Issue 9

An. Carpinteri et alii, Frattura ed Integrità Strutturale, 9 (2009) 46 - 54; DOI: 10.3221/IGF-ESIS.09.05 50 with u  = ultimate tensile strength. Equation (7) is based on the well-known linear interaction between normal stress amplitude and normal stress mean value (diagram of Goodman). In order to transform the actual periodic multiaxial stress state into an equivalent uniaxial normal stress state (with amplitude eqa ,  ), Equation (6) can be rewritten as follows: 1, 2 2 1, 1, 2 , ,                  af a af af eqa eqa C N (8) For fatigue strength assessment at finite life, the fatigue limits 1,   af and 1,   af appearing in Eqs (6) and (8) should be replaced by the corresponding fatigue strengths. Hence, using a Basquin-like relationship for both fully reversed normal stress (   m f af af NN 0 1, 1,     , with    1, af fatigue strength for fully reversed normal stress at finite life f N , and 0 N = reference number of loading cycles, e.g. 2  10 6 ) and fully reversed shear stress (   * 0 1, 1, m f af af NN     , with    1, af fatigue strength for fully reversed shear stress at finite life f N ), Equation (8) becomes:   m f af a m f m f af af eqa N N C N N N N N                                     0 1, 2 *2 0 2 0 2 1, 1, 2 , (9) where the equivalent normal stress amplitude, eqa N ,  , at finite life f N is given by:                  u m m f af a eqa N N N N N 0 1, , (10) Now substituting Eq.(10) into Eq.(9), the number f N of loading cycles to failure can be determined by solving the non- linear equation obtained. E XPERIMENTAL APPLICATIONS AND DISCUSSION n the present section, the above fatigue criterion is applied to some experimental results, obtained from finite-life fatigue tests, related to welded joints subjected to bending (or tension), torsion, in-phase or out-of-phase combined bending (or tension) and torsion [11, 19-21]. Some mechanical characteristics of the materials examined are reported in Ref. [18] . The values of the following material parameters: 1,   af , 1,   af , m and * m , required by the proposed criterion to evaluate fatigue life, are those determined in Ref .[25] by Susmel and Tovo, who analysed the experimental data reported in Refs [11, 19-21]. Note that such parameters have been deduced by Susmel and Tovo [25] analysing the above experimental data found in the literature, except for the data set reported in Ref .[19] , since the S-N curve related to bending cannot be determined due to the limited number of experimental results. Therefore, the values given by Eurocode 3 [2] are herein adopted for the above parameters. The geometries of the specimens examined are circular tube-to-plate joints, box beams with longitudinal attachments and square tube-to-plate joints. The most critical point (point P) for fatigue crack initiation is assumed to be at the weld toe, since cracks in welded structural components often initiate along the weld toes, where high stress concentrations and local geometric irregularities exist. I