Issue 41

V.M. Machado et alii, Frattura ed Integrità Strutturale, 41 (2017) 236-244; DOI: 10.3221/IGF-ESIS.41.32 239 propagate during their service lives. However, despite self-evident, this prudent requirement is still not included in most SN and  N fatigue design routines used in practice. In fact, most long-life designs just intend to maintain the service stresses at the structural component’s critical point below its fatigue limit,  <  S LR /  F , where  F is a suitable safety factor for fatigue applications. So, although such calculations can be quite complex (e.g. when analyzing fatigue crack initiation caused by random multiaxial non-proportional loads), their so-called safe-life philosophy is not intrinsically safe. However, despite neglecting the effect of any cracks or crack-like defects, most long-life fatigue designs do work quite well in practice. This means that they are in fact somehow tolerant to undetectable or to functionally-admissible short cracks. Nevertheless, the question “how much tolerant” cannot be answered by SN and  N procedures alone. This potentially important problem can be dealt with by adding short crack concepts to their infinite life design criteria, which may be given (in its simplest version) by                 R 12 th F R K a g a w 1 a a ( ) ( ) , R R th L      2 R a 1 K S ( ) ( ) (4) Since the fatigue limit  S LR at a given fixed {  , R } condition already reflects the effect of microstructural defects inherent to the material, Eq. (4) complements it by describing the tolerance to small cracks that may go unnoticed in actual service conditions. A practical example can illustrate well how these ideas can be useful in engineering applications. Due to a rare manufacturing problem, a batch of a small but important structural component was delivered with tiny scratch-like elongated surface cracks only detectable by under a microscope, causing some serious unexpected failures when mounted in the machine it usually worked forever. The question is how to estimate the effect of such small crack-like defects in the fatigue strength of those components, knowing that each piece has a 2 by 3.4mm rectangular cross-section and is made of a steel with ultimate strength S U = 990MPa and (uncracked) fatigue limit S L = 246MPa . The piece fatigue limit is about S U /4 , whereas steels typically have S L  S U /2  495MPa . This difference may be due to a surface finish factor k sf  0.5 , a value between those proposed by Juvinall for S U  1GPa steels with cold-drawn or machined surfaces , 0.45  k sf  0.7 [13]. Although surface finish should not affect the growth of fatigue cracks, the measured value could be due to other factors as well, like e.g. tensile residual stresses near the piece surface. Hence, the only safe option is to use S L  246MPa to evaluate the short crack effects, estimating the fatigue limit at R >  1 (or at  m > 0 ) e.g. by Goodman as S L (R)  S LR  S L S U ( 1  R ) / [ S U ( 1  R )  S L ( 1  R )] . The FCG threshold is also needed to model short crack effects. If data is not available, as in this case, it must be estimated e.g. by  K th ( R  0.17 )   K th0 = 6MPa  m and  K thR ( R > 0.17)  7  ( 1  0.85R ) [4]. This risky practice increases the prediction uncertainty, but it was the only option available. However, this estimate is conservative regarding typical data, which tend to indicate 6 <  K th0 < 12MPa  m . Moreover, it assumes  K thR ( R < 0 )   K th0 , usually a safe estimate as well (unless the load history contains severe compressive underloads that may accelerate the crack, not the case here). Using the SIF of an edge-cracked strip of width w loaded in mode I [4], Fig. 2 shows the tolerable stress ranges under pulsating axial loads estimated within a fatigue safety factor  F by:                                  0 th F 0 12 3 0 K a a a 2w a a a 0 752 2 02 0 37 1 1 w a 2w 2w 2w a sec tan . . . sin (5) This simple (but quite reasonable) model indicates that the studied structural component tolerates well small edge cracks up to a  30  m , since they almost do not affect its original fatigue limits. However, since this conclusion is based on estimated properties, Fig. 3 evaluates the influence of the threshold  K th0 and of the data-fitting exponent  on the values estimated for the tolerable stress ranges, enhancing how important it is to measure them to obtain less-scattered predictions. Nevertheless, in spite of this scatter, such estimates can be very useful for designers and quality control engineers. They can be used e.g. as a quantitative tool if a production or an operational accident damages the surface of otherwise well-behaved components, to help deciding whether they can be kept in service or must be recalled. These estimates provide interesting results, but they have some intrinsic limitations. They assume the short crack grows unidimensionally, thus can be characterized by its size a only, when surface flaws much smaller than the piece dimensions probably look like small surface or corner cracks, and should be treated as so. 2D cracks grow by fatigue in two directions, usually changing their shape at every load cycle, although maintaining their original plane under mode I loads, see [4]. In