NUMERICAL ESTIMATION OF FATIGUE LIFE OF AEROENGINE … · 2016-09-01 · NUMERICAL ESTIMATION OF...

SASTECH Journal 47 Volume 9, Issue 2, September 2010

NUMERICAL ESTIMATION OF FATIGUE LIFE OF AEROENGINE FAN BLADES

Binesh philip1, *N. C. Mahendra Babu2 1Student, M. Sc. [Engg.], 2

Keywords: Fan, Compressor, High Cycle Fatigue, von Mises Stress, Modal and Harmonic Analysis

Professor, M.S. Ramaiah School of Advanced Studies, Bangalore 560 054 *Contact Author e-mail: [email protected]

Abstract During every startup and shutdown of an aviation gas turbine, the fan blades are subjected to centrifugal, gas

bending and vibratory loads. This repeated loading and unloading can reduce the life of fan blades. Previous works on fan blades have focused mainly on fatigue life estimation in the vicinity of foreign object damage. There is no evidence of fatigue life estimation from centrifugal, gas bending load and dynamic load.

As it is important to assess the fatigue life of the blade subjected to static and dynamic loads, the analysis is divided into two parts. In the first part, the blade is subjected to static loading that is centrifugal and gas bending load. Based on stress results, a decision is made whether to proceed with stress based fatigue life assessment or strain based fatigue life assessment. In case of dynamic loading, the blade is subjected to a tip load. Harmonic analysis is carried out to study the alternating stresses. The equivalent endurance stress obtained is checked against the S-N curve to obtain the HCF life under dynamic loading.

Results obtained are based on the above process. In case of static loading, it is observed that the dovetail regions will have a minimum life in LCF. And in case of dynamic loading, it is observed that the maximum speed of the fan blade is close to one of the blade passing frequencies. Hence, the deflections are predominantly similar. It is also observed that under dynamic loading, the aerofoil is having a minimum life in HCF.

1. INTRODUCTION Aircraft engines or otherwise known as gas

turbines are power plants that suck in air, compress it, mix the compressed air with the right proportion of fuel, burn the mixture in the combustor and expand it in the turbine. All these processes are driven by large number of rotating parts. When a gas turbine is in operation, the different parts of the engine are subjected to extreme loading such as centrifugal loads, thermal loads, gas bending loads, aerodynamic loads, vibration loads, etc. these loads can induce a plastic damage into the components. During each operation, there is a certain amount of permanent damage induced in the system. This could ultimately lead to fatigue failure. Such a failure, if not predicted, can results in catastrophic damage leading to loss of both human and property. Engine designers, therefore, design their components for safe life, that is the components are designed to survive a definite period of time. During every maintenance cycle, the components are either replaced or repaired. This decision is either based on past experience or fatigue calculation.

This paper deals with an analytical procedure to quantify the fatigue life of a 1st

During every startup and shutdown of the engine, the fan blade is subjected to steady and vibration loads. Steady loads arise from the centrifugal and gas bending loads whereas vibration loads arise from blade row interactions. Vibration can also arise from rotor instability, aerodynamic excitation occurring in upstream vanes, downstream struts and blades.

Aeromechanical instability in blades is accompanied by aerofoil flutter and acoustic fatigue of sheet metal components in the combustor, nozzle and augmenter. The steady loads induce a permanent damage into the blade. The fatigue life of the blade under such conditions is computed by Low Cycle Fatigue (LCF) analysis. In case of vibration loads, the fatigue life of the blade is computed by High Cycle Fatigue (HCF) analysis.

Low cycle fatigue is due to high amplitude low frequency loading, comprising one startup-shutdown cycle. It is also known as a stress block. During each LCF, certain regions of the blade undergo plastic deformation. Hence, the life of such the regions is assessed by strain based approach. But in case of regions that are elastically deformed, a stress based approach is used to compute the fatigue life.

stage fan blade. This blade, being at the starting of the engine, is subjected to centrifugal, gas bending and dynamic loads. All the loads are dependent on the speed of the engine. As the speed increases, the centrifugal force, gas bending load and dynamic load also increase. Dynamic load arises from pressure fluctuations between blade tip and casing.

Unprecedented failures in the past have led to research on fatigue life estimation. Both experimental and numerical fatigue life estimation has been carried out. Dungey and Bowen [1] carried out experimental studies on a cross-rolled Ti-6Al-4V plate to assess the effect of HCF on LCF. In this study, it is concluded that large vibrational amplitude reduced the fatigue life considerably. Ren and Nicholas [2] carried out experimental analysis to study the effect of prestrain on subsequent HCF cycles. They carried out tests on Nickel-based superalloy, Udiment-720. From this test it was concluded that 10% prior LCF consumption could reduce the HCF limit by 33%. Russ [3] also studied the effect of LCF cycles on subsequent HCF cycles. From the study it is concluded that the introduction of LCF effectively increased the FCG rate of subsequent high R cycles. From this study it is also concluded that the load interactions have lower life as compared to the one with higher no-load interaction. Byrne et al [4] also observed similar behaviour on Ti-6Al-4V specimens. From the


experiments it was concluded that periodic LCF overloads reduced the effect of FCG rate. Another observation in these experiments was that an increase in the prior LCF cycles to the loading block increased the FCG rates proportionately prior to the onset of HCF activity and reduced the effect of HCF at onset. Byrne et al [5] studied the effect of FOD on subsequent low and high cycle fatigue crack growth behaviour. From this study, they concluded that the residual stress from FOD played an important role in fatigue life. It is also concluded that the FOD damages are preferred sites of crack propagation.

Several theoretical studies have also been carried out in the past to study the fatigue life estimation. Li et al [6] studied fatigue life models subjected to multiaxial loading. They carried out elastoplastic analysis on Steel specimens to determine fatigue life. The theoretical studies were supported by experimental approach. From this study it was concluded that multilinear kinematic hardening was best suited for fatigue life estimation. Mall et al [7] carried out hybrid experimental- numerical studies on fatigue life of Ti-6Al-4V plates subjected to Foreign Object Damage (FOD). From the study it was observed that there was sufficient reduction on fatigue strength from a prior FOD. Dowson et al [8] studied the effects of cyclic loading on elastic modulus, yield strength and plastic strain development. The theoretical analysis was supported by experimental studies and they found a good match in results. The above study addressed the complete failure of the component and did not differentiate between crack initiation and crack propagation. Fatigue life estimation is addressed in the vicinity of the FOD and none of the published papers address the fatigue life estimation of the fan blades. Component based fatigue life estimation is not addressed in any of these papers. In the current study a numerical approach is developed to evaluate the fatigue life of fan blades.

Fig. 1 Overall dimension of fan blade

2. GEOMETRIC MODEL The part considered for fatigue life estimation is a

fan blade taken from a turbojet aviation gas turbine. Made of Ti-6Al-4V material, each blade weighs about 687grams. The overall dimensions of the fan blade are shown in Fig. 1. The maximum rotational speed of the blade is 10,600 rpm, with corresponding tip speed of 429.58 m/s. The speed falls within the range given in Table 1.

Certain assumptions are considered due to inadequacy of data

• The loading conditions are with respect to sea level.

• Only structural damping is considered in the analysis.

Table 1 Range of axial flow compressor design parameters [9].

3. METHODOLOGY As the fan blade is spinning at full speed, it is

subjected to steady centrifugal and gas bending loads. This can lead to low cycle fatigue, whereas excitation from secondary flows between blade and casing lead to high cycle fatigue. The procedure for fatigue life estimation is represented as a flow chart in Fig. 2.

4. FINITE ELEMENT MODEL As depicted in the methodology flow chart (Fig. 2),

it is important to have a finite element model. The quality of results is dependent on the quality of FE model. Denser the mesh used for analysis, better will be the results. The FE model is generated in HYPERMESH. The FE element library contains a variety of element types. The use of these elements is governed by the type of problem, time for solving the problem and quality of results. It is also advisable to have best quality mesh for fatigue life assessment. For the current problem, a mesh convergence study was carried out to decide on the quality of mesh.

4.1 Mesh Convergence Studies

In order to mesh the fan blade, a mesh convergence study was carried out. It was for the type of the element used and the density of the mesh. A cantilever beam was considered for the study, as shown in Fig. 3.


Fig. 2 Flowchart of HCF- LCF assessment

Fig. 3 Cantilever beam It was subjected to its own weight of 1G load, and

material properties of Ti-6Al-4V were considered for the analysis. Five FE models of the beam were generated using:

• Only first order hexagonal element (8-Node)

• Only first order tetrahedral element (4-Node)

• Only second order tetrahedral element (10Node)

The element shapes are shown in Fig.4.

Fig. 4 Element shapes Case (iii) is further analysed with increased mesh

density. Summary of different cases analysed is shown in Table 2. Corresponding FE models are shown in Fig.5.

Fig. 5 FE models for 5 cases

Table 2 Mesh information

Linear static analysis was carried out for all these

cases and bending stress was plotted against analytical results. X-direction stress results are captured at each node on the top face, from the fixed to the free end. The results are plotted on a graph and are verified against the theoretical calculations has shown in Fig. 6.

Fig. 6 Bending stress for different cases and analytical results

From the graph it is observed that as the mesh density increases the results get closer to the theoretical results. Based on these results, the fan blade is meshed with 10- Node tetrahedron element and with a density of around 0.36 mm. Regions such as fillets of airfoil-platform interface, fillets at neck of dovetail and other fillet regions are more densely meshed for better prediction of results. The total number of elements in the fan blade is 125 332 and the total number of nodes is 202 349. FE model of the fan blade is shown in Fig. 7.


Fig. 7 FE model of fan blade

4.2 Material Property

A widely used material for fan and compressor blades is Ti-6Al-4V because of its low density and high strength. The material properties [10], considered at room temperature, are given in the Table 3.

Table 3 Material properties of Ti-6Al-4V

4.3 Boundary Conditions

Another important input to the analysis is the application of boundary conditions. In reality, the blade is clamped to the disc at the dovetail. The rotation of the disc spins the blade. Boundary conditions are shown in Fig. 8.

Fig. 8 Boundary conditions at dovetail of fan blade

4.4 Loading Conditions

The blade is subjected to other types of loads when it is spinning at full speed. One of these is the gas bending load, which tends to push the blade in tangential and axial direction. Calculation of gas bending load is done according to ref [11], [12] and [13]. Apart from the gas bending load, there is a

secondary flow between the blade tip and casing. This can induce a vibratory load in radially downward direction. This load determines the life of the fan blade. Analysis is carried out taking into consideration the above loads.

5. ANALYSIS

5.1 Static Analysis

Static analysis is carried out to determine the LCF. Stress distribution is also studied from static analysis. The results from this analysis determine whether to proceed with stress based approach or strain-based approach. In case of a strain based approach, stress-strain curve is also input to the analysis [10]. Multilinear kinematic hardening model is considered for the analysis as it takes into account the cyclic effects [14]. The stress-strain curve is shown in Fig. 9.

Fig. 9 Stress-strain plot from MIL handbook

5.2 Dynamic Analysis

As discussed in the loading section, the fan blade is also subjected to pressure fluctuations at the blade tip in the radial direction. Vibration characteristics of the blade are studied from modal analysis. Prestressed modal analysis is carried out at different speeds ranging from 0 to 10600 rpm [14]. The natural frequencies from the analysis are plotted on a Campbell diagram. As there are 24 blades in the first stage fan, a 24X line is drawn to check for interactions. Campbell diagram and mode shapes give a better understanding of the response of the blade. The amplitude of the response is determined from harmonic analysis.

Loading for harmonic analysis is obtained from pressure fluctuations between the blade tip and the casing. Analysis is carried out for full speed. Radial force equivalent to pressure fluctuations is applied in the downward direction [15], as shown in Fig.10. Structural damping of 20% is considered for the analysis.

6. FATIGUE LIFE ASSESSMENT The strains and stresses obtained from static and

dynamic analyses are used for fatigue life assessment. The strains obtained from static analysis are used for LCF whereas the vibratory stresses obtained from harmonic analysis are used for HCF.


Fig. 10 Excitation force applied at blade tip

6.1 Evaluation of LCF for fan blade

Fatigue strength properties are needed for LCF assessment [16].

Fatigue strength exponent ( ) 1260.0−=b

Fatigue ductility coefficient 8.2=

′

fε

Fatigue ductility exponent ( ) 86.0−=c

The total life is calculated using strain life relation [11]

( ) ( ) plastic

cff

elastic

bf

f NNE

222

εσε ′+′

=∆

Fig. 11 Goodman diagram

6.2 Evaluation of HCF for fan blade

HCF assessment is carried out based on dynamic analysis. It is obtained from the equation

( )bffen N2′= σσ as per ref. [17] and [18]. Endurance

stress enσ is obtained from intercept of Goodman diagram, as shown in Fig. 11.

The mean stress and alternating stresses are obtained from static and dynamic analyses.

7. RESULTS AND DISCUSSIONS Analysis is carried to assess the life of the fan

blade. As discussed in the previous section, the LCF is determined from static analysis, whereas HCF is determined from dynamic analysis.

7.1 Static Analysis

Different regions of the blade such as dovetail roots and roots of the aerofoil experience high centrifugal stresses when the blade spins at 10600 rpm along with the gas bending load. As the state of stress is multiaxial, von Mises stress is considered for life calculation. Figure 12 shows results of static analysis.

Fig. 12 von Mises stress of full blade Maximum von Mises stress of 1740 MPa is

observed at the dovetail root. But the yield strength of the material is only 985 MPa. Hence, fatigue cannot be computed considering stress based approach. Material non-linear analysis is carried out to study the plastic strain at the dovetail roots as shown in Fig. 13. The total strain is shown in Fig. 14.

Fig. 13 Plastic strain


Fig. 14 Total strain

7.2 LCF Calculation

The life at the dovetail root, calculated based on Section 6.1, is cyclesN f 3978= . LCF cycles at

different regions are shown in Fig. 15.

Fig. 15 LCF plot of fan blade

7.3 Modal Analysis

As discussed in the previous section, the modal analysis is carried out at different speeds to study the vibration characteristics. Frequencies are plotted on a Campbell diagram, as shown in Fig. 16.

Fig. 16 Campbell diagram As there are 24 blades in the first stage disc, each

blade is subjected to 24 excitations during each revolution. Mode shapes are shown in Fig. 17. It is observed that at almost all the frequencies, maximum deflection occurrs only at the tip. The fan blades would survive only a few seconds if they operate at the blade passing frequencies. When the blades are spinning at full speed, the most probable mode shape would be the 14th mode.

Fig. 17 Mode shapes


Fig. 18 Maximum displacement at 4240Hz

7.4 Harmonic Analysis

A force representing the cyclic load is applied at the tip of the blade in radially downward direction. Maximum displacement obtained is shown in Fig. 18.

The displacement obtained is similar to the 14th mode shape. Von Mises stress results are shown in Fig.19. It is observed that the maximum stress does not exceed the yield strength of the material.

Fig. 19 Maximum alternating stress

Fig. 20 High cycle fatigue plot

7.5 Stress Based Fatigue Calculation Procedure

Alternating stress σa from harmonic analysis and mean stress σm

8. CONCLUSIONS

from static analysis is plotted on a Goodman diagram to obtain the endurance stress. The endurance stress is substituted in the S-N equation to compute the life. Figure 20 shows the HCF plot of the fan blade.

Based on this study, a methodology is derived to analytically compute the fatigue life of typical aero engine fan blades. Some of the important conclusions derived from this analysis are:

• Failure of dovetail region of the blade is by LCF. It is also stated in some of the previous works.

• Failure of the dovetail is also by HCF and damage could be immediate if the blade is operated at the blade passing frequency.

• Major source of failure of the blade is by foreign object damage and there are lots of studies being carried out on HCF damage from FOD.

• Gas bending loads play an important role in the LCF of the blade.

• The gap between the casing and the fan blade tip can contribute to cyclic loading in the radially inward direction.

• Campbell diagram is important to understand the blade natural frequencies at the operating speeds. This could enable the designer to keep the operating speeds away from the blade natural frequencies, thereby preventing HCF damage.

9. REFERENCES [1] Dungey. C and Bowen. P, The effect of combined

cycle fatigue upon the fatigue performance of Ti-6Al-4V fan blade material, Elsevier, Journal of Materials Processing Technology Vol. 153-154 pp. 374-379, 2004.

[2] Weiju Ren, Theodore Nicholas, Effects and Mechanisms of Low Cycle Fatigue and Plastic Deformation on Subsequent High Cycle Fatigue Limit in Nickel-base Superalloy Udimet 720, Elsevier, Material Science and Engineering A Vol. 332 pp. 236-248, 2002.

[3] Stephan M. Russ, Effect of LCF on HCF Crack Growth of Ti-17, Elsevier, International Journal of Fatigue Vol. 27 pp. 1628-1636, 2005.

[4] J. Byrne et al., Influence of LCF Overloads on Combined HCF/LCF Crack Growth, International Journal of Fatigue Vol. 25 pp. 827-834, 2003.

[5] J. Byrne et al., Fatigue Crack Growth from Foreign Object Damage under Combined Low and High Cycle Loading. Part I: Experimental Studies, Elsevier, International Journal of Fatigue, Vol. 29, pp. 1339-1349, (2007)

[6] B. Li et al., Simulation of Cyclic Stress/Strain Evolutions for Multiaxial Fatigue Life Prediction, Elsevier, International Journal of Fatigue, Vol. 28 pp. 451-458, 2006.

[7] Shankar Mall et al., Effect of Predamage from Low Cycle Fatigue on High Cycle Fatigue Strength of Ti-6Al-4V, Elsevier, International Journal of Fatigue, Vol. 25, pp. 1109-1116, 2003.

[8] A. L. Dowson et al., Development of a Finite Element Based Strain Accumulation Model for the Prediction of Fatigue Lives in Highly Stressed Ti


Components, International Journal of Fatigue, Vol. 17, No. 6, pp. 385-398, 1995.

[9] Jack D. Mattingly, William H. Heiser, David T. Pratt, Aircraft Engine Design, 2nd

[10] Military Handbook, Metallic Materials and Elements for Aerospace Vehicle Structures, MIL-HDBK-5H; 1

Ed., AIAA, Inc., Education Series, 1801, Alexander Bell Drive, Reston, VA 20191-4344.

st

[11] Kogenhop. O, Propagation Lifetime Calculation of the P&W Compressor Fan Disc – Life Prediction Based on Crack Growth, NLR-TP-2000-302, 31

December 1998.

st

[12] H Cohen et al., Gas Turbine Theory, 4

May 2000.

th

[13] Jack D. Mattingly, William H. Heiser, David T. Pratt, Aircraft Engine Design, Second Edition, AIAA, Inc., Education Series, 1801, Alexander Bell Drive, Reston, VA 20191-4344.

Edition, 1996, Longman Group Limited, England

[14] Ansys documentation.

[15] Institution of Mechanical Engineers (Great Britain), International Conference of Fans, Fluid Machinery Group, WILEY, 1807.

[16] M. P. Szolwinski, J. F. Matlik, T. N. Farris, Effects of HCF Loading on Fretting Fatigue Crack Nucleation, ELSEVIER, International Journal of Fatigue, Vol. 21 671-677, 1999.

[17] Julie. A. Bannantine, Jess J. Comer and James L. Handrock, Fundamentals of Metal Fatigue Analysis, Prentice Hall, Upper Saddle River, NJ 07458.

[18] http://www.fatiguecalculator.com accessed on 21/10/2009

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