Issue 24

A. A. Shanyavskiy, Frattura ed Integrità Strutturale, 24 (2013) 13-25; DOI: 10.3221/IGF-ESIS.24.03 22 exceed the number of flights of an aircraft and, in some discs, respond to over 50% operating time (assuming one striation formed by one start-and-shut-down cycle of the engine (see Tab. 2). Validity of using the above-mentioned relationship was evaluated based on the test results obtained for P-3 disk installed in an engine (see Fig.8). Having quantitatively estimated the fractographic parameters of fatigue fracture of turbine disks bench tested by ECP loading in an engine, we established that a single fatigue striation with a respective crack increment formed per each one-flight cycle under the takeoff conditions. The stresses applied to the disk during ECP were significantly lower in such a bench test regime than in service. Using the fracture-mechanics approach, we compared the stressed states of the disks in the bench tests and in service. For the discussed case of semi-elliptic crack a well-known formula of e K equivalent stress-intensity factor is applicable [17]:     / / e e K a c a        (2) In Eq.2, Ф(с/а) is the elliptic integral of the secondary type, whose value depends on the ratio (с/а) of semi-elliptic-crack axes in any crack-growth direction. In our case, term “equivalent” means that fractographic estimation of stresses based on fatigue striations value related to material reaction on its complicated stress-state. This reaction is equivalent in stress level with opened propagated crack by Mode I. The Eq.2 can be applied correctly to the crack starting from a distance of 1 mm or greater from the in-hole surface of the disk: at that distance, effect of the surface-stress concentration is negligibly for crack-growth over the length in 1 mm. However, the calculated equivalent stress is totally expressive of all the strengthening-and-weakening effects of prominent plastic deformation typical of even the very first loading cycle of low-cycle fatigue. We should stress on that the cracks to be in-service detected belong to a small kind as concerns a crack length (within 1 mm) and the growth behavior of fatigue- striation spacing (linearly dependent of the crack length). For such cracks, using the concepts of strain-range or J-integral would be of greater accuracy and meaning than the concept of stress because of well-developed plastic deformation. Nevertheless, when estimating a relationship between the characteristics of material behavior in service and in bench tests, the concept of equivalent stress remains still proper. Indeed, irrelevant to the way of loading, a value of striation spacing always corresponds to just a respective unique value of stress-intensity factor, completely determined by a respective equivalent stress [4, 6]. The disk material exhibits maximum stress intensity factor max ( ) e K = 70 MPa m 1/2 at the moment that the growth behavior of a fatigue crack changes from steady to unsteady, the value of fatigue-striation spacing being close to 1.2  m. One can see that both from the Paris’ curve in term of crack growth rate and fracture morphology of the material. We calculated elliptic integrals for the boundaries between Zone-I and Zone-II fractures of the broken P-1 and P-2 disks and for the line of 1.2  m striation spacing in one of the opened cracks which were also discovered in P-1 disk; the integrals appeared 1.0158, 1.0325, and 1.09, respectively. With the cracks dimensions and the respective above-calculated values substituted to Eq.1, we calculated  e as 1130, 1320, and 1180 MPa. The calculations could be done owing to fractographic examination of those broken disks and artificially opened fatigue crack. Thus estimated equivalent stresses approximate to those acquired from the finite-element analysis of a complex stressed state of a disk with the shear stresses taken into account [11]. The above stress figures appear to exceed more than twice the stress level commonly acceptable for the disks. Accordingly, the disks bolted to the shaft through the holes in this particular way must be of a low expected durability. We compared how much the disks were loaded in the bench-tests and in service. In so doing, we assumed that the stress- intensity factors are the same for the same values of fatigue-striation spacing irrespective of the loading prehistory of the disks because there were not discovered difference in material properties for all investigated disks. The stress- and strain- intensity factors were both discussed as representative of a stress pattern whether in bench-tests or service. From a comparative analysis, one can have a characteristic indicating how much the disks were stressed relative to one another. Hence, we can write,     0 e e t K K  for  = 1.2 mm (3) or         1/2 0 0 0 / / / / e e t t t a a      (4)