P. Gallo et alii, Frattura ed Integrità Strutturale, 34 (2015) 180-189; DOI: 10.3221/IGF-ESIS.34.19 181 surface roughness on the crack initiation. These topics, especially if considering notched components at high temperature and high number of cycles, are ignored in the modern literature. However, it is possible to find some interesting works briefly reported hereafter. Dealing with un-notched specimens, the fatigue behavior of different materials at high temperature has been investigated in [1–3]. In [1] an experimental investigation was conducted on 22Cr-20Ni-18Co-Fe alloy at elevated temperature using plain specimens. Fatigue tests were carried out at a constant temperature (871°C) while the strain ranged from 0.265 to 1.5 %. The fatigue lives varied from 10 3 to 10 6 cycles to failure. Cyclic deformation properties of the tested material were obtained from the tests and three fatigue models were applied discussing the advantages and drawbacks of each model. The fatigue properties and crack growth mechanism of a 2.25Cr–1Mo steel were investigated in [2]. The work was aimed to study the fatigue life up to 10 7 cycles of structural components used in hot and high-pressure environments. The tests were conducted on un-notched specimens in a temperature range varying between 20 and 500°C. The high-cycle fatigue life was found to be strongly influenced by the density and size of interior inclusions. While results from un-notched materials are not so rare in the past and recent literature as just discussed, only few systematic investigations have been performed on notched specimens under fatigue loading at high temperature at medium-high cycle fatigue [4–6]. In [4,5], the notched fatigue strength of the nickel-base superalloy Inconel 718 was investigated under rotating bending loading at room temperature and 500°C in air. The linear notch mechanics was employed to assess the fatigue strength at elevated temperatures being for that material the small-scale yielding condition satisfied also at elevated temperature. The effect of notch types and stress concentration factors on low cycle fatigue life and cracking of the DZ125 directionally solidified superalloy was experimentally investigated by Shi et al. [7]. Single-edge notched specimens with V and U type geometries were tested at 850 °C with a stress ratio R=0.1. The main conclusion of the paper was that K t can be considered as a key parameter controlling the notch fatigue at least when the absolute dimensions of the tested notched specimens are similar. In some recent contributions, the present authors have summarized the results from uniaxial tension load-controlled fatigue tests performed at high temperature on different materials. Berto et al. [8] investigated the high temperature fatigue up to 650°C of notched and un-notched Cu-Be specimens. All fatigue data have been reanalyzed there in terms of the mean value of the strain energy density evaluated, for the notched specimens, over a finite size control volume surrounding the highly stressed zone at the hole edge. This has permitted to summarize all fatigue data in a quite narrow scatter band. Gallo et al. [9] presented data from uniaxial-load controlled fatigue tests on notched specimens made of titanium Grade 2 at 500°C. Two geometries were considered: semicircular notches and plates weakened by lateral symmetric V-notches. Also in this case, the fatigue data from un-notched and notched specimens have been reanalyzed in terms of the mean value of the strain energy density. This has permitted to summarize all fatigue data in a single narrow scatter band, regardless of the specimen geometries. Other authors have recently extended linear elastic approaches to assess high temperature fatigue, such as Louks and Susmel [10] that investigated the accuracy of the linear-elastic Theory of Critical Distances (TCD) in estimating high-cycle fatigue strength of notched metallic materials, experiencing elevated temperatures during in-service operations with very sound results. The number of paper remains very poor if considering works on the influence of the surface roughness on the fatigue behavior at high temperature. However it is a very interesting topic from industrial viewpoint since the investigation of the cooling channels roughness on the high temperature behaviour and the cracks initiation can lead to several advantages: first of all, it defines quantitatively the influence of the surface roughness on the fatigue performances, and therefore justifies the costs to obtain a high surface finishes quality. This makes possible to evaluate in terms of cost-benefit analysis the choice of imposing a low surface roughness or, otherwise, high surface roughness. An interesting work is presented by Kim et al. [11] on the sensitivity of surface crack initiation to surface roughness in LCF at 550 °C of AISI 404L and Cr-Mo-V steel, in a pure argon atmosphere, also under creep-fatigue interaction condition. The creep-fatigue interaction was achieved by the introduction of tensile hold time. Two different states of surface finishes were obtained by mechanical polishing with emery papers of grade 80 and 1200 respectively. For Cr-Mo- V steel specimens, the maximum value for the depth of the surface polished with emery paper 80 and 1200 are about 8.0 and 0.4 μm respectively. The result of the tests shown that for Cr-Mo-V steel the fatigue life of the specimen polished with emery paper no. 80 is significantly reduced (about 50%) compared with that of the specimen polished with emery paper no. 1200. The same trend was registered independent of the creep-fatigue interaction condition, which is a very important consideration. Since the surface roughness affects only the surface phenomena like crack initiation, they concluded that the number of cycles for crack initiation was a large fraction of the fatigue life, both in the case of pure fatigue or fatigue-creep interaction. This is a very important conclusion because supports the significance to investigate the influence of the surface roughness on the crack initiation since this phase is the one that involves a large fraction of fatigue life. Moreover, they observed that no grain boundary cavitation was detected during the tests and the fracture