On Design of Fatigue Resistance Metallic Parts

This paper is devoted to design of metallic parts exposed to low cycle fatigue. Two flat discs, as representatives of these parts, were discussed. The first with 8, and the second with 64 eccentrically arranged holes. Their resistance to low cycle fatigue was investigated. Cyclic properties of two aerospace steels nominated for workmanship, plus planned revolves per minute and revolves per minute of 5% above planned, are taken into account. On the base of estimated low cycle fatigue life data, good design solution was discovered. On the other hand, it was shown that the both mentioned discs would have a large drop of resistance to low cycle fatigue for revolves per minute of 5% above planned.


Introduction
HERE are many metallic parts of machine systems that are required to have satisfying fatigue resistance. Among them are certainly the compressor and turbine disks of aircraft engines, in which resistance to low cycle fatigue (LCF) is important.
Required resistance to LCF of certain disk, or its required low cycle fatigue life (LCFL), can be achieved by good combination assigned geometry, a material chosen for workmanship, and the load level. During assigning of geometry, a designer should devote attention to the stressed areas, as which are rims, hubs and holes of different purposes, in which, to a greater or lesser extent, local plastic strains can be provoked.
This time, the holes of different purposes, their size, number and arrangement, are interesting for us. Here's why. The aircraft accident described in [1] had occurred because of the crack initiation and fracture in the area of holes of one JTD8-15 engine compressor disk. Because of stressed holes of fractured fan disk of the left engine, of aircraft MD-88, occurred accident described in [2]. In the papers [3], [4] and [5], it is discovered that areas with holes are the most stressed areas of analyzed aircraft engine disks.
Useful conclusions regarding the design of fatigue-resistant aircraft engine disks, which will have holes of different purposes, can be drawn from discussing of flat disks.
Here we will discuss two flat disks with eccentrically arranged holes, and we will follow them under the basic marks D1 and D2.
Everything, what we will say, it will be a supplement to the research described in [6] and [7].

Geometries of disks
The flat disks D1 and D2 with their geometries are shown in Fig.1.
Both disks have the same thicknesses (20 mm). The flat disk D1 has the central hole with radius R60 and eight eccentrically arranged holes 60. The centers of these holes lay on the circular R120.
Beside of central hole and eight eccentrically arranged holes 60, the flat disk D2 has eight eccentrically arranged holes 30 whose centers lay on the circular R150, and fortyeight holes 5 whose centers belong to circulars R90, R100, R125 and R165 (total 64 eccentrically arranged holes).

Materials
Two steels nominated for workmanship of our flat disks are: steel 13H11N2V2MF (Steel S1) and steel AISI 304 (Steel S2). Poisson's coefficients of these steels are the same ( = 0.29), while their mass densities are different and amount: Cyclic properties of steels S1 and S2 are included in Table 1. The estimation of the resistance to LCF, or estimation of LCFL of metallic parts, is based on the application of the next three equations: The first equation in (1) is the equation of the cyclic stressstrain curve, the second presents Massing's curve, and the third is the equation of the basic strain-life curve [9]. These curves for the certain metallic material, we obtain by the testing of specimens in the controlled strains regime, when is For steel S2, the forms of those equations are:  Figure 2. Cyclic stress-strain curves of steels S1 and S2 Cyclic stress-strain curves, Massing's curves and the basic strain-life curves of the steels S1 and S2 are shown in the next figures.  According to materials nominated for the flat disks workmanship, to the basic marks D1 and D2, we will add S1 or S2, and practically we will have a job with four disks: D1S1, D1S2, D2S1 and D2S2.

Loads
Suppose that flat disks D1 and D2 will be loaded by own centrifugal forces provoked by imaginary spin tests ST1 and ST2, with diagrams included in Fig. 5. In the spin test ST1, the first test block is ABB'A' and the other blocks are A'BB'A' with maximal planned revolves per minute (RPM) 15000 (100%). Similarly, for the spin test ST2 we have blocks ACC'A' and A'CC'A' with maximal RPM of 5% above maximal planned, and it is 15750 (105%). The quotient between 15750 RPM and 15000 RPM is 1.05.

Local stress-strain responses
Local stress-strain responses of the flat disks D1 and D2 are connected with their critical points. If they loaded by own centrifugal forces, according to [6] and [7], the critical points will be points P 1 and P 2 . Position of these points is identified in Fig 6. They belong to the contours of the holes 60 and the circular R90.
The data on local stress responses, for the case of ideal elasticity (the data on linear stress responses at critical points of the flat disks), are contained in The index 1 j  refers to disk D1 and its critical point P 1 , while the index 2 j  refers to disk D2 and its critical point P 2 .
Theoretical or geometric stress concentration factors , t j K in (4) are taken from [6].
and they are connected with all points that lay on the circular R90, of the flat disks without eccentrically arranged holes. are not real values. However, although they unreal, from the levels of these stresses, using Neuber's hyperbola [9] or some of its modification, as it as Sonsino-Birger's modification in [10] and [11], we can move to the level of real stress-strain response (nonlinear stress-strain response) at the critical points.
Nonlinear stress-strain response at the critical points of our flat disks, taking into account spin tests ST1 and ST2, was described by stabilized hysteresis loops which were modeled using corresponding Massing's curves of steels S1 and S2.
The upper points of the stabilized hysteresis loops were determined graphically (see [6]), as the intersection points between Sonsino-Birger's curves , , , and cyclic stress-strain curves defined by the first equations in (2) and (3). Coordinates of the i-th intersection point are: . All these coordinates we have in Table 3.
and the second equations in (2) and (3). For our imaginary tests ST1 and ST2 Sonsino-Birger's curves in (6) and (7)  For example, graphically determined nonlinear stress-strain responses at critical points of disks D1S1 and D1S2, for spin test ST1 and ST2, that defined by stabilized hysteresis loops, are shown in Fig. 7 and Fig. 8.
The intersection points between Sonsino-Birger's curves in (6) and lines define local stress response of the flat disks, for the case of ideal elasticity (linear stress response). All data on nonlinear stress-strain responses at critical points of the flat disks are included in Table 4.

Fatigue resistance estimation and results discussion
Fatigue resistance estimation or LCFL estimation of the flat disks was carried out using Morrow's strain-life curve, that is defined in [9], and given in the general form: we obtained the second four data for f fi i N N LCFL   . The first equations in the system (10) and (11) are equations of Morrow's strain-life curves which refer on steels S1 and S2. The values for , m i  and i   , in them, were taken from Table 4.
Results of estimated fatigue resistance, or estimated LCFL, expressed in test blocks of the spin tests ST1 and ST2, are contained in Table 5. Graphically determined LCFL of disks D1S1 and D1S2 exposed to spin test ST1, we have in Fig. 9. Figure 9. Graphically determined LCFL of disks D1S1 and D1S2 exposed to spin test ST1 The data on estimated LCFL are shown by histogram in Fig.10.

Conclusion
If we had a request to replace disk D1S1 with a new disk that would be overloaded by 5% above the planned load and would have LCFL at least 20% longer, we would conclude that we could replace it with disk D2S2. Because this disk is discovered as a good design solution.
The parts of machines, exposed to LCF, should not be forced, because with a small percentage increase in load, in a much higher percentage, their fatigue resistance can be reduced.
If it is necessary to overload the machine part exposed to LCF, then it is necessary to start with its redesigning. It is necessary to change its geometry or choose a new material for its workmanship, or both.
In the future research it would be interesting to carry out experimental spin tests for discussed flat disks and obtained results of LCFL compare with here estimated.
On the other hand, it would be interesting, through the boundary conditions, simulate the action of centrifugal forces of rims and blades of aircraft engine compressor and turbine discs, and investigate their influence on LCFL of flat disks that here were discussed.
The methodology of the fatigue resistance estimation of the flat disks with eccentrically arranged holes, can be applied and for the other metallic parts.