Issue 33

F. Castro et alii, Frattura ed Integrità Strutturale, 33 (2015) 444-450; DOI: 10.3221/IGF-ESIS.33.49 445 Wöhler Curve Method (MWCM) [11] was applied at a point located at a critical distance below the trailing edge of the contact. Estimates of fretting fatigue thresholds fell within an error interval of ±20% when compared to experimental data. The methodology proposed by Araújo et al. [6] is only applicable to design situations involving threshold conditions. In this paper, an extension of this approach to the medium-cycle fatigue regime is presented. A first attempt to assess the new methodology is carried out based on available fretting fatigue tests [1]. M ULTIAXIAL FATIGUE LIFE ESTIMATION he MWCM [10-12] is a multiaxial stress-based critical plane approach where the driving parameters for crack nucleation are the maximum shear stress amplitude,  a , and the maximum normal stress acting on the maximum shear stress plane,  n,max . Once the values of  a and  n,max have been evaluated, the stress ratio  is defined as n,max a     (1) It is noteworthy that  is sensitive not only to mean stresses, but also to the degree of multiaxiality and non- proportionality of the stress path [10]. Also, it is worth recalling that for an unnotched specimen under fully reversed uniaxial loading the  ratio is equal to unity, whereas under fully reversed torsional loading  equals zero [10]. The MWCM is based on a modified Wöhler diagram where  a is plotted against the number of cycles to failure, N f (Fig. 1). This diagram is made of different fatigue curves, each one corresponding to a certain value of  ratio and being unambiguously described by its negative inverse slope  and by a reference shear stress amplitude,  A,Ref , corresponding to an appropriate number of cycles to failure, N A . To obtain the diagram, one should properly define the  vs.  and  A,Ref vs.  relationships, and correctly calibrate them by running appropriate experiments. The following linear relationships have been found by Lazzarin and Susmel [12] to correlate a wide range of experimental data: ( ) b a      (2) A,Ref ( ) c d      (3) where a , b , c and d are material constants. When these constants are obtained from fully-reversed uniaxial and torsional tests on plain specimens, Eqs. (2) and (3) are stated as Figure 1 : Modified Wöhler diagram. ( ) [ ( ) ( 1 0)] ( )0                (4) 0 A,Ref 0 0 ( ) 2                (5) where  (  =1) and  0 are, respectively, the inverse slope of the modified Wöhler curve and the fatigue limit under uniaxial loading condition, whereas  (  =0) and  0 are the corresponding quantities for torsional loading. It is noteworthy that, for T