Growth of very long ‘‘short cracks’’ initiated at holes P. Lorenzino, A. Navarro ⇑ Departamento de Ingeniería Mecánica y de los Materiales, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain article info Article history: Received 30 September 2013 Received in revised form 26 March 2014 Accepted 26 March 2014 Available online xxxx Keywords: Short crack Microstructural barrier Grain size Notch Fatigue crack initiation abstract The initiation and growth behavior of very long microstructurally short fatigue cracks formed at circular holes is described. Very long here means cracks which are several millimeters or even centimeters long. Microstructurally short refer to the fact that these cracks, in spite of their physical length, are still smaller than the grain size of the material and thus exhibit the characteristic features of such cracks. Growth retardation or even halt at grain boundaries and fluctuating crack growth rates can readily be observed with the naked eye by employing a experimental technique which allows one to increase the grain size of Al1050 Aluminum alloy until the centimeter scale by applying a series of mechanical and heat treatments. Once the thermo-mechanical treatment is completed and the desired grain size obtained, a circular notch is machined on each specimen, and the samples are subjected to fatigue loading. With this method, interactions between cracks and microstructural barriers can be studied with an unprecedented level of ease and detail. An interesting observation is that the location of the crack initiation point along the hole contour varies greatly with the ratio between the hole diameter and the grain size: for large ratios, the initiation point is located close to the point corresponding to the maximum circumferential stress (the horizontal symmetry axis in our case), but for smaller ratios, however, the point of crack initiation moves markedly away from the symmetry axis. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction The problem of the characterization of the crack tip stress and strain fields for fatigue problem has a long history. The inauspi- cious beginnings of the characterization of fatigue crack growth rate of long cracks by the stress intensity factor range as described in the Paris law is a well-known episode in fracture mechanics lore. There, a single parameter embodies the physics of the problem and crack growth rate can be expressed as a unique function of DK irre- spective of the geometry of the component or the type of load applied. Dimensional analysis arguments (Navarro and de los Rios [1]) show that fatigue crack growth rate can indeed be expected to depend on DK alone when the size of the plastic zone relative to the crack length does not change. Consider a fatigue crack growing in an infinite medium (see Fig. 1, taken from [1]). As it is well known, the growth of a crack by fatigue depends on the plasticity generated at the tip of the crack. The dimensional analysis should then consider the length a of the crack and a new characteristic length c representing the extent of the plastic zone. Then, the rate of crack growth can be shown to be given by da dN ¼ C  DK m  a c  n ð1Þ But, of course, for long cracks and for the values of applied stress in which LEFM is considered to hold, s=s y < 0:3, the Dugdale relation a c ¼ cos p 2 s s y   ð2Þ gives values of between 0.9 and 1 for the ratio a=c, and therefore, neglecting this variation above, the Paris law is obtained da dN ¼ C   DK m ð3Þ When plasticity is more extensive, the term a=c should be taken into account and the parameter DK on its own does not describe physical similarity either. Attention is also drawn to the idea that the Dug- dale-type relationship describes the self-similar growth of the crack across an ideal homogeneous body, where there is no distinguish- able microstructural feature that may be used to define any intrinsic unit of length. It is only in these conditions that single parameter characterizations of fatigue crack growth would be applicable. Microstructurally short fatigue crack growth is thus a prime example of a situation where a single parameter characterization of the crack stress and strain fields does not seem to be entirely appropriate. It is a very important problem from the practical point http://dx.doi.org/10.1016/j.ijfatigue.2014.03.023 0142-1123/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +34 954487311; fax: +34 954487295. E-mail address: navarro@us.es (A. Navarro). International Journal of Fatigue xxx (2014) xxx–xxx Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue Please cite this article in press as: Lorenzino P, Navarro A. Growth of very long ‘‘short cracks’’ initiated at holes. Int J Fatigue (2014), http://dx.doi.org/ 10.1016/j.ijfatigue.2014.03.023