Issue 16

L. Susmel, Frattura ed Integrità Strutturale, 16 (2011) 5-17; DOI : 10.3221/IGF-ESIS.16.01 6 Wöhler Curve Method (MWCM) [11]. In more detail, initially we checked the accuracy and reliability of such a criterion in estimating both high-cycle fatigue damage [12, 13] and lifetime [14, 15] of plain engineering materials subjected to multiaxial fatigue loading. Subsequently, attention has been focused on the problem of estimating multiaxial fatigue damage in the presence of stress concentration phenomena [16-19], by also investigating the related problem of designing welded connections against multiaxial fatigue [20-24]. Recently, basing his investigation on several experimental results taken from the literature, Jan Papuga [25] has performed a systematic comparison amongst different criteria in order to select the most accurate one in estimating high-cycle fatigue damage in plain engineering materials subjected to multiaxial loading paths. According to his calculations, he has come to the conclusion that the use of the MWCM results in poor estimates, especially when superimposed static stresses are involved. In our opinion, such an erroneous conclusion has to be ascribed to the fact that Dr. Papuga has applied our approach in a wrong way, by systematically miscalculating the stress quantities relative to the critical planes. Accordingly, in the present paper the main features of the MWCM are initially reviewed by focusing attention mainly on the problem of determining the so-called mean stress sensitivity index. Subsequently, it is proven, through 704 experimental endurance limits generated by testing both plain and notched samples made of 71 different materials, that, when the MWCM is used correctly, it is capable of estimates falling mainly within an error interval of ±10%. F UNDAMENTALS OF THE MWCM he MWCM is a critical plane approach which estimates multiaxial fatigue damage through the maximum shear stress amplitude,  a , as well as through the mean value,  n,m , and the amplitude,  n,a , of the stress perpendicular to the critical plane. According to the fatigue damage model the MWCM is based on [11], the critical plane is defined as that material plane experiencing the maximum shear stress amplitude,  a . From a practical point of view, the combined effect of both  a ,  n,m and  n,a are taken into account simultaneously through the following stress index [13]: a an mn eff m     , ,    (1) In the above identity, mean stress sensitivity index m [13] is a material property to be determined experimentally whose main features will be investigated in the next section in great detail. As to ratio  eff instead, thanks the way it is defined, such a stress index is seen to be sensitive not only to the presence of superimposed static stresses, but also to the degree of non-proportionality of the applied loading path [11]. Turning back to the MWCM, the way it estimates fatigue damage under multiaxial fatigue loading is schematically shown by the modified Wöhler diagram reported in Fig. 1a. The above log-log diagram plots the shear stress amplitude relative to the critical plane,  a , against the number of cycles to failure, N f . By performing a systematic reanalysis based on numerous experimental data [12, 14, 15], it was proven that, as index  eff varies, different fatigue curves are obtained (Fig. 1a). In particular, it was observed that fatigue damage tends to increase as  eff increases: this results in the fact that the corresponding fatigue curve tends to shift downward in the above diagram with increasing of  eff (Fig. 1a). According to the classical log-log schematisation used to summarise fatigue data, the position and the negative inverse slope of any Modified Wöhler curve can unambiguously be defined through the following linear relationships [11, 12, 15]:           k (2)   b a f       Re (3) In the above definitions, k  (  eff ) is the negative inverse slope, while  Ref (  eff ) is the reference shear stress amplitude extrapolated at N A cycles to failure (see Fig. 1a). Further,  ,  , a and b are material constants to be determined experimentally. In particular, by remembering that  eff is equal to unity under fully-reversed loading and to zero under torsional loading [11], constants a and b in Eq. (3) can be calculated directly as follows:   A eff A A eff f                2 Re , (4) T