PSI - Issue 37

Jesús Toribio et al. / Procedia Structural Integrity 37 (2022) 1029–1036 Jesús Toribio / Procedia Structural Integrity 00 (2021) 000 – 000

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Fig. 2b shows analogous K -results at the center of an intermediate crack ( a/b =0.5). Results behave in a similar manner to that of the straight crack, i.e., clear SIF overestimation of the results by Levan and Royer and lower K values if bending is restrained. However, other results are closer between them, so that a unique SIF solution could be taken and again results by Astiz perform the best. Previous comments also apply to the center of circular cracks ( a/b =1.0), cf. Fig. 2c. In this case numerical results fit even more closely, so that no over- or under-estimation of SIF is detected and a really unique polynomial expression could be extracted form the general trend. In this case of a circular crack, the SIF is not maximum at the crack center, but at the crack ends (sample surface). In the matter of the crack ends (specimen surface), only results by Carpinteri, Levan-Royer, Shih-Chen and Shin Cai (with free ends and constrained ends) are available in usable form, cf. Fig. 3. These three plots always show the same trend: (i) overestimation of K in the case of Levan and Royer (ii) underestimation of K in the case of constrained ends ( C -solution by Shin and Cai). In addition to the described review of K -solutions published in the scientific literature, and to have a complete picture of the problem, previous results are compared with the solutions proposed by the British Standard BSI 7910:1999 in Figs. 4 and 5 in the matter of the crack center (point A) and the cylinder surface (point B). The British Standard BSI 7910:1999 exhibits some weak points with regard to the SIF calculated from the paper by James and Mills (1988). In particular, it only considers the straight-fronted and circular cracks, but no other aspect ratios (different a / b) . In addition, it is simply a uniparametric K -solution as a function of only the relative crack depth a / D , so that the curvilinear coordinate representing the specific location at the crack front is not taken into account and, moreover, results at the crack center and at the cylinder surface are frequently mixed with really unacceptable scattering band. This important issue of the different SIF values at the crack center and at the cylinder surface is addressed and clarified by Toribio (1992a). The numerical results by Levan and Royer clearly overestimate the SIF over the whole range of crack depths (from shallow to deep cracks) and crack aspect ratios (from quasi-straight to very curved cracks). This over-estimation of K , although leading to conservative engineering design associated with lower risk of catastrophic failure, might lead to an undesired increment of costs, so that this solution should be disregarded. Moreover, results by Couroneau and Royer (slightly below the general trend) fairly contradict those by Levan and Royer (well above the average trend), a reason why the latter should be disregarded too as not very adequate. With regard to the results by Shih and Chen, they should be used with caution, since in some cases the fitting procedure produces negative K -values (Cai and Shin, 2004) so that it must be used with care in engineering since could provide non-conservative underestimation of SIF, or even an absurd negative value. Other numerical results of the SIF at the crack center or surface of a semielliptical part-through crack (Valiente, Astiz, Carpinteri, Shin-Cai) work really well when plotted against the relative crack depth (see Figs. 2 and 3), with In fracture mechanics approaches, damage tolerance analyses or structural integrity assessments in engineering, the solutions that should be taken in consideration are those by Valiente, Astiz, Carpinteri and Shin-Cai (both for free ends and for constrained ends). The summary of the characteristics of these solutions is as follows: (i) Valiente proposed a couple of one-parameter K -solutions (global and local) as a function of only the relative crack depth ( a/D ), they being valid only for the crack center of straight-fronted edge cracks. (ii) Astiz and Carpinteri computed a two-parameter K -solution as a function of both the relative crack depth ( a/D ) and the crack aspect ratio ( a/b) . When the SIF value is required not only at the crack center but also at the crack surface, the two-parameter K -solution obtained by Carpinteri is a reasonable option. (iii) Shin and Cai obtained a couple of three-parameter K -solutions (for free and constrained ends) as a function of the relative crack depth ( a/D ), the crack aspect ratio ( a/b) and the position at the crack front ( x/h ), cf. Fig. 1. These solutions are very adequate for analysis of crack shape evolution in fatigue crack propagation. the logical increasing trend of K versus a/D . 4. On the most adequate SIF solutions