Issue 38

H. Wu et alii, Frattura ed Integrità Strutturale, 38 (2016) 99-105; DOI: 10.3221/IGF-ESIS.38.13 100 Case B shear microcracks, which grow on planes that make an angle  = 45 o with the free surface, see Fig. 1. To compact and hopefully clarify the critical plane notation in this work, Case A tensile planes are represented as A90(T), Case A shear as A90(S), and Case B shear as B45(S), where 90 or 45 come from their   angles in degrees with respect to the free surface. A90(T) or A90(S) microcracks only involve one normal and one shear stress/strain component, so normal or shear ranges are quite easy to calculate under variable amplitude loading (VAL) conditions using classic uniaxial rainflow procedures. However, B45(S) microcracks involve in general two shear components, an in-plane stress  A (or strain  A ) and an out-of- plane  B (or  B ), see Fig. 1, which must be properly combined to evaluate their joint effect on fatigue damage. Figure 1 : Non-proportional shear strain path  B   A (or shear stress path  B   A ) acting on a B45 candidate plane (at 45 o from the free surface), for a general loading history. The combination of both usually non-zero  B and  A ranges may cause the initiation of a combined Mode II-III B45(S) microcrack, with  B mainly contributing to increase its depth while  A is mainly tending to increase its width. The combination of  B and  A into an equivalent range  is not a trivial step under general NP loadings, where the  B and the  A histories may be (and usually are) out of phase. This process requires first a 2D rainflow algorithm such as the Modified Wang Brown method [2] to identify every load event from the  B   A (or  B   A ) history. Then, for each identified load event, its path segments are used to calculate a path-equivalent shear stress  (or strain  ) range. The simplest approach for the  B   A diagram is to assume a path- equivalent A B 2 2         for each identified load event, as discussed in [3]. However, this simple equivalent range expression would not be able to tell apart e.g. a rectangular from a less damaging cross-shaped  B   A path with same  B and  A , because both would wrongfully generate the same equivalent shear stress range  . Hence, this path-equivalent range is not a suitable solution to solve these problems in practical applications. Another possible approach is to use the so-called convex-enclosure methods, which try to find circles, ellipses, or rectangles that circumscribe the load-event path in such 2D  B   A or  B   A diagrams. For instance, Dang Van’s pioneer Minimum Ball method [4] searches for the circle with minimum radius that circumscribes each identified load path; the minimum ellipse methods [5-6] search for an ellipse with semi-axes a and b that circumscribes the entire path with minimum area  a  b or minimum “ellipse norm” [a 2 + b 2 ] 0.5 ; and the maximum rectangular hull methods search for a minimum rectangle that circumscribes the path with maximum area or maximum diagonal [7]. The value of the path- equivalent  or  would be assumed as the circle diameter, the ellipse norm, or the rectangle diagonal, which is then used for fatigue damage calculation purposes. However, such convex-enclosure algorithms do not consider the actual shape of the loading path. Instead they substitute the actual load path by some convex enclosures associated with them. Therefore, an infinite number of loading paths associated with different fatigue lives could have the same convex enclosure, wrongfully predicting the same damage if such simplified path-equivalent algorithms are used to calculate it. This issue has been solved with the Moment-Of-Inertia (MOI) method, which has been proposed in [8-9] to estimate path-equivalent stress and strain ranges, as well as their mean components, considering the influence of the shape of the