Issue 35

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 35 (2016) 456-471; DOI: 10.3221/IGF-ESIS.35.52 462 Figure 3 : Definitions of K Values, Schijve [50]. The application of  K eff is considerably complicated by two problems: (1) small cracks and (2) threshold  K values (  K th ). Small cracks can be significant because in many cases a relatively large part of the fatigue life is spent in the small crack length regime. The threshold problem is particularly relevant for fatigue under variable amplitude spectrum, if the spectrum includes many “small” cycles. It is important to know whether the small cycles do exceed a threshold  K value, and to which extension it will occur. The application of similitude concept in structures can help so much, but the results correlation is not satisfactory and the arguments normally are:  The similarity can be violated because the crack growth mechanism are no longer similar  The crack can be too small for adopting K as a unique field parameter   K eff and others conditions being nominally similar, it is possible that other crack tip aspects also affect crack growth, such as crack tip blunting and strain hardening, Schijve [50]. Newman and Armen [51-53] and Ohji et al. [54] were the first to conduct the two dimensional analysis of the crack growth process. Their results under plane stress conditions were in quantitative agreement with experimental results by Elber [28], and showed that crack opening stresses were a function of R ratio (S min /S max ) and the stress level (S max /  0 ), where  0 is the flow stress i.e: the average between  ys and  u . Blom and Holm [55] and Fleck and Newman [56-57] studied crack growth and closure under plane-strain conditions and found that cracks did close but the cracks opening levels were much lower than those under plane stress conditions considering same loading condition. Sehitoglu et al. [58] found later that the residual plastic deformations that cause closure came from the crack. McClung [59-61] performed extensive finite element crack closure calculations on small cracks at holes, and various fatigue crack growth models. Newman [62] found that S max /  0 could correlate the crack opening stresses for different flow stresses (  0 ). This average value was used as stress level in the plastic zone for the middle crack tension specimen, McClung [61] found that K analogy, using K max /K 0 could correlate the crack opening stresses for different crack configurations for small scale yielding conditions where K 0 =  o  (  a) . ( K -analogy assumes that the stress-intensity factor controls the development of closure and crack-opening stresses and that, by matching the K solution among different cracked specimens, an estimate can be made for the crack opening stresses). Matos & Nowell [63] present a literature review of the phenomenon of plasticity-induced fatigue crack closure under plane strain conditions and mention that there are controversial topics concerning the mechanics of crack propagation. In general there is no consensus in the scientific community. Fleck [64] used finite elements to simulate plasticity induced crack closure under plane strain conditions and predicted that the nature of the closure process changes from continuous to discontinuous after a sufficient increment of crack growth. He suggested that closure involves only a few elements relatively distant from the current crack tip and the closure levels decay steadily as the crack grows beyond its initial length. In the limit, the closure would not occur at all. Tab. 3 presents an adapted chronologic review crack advance scheme from Matos & Nowell [63].