Experimental and numerical analyses of the cyclic behavior of austenitic stainless steels after prior inelastic histories

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Highlights

  • Cyclic stress-strain curve depends strongly on the previous elastoplastic loading history.

  • Both 304 and 316 SS exhibit significant relaxation even at room temperature.

  • For a qualitative point of view, the MM model leads to correct predictions about the strain memory effect.

  • The MM fails in describing accurately the stabilized cyclic behavior.

  • The prediction of the cross-hardening responses is generally satisfactory.

Abstract

The work deals with the cyclic behavior of 304 L and 316 L austenitic stainless steels subjected to stress or strain control. Particular attention is being given to the analysis of situations where the cyclic loading under a given amplitude was preceded by inelastic pre-deformation. The obtained results show that the cyclic stress-strain curve is not unique, as it depends on the maximum strain range reached previously. For the tests starting by a relaxation, the significant additional strain hardening was demonstrated when crossing from axial loading to the equivalent shear loading. A comparison between experimental results and those obtained by simulation shows that the MultiMechanism model (MM) prediction has a good qualitative agreement with the experimental results in the description of the different cyclic behavior phenomena investigated in this work with relatively small number of parameters. However, the MM model should be improved in order to better take into account certain situations like the strain hardening phenomenon exhibited in the sequential tests described here.

Introduction

Structural integrity has always been an obstacle to industrial development. Experience shows that fracture of structures and mechanical parts in different industries during service life are most often due to the fatigue. For a safe design of critical components, an accurate description of the stress–strain responses of materials under proportional and non-proportional cyclic paths requires powerful constitutive models to ensure reliable and accurate fatigue life prediction.

Austenitic stainless steels are intensively used in many industrial applications such as aeronautics, nuclear power plants, pressure vessels and pipes due to their excellent mechanical properties such as ductility, tenacity and strain hardening as well as their high corrosion resistance. Its behavior is strongly influenced by many different parameters and loading conditions. Experimental studies show that austenitic stainless steels (304 L and 316 L) have a significant additional cyclic hardening (over-strengthening) under non-proportional loading [[1], [2], [3], [4], [5]], it occurs in the first cycles to stabilize in a few tens of cycles. Furthermore, a phenomenon called ‘‘cross-hardening effect” has been demonstrated; appearing when a proportional cyclic loading in a given direction is followed by a subsequent proportional cyclic loading in another direction. Significant cyclic over-hardening was then observed just after the change of the loading direction, followed generally by cyclic softening and stabilization. The effect of this phenomenon on the ratcheting has been studied for 316 L and 304 L stainless steels, the generated over-hardening seems to slow the ratcheting rate of this grades of stainless steels [4,6]. The strain memory effect on subsequent cyclic behavior of the austenitic stainless steels has been investigated [[7], [8], [9], [10], [11]]. For 316 L stainless steel, cyclic tests were carried out for maximum total strain amplitudes of 1%, 2%, 2.5% and 3% [7,9]. The results show that the Cyclic Stress-Strain Curve (CSSC) is not unique and clearly depends on the previous loading history. Other results indicate the existence of a threshold below which this effect of strain memory is not observable on the CSSC. Indeed, for small plastic deformation amplitudes lower than 0.4%, 316 L stainless steel did not show a cross effect on the CSSC [12]. The ratcheting phenomenon for austenitic stainless steels has been studied many times, depending on the stress amplitude, the mean stress [13], the rate-dependence and the history of the loading and temperature [6,[13], [14], [15], [16], [17], [18], [19]]. Recent work on the 304 L SS has highlighted a significant coupling between the ratcheting and creep. Indeed, the contribution of these viscous phenomena has been studied using ratcheting tests for which the material has been subjected to a preliminary creep test in order to dissipate the viscous effects [20]. Experimental results show that, after the creep phase, no significant cyclic accumulation of the plastic strain was observed. This means that most of the cyclic accumulation of plastic deformation observed for classical ratcheting tests on the material under consideration appears to be mainly due to creep. Contrary to what is generally admitted in the literature, the ratcheting seems very weak for this material at room temperature.

In order to take into account the various aspects of the cyclic behavior of austenitic stainless steels during the design of industrial components, numerous studies have been published on the modeling of the different phenomena observed experimentally [19,[21], [22], [23], [24], [25], [26]]. Two types of phenomenological models have been developed, the Chaboche type models [[25], [26], [27], [28], [29]] and the multimechanism type models [20,21,23,[30], [31], [32], [33], [34]] adopted in this work. The first version of the MM model has been proposed by Cailletaud and Sai in 1995, the theoretical background can be found in Ref. [23]. The main originality of the MM model is the decomposition of the inelastic strain in two components each one representing one mechanism (2 M). Both mechanisms are combined in one loading function to define one criterion (1C). Thanks to this approach, the MM model is a possible alternative to the Chaboche model for modeling the complex behavior of materials. Several improvements of this model have been proposed to better take into account the various inelastic phenomena and complex material behavior like: cyclic hardening and softening, rate-dependence of the behavior, additional hardening under non-proportional loading path, strain hardening memory, cyclic accumulation of the inelastic strain under creep or classical ratcheting test and anisotropy of cyclic behavior [21,[30], [31], [32], [33], [34], [35]].

In the last two decades, the capabilities of the MM model have been demonstrated by simulating a number of proportional and non-proportional cyclic loading paths on different materials. Many numerical studies of 304 SS ratcheting behavior have been reported especially in Refs. [13,[16], [17], [18], [19], [20], [21],[36], [37], [38], [39]]. The description of the multiaxial ratcheting by the MM model has been improved through the modification of the kinematic hardening rules, leading to the definition of new formulation in order to ensure the thermodynamic consistency of the model [20,33,34]. Furthermore, in the light of the experimental results obtained in Taleb and Hauet work [6], an improved version of the multimechanism model was proposed in Ref. [21] where the modeling of the isotropic hardening was revisited in order to take into account the over-hardening due to non-proportional loading paths as well as the strain memory phenomenon. Moreover, the contribution of creep in the cyclic accumulation of the inelastic strain in the behavior of the austenitic stainless steel (304 L) necessitates the use of rate-dependent constitutive equations. In this context, the capabilities of the multimechanism model have been demonstrated in simulating the classical ratcheting as well as the creep-ratcheting tests performed in Ref. [20]. The predictions were particularly satisfactory for non-proportional loading paths. A particular attention has been paid to the identification process in order to capture the main important phenomena encountered in the tests performed: relative parts of isotropic and kinematic hardening, time dependent effects, non-proportionality effect and strain memory. For that, the MM model requires the determination of 17 material parameters.

In this work, we are interested by the multimechanism modeling of some complex cyclic behavior phenomena demonstrated by two types of austenitic stainless steels: strain memory effect on the cyclic stress-strain curve (CSSC) and effect of the relaxation of the axial stress on the subsequent cyclic behavior. After the introduction, the obtained experimental results are summarized in the second section. The third and fourth sections are devoted, successively, to the presentation of the main constitutive equations of the multimechanism model and the identification of the material parameters. In the fifth section, a comparison between the experimental results and those obtained by simulation will be presented. Some concluding remarks are given in the last section.

Section snippets

Materials

Two austenitic stainless steels (304 L and 316 L) have been considered in this study. Their average chemical compositions are given in Table 1.

Specimen and experimental device

Thin-walled tubular specimens have been used in this study. The gage length is equal to 46 mm where a central part of 25 mm is used for the extensometry. In the latter zone, the outer and inner diameters are equal to 20 mm and 17 mm respectively (Fig. 1) which is in accordance with ASTM Standard E2207 [40] in order to reduce the effect of the strain

Constitutive equations

Among the models available in the literature, we chose to detail for this study the multimechanism (MM) model in its version called 2M1C (two mechanisms and one criterion). The set of constitutive equations of the MM model is given here considering the Taleb and Cailletaud version described in Refs. [21]. For further details, the reader is referred to the original paper for full equation set.

Two mechanisms are combined in one loading function f to define one criterion. The inelastic strain is

Test results and discussion

The simulation was performed using ZeBuLoN finite element code in which the MM model is implemented. A comparison between the experimental results and those obtained by simulation are presented below.

Conclusion

In addition to some experimental investigations, this work has enabled the evaluation of the multimechanism model (MM) in terms of its predictive capabilities about the cyclic behavior of austenitic stainless steels: strain memory effect on cyclic stress-strain curves, the relaxation of the axial stress effect on the subsequent cyclic behavior.

A comparison between the experimental sequential tests results and those obtained by simulation shows that the MM model simulation has a good qualitative

Credit author statement

Adel Belattar: Conceptualization, Methodology, Data curation, Writing – original draft preparation, Visualization, Investigation. Lakhdar Taleb: Supervision, Software, Validation, Resources, Writing- Reviewing and Editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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