Multiaxial fatigue of V-notched steel specimens: a non-conventional application of the local energy method

Abstract

A B S T R A C T The paper deals with the multi-axial fatigue strength of notched specimens made of 39NiCrMo3 hardened and tempered steel. Circumferentially V-notched specimens were subjected to combined tension and torsion loading, both in-phase and out-of-phase, under two nominal load ratios, R = −1 and R = 0, also taking into account the influence of the biaxiality ratio, λ = τ a /σ a . The notch geometry of all axi-symmetric specimens was a notch tip radius of 0.1 mm, a notch depth of 4 mm, an included V-notch angle of 90 • and a net section diameter of 12 mm. The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading on plain and notched specimens. Furthermore the fracture surfaces are examined and the size of nonpropagating cracks measured from some run-out specimens at 5 million cycles. Finally, all results are presented in terms of the local strain energy density averaged in a given control volume close to the V-notch tip. The control volume is found to be dependent on the loading mode.Keywords multiaxial fatigue; notch stress intensity factor (NSIF); strain energy density (SED); torsion loading; V-notched. N O M E N C L A T U R E2α = V-notch included angle = Phase angle λ = Biaxiality ratio, τ a /σ a λ 1 = Eigenvalue of the mode I stress distribution, according to Williams's solution λ 3 = Eigenvalue of the mode III stress distribution ρ = Notch root radius σ a = Nominal stress amplitude referred to the net area of the specimens τ a = Nominal stress amplitude due to torsion loading (on the net area) σ A, τ A = Fatigue strength (in terms of stress amplitudes on the net area) at N A cycles to failure σ y = Yield stress σ y = Cyclic yield stress c np = Non-propagating crack length according to Yu, Tanaka and Akiniwa's model e 1 , e 3 = Parameters used for the energy density evaluation k = Inverse slope of the fatigue curves K 1 , K 3 = Mode I and mode III notch stress intensity factors (NSIFs) K th = Threshold value of the stress intensity factor K IIIsh th = Shielding stress intensity factor under mode III loading according to Yu et al. k 1 , k 3 = Non-dimensional factors used in the NSIF expressions Correspondence: P. Lazzarin.

Fracture behaviour of notched round bars made of PMMA subjected to torsion at −60°C

“…(3) and, for the crack case, e 3 = 0.4138, as shown in [62][63][64], By considering the average values of the critical stress T c measured from the semicircular specimens as described above and the average value of the critical stress intensity factor J< mc (see Tables 6 and 7), the control volume radius becomes: Contrary to Ref. [61], where the presence of large scale yielding did not allow to establish a priori the value of the radius, in the present contribution the radius has been determined from measurements with smooth notched specimens and cracked specimens [19,21].…”

“…About 1200 experimental data under mode I and mixed mode conditions (I + II) were summarised in Refs [40,42]. Recently the SED approach was also applied to summarise a number of fatigue data from V-notched specimens subjected to uniaxial and multiaxial loading [63,64]. Under torsion loading a number of non-linear elastic effects were detected resulting in a control volume dependent on the loading mode [61].…”

“…notch opening angle and tip radius). A non-conventional approach of these data in terms of strain energy density, as an extension of previous contributions [62][63][64], has been carried out showing a good agreement between experimental results and theoretical fracture assessment but only when the notch root radius is lower than or equal to 5 mm.…”

“…According to [62][63][64], the radius of the control volume for a bar with a circumferential crack subjected to torsion can be obtained through the following expression:…”

Crack initiation life in notched Ti-6Al-4V titanium bars under uniaxial and multiaxial fatigue: synthesis based on the averaged strain energy density approach

“…n the recent literature [1][2][3][4][5][6], an unexpected notch-strengthening phenomenon was found in circumferentially notched specimens under pure torsion or combined tension-torsion multiaxial fatigue loadings. The fatigue life of notched bars resulted longer than that of smooth ones, the higher the stress concentration factor under the same load amplitude.…”