The deformation and fracture of gas turbine parts like turbine blades which are subjected to hightemperature and other mechanical loads, depends mainly on temperature and time and hencedue to creep. For reliable operation of a gas turbine, life prediction of the components of theturbine is of prime importance so that the damages can be detected and repaired before it getsproblematic. In the present study, a low-pressure turbine disc is analyzed for the stress fieldunder mechanical and thermal loading. The mechanical thermal loads and boundary conditionsare imposed in the finite element analysis software ANSYS. A time hardening model is used topredict the stress relaxation and creep strain accumulations in the component with respect totime. The Larson-Miller Parameter (LMP) data is used to evaluate the constants used in thiscreep analysis. By defining the model through these constants, stress relaxation feature wascaptured and the total time in hours for an accumulated creep strain of 0.1% was calculated.The time required for the accumulation of the creep strain, without considering the stress relaxationphenomena was observed to be conservative by an order. Thus the considerations given tocreep play a vital role in the design of machine components especially the aero gas turbineengine components, which are primarily subjected to severe mechanical and thermal loads.
Keywords: Gas turbine, Creep life, Larson miller parameter, Stress relaxation
INTRODUCTIONMetals subjected to a constant load atelevated temperatures will undergo ‘creep’,a time dependent increase in length. Theterms ‘high’ and ‘low’ temperature in thiscontext are to the absolute meltingtemperature of the metal. At homologoustemperatures of more than 0.5 Tm, creep isof engineering significance.
ISSN 2278 – 0149 www.ijmerr.comVol. 3, No. 3, July 2014
1 Department of Mechanical Engg., AIT, Chikmagalur.
Creep, which is the continuousaccumulation of deformations and hencestrains of a material, most of which isirreversible, under constant loads at elevatedtemperatures maintained over a period oftime, is a life limiting criterion for the design ofthe turbine discs. Creep resistance is one ofthe many requirements that most be met bythe aero engine components subjected to
Research Paper
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Int. J. Mech. Eng. & Rob. Res. 2014 Abhishek S Makunte and Ramesh B N, 2014
elevated temperatures. Precise information onthe deformation is, therefore, required for theanalysis and design of aircraft enginecomponents particularly the turbine discs andblades.
Unlike ordinary strength calculations, whichhave the object of determining the absolutestrength of a component, the object creepcalculations is to ensure that the componentwill not fail to perform its structural function withina certain specified life period of time.
The following requirements are applied tothe component. The total deformation shouldnot exceed a certain predefined value inaccordance with the structural function of thecomponent. Failure should not occur duringservice life.
The blade is expected to exhibit areasonable short time creep life of the orderof 10 hours, in this condition. Such a low valueof life is acceptable as the total time spent bythe blade in this condition would be very shortduring its service life whereas, in the cruisecondition the blade is subjected to less severethermal and mechanical environments andalso the component spends comparativelylonger period in this condition in its service.Hence, it is expected to have a much longercreep life in this condition. The blade has tomeet the specified safety standards in eachof such operating conditions.
CREEP ANALYSISTime-Hardening HypothesisThe time hardening model, suggested for thefirst time by Davenport (1838) and developedby Kachanov (1960), is also known as the flowtheory or the second variant of the ageing
theory. It assumes that at constant temperaturethere exists the relationship between the creepstrain rate the stress , and the time t.
F(, t, T) = 0 ...(1)
The creep strain is generally assumed todepend on the stress, temperature and time(or strain) and is generally written in rate formin order to include, in some measure, thehistory dependence of the creep process.
c = An tm ...(2)
It is assumed to be valid for uni-axialcreep under constant stress andtemperature. A,n,m are parameters, dependon temperature and time. If at a time ti thetotal stress is i, it is represented in thecreep curve by point Mi
. If the stress isassumed to remain constant for a small timestep, creep fol lows the curve thatcorresponds to the stress i and starts frompoint M i. In a time interval t, a creepdeformation of c accumulates. This waythe change in creep strains in the timeinterval is calculated. Adding theseincremental creep strains to thecorresponding free strains of each linearelement the redistributed stress at that pointis evaluated.
Now creep occurs along the curve thatcorresponds to new stress value i + 1commencing from the point at which elapsedtime is ti+1 = ti + t. In order to find this pointon the new creep curve a vertical line isdrawn from the end of the incremental creepstrain on the previous creep to meet the newcurve at point M+1. Continuing this processthe relaxation curves are constructed. Thetotal elapsed time gives the creep life for theaccumulated creep strain at that point.
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Int. J. Mech. Eng. & Rob. Res. 2014 Abhishek S Makunte and Ramesh B N, 2014
FINITE ELEMENT OF THE DISCThe solid model of the disc and the 2-daxisymmetric model with dimensions arepresented in the Figures 1 and 2 respectively.The 2-d axisymmetric model was made into asurface and the free meshing of the surfacewas carried out in catia. The mesh wasgenerated using the plane-axisymmetricelement. The method model is then importedto ansys and further analysis is carried. Herethe geometry, material properties and loadsare axial symmetric and hence the problem ismathematically two-dimensional. The turbinedisc being thicker can have strong non-linearstress distribution across the thickness and theanalysis has to be performed at critical timepoints using eight node isoperimetric 2-daxisymmetric elements.
Solid Model of a Typical GasTurbine DiscMaterial CompositionThe commercial name of the material of thedisc is INCONEL718, a nickel based super
alloy. Its composition is presented below (http://www.hightempmetals.com/techdata/hitempInconel718data.php).
A1 = 0.4%-1.0%
C = 0.08%
Cr = 14.0%-17.0%
Fe = 5.0%-9.0%
Ni = 0.7 min
Ti = 2.25%-2.75%
Cb +Ta = 0.7%-1.2%
AssumptionsIn the computation of creep strainaccumulation certain assumptions would needto be made.
1. The most important of them is that the discmaterial is perfectly elastic. There isconsiderable amount of literature on tensioncreep under constant load and constanttemperature conditions. However, whenone considers creep under compressionloads extensive creep data are still lacking.
Figure 1: Solid Model of a Gas Turbine Disc
Figure 2: Loads for Thermal Analysis
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Int. J. Mech. Eng. & Rob. Res. 2014 Abhishek S Makunte and Ramesh B N, 2014
2. It is assumed that the material shows samecreep and long time rupture behavior undercompressive load as in the tensile load,apart from the sign of the creep strain.
3. Steady state conditions of temperature andcentrifugal stress exist.
4. Plane section remains plane before andafter creep deformation.
Practical creep strength calculations incomponents like gas turbine rotor blade anddiscs need a theoretical description of thecreep process in order to evaluate the strainafter a certain time and the conditions offailure. The dependency of creep rate onstress is very non-linear. A small increase instress at high temperatures can cause aconsiderable increase in creep resultsbetween creep results obtained at differenttemperatures.
RESULTS AND DISCUSSIONThe results of the analysis performed inANSYS with four different stages mentionedearlier are presented here. The radial stressand the vonmises stress distribution plots arepresented for all the four cases.
Radial and Vonmises StressesDistribution in Different StagesStage 1: Here, only the body force due torotation was considered. The angular velocity, = 1156.8 rad/sec was imposed. Figure 3shows the distribution of radial stress for disc.The disc was constrained along the axialdirection and is allowed to grow in the radialdirection. Then radial stress is seen as shownin the Figure 3.
Because of the body force and angularvelocity of 1156.8 rad/sec, the maximum stress
(100.902) will be developed in the disc at therim and minimum stress in seen at the endparts of the rim and bore.
The vonmises stress is also considered forthe same body force and angular velocity of1156.8 rad/sec the maximum stress of(176.162 MPa) is seen in the disc at the endpart of rim and minimum stress is seen at theend part of the bore, as shown in the Figure 4.
Figure 3: Radial Stress Distribution(Stage 1)
Figure 4: Vonmises Stress Distribution(Stage 1)
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Int. J. Mech. Eng. & Rob. Res. 2014 Abhishek S Makunte and Ramesh B N, 2014
S. No. Stress Value in MPa Location in the Disc Temperaure in C°
1. Radial stress 100.92 Web 422.26
2. Vonmises stress 176.162 Bore 390.29
Table 1: Maximum Values of Radial and Vonmises Stage Distribution
Stage 2: In this stage the body forces due torotation along with blade loads wereconsidered. The calculated value of blade =20104.2 Kgf
In the above case body force and angularvelocity is considered but in this case alongwith this loads are considered. Here thecalculated values of the blade load is taken,i.e. = 20104.2 Kgf as shown in Figure 5.
Because of this, maximum stress (112.424MPa) will be seen in the disc at the rim lowerend and minimum stress is seen at the end
part of the rim and lower side of the bore. Thedisc was constrained along the axial directionand is allowed to grow in the radial direction.
Vonmises stress is obtained for the sameabove case which is as shown in the aboveFigure 6. The maximum vonmises stress(187.378 MPa) is developed at the end partof the rim and minimum stress developed atthe lower end part of the bore.
Stage 3: Here the thermal gradient was superimposed in addition to the above two stagesof loading. The thermal gradient was obtainedby performing a heat transfer analysis on the
Figure 5: Radial Stress Distribution(Stage 2)
Figure 6: Vonmises Stress Distribution(Stage 2)
S. No. Stress Value in MPa Location in the Disc Temperaure in C°
1. Radial stress 112.424 Web 422.26
2. Vonmises stress 183.378 Bore 390.29
Table 2: Maximum Values of Radial and Vonmises Stage Distribution
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Int. J. Mech. Eng. & Rob. Res. 2014 Abhishek S Makunte and Ramesh B N, 2014
disc. The stress plots obtained in the stage 3are the pre-stressed relaxation plots. In stage3, all the three, i.e., body forces, blade loadsand thermal gradient were considered.
For the above same stage vonmisesstresses are obtained which is shown in theFigure 8. The maximum vonmises stress(208.261 MPa) is seen at end part of the rim
Figure 7: Radial Stress Distribution(Stage 3)
Figure 8: Vonmises Stress Distribution(Stage 3)
S. No. Stress Value in MPa Location in the Disc Temperaure in C°
1. Radial stress 127.81 Web 422.26
2. Vonmises stress 208.261 Bore 390.29
Table 3: Maximum Values of Radial and Vonmises Stage Distribution
Figure 9: Radial Stress Distribution(Stage 4)
Figure 10: Vonmises Stress Distribution(Stage 4)
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Int. J. Mech. Eng. & Rob. Res. 2014 Abhishek S Makunte and Ramesh B N, 2014
and minimum stress is seen at the end of thebore.
Stage 4: In addition to the above-mentionedfour stages of loadings, the creep materialproperties were defined here. The values ofthe three constants evaluated previously weredefined here and the disc was made to run for10 hours and the creep analysis was carriedout. The stress plots obtained in the stage 4are the post stress relaxation plots.
Vonmises stress distribution for stage 4 isas shown in Figure 9. The maximum vonmisesstress (209.434 MPa) is found to be at upperend part of the rim and minimum stress is seenat end part of bore.
Figure 10 shows the deformed shape of thedisc at end of rim quenching. Figure 10 showsthe deformed shape of the disc along with un-
deformed shape at end of rim quenching.Figure 11 shows the deformed shape of thedisc along with un-deformed edge at end ofrim quenching
S. No. Stress Value in MPa Location in the Disc Temperaure in C°
1. Radial stress 126.935 Web 422.26
2. Vonmises stress 209.434 Bore 390.29
Table 4: Maximum Values of Radial and Vonmises Stage Distribution
Figure 11: Deformed Shape of the Discat End of Rim Quenching
Figure 12: Deformed Shape of the DiscAlong with Undeformed Shape at End
of Rim Quenching
Figure 13: Deformed Shape of the DiscAlong with Undeformed Edge at End
of Rim Quenching
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Int. J. Mech. Eng. & Rob. Res. 2014 Abhishek S Makunte and Ramesh B N, 2014
Life EstimationThe maximum value of the radial stress andVonmises stress obtained in stage 3 areshown in figure 10 and 11 respectively. Table5, given below lists the maximum value of theradial stress and vonmises stress with locationof occurrence of the maximum value and thetemperature at that location for stage 3. Thestage 3 presents the result prior to the stressrelaxation.
Similarly, the maximum value of the radialstress and vonmises stress obtained in thestage 4 are shown in the Figures 10 and 11respectively. The Table 6, given below lists themaximum value of the radial stress andvonmises stress with location of occurrenceof the maximum value and temperature at thelocation for stage 4. The stage 4 presents theresult after the stress relaxation.
It can be noticed that the radial stress hasrelaxed from a value of 127.81 mpa in stage 3
to a value of 126.935 mpa in stage 4. Similarlyvonmises stress has relaxed from a value of208.261 mpa in stage 3 to a value of 209.434mpa in stage 4.
The life of the disc was estimated from therelaxed stress value in the Table 7 and theircorresponding LMP values for the four stressvalues were interpolated from the availablecreep properties of INCONEL-718.
The estimated life value for stage 3 andstage 4 and their comparison is made in thetable.
Hence it is evident from the result that onincorporating the creep properties, the stressrelaxation is more, hence the exact life of thedisc is evaluated from the relaxed value of thestresses. If the creep effects are notconsidered, the stress will not be relaxed andthe value of life obtained with that stress valuewould be an under estimation of the life of thedisc.
S. No. Stress Value in MPa Location in the Disc Temperaure in C°
1. Radial Stress 127.81 Web 422.26
2. Vonmises stress 208.261 Bore 390.2
Table 5: Pre-Relaxation Result (Stage 3)
S. No. Stress Value in MPa Location in the Disc Temperaure in C°
Int. J. Mech. Eng. & Rob. Res. 2014 Abhishek S Makunte and Ramesh B N, 2014
CONCLUSIONIn this project we have sought to explain thecreep life estimation of aero gas turbine disc.Some of the salient features of this work areas follows.
• The Finite Element analysis of the 2-D axi-symmetric model of the disc was carriedout, considering the mechanical and thermalloads.
• The material constants required for the timehardening model were evaluated usingLMP data for different values of percentageaccumulation of creep strain in the disc.
• The least square error approximation wasemployed to evaluate the value of the threeconstants. By defining the model throughthese constants, stress relaxation featurewas captured and the total time in hours foran accumulated creep strain of 0.1% wascalculated.
• The time required for the accumulation ofthe creep strain, without considering thestress relaxation phenomena wasobserved to be conservative by an order.Thus the considerations given to creep playa vital role in the design of machinecomponents especially the aero gas turbineengine components, which are primarilysubjected to severe mechanical andthermal loads.
• The evaluated value of life of the aero gasturbine disc, upon considering the creepproperties was higher than the case withoutthat consideration. Thus it can be concludedthat the process of evaluating the life of theaero gas turbine disc would be anunderestimation, if the creep properties areignored.
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