The present paper discusses the evolution of a critical plane‐based multiaxial high‐cycle fatigue criterion, known as Carpinteri–Spagnoli criterion. By proposing appropriate changes to the original formulation, the extended versions of the aforementioned criterion are able to assess smooth and notched metallic structural components subjected to different fatigue loading conditions, such as multiaxial in‐phase and out‐of‐phase synchronous cyclic loading, asynchronous cyclic loading and random loading. The results obtained through this criterion are compared with some experimental results related to relevant data reported in the literature.

In this work, a refined interelement diffuse fracture theoretical model, based on a cohesive finite element approach, is proposed for concrete and other quasibrittle materials. This model takes advantage of a novel micromechanics‐based calibration technique for reducing the artificial compliance associated with the adopted intrinsic formulation. By means of this technique, the required values for the elastic stiffness parameters to obtain nearly invisible cohesive interfaces are provided. Furthermore, the mesh‐induced toughening effect, essentially related to the artificial crack tortuosity caused by the different orientations of the interelement cohesive interfaces, is numerically investigated by performing comparisons with an additional fracture model, newly introduced for the purpose of numerical validation. These comparisons are presented to assess the reliability and the numerical accuracy of the proposed fracture approach.

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A B S T R A C T The myriad applicability of the frequency-domain critical plane criterion is outlined in order to evaluate and track the progression of fatigue damage in metallic structures subjected to high-cycle multiaxial random vibrations. The fatigue assessment using the given criterion is performed according to the following stages: (i) critical plane definition, (ii) power spectral density evaluation of an equivalent normal stress and (iii) computation of the damage precursor and fatigue life. The frequency-domain critical plane criterion is validated using experimental results related to (a) AISI 1095 steel cantilever beams under nonlinear base vibration, (b) 18G2A steel and (c) 10HNAP steel round specimens under random non-proportional combined flexural and torsional loads.Keywords damage precursor; frequency domain; high-cycle fatigue; multiaxial loading; random loading; vibration fatigue. Z ' = rotated frame Puvw = reference system related to the critical plane S eq (ω) = equivalent PSD function s xyz (t) = stress vector in PXYZT = time interval of observation T cal = fatigue life determined through calculations T exp = fatigue life through experiments α n = nth bandwidth parameter, with n = 1,2,3, … γ = rotation about the w axiŝ 1;2 and3 = rotation about the X ' axis λ n = nth spectral moment, with n = 1,2,3, … σ af = fatigue limit for fully reversed normal stress (R = À 1) σ 2 6';6' = variance of s 6 ' t ð Þ σ 2 6};6} = variance of s 6 } t ð Þ τ af = fatigue limit for fully reversed shear stress (R = À 1) ω = pulsation Correspondence: S. Vantadori.

In the present paper, some research results determined by the authors during the last two decades are reviewed. The influence of notches (geometrical discontinuities) on the fatigue life of metallic structural components is analysed. In particular, notches with different shapes (therefore characterised by different values of the stress concentration factor) are examined in the case of both double‐curvature shells and round bars under mode I loading. An elliptical‐arc surface crack is assumed to exist at the notch root. The stress intensity factor (SIF) is numerically evaluated, and the crack propagation under cyclic loading is analysed through a numerical procedure, which takes into account the aforementioned SIF.

The goal of the present paper is to discuss the reliability of a strain-based multiaxial Low-Cycle Fatigue (LCF) criterion, recently proposed by some of the present authors, in estimating the fatigue lifetime of metallic structural components weakened by sharp notches. Such a criterion, based on the critical plane approach, is formulated according to the control volume concept related to the Strain Energy Density (SED) criterion: a material point located at a certain distance from the notch tip is assumed to be the verification point where to perform the fatigue assessment. The above distance is assumed to be a function of both the biaxiality ratio (applied shear stress amplitude over normal stress amplitude)  phase angle between transversal normal strain t  and axial normal strain z  ur  , ut  , uz  direction cosines of u -axis vr  , vt  , vz  direction cosines of v -axis wr  , wt  , wz  direction cosines of w -axis  phase angle between shear strain zt  and axial normal strain z  a  Manson-Coffin shear strain amplitude zt  shear strain  angle between the averaged principal strain direction 1 and the normal w to the critical plane

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