular) specimen by torque or by a combination of tension and torque to reach multiaxial loading conditions (see e.g., [24], [25], [26]). In order to have a defined position of the crack for measurement of its length, starter notches or precracks are commonly prepared in the specimens. Multiaxial in-phase and out-of-phase loading using such specimens was studied e.g. in the works of Vormwald et al. [25], [27].

It should be noted that the research of mixed mode encounters several problems, since the mixed-mode loaded cracks tend to deviate from the original crack plane to reach local mode I loading. Very limited data can be found for stable shear-mode crack propagation. One example was studied and published in [28], where the precracks were introduced by cyclic tensile loading and subsequently the orientation of the specimen was changed so that the precracks were loaded by pure shear modes. The cracks propagated coplanarly (in the shear mode) only under large-scale yielding. Under small-scale yielding, the shear-mode loaded cracks grow under dominant local mode I mechanism, with the exception of single-phase bcc metals, where a crystallographic coplanar (local mode II) crack growth is easy to realize owing to low angles between the slips planes [29], [30]. In relation to that, shear-mode cracks are typical for natural initiation in smooth (unnotched) specimens due to localization of cyclic plastic deformation in the slip planes. In the case of crack initiation at a defect, the orientation of cracks in multiaxial LCF regime was studied in [31]. There is a transition size of the defect, under which the crack does not deflect to a local mode I growth. It happens for defects with small radii (tens of micrometers), which is related to large amplitudes of loading of the specimen. In the case of the specimens used in the present work, the hole diameter was large enough for the cracks to always naturally initiate in mode I. This situation most probably occurs in the majority of applications, where fatigue cracks initiate at defects.

There is often confusion around the terminology, since many authors mistakenly refer to multiaxially loaded specimens as “mixed-mode” scenarios. If the crack is loaded locally in mode I, its behaviour should not be different from any other case of mode I loading. Therefore, such experiments should not be regarded as measurement of some unknown material behaviour under mixed-mode loading. Instead, these experiments should verify that the local mode I crack driving force is computed correctly with respect to the complex configuration of geometry, external loading and crack path. If the crack driving force is computed correctly, it should be possible to take the material data obtained for axial loading and to use them for multiaxial in-phase loading scenarios. This would simplify substantially the testing procedures, since uniaxial data are much easier to obtain and no additional tests would be needed. One of the purposes of this work is to test this approach on specimens loaded by combinations of tension and torsion made of the 316L steel used in many applications with high demands on safety in long-term operation in corrosive environment, e.g. in energy industry or implants [32], [33].

In the presented study, significantly different fatigue lives were observed under axial loading and under torsional loading for equal loading in terms of the equivalent strain amplitude. Therefore, another purpose of this work was to provide explanation of such behaviour and to find out whether there is a principal difference between material fatigue behaviour under tension and torsion loading or a unifying description can be found. As mentioned earlier, a description taking into account crack propagation would be advantageous, since the low-cycle fatigue problems in many applications (e.g. pressure pipes, boilers) are connected to failure of bodies with complex geometry with the presence of stress concentrators or defects. The results obtained for laboratory specimens could be then transferred to real applications.