Issue 33

M. Vormwald, Frattura ed Integrità Strutturale, 33 (2015) 253-261; DOI: 10.3221/IGF-ESIS.33.31 254 M ULTIAXIAL FATIGUE CRACK INITIATION he macroscopic appearance of early fatigue crack initiation is similar under uniaxial, proportional, or non- proportional loading. In all cases short cracks initiate at microscopically small defects. A stage of stable fatigue crack growth follows. The crack selects a plane of growth which is usually termed critical plane. Therefore, the critical plane approaches to multiaxial fatigue assessment are among the most preferred approaches. Variants of this approach are explained in the standard text book of Socie and Marquis [3]. As an example, Fig. 1 shows fatigue cracks initiated under uniaxial and severely non-proportional multiaxial loading. The crack growth has been monitored by Hoffmeyer [4] who applied the replica technique. A part of this investigation has been published earlier in references [5] and [6] where more details can be found. a) 50  m b) Figure 1 : Appearance of short fatigue cracks in AW5083 (also nominated as AlMg4.5Mn or Al5083), a) uniaxial loading with 0.3% a   , b) multiaxial non-proportional pseudo-random strain sequence, straight-line cumulative frequency distribution ,max 0.346% a   , ,max 0.6% a   and a phase shift of 90° between the normal and the shear strain signal, Hoffmeyer [4]. Challenge 1: Crack driving force It suggested itself to model the mechanisms by means of fracture mechanics [7-19]. Naturally initiating cracks require stress and strain amplitudes of a magnitude that usually prevents the application of linear elastic fracture mechanics. A crack driving force from the collection of elastic-plastic fracture mechanics is selected. The first challenge is to define a reasonable and applicable formulation. Strain based intensity factors and variants of the cyclic J  -integral are used. Here, some results are reported which adapted a formulation based on approximation formulas assumed to provide an estimate of the J  -integral. 2 I,eff I ,eff 2 x J Y W a     (1) 2 II,eff II eff / (1 ) xz J Y W U a       (2) 2 III,eff III eff xy J Y W U a     (3) These formulas are supposed to be valid for semi-circular surface cracks. The x -coordinate is perpendicular to the crack area. Besides geometry factors Y for the three opening modes, the estimates rely on a proportionality between the direction-related portions of the strain energy density range, ij W  , and the corresponding mode-related J  -integral. A numerical check of the accuracy of this assumption is pending. T