A Path‐independent Parameter for Fatigue Under Proportional and Non‐proportional Loading

Abstract

A path-independent multiaxial fatigue damage criterion is proposed based on critical plane concepts: fatigue crack growth is controlled by the maximum shear strain, and an important secondary effect is due to the normal strain excursion over one reversal of the maximum shear strain. The effect of loading path on fatigue endurance is quantified by the normal strain excursion. Only one multiaxial material constant is required in the model which can be determined from uniaxial test data plus one torsional result. The parameter can be easily integrated with a shear strain-life relationship to predict low cycle fatigue lifetime. Experimental data of four different materials: En1 5R steel, I % Cr-Mo-V steel, 304 stainless steel, and 316 stainless steel at two temperatures were used to verify the criterion. It is shown that the proposed parameter can satisfactorily correlate test results for various proportional and non-proportional straining paths. NOMENCLATURE b. c = fatigue strength and ductility exponents E = Young's modulus F = rotation factor g = cross hardening coefficient factor K ' , n' = cyclic strength coefficient and strain hardening exponent Nf = fatigue lifetime S = normal strain effect coefficient f = effective shear strain yma, = maximum shear strain t e q , ueq = equivalent strain and stress tn = normal strain across maximum shear plane t: = normal strain excursion between turning points of maximum shear strain v,, vpr vCR = elastic, plastic, and effective Poisson's ratios u;, t i = fatigue strength and ductility coefficients ofl, zfl = uniaxial and torsional fatigue limits

Fatigue life under non-Gaussian random loading from various models

“…This paper deals with the comparison of some selected models of fatigue life estimation under stationary non-Gaussian random axial loading on the basis of experimental data obtained for the 10HNAP steel in high cycle fatigue (HCF). In this paper the following models for multiaxial loading are analyzed and their predictions compared with experiments: SmithWatson-Topper damage parameter used by BannantineSocie [5], Fatemi-Socie [5,6], Socie for HCF [7], WangBrown [8,9], Morel [10,11] and Łagoda-Macha [1][2][3][4]. n in spherical coordinates system m s = l 0 variance of a stress history s(t) s a max maximum amplitude in the history of stress after cycle counting by means of the rainf ow algorithm s af fatigue limit in fully reversed tension-compression y angle, from f xed axis in the plane P n →, to def ne the direction where the resolved shear stress is computed…”

Fatigue life prediction of titanium alloy for block loading using the hybrid approach of critical plane and continuum damage mechanics

“…Calibrated coefficients from the axial loads are determined using the solid specimen, as the experimental fatigue life for the axial load is determined using a solid specimen [48]. The experimental fatigue life results for titanium alloy BT9 are given in Table 3, and were determined using the tubular specimen Experimental [33] Experimental [48] Fatigue life prediction of titanium alloy for block loading using the hybrid approach of critical plane and continuum damage mechanics [48]. The predicted fatigue, along with the experimental fatigue lives for blocks of loading, are presented in Table 3.…”

“…The accuracy of the proposed model can be further improved by applying the block loading as a full or filtered profile so that only high damage cycles remain and the sequence effect of previous loading cycles can be captured. Experimental [33] Experimental [48] Fatemi Socie Model [48] mainly due to the difference of specimen geometry, as well as the fact that the axial, torsion and out-of-phase profiles are only used for coefficient calibration to estimate the fatigue life for block loads. Generally, the model has shown good accuracy and is simple to apply.…”

“…Wang and Brown [33] have proposed a modification of the model proposed by [34], adding the capability to handle the strain path effect. The model is expressed in Eq.…”

Multiaxial fatigue property of type 316 stainless steel using hollow cylinder specimen under combined pull loading and inner pressure

“…The equivalent stress based on von Mises (Mises stress) is generally used in that design for structures under multiaxial loading. In recent literatures of multiaxial fatigue, it is reported that fatigue life evaluated by the Mises stress is overestimated [1][2][3][4][5][6][7][8] and the M magnitude depends on loading path [9][10][11][12][13][14][15][16]. In the multiaxial fatigue under non-proportional loading in which directions of principal stress and strain are changed in a cycle, it has been reported that fatigue lives are reduced accompanying with additional hardening which depends on both loading path and material [4][5][6][7][8][9][10][11][12][13][14][15][16].…”