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A B S T R A C T In the present paper, the fatigue strength estimation capabilities of the modified C-S (Carpinteri-Spagnoli) criterion are improved by employing the Maximum Rectangular Hull (MRH) method proposed by the first author. The C-S criterion is a multiaxial high-cycle fatigue criterion based on the critical plane approach and takes into account both shear stress (Mode II) and normal stress (Mode I) mechanisms to evaluate the orientation of the critical plane. The fatigue damage parameter used is given by a nonlinear combination of the equivalent normal stress amplitude, N a,eq , and the shear stress amplitude, C a , acting on the critical plane. In the present paper, the shear stress amplitude is evaluated through the MRH method. Some experimental data available in the literature are compared with the theoretical estimations, concluding that the multiaxial fatigue strength evaluations provided by the C-S criterion are improved when C a is computed applying the MRH method instead of the Minimum Bounding Circle (MBC) method.Keywords critical plane approach; modified C-S criterion; multiaxial high-cycle fatigue; Maximum Rectangular Hull method; stress-based criterion. N O M E N C L A T U R Ea = amplitude C = shear stress vector acting on the critical plane C a = shear stress amplitude C 1,a (ξ), C 2,a (ξ) = half sides of the rectangular hull f y = material yield stress I = error index m = mean value max = maximum value N = normal stress vector perpendicular to the critical plane N a,eq = equivalent normal stress amplitude PXYZ = fixed frame P123 = frame of the principal stress axes P123 = frame of the weighted mean principal stress axes S w = stress vector at material point P, related to the critical plane t = time T = observation time interval w = vector normal to the critical plane α = phase angle between longitudinal (axial) normal stress σ x and tangential (hoop/circumferential) normal stress σ y β = phase angle between longitudinal (axial) normal stress σ x and shear stress τ xy

Low fracture toughness of concrete represents a serious shortcoming. An effective way to improve the concrete toughness is represented by the dispersion (during mixing) of discontinuous fibres into the concrete mix. The principal beneficial effect of fibres is the crack bridging in the cementitious matrix, providing resistance to crack propagation before fibre debonding and/or pulling out or failure. In the present paper, the fracture behaviour of FRC (fibre reinforced concrete) specimens is examined, with micro-synthetic polypropylene fibrillated fibres being randomly distributed in concrete. The modified two-parameter model, proposed by the authors to calculate Mode I plain-stain fracture toughness for quasi-brittle material, is able to take into account the possible crack deflection (kinked crack) during stable crack propagation.

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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.