Issue 41

A. Carpinteri et alii, Frattura ed Integrità Strutturale, 41 (2017) 66-70; DOI: 10.3221/IGF-ESIS.41.10 67 Since the pioneering work by Neuber [2], a big effort has been made by the scientific community in order to devise suitable criteria for accurately assessing the fatigue strength/life of structures weakened by either blunt or sharp notches, subjected to complex time-varying loading. Nowadays, a universally accepted criterion does not exist yet, and hence the multiaxial fatigue analysis of notched components is a research topic still open. Reviews of the most promising fatigue criteria for fatigue assessment of notched metallic components can be found in Refs [3,4]. Several multiaxial fatigue criteria available in the literature represent a reformulation of their counterparts for smooth components, by considering the detrimental effect of the stress/strain concentration phenomena on the material fatigue strength. Such criteria usually reduce the complex multiaxial stress/strain state to an equivalent uniaxial condition: they are stress-based in High-Cycle Fatigue (HCF), whereas they are strain-based in Low-Cycle Fatigue (LCF). According to the above remarks, the present authors have recently proposed a strain-based multiaxial fatigue criterion in order to estimate the fatigue life of severely notched specimens under LCF [5]. Such a criterion is an extension of the critical plane-based multiaxial fatigue criterion proposed by Carpinteri et al. for smooth specimens [6,7] to the case of notched ones. The above extension is formulated by implementing the concept of the control volume, related to the Strain Energy Density (SED) criterion proposed by Lazzarin et al. [8,9]. More precisely, the fatigue life assessment is performed by taking into account the strain state at a material point (named verification point) located at a certain distance from the notch tip, depending such a distance on both the biaxiality ratio  (remote shear stress amplitude over remote normal stress amplitude) and the control volume radii under loading conditions of Mode I and Mode III. The goal of the present paper is to discuss the accuracy and reliability of the joined application of the strain-based criterion together with the control volume concept [5] in estimating multiaxial fatigue lifetime of structural components weakened by notches. In particular, the results obtained by employing the criterion proposed in Ref. [5] are compared with some experimental data recently published [10], related to circumferentially V-notched round bars made of titanium grade 5 alloy (Ti-6Al-4V) under both uniaxial and multiaxial fatigue loadings. C RITERION FORMULATION FOR NOTCHED COMPONENTS n order to check the accuracy of the strain-based multiaxial fatigue criterion together with the control volume concept (related to the SED criterion) in estimating fatigue life of notched components, we briefly outline the analytical basis of such a criterion (details may be found in Ref. [5]). The fatigue life assessment is carried out at a verification point (point P ), which is distant r from the notch tip. Such a distance r , measured along the notch bisector line, is a function of both the biaxiality ratio  and the control volume radii provided by the SED criterion [8,9]:         1.484 0.221 11.3 m m r R R (1) where m R is the mean control volume radius, computed by averaging the control volume radius related to Mode I, 1 R , and that related to Mode III, 3 R . According to the SED criterion, such radii depend on the mean values of Mode I and Mode III Notch Stress Intensity Factors (NSIFs) ranges, and on Mode I and Mode III HCF strengths of both smooth specimens and the notch geometry. Once the position of the verification point P is determined according to Eq. (1), the strain tensor at such a point is obtained from a finite element analysis by examining a tridimensional model. After the strain state at point P is deduced, the averaged directions of the principal strain axes can be determined on the basis of their instantaneous directions by means of the averaged values of the principal Euler angles. The orientation of the critical plane is linked to the above averaged directions through the off-angle  :                               2 3 1 1 45 2 2 1 a a eff (2) where  eff is the effective Poisson ratio, and  a and  a are defined by the well-known tensile and torsional Manson- Coffin equations, respectively. I