Issue 30

M. Da Fonte et alii, Frattura ed Integrità Strutturale, 30 (2014) 360-368; DOI: 10.3221/IGF-ESIS.30.43 365 DISCUSSION Stress Intensity Factors ssuming that cracks have always a semi-elliptical shape as shown in Fig. 4, the points on crack front at deepest crack depth (A) and where the crack intersects the external surface (points B and C) are the most important ones. The semi-ellipse axes are obtained according to the equation b=2s/π experimentally obtained [1, 9], and Eq. (1) was deducted.   2 2 2 cos 1 b r 1 sen r a       (1) The major research field of fracture mechanics is the determination of the Stress Intensity Factors. In this study, SIF for mode I and mode III along the crack front of semi-elliptical surface cracks normal to the axis in shafts subjected to bending, torsion and bending-torsion simultaneously, determined by a three-dimensional finite-element analysis [12] will be used. The total arc crack length 2s was chosen as the experimentally obtained crack parameter in fatigue crack growth tests and according to Shiratori et al [11] and Freitas et al [12]. Therefore the mode I Stress Intensity Factor K I for any point along the surface crack was obtained by the equation: s B) , , (F K s a b r b I I    (2) where B S is the remote applied bending stress, s is the half arc crack length and F I is the boundary correction factor or the dimensionless SIF for mode I which is a function of the semi-elliptical crack shape (b/a), relative crack depth (b/r) and of the position points along the crack front defined by the parametric angle Φ , Fig. 3, which was determined taking into account the FEM calculations presented in [12]. As indicated before, limited results for the SIF of semi-elliptical surface cracks in round bars subjected to torsion stress levels are available, and the results presented in [12] are used in this paper. Therefore, SIF K III will be obtained using the same geometric parameters that were used for mode I (bending): s T) , , ( F K s a b r b III III    (3) where T S is the remote applied torsion stress on the outer surface of the shaft, s is the half arc crack length and F III is the boundary correction factor for mode III which is a function of the semi-elliptical crack shape (b/a), relative crack depth (b/r) and of the position along the crack front determined by the referred parametric angle Φ in Fig. 3 that was determined taking into account the FEM calculations described in [12]. Mixed-mode crack growth under multiaxial loading Most of fatigue crack growth studies have been done on single-mode loading and usually are performed under mode I loading condition. However, single-mode loading seldom occurs in practice, and in many cases cracks are not normal to the maximum principal stress direction. The multiaxial mixed-mode fatigue crack growth is a common problem in many engineering structures and components. For long cracks, the propagation mechanisms are often analyzed using linear elastic fracture mechanics approach. Under combined axial and torsion loading, the surface corner of the semi-elliptical crack has mixed mode I+mode II, but at maximum depth of the semi-elliptical cracks has only mixed mode I+mode III [12]. For mixed-mode loading, one can assume that the fatigue crack growth rate may be expressed by the Paris law where the stress intensity factor range is replaced by an equivalent SIF range, ∆K eq :   m eq KC dN da   (4) There are many approaches proposed to define the equivalent SIF range ∆K eq for mixed-mode loadings. One of them is based on the addition of the Irwin’s elastic energy release rate, G parameters for the three loading modes:       2 1 2 III 2 II 2 I 2 1 total eq K v 1 K K E G K          (5) A