Issue 41

M. Vormwald et alii, Frattura ed Integrità Strutturale, 41 (2017) 314-322; DOI: 10.3221/IGF-ESIS.41.42 315 generally accepted and validated formulation of a crack force parameter still needs to be identified [2]. Moreover, experimental investigations for the 3D mixed mode load to validate existing predicting assumptions need to be further developed [4]. The present paper discusses 2D and 3D formulations for equivalent SIFs for complex mode problems, presented by Erdogan and Sih [9], by Schöllmann et al. [3] and by Richard et al. [4-6], under the light of experiments carried out by Vormwald and his co-workers [10, 11]. These experiments used digital image correlation, DIC, to measure full-field displacement and derived data for 3D tested specimens. The acquired data made possible the determination of relative crack flank opening displacements, COD, and their associated mode I, II and III SIFs, as well as the calculation of equivalent SIFs and tangents to crack paths for cases of mixed-mode variations (inside one cycle and from cycle to cycle) using the above mentioned formulations. E XPERIMENTAL METHODS onstant amplitude fatigue tests have been performed using thin-walled tubes under alternated tension- compression (force F ranging from 45kN to -45kN) and torsion (moment M ranging from 532 Nm to -532 Nm). Data was acquired from five different loading sequences applied to individual specimens [2-3]: pure alternated tension-compression loading (specimen R-028), pure alternated torsion loading (specimen R-029), proportional alternated tension and torsion loading (specimen R-030), and out-of-phase loading with phase angles of 45° (specimen R-033) and 90° (specimen R-031). The load ratio was R F = R M = -1. The specimen geometry is shown in Fig. 1. The specimens were machined from longitudinally welded tubes. The individual specimens were saw-cut and the slits or notches were milled. Two holes, with a diameter of 4 mm, were drilled with a distance of 10 mm from the centers of the holes (length of an arc measured at the outer surface). The notch was positioned opposite to the longitudinal weld. The material was constructional steel S235 with the following mechanical properties: Young’s modulus, E = 214GPa, yield strength (0.2% plastic offset), S y = 310MPa, ultimate tensile strength S u = 435MPa, and the parameters of the cyclic Ramberg-Osgood stress-strain curve, K’ and n’ , respectively equal to 1170MPa and 0.239. Figure 1 : Specimen geometry (mm) The experiments have been conducted under load and moment control, respectively, using a servo-hydraulic, four-pillar tension-torsion testing machine with frequencies between 0.1 Hz (when necessary, during 3 cycles for DIC data acquisition) and 2 Hz. The cracks were assumed to be through-wall cracks with a straight crack front. The crack length is defined as the arc length with the arc measured starting at the crack initiation location. Depending on the loading type, two, or four cracks were observed [10, 11]. D ETERMINATION OF STRESS INTENSITY FACTORS FROM CRACK - FLANK OPENING DISPLACEMENTS he determination of SIFs, K i (i = I, II, III) was based on their relationship with relative crack flank opening displacements, COD i , [12] as given by Eqs. (1). Generally, points A and B are symmetrically located over the crack faces (  ~+π) and near the crack tip (small local crack path curvature and coordinate r << crack length a), as illustrated in Fig. 2. In Eq. (1) U’, V’ are in plane displacements respectively in the parallel and orthogonal crack directions and W’ is the out of plane displacement. Polar coordinates are referred to the tangent and orthogonal axes relative to the crack line. C T