Microsoft Word - numero_50_art_7_2531 N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 54 Characterization of the stress-strain state in a gas turbine engine compressor disc taking into account damage accumulation Natalia Boychenko, Ivan Ishtyryakov Institute of Power Engineering and Advanced Technologies, FRC Kazan Scientific Center, Russian Academy of Sciences, Russia nataboi@ya.ru, ivan_200999@mail.ru ABSTRACT. A stress-strain state analysis of a gas turbine engine compressor disc was conducted with consideration to the accumulation of damages under various loading conditions in the temperature range. Characterization of constraint effects was performed using the local stress triaxiality h, TZ-factor and In-factors for various crack sizes and different operation conditions. The distributions of elastic, plastic and creep stress intensity factors were determined by numerical calculation. Results for several crack front positions, temperature values and disc rotation angular velocity were obtained. The differences in the behaviour of elastic and nonlinear fracture resistance parameters were observed on the basis of loading conditions, crack geometry and temperature. Nonlinear stress intensity factors are preferred as the fracture resistance parameters of materials and structures. KEYWORDS. Compressor disc; Creep; Damage; Surface flaw; Plastic stress intensity factor; Creep stress intensity factor. Citation: Boychenko N., Ishtyryakov I., Parametric study of stress-strain state in gas turbine engine compressor disc taking into account damage accumulation, Frattura ed Integrità Strutturale, 50 (2019) 54-67. Received: 28.05.2019 Accepted: 07.07.2019 Published: 01.10.2019 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION as turbine engines (GTE) are the main power plants in modern aviation. Many types of engines in land and marine engineering are based on GTEs. GTEs are operated under extremely high temperatures and loads for long periods of time. The temperature ranges from -60°C to +1700°C, air pressure can reach 300 MPa, and gas flow rate exceeds the sonic velocity. The main loads are derived from centrifugal forces on the rotating parts of the rotor; a rotation frequency reaches 5000 1/s, and the circumferential speed is –450 m/s. High-strength materials, efficient technological processes and advanced design solutions are used to implement highly reliable parameters. Titanium alloys and stainless steels are often used for highly loaded rotor components, and heat-resistant nickel-based alloys are used for high-temperature turbine components [1, 2]. When in operation, the discs subjected to centrifugal and thermal loads are the most loaded part of the rotors. The compressor disc has various concentrators in the form of grooves, holes, mating surfaces and recesses, etc. In some cases, stresses near concentrators may exceed the yield strength, and plastic stains will occur [3, 4]. G http://www.gruppofrattura.it/VA/50/2531.mp4 N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 55 This study aims to explore elastic and nonlinear fracture resistance parameters and analyse constraint parameters taking into account accumulation of damages under various loading conditions within a temperature range. THE SUBJECT UNDER STUDY AND MATERIAL PROPERTIES n this study, the stress-strain state and the fracture resistance parameters in an aircraft GTE compressor disc (Fig. 1a) were analysed. Slot fillets under the blade are the concentrated stress areas in the compressor disc of the aircraft GTE [3, 5-7]. The ‘dovetail’ type attachment had a broach angle of 26 at the axis of rotation, and partial-through surface cracks occurred in the disc and blade attachment [7, 8-10] (Fig. 1b). The crack propagation usually starts from a quarter elliptical corner surface flows [9, 11]. Crack developed in slot fillet near the disc outer surface. Further, the growing crack intersected the entire thickness of the disc. As a result, the disc rim ruptured (Fig. 1c) [9, 11]. a) b) c) Figure 1: GTE compressor disc (a) and operation damages of disc and «dovetail type» blade attachment (b, c). Numerical analyses of the stress-strain state under the operating loading conditions were conducted in this study at various temperatures and crack sizes. The first part of numerical calculations focused on the stress-strain state analysis of the compressor disc without cracks. The second part was devoted to the analysis of the compressor disc with operational damage in the slot fillet of the – ‘dovetail’ type disc and its blade attachments. Three types of curvilinear crack geometry were considered. All calculations were performed at room (23°С) and elevated (300°С and 370°С) temperatures with a rotor angular velocity of 925 and 1000 rad/sec. Elastic, plastic and creep conditions were considered. Damage accumulation was analysed in consideration of creep conditions. Thus, numerical investigations were performed for given combinations of the main parameters, such as the angular velocity of the compressor disc, temperature, shape and size of the defect and the elastic, plastic and creep properties of the material. The combinations of the parameters used in the numerical calculations are presented in Tab. 1. Angular velocity, rad/s Temp., °С Disc without crack Disc with surface crack: а=0.34mm, с=0.71mm а=0.76mm, с=1.32mm а=1.5mm, с=2.2mm Elastic Plastic Creep Damage Elastic Plastic Creep Damage 925 23 + + - - + + - - 300 + + + + + + + + 370 + + + + + + + + 1000 23 + + - - + + - - 300 + + + + + + + + 370 + + + + + + + + Table 1: Various parameters employed in the numerical calculations. The compressor disc considered for the numerical calculations was made of titanium alloy VT3-1. The main mechanical properties of the material analysed at three temperatures are summarized in Tab. 2, where, σ0.2 – yield stress, σut – true ultimate tensile stress, Е – Young's modulus, n – strain hardening exponent, α – strain hardening coefficient. I N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 56 Temperature, °С 0.2 MPa ut MPa E GPa n α 23 1004 1602 100 12.88 1.11 300 753 1515 96 8.91 0.99 370 699 1500 97 8.43 0.97 Table 2: Summary of the main mechanical properties of titanium alloy VT3-1 at room and elevated temperatures. The Norton law was used to describe a material’s behaviour under the creep conditions: n cr B   (1) where cr is the creep strain rate, B is the creep coefficient, ncr is the creep exponent, and σ is the stress. The creep properties for titanium alloy VT3-1 are listed in Tab. 3. Material Temperature, °С Creep equation Creep constant B, (MPa)-n hour-1 ncr VT3-1 300 9 1.63423 10cr     3·10-9 1.6342 370 9 1.93371 10cr     10-9 1.9337 Table 3: Creep properties of titanium alloy VT3-1 at 300°С и 370°С. In this study, the model proposed by Shlyannikov and Tumanov for the damage accumulation rate [12, 13] was used to assess the creep damage behaviour:     1 / 1 1 n n i i в m f bd dt t                   (2) 22 1 3 i b     ;         2 2 1 1 1 1                ;   221 1 1 i            where 0 1  is the measure of damage, with 0  denoting the undamaged state and 1  the fully damaged state;  is the experimental material constant, which is determined as the ratio of uniaxial tensile strength to compression strength = t /c. For brittle fracture  = 0, whereas  = 1 is for ductile fracture tf is the time for the fracture to occur under creep conditions, m is the constant in the law of damage accumulation, 2 1    is the principal stress ratio, and  is the Poisson's ratio. Eqn. (2) allows us to consider the complex stress state. Knowing only the constants of the Norton law equation and the time to fracture at least at one level of the effective nominal stresses is enough to determine the constants of Eqn. (2) [12, 13]. Eqn. (2) was integrated into the ANSYS finite element (FE) code [14]. A full-field 3D FE analysis was conducted using the ANSYS code to determine the stress-strain state parameters of the GTE compressor disc with the considered geometry. N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 57 ELASTIC-PLASTIC STRESS FIELDS IN THE GTE COMPRESSOR DISC he first part of this study is concerned with the stress–strain state analysis of the compressor disc without cracks. FEM calculations were performed to determine the stress and strain distributions under different loading conditions within a specified temperature range. The 3D segment of the disc with blades was simulated due to the cyclic symmetry property of the disc. A 20-node quadrilateral isoparametric 3D solid FE model represented the 3D compressor disc configuration (Fig. 2). The displacements of the radial sections of the disc corresponded to the XOY, YOZ and XOZ planes and were limited under normal. The interaction between the blade root and the mounting holes of the disc was modelled using contact elements. The 3D FE model of the aircraft GTE compressor disc D-36 are presented in Fig. 2a. The global elastic–plastic equivalent, von Mises stress distributions and local nonlinear strain zone in a compressor disc with an angular velocity of 925 rad/s at room temperature are shown in Figs. 2b and 2c. a) b) c) d) Figure 2: The 3D FE model (a), Global von Mises stress distributions (b), local nonlinear strains zone (c) and damage distribution (d) in aircraft GTE compressor disc. Results indicated that the main high-loaded areas of the disc are the slot fillets under the blade in which the maximum stresses exceed the yield strength of the titanium alloy VT3-1 at the temperature considered. A similar pattern was observed for all other combinations of the angular velocity and temperatures listed in Tab. 1. The stress and strain level in the disc depends on the temperature and the angular velocity. T N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 58 Fig. 2d shows the damage field in the slot fillets of the compressor disc at 370°C. An area of defect nucleation in the slot fillet was determined on the basis of the maximum value of the damage. This area coincides with the localization of real cracks occurring in the compressor disc during the operation. The obtained area of defect nucleation was used as a basis for the second part of the work. STRESS-STRAIN STATE OF THE GTE COMPRESSOR DISC WITH OPERATIONAL DAMAGES he second part of the numerical study is concerned with the stress–strain state analysis of the GTE compressor disc with cracks. The location of the surface defect was chosen in accordance with the direction previously determined at the first stage of this study. The initial crack inclination (nearly 45°) was defined in a manner consistent with the results of the full-size compressor disc’s experimental low cycle fatigue tests. The position of the quarter-elliptic crack fronts in the compressor disc and the size of the simulated defects are presented in Fig. 3. The crack was modelled as a notch with a crack tip curvature radius r = 0.002mm, where a is the crack depth, and c is the crack size on the free surface of the disc. To compare the behaviour of the governing parameters along the corner quarter-elliptical crack front, we use normalized coordinates in the following forms: 0 0 0 0 cos , sinx y       cos , sin c c c c x y       cos , sini i i ix y       ,  0 0, , i c c         (3) 0 0 0 0 , i ii i c c x x y y X Y x x y y        2 21 , 0,1 2 i i i iR X Y R   where 0 is an angle denoting the position of the crack front point on the free surface of the disc. c is an angle that corresponds to the crack front point placed on the slot key’s surface (Fig. 3). In this study, a dimensionless variable R was used in a range from 0 to 1, where R=0.0 indicates the exterior surface of the compressor disc (point B), and R=1.0 corresponds to the slot surface (point A). Once the location of the crack and the size of the crack are identified, the region around the crack should be meshed appropriately to calculate the nonlinear fracture resistance parameters accurately. A quarter-elliptical part-though crack was inserted in the compressor disc FE model (Fig. 4) in the area of the disc and blade attachment. A full-field 3D FE analysis was performed to obtain the stress and strain fields along the corner crack front in the compressor disc when subjected to different combinations of angular velocities, temperatures and crack front positions (Tab. 1). Fig. 5 shows typical plots of the nonlinear strain zones along the curvilinear crack front in the compressor disc for plastic, creep and damage solutions. The nonlinear strain zone pertains to when the zone within the total strain intensity exceeds the yield strain value. Results show that under the operating loading conditions, the distribution of strains (Fig. 5) were non-symmetrical due to mode mixity, and the nonlinear zone was larger in the slot key relative to the free surface of the disc. The maximum value of strain intensity was located in the slot fillet’s inner surface for all considered combinations of variable parameters and is presented in Tab. 1. The crack was assumed to grow primarily along the thickness of the disc. This assumption was confirmed by the data on the crack paths in the slot key fillet [8]. The nonlinear strain zone under creep conditions was significantly larger than that under the plastic solution. Strain intensity increased due to damages under creep conditions. Thus, an account the damages allows a more conservative estimate of the degradation of the material properties and stress–strain state parameters. T N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 59 Crack front point A с, mm point B a, mm front 1 0.71 0.34 front 2 1.32 0.76 front 3 2.22 1.5 Figure 3: Crack front positions and sizes in the slot fillet of aircraft GTE compressor disc. Figure 4: The 3D FE meshes of slot fillet of compressor disc with а quarter-elliptical part-though crack. A B (B) (A) N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 60 Plastic solution Creep Damage Figure 5: Strains intensity distributions in the compressor disc with а crack in a slot fillet. Figure 6: Contours of creep damage around crack tip on slot fillet surface (point A) and free surface (point B) of compressor disc with angular velocity 925 rad/s. Fig. 6 shows the contours of the damaged zones around the crack tip in the slot fillet of the compressor disc with an angular velocity of 925 rad/s at 300°C and 370°C. Results are presented for two sections: the inner surface of the slot fillet (Fig. 3 point A) and the free surface of the disc (Fig. 3 point B). The crack front positions are indicated by the numbers 1 and 3, respectively. The contours of the damaged zone for the second crack front occupied an intermediate position. As shown in Fig. 6, the measure of damage depended on the temperature, crack size and on the point along the crack front. The shape of the damage contours in the slot fillet and on the free surface (points A and B correspondingly) were significantly different. On the inner surface of the slot fillet, the damaged zone was close to symmetrical; meanwhile, substantial asymmetry was observed on the free surface of the disc. Moreover, the asymmetry of the damaged zone on the free surface increased with the increasing crack size. N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 61 NONLINEAR FRACTURE RESISTANCE AND CONSTRAINT PARAMETERS IN THE GTE COMPRESSOR DISC Elastic and plastic stress intensity factors hlyannikov et al. [5] showed that the stress–strain state in the rotating disc obtained from FE calculations was biaxial indicating that the structure around the slot fillets of the key was subjected to radial and tangential stresses. Stress biaxiality ratio rr    is a function of the current value of the disc radius and varies from η=−0.27 to η=+0.29 [3]. The data presented in Fig. 8 also indicates a mixed mode behaviour along the crack front in the compressor disc. Different from pure mode I, calculating the two fracture parameters was necessary to study the influence of the mixed mode loading conditions on fracture resistance parameters, namely, Modes I and II stress intensity factors (SIFs) KI and K2. Shlyannikov [15] generalised the numerical method of calculating the geometry-dependent correction factors Y1 and Y2 for SIF KI and K2 under mixed mode fracture. This study directly used the results of the FE solution for calculating SIF KI and K2 ahead of the crack tip (θ=0º):    2 22 2 21 2 1 24eqvK K K K K   (6) 1 2 FEMK r  2 2 FEM rK r  where FEMi represents the stresses obtained from the FE solution, and r and θ – are the polar coordinates centred at the crack tip. The plastic stress intensity factor was introduced in [3, 16-17] as the unified fracture resistance parameter for fatigue crack growth rate characterization. For the compressor disc, the plastic SIF Kp in pure Mode I (or pure Mode II) can be expressed directly in terms of the corresponding elastic equivalent SIF Keqv. This is shown in [18]:    1 2 1 1 1 4 n eqv P y n K K I w                 (7) where 3 4   ,  is the Poisson’s ratio, In is the governing parameter of the elastic–plastic stress–strain fields in the form of In factor, α and n are the hardening parameters, y is the yield stress, and w is the characteristic size (in this case, the width of key). In the asymptotic HRR solution [19-21], the In is dependent only on the plastic properties of the material, namely, the strain-hardening exponent n. Shih [22] modified the HRR solution for the plane strain problem and found that the In becomes dependent on the mode mixing parameter Mp under mixed mode, small-scale yielding,. Shlyannikov and Tumanov [16] developed a method to determine the In factor. This method considers the influence of the specimen and crack geometry [16]:     , , , ( , , , )FEM FEMn p PI M n a w M n a w d         (8)     1, , , cos 1 FEMFEM n P e n M n a w n        sin FEM FEM FEM FEM FEM FEMr rr r r du du u u d d                               (9)  1 cos . 1 FEM FEM FEM FEM rr r ru u n         S N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 62 A detailed description of the governing parameter in the form of In-factor definition is given in [16]. It is shown that In- factor is sensitive to the constraint effects and can be used as constraint parameter. Stressstrain fields under extensive creep can be written in terms of creep stress intensity factor Kcr in the following form [23]: 1 * 1 0 1 crn cr cr n C K BI L        (10) where B and ncr are creep constants, cr nI is the governing parameter of the stress–strain fields for power-law creeping materials, and С* is the С-integral under extensive creep. Methods for determining C-integral at various creep stages and conditions are given in [23-26]. A numerical method was introduced by Shlyannikov [23] to determine the governing parameters of the creep-crack tip fields in terms of the In integral for power-law creeping materials. This method can be also be used to analyse the creep- damaged material’s fracture resistance characteristics. Kcr is the most effective crack tip parameter in correlating the creep– fatigue crack growth rates in power plant materials and can be used for practical purposes [23, 24]. Constraint parameters distributions The stress-strain state analysis of the compressor disc with corner cracks should be performed taking into account in- plane and out-of-plane constraint effects. Shlyannikov et al. [27, 28] showed that different traditional approaches which can successfully describe the in-plane constraint are inaccurate for describing 3D surface cracks. In [29], constraint parameters were analysed as a function of cyclic tension loading and temperature conditions. Characterization of the constraint effects in the present study was performed using the local stress triaxiality h, TZ-factor, In-factor and cr nI for specified combinations of crack sizes and loading conditions. All parameters were determined at the crack tip distance range of r/a=0.01, where the numerical solution provides a stabilised result. A local parameter of the crack-tip constraint was proposed in [30] as a secondary fracture parameter because the validity of some concepts previously mentioned depends on the chosen reference field. This stress triaxiality parameter is described as follows: 3 3 2 kk ij ijh s s        (4) where kk and ijs are hydrostatic and deviatoric stresses, respectively. As the function of the first invariant of the stress tensor and the second invariant of the stress deviator, the stress triaxiality parameter is a local measure of the in-plane and out-of-plane constraint effects that is independent of any reference field. The TZ-factor [31] has been recognized to present a measure of the out-of-plane constraint and can be expressed as the ratio of the normal stress components: zz z xx yy T      (5) where  is the Poisson’s ratio, zz is the out-of-plane stress, and xx and yy are the in-plane stresses. Fig. 7 depicts the effect of temperature on the constraint parameters for plastic and creep solutions. Results for two crack front positions (initial and final [front 1 and 3, respectively]) are presented. The Tz-factor and stress triaxiality h change in character along the crack tip from the free surface (R=0) and across the mid-plane (0> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /DEU /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. 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