Low-cycle fatigue behavior and life prediction of CP-Ti under non-proportional and multiaxial loading

https://doi.org/10.1016/j.engfracmech.2021.107930Get rights and content

Highlights

  • The maximum principal strain critical plane is more effective under both IP and OP loading.

  • FS model and KBM-P model can be applied to both IP and OP loading in a general form.

  • MLCF life prediction model based on newly defined αNf and α are established.

Abstract

Non-proportional multiaxial low-cycle fatigue (MLCF) tests were performed on CP-Ti at different multiaxial strain ratios. The optical microscopy observations and life prediction models verified that the critical plane of CP-Ti was the maximum principal strain plane and that it was effective under non-proportional loading. A non-proportional life coefficient and strain energy density coefficient are proposed. Typical MLCF life prediction models, such as the ESN, FS, KBM, and KBM-P models, are discussed under non-proportional loading. Finally, by associating the newly defined non-proportional life coefficient with the non-proportional hardening factor, two comprehensive non-proportional MLCF life prediction models are established, which have higher accuracies than those of previous models.

Introduction

Commercially pure titanium (CP-Ti) and titanium alloys are widely used in the chemical, marine, and aviation industries because of their light weight, high strength, and good corrosion resistance [1]. Due to the service requirements of rotating aero engines, there have been numerous studies [2], [3], [4], [5], [6] on the proportional and non-proportional multiaxial cycle fatigue (MCF) properties of titanium alloys. However, with the recent development of sophisticated manufacturing processes, traditional chemical process equipment must also consider the MCF performance of materials [7], [8]. As a widely used material in chemical process machinery, the MCF performance of CP-Ti, particularly the non-proportional MCF performance close to the actual operating loading conditions, requires further research and exploration.

Compared with proportional loading, non-proportional loading introduces a change in the phase angle. Axial and torsional loading change from synchronous to asynchronous loading. In previous research, numerous materials, such as 304L stainless steel [9], [10], 800H stainless steel [11], 16MnR steel [12], and 1050 steel [13], have been reported to exhibit non-proportional cyclic hardening phenomena. The degree of non-proportional hardening is related to the applied strain amplitude and loading path [13], [14], [15], [16]. 7075-T651 aluminum alloy exhibits lower fatigue life in two-step loading spectra [17]. Kanazawa et al.[18] first related the non-proportional cyclic hardening phenomenon to a change in the slip plane. The rotation of the maximum shear plane under non-proportional loading causes the slip plane to change from one crystallographic slip system to another. Doong et al.[19] compared the non-proportional hardening coefficients of materials with different stacking fault energies (SFEs). They found that 304L stainless steel (low SFE) has a high non-proportional hardening coefficient, whereas polycrystalline 1100 aluminum (high SFE) has a low non-proportional hardening coefficient. They concluded that the degree of non-proportional hardening decreases with increasing SFE. On this basis, Borodii and Shukaev [20] combined the non-proportional hardening coefficients of materials with various SFEs and proposed a non-proportional coefficient prediction model based on the material strength parameter. Nima et al.[13] observed that the cyclic hardening characteristics of a material are consistent with the non-proportional cyclic hardening characteristics. Materials with cyclic hardening characteristics also exhibit non-proportional cyclic hardening characteristics, while materials with cyclic softening characteristics exhibit almost no non-proportional hardening. They proposed a quantitative relationship between the cyclic hardening coefficient and the non-proportional cyclic hardening coefficient to predict the non-proportional cyclic hardening coefficient.

Presently, multiaxial fatigue life prediction is an active area of research. Multiaxial fatigue life prediction can be roughly divided into three categories: equivalent, critical plane, and energy methods. With reference to the Lagrangian equivalent strain, Amanda et al.[21] proposed a method to standardize the multiaxial fatigue test data of Nitinol materials. They used the improved Coffin–Manson method to obtain a fatigue life prediction model of Nitinol alloys under multiaxial loading. Owing to the weak correlation between the equivalent stress or equivalent strain and the loading path during non-proportional loading, the equivalent method was slowly rejected. However, owing to its ease of use, equivalent stress and equivalent strain methods are still widely used in engineering. Owing to the selection of fatigue parameters, most energy and critical plane methods can accurately reflect the influence of the loading path on the multiaxial fatigue behavior. The most widely accepted critical plane fatigue life prediction equations are the Findley [22] model (which uses stress parameters), the Kandil, Brown and Miller [22], [23] model (which uses strain parameters), and the Fatemi [24] model (which uses both stress and strain parameters). These models have various advantages and disadvantages according to the differences in the material failure modes and test loading methods. Andrea et al. [25] proposed a strain-based multiaxial fatigue criterion connected to a critical plane approach. They extended the Carpinteri–Spagnoli (C–S) criterion for high-cycle fatigue to the range of low/medium-cycle fatigue. Wu et al. [26] conducted multiaxial fatigue tests under proportional and non-proportional loading on TC4 alloys. They found that the critical plane method based on the shear strain Wu–Hu–Song (WHS) approach could predict the fatigue life more accurately. Smith et al. [27] proposed the SWT model using the strain energy density on the critical plane as the fatigue parameter. This method combines critical plane and energy methods. Liu et al. [28] proposed a method based on the virtual strain energy (VSE) concept to predict multiaxial fatigue lives under in-phase and out-of-phase biaxial loading conditions. This method consistently predicted the multiaxial fatigue life of 316L stainless steel with high accuracy. Xue et al. [29] defined an equivalent strain amplitude (ESA) alternative fatigue damage parameter to overcome the deficiency of the modified generalized strain amplitude (MGSA) damage parameter [30]. This method combines the concept of energy on the critical surface and proposes a multiaxial fatigue damage parameter without a weight coefficient. The predictions were satisfactory and conservative, particularly under random multiaxial loading conditions. Li et al. [31] proposed a real-time damage evaluation method for multiaxial thermo-mechanical fatigue which considered influence of temperature on the damage accumulation and effect of non-proportional additional hardening on all damages. Berti et al. [32] evaluated how the use of different multiaxial fatigue criteria may affect the fatigue assessment for Nitinol peripheral stents. The results showed that the von Mises is the most conservative criterion. The critical plane approaches yield more realistic approximations.

Few studies have been conducted on the non-proportional multiaxial fatigue behavior of CP-Ti, particularly for different multiaxial strain ratios. Existing studies on experimentally varying the multiaxial strain ratio are mostly focused on the influence of the loading path on the multiaxial low-cycle fatigue (MLCF) behavior. There are relatively few studies on the effect of the multiaxial strain ratio on the MLCF behavior under proportional and non-proportional loading. Moreover, the hardening and stress–strain response of CP-Ti under non-proportional multiaxial loading requires further experimental study. In this study, the non-proportional multiaxial fatigue behavior of CP-Ti under various multiaxial strain ratios was investigated in detail. The test results under non-proportional loading were compared with the results under proportional loading. The cyclic stress–strain response and fatigue life data of CP-Ti under non-proportional loading obtained through the strain-controlled MLCF tests were compared with the relevant data under proportional loading to obtain the non-proportional hardening characteristics and fatigue life prediction of CP-Ti under non-proportional loading. Furthermore, the versatility of various fatigue life prediction models under proportional and non-proportional loading was compared. Finally, by associating the newly defined non-proportional life coefficient with the non-proportional hardening factor, two comprehensive non-proportional MLCF life prediction models are proposed.

Section snippets

Materials and experimental procedures

CP-Ti was used as the material in this study. Its chemical composition and mechanical properties are listed in Table 1, Table 2, respectively. Fatigue specimens were cut directly from the CP-Ti plate by wire cutting and lathe processing according to ASTM E2207, as shown in Fig. 1 [33]. The fatigue specimens were cut along the rolling direction of the CP-Ti plate.

Non-proportional MLCF tests were performed using an MTS 809 material test system under non-proportional strain-controlled mode at room

MLCF hysteresis loops of CP-Ti under IP and OP loading

The fatigue test data for OP loading are listed in Table 3. The axial and torsional stress amplitudes were obtained from the data at half the fatigue life. The von Mises equivalence criterion under tension and torsion loading was used to calculate the equivalent strain and stress (Eqs. (1), (2), respectively)[34].Δεequiv/2=(Δε/2)2+(Δγ/2)2/3Δσequiv/2=(Δσ/2)2+3(Δτ/2)2where Δε/2 and Δγ/2 are the axial and shear strain amplitudes, respectively, and Δσ/2 and Δτ/2 are the axial and shear stress

Conclusions

  • (1)

    Compared with that under IP loading, the axial strain energy density of CP-Ti under OP loading gradually increased with increasing multiaxial strain ratio. For the torsional hysteresis loops, compared with those under IP loading, the peak and valley values of the stress response under OP loading markedly increased and decreased, respectively. This is a manifestation of non-proportional hardening.

  • (2)

    Because the axial stress and torsional stress under OP loading were asynchronous, the influence of

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.

Acknowledgements

The authors gratefully acknowledge the financial supports of the National Natural Science Foundation of China (5197527, 51905260) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX20_1070).

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