On the fatigue limit of ductile metals under complex multiaxial loading

doi:10.1016/S0142-1123(99)00107-3

International Journal of Fatigue

Volume 22, Issue 2, February 2000, Pages 137-145

https://doi.org/10.1016/S0142-1123(99)00107-3 Get rights and content

Abstract

The classical strength hypotheses are not applicable for the calculation of the fatigue limit under multiaxial loading with changing directions of the principal stresses. Hitherto, two groups of concepts have been proposed, the critical plane approach and the integral approach. In the present paper it is shown that with the integral approach, in particular the Shear Stress Intensity Hypothesis SIH, a good estimation can be achieved with complex periodical loads. This is verified using the results of 179 test series with ferritic and ferritic perlitic steel with a range of the tensile strength of R_m=400–1600 MPa. References will be given to further hypotheses and developments.

Section snippets

Initial situation

In 1945, Nishihara and Kawamoto published an important study with respect to multiaxial test results [1]. For the combination of normal and shear stresses, the effect of the phase difference on the endurance limit proved to be very small, Fig. 1, as confirmed by later investigations [2]. In the case of S–N-curves a phase difference between the normal and shear stresses results in a reduction of the number of cycles to fracture [3]. If it is assumed that the endurance limit is determined by the

Requirements on a strength hypothesis for variable principal stress directions

The demand for invariance of a fixed coordinate system is sufficient for the static calculation for determining the beginning of yield and for the calculation of the endurance limit under cyclic load for proportional loading with a constant principal stress direction. In the case of changing principal stress direction two further criteria must be satisfied:

•
the invariance of the principal stress system and
•
recording of the temporal and spatial variation of the stress tensor.

The latter condition

Integral approach

In analogy with Eq. (4) an integration of the square of the shear stress amplitude can be performed over all sectional planes γϕ for fully reversed stress. This yields the equivalent-stress amplitude, $σ_{equ,a} = 15 8π ∫ γ=0 π ∫ ϕ=0 2π τ^{2}_{γϕa} · sin γ· dγ· dϕ^{12}$ If one principal stress direction is constant, for instance, in the case of a planar stress state on the surface of a structural component, Eq. (5) can be simplified: Instead of integrating over the entire volume element, the integration over one degree of

Shear stress intensity hypothesis SIH

For the example of the SIH [2], [7], [8], [9], [10] the possibilities offered by the integral approach are described in the following. The reduced stress amplitude is given by, compare Fig. 5, $σ_{equ,a} = 15 8π ∫ γ=0 π ∫ ϕ=0 2π aτ^{2}_{γϕα} 1+mτ^{2}_{γϕm} +bσ^{2}_{γϕa} 1+nσ_{γϕm} sin γ dγ dϕ^{12}$

The failure condition is $σ_{equ,a} =σ_{W}$

The constants a, b, m, and n are obtained from the tensile-compressive fatigue strength σ_w, torsional fatigue strength τ_w, pulsating tensile strength σ_Sch, and pulsating torsional strength τ_Sch, see Table 1.

The

Criticism by I.V. Papadopoulos et al.

In [14] Papadopoulos et al. have commented on various hypotheses proposed in the literature. Three categories are thereby distinguished:

•
Critical plane approaches (Findley, Matake, Robert, McDiarmid, Dietmann)
•
Approaches based on the stress invariants (Marin, Sines, Crossland, Kakuno–Kawada)
•
Criteria based on stress averages within the elementary volume (Grubisic and Simbürger, Liu and Zenner)

In the following, only the criticism concerning the final category is discussed.

Summary

With the hypotheses of the integral approach, the fatigue limit for ductile metallic materials under complex multiaxial loading can be calculated with high accuracy (e.g. combined alternating and static stresses, phase differences, different frequencies, and sinusoidal as well as nonsinusoidal waveforms). This is shown for example with the Shear Stress Intensity Hypothesis SIH using results from 179 test series with ferritic and ferritic perlitic steel. The SIH is applicable in a range of 0.577≤

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Citation Excerpt :
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According to many researchers, there is a correlation between additional non-proportional hardening and fatigue life drop under the non-proportional loadings. This opinion results in many multiaxial fatigue life prediction models relating the fatigue life with non-proportional hardening parameter. At the same time there is a significant number of researchers, who believe that such a relationship is not a general principle and fatigue damage parameters cannot be formulated based on it. Since the scientific discussion on this dispute in literature is rather fragmentary, this paper tries to answer the question about the character of relationship between non-proportional hardening and fatigue life. For this purpose, the views of both sides and associated multiaxial fatigue models are presented at first. Secondly, own fatigue tests were carried out under proportional and non-proportional loadings on 5 materials. The analysis of own experimental results was extended to include literature data regarding another 25 materials. In the summary, it was found that the relationship between additional non-proportional hardening coefficient and fatigue life should not be the base for the multiaxial fatigue models.

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On the fatigue limit of ductile metals under complex multiaxial loading

Abstract

Section snippets

Initial situation

Requirements on a strength hypothesis for variable principal stress directions

Integral approach

Shear stress intensity hypothesis SIH

Criticism by I.V. Papadopoulos et al.

Summary

Int. J. Fatigue

Int. Journal of Fatigue

The strength of metals under combined alternating bending and torsion with phase difference

Mem. of the College of Eng., Kyoto Imperial University

On a new multiaxial fatigue criterion based on a selective integration approach

Proc. of the Sixth International Fatigue Congress, Fatigue 96

High cycle multiaxial fatigue energetic criterion taking into account the volumetric distribution of stresses

Proc. of the 5th Int. Conf. on Biaxial/Multiaxial Fatigue & Fracture, Cracow

Eine Festigkeitshypothese für die Dauerfestigkeit bei beliebigen Beanspruchungskombinationen

Konstruktion

Schubspannungsintensitätshypothese — Erweiterung und experimentelle Abstützung einer neuen Festigkeitshypothese für schwingende Beanspruchung

Konstruktion

Berechnung der Dauerschwingfestigkeit bei mehrachsiger Beanspruchung

Mat.-wiss. u. Werkstofftech

Weakest link theory and multiaxial criteria

Proc. of the 5th Int. Conf. on Biaxial/Multiaxial Fatigue and Fracture, Cracow

Mechanics of solid materials