Issue 35

R.A. Cardoso et alii, Frattura ed Integrità Strutturale, 35 (2016) 405-413; DOI: 10.3221/IGF-ESIS.35.46 406 divided in two groups: type 1 when crack initiation is mainly influenced by the range of the shear stress Δ τ , and type 2 when the range of normal stress Δ σ n governs the process. Figure 1 : Scheme of classical stages of crack initiation and short crack propagation. In [3], where tests were conducted in low carbon steel weakened by U-notches to study the high cycle fatigue cracking behaviour, was verified that Stage I, in this kind of stress raiser, is governed by a mixed mode, since the crack profile in Stage I was not parallel to the notch bisector line. It was also noted that the irregular mixed mode dominated path was confined within a distance from the notch tip of the order of L , the material characteristic length, Eq. (1). 2 1 1             th K L (1) where Δ σ -1 is the plain fatigue limit and Δ K th is the threshold value of stress intensity factor range, both for a load ratio of -1. Considering these assumptions, two multiaxial criteria based on the theory of critical distances will be applied to estimate the initial crack direction, Fig. 2. Early stage of crack propagation-The critical direction method combined with the TCD (the critical direction method) The theory of critical distances (TCD) [4] can be used in association with any fatigue criterion [5]. So based on the hypothesis that in stage I one may have cracks dominated by the maximum range of normal stress (crack type 2), the crack orientation will be defined here by a line of length 2L, inclined by an angle θ σ with respect to the y axis, which maximizes θ in Eq. (2), Fig. 2a. Therefore, an important aspect that one should notice in Eq. (2) is that the maximum range of normal stress is always computed perpendicular to the line defined by angle θ , i.e, the line 2L (inclined by θ ) is discretized in many material points and the maximum normal stress range is calculated for the same plane θ for all these points. This procedure provides the critical orientation θ σ that a crack of length 2L would have in theory in its stages of initiation and early growth. A similar approach can be used to find the direction that minimizes the shear stress amplitude, Δ τ , Eq. (3). The mechanical basis to support this hypothesis is the fact that, in these planes, less energy is wasted with friction and consequently more energy is available for crack propagation [7].          dr r L L ) ,( 2 1 max 2 0       (2)          dr r L L r ) ,( 2 1 min 2 0       (3) In Eqs. 2 and 3 the integrals are carried out over a constant length 2L, as defined by the so-called Line Method (LM). In a similar way one could assume the point or the area method (for 2D problems) [6], but these will not be assessed here due to space constraints.