Issue 9

An. Carpinteri et alii, Frattura ed Integrità Strutturale, 9 (2009) 46 – 54 ; DOI: 10.3221/IGF-ESIS.09.05 47 Several methods are available in the literature to perform fatigue strength and service life assessment of welded joints under uniaxial fatigue loading [1]. The most common uniaxial approach, encapsulated by most of the standard codes in force for metallic structures [2] , proceeds by comparing the nominal stress amplitudes applied to the joint with the nominal stress values obtained from S-N curves. Local approaches based on local parameters have recently attracted increasing attention in the research community: for example, structural stress and strain approaches [3,4] , notch stress and strain approaches [5,6] , fracture mechanics approaches [7,8], critical distance approaches [9,10] . The fatigue assessment of welded joints employing local parameters becomes more complex when multiaxial fatigue stress-strain states are present in the vicinity of welded joints. When a weld structure is subjected to in-phase multiaxial fatigue loading, the stress-strain state can be reduced to an equivalent stress/strain based on conventional hypotheses used for static strength evaluation (e.g. see the von Mises criterion or the Tresca criterion). However, some experimental results [11] on welded steel joints show a decrease of fatigue life in presence of out-of-phase multiaxial loadings as compared to fatigue life under in-phase multiaxial loadings. The critical plane-based multiaxial fatigue criterion proposed by Carpinteri and Spagnoli (the C-S criterion) for smooth and notched specimens [12-17] has recently been extended to welded structural components by employing the nominal stresses [18]. In the present paper, a comparison between lifetime predictions and experimental data available in the literature [11, 19-21] is carried out, for both in-phase and out-of-phase biaxial cyclic loadings with constant amplitude. T HE C-S CRITERION multiaxial fatigue criterion based on the so-called critical plane approach has been proposed by Carpinteri and Spagnoli to estimate the high-cycle fatigue strength (either endurance limit or fatigue lifetime) of both smooth and notched structural components [12-17] . The main steps of the C-S criterion are as follows: (i) Averaged directions of the principal stress axes are determined on the basis of their instantaneous directions; (ii) The orientation of the initial (hereafter termed critical) crack plane and that of the final fracture plane are linked to the averaged directions of the principal stress axes (two material parameters are required at this step: fatigue limit 1,   af under fully reversed normal stress, and fatigue limit 1,   af under fully reversed shear stress); (iii) The mean value and the amplitude (in a loading cycle) of the normal stress and shear stress, respectively, acting on the critical plane are computed; (iv) The fatigue strength estimation is performed via a quadratic combination of normal and shear stress components acting on the above critical plane (in the case of finite-life fatigue evaluation, two further material parameters are required at this step: the slope m of the S-N curve in the high-cycle regime under fully reversed normal stress, and the slope * m of the S-N curve in the high-cycle regime under fully reversed shear stress). In the following sub-sections, the C-S criterion is briefly reviewed, and an extension to the fatigue assessment of welded structural components under in- and out-of-phase loadings is discussed [18] . Averaged directions of the principal stress axes At a given material point P , the direction cosines of the instantaneous principal stress directions 1 , 2 and 3 (being       t t t 3 2 1    ) with respect to a fixed PXYZ frame can be worked out from the time-varying stress tensor   t σ . Then the orthogonal coordinate system P123 with origin at point P and axes coincident with the principal stress directions (Fig.1) can be defined through the ‘principal Euler angles’,    , , , which represent three counter-clockwise sequential rotations around the Z -axis, Y  -axis and 3 -axis, respectively (   2 0  ;    0 ;   2 0   ). The procedure to obtain the principal Euler angles from the direction cosines of the principal stress directions consists of two stages, described in Ref .[12] . The averaged directions of the principal stress axes 2ˆ,1ˆ and 3ˆ are obtained from the averaged values    ˆ ,ˆ ,ˆ of the principal Euler angles. Such values are computed by independently averaging the instantaneous values       t t t    , , as follows [12,13]:     dt tWt W T   0 1 ˆ       dt tWt W T   0 1 ˆ       dt tWt W T   0 1 ˆ   (1) A