Simulation of fatigue failure in composite axial compressor blades

8
Simulation of fatigue failure in composite axial compressor blades Qubo Li a,, Janusz Piechna b , Norbert Müeller a a Turbomachinery Laboratory, Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226, USA b Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Warsaw, Poland article info Article history: Received 3 August 2010 Accepted 23 November 2010 Available online 2 December 2010 Keywords: Composite axial impeller Fatigue Finite element method Damage accumulation abstract Centrifugal forces are generated by a spinning impeller, of magnitudes that create large stresses. Aerody- namic forces are also imparted on an impeller blade, which varies with time and position. These two forces play different roles during compressor events. Damage accumulated from these events results in the fatigue failure of impeller material and structure. Therefore, it is important to design an impeller against dynamic and fatigue failure. The finite element method has been used in the study of impeller fracture mechanics and is regarded as an important tool in the design and analysis of material and struc- tures. Novel axial composite impellers, manufactured through filament winding technology, were invented and studied at Michigan State University. These impellers will be used to compress water vapor so as to use it as a refrigerant. In this study dynamic and fatigue behavior of two types of composite impellers 8B and 8C, were analyzed using commercial code ANSYS. Firstly, load cases were identified calculated and evaluated. Static analysis was then performed with a full 3-D finite element model. The critical zone where fatigue failure begins was extracted and used to determine life assessment positions. Secondly, aerodynamic forces imparted on the blade were obtained from FLUENT, so that damage from dynamic stresses could be calculated. Finally, based on the FEM and FLUENT simulation results, a linear damage accumulation model was employed as a damage estimation rule to predict life of the two composite impellers. A conservative life of 6498 h for 8B was calculated by this method, as was a life of 5435 h of 8C. Based on the method, safe fatigue life reduces for about 32% in case of 8B and 40% in case of 8C com- pared with conventional approaches where aerodynamic forces are omitted. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Of all the statistical data regarding fracture failure, the study of these events in rotating parts and structures account for more than 80% of the cases [1]. This relates to the high degree of interest in the failure of complicated rotating and moving systems. The root causes behind these failures vary a lot based on different operating conditions, such as high rotational speed and elevated tempera- ture. In general, compressor blade failures can be grouped into two categories: (a) fatigue, including both high-cycle fatigue (HCF) and low-cycle fatigue (LCF) [2–6] and (b) creep rupture [7]. Blade fatigue failures are often related to anomalies in mechanical behaviors and manufacturing defects. Because the mechanical per- formance requirements of compressor blades have high theoretical significance and application value, a precise life prediction is very important. Fig. 1 shows a comparison between different industrial components and their expected life cycles. Considering centrifugal stresses for the life prediction of impel- ler blade components, we examine the non-steady-state usage. Typically there is a high accelerating stage during every start-up, where low-cycle fatigue problems exist. The same problem hap- pens at every shut-down period where the deceleration effects cause large LCF problems. In this case, because of large loading changes from centrifugal forces within a short time, low-cycle fati- gue approaches are suitable to calculate damage in these two periods. From an aerodynamic viewpoint, when rotor blades rotate, the pressure difference from the suction side and pressure side changes periodically due to the aerodynamic impact from stator. These pressure differences change periodically which produce cyc- lic loads on rotor blades. Since this aerodynamic force is typically small compared with centrifugal force, it is usually neglected by investigators [8]. A relative small pressure stress coming from blade’s suction side and pressure side would generate dynamic pressure force changes along the blade’s rotating angle. This force is far less than many materials’ elastic force limit, and investigation of damage accumulation in this period can be done via high-cycle fatigue approaches. Under high temperature and high rpm condi- tions, this relatively small oscillating force coupled with a high centrifugal force would impact the impeller blades fatigue life, and possibly shorten the service life significantly. In published 0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.11.051 Corresponding author. E-mail address: [email protected] (Q. Li). Materials and Design 32 (2011) 2058–2065 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes

Transcript of Simulation of fatigue failure in composite axial compressor blades

Materials and Design 32 (2011) 2058–2065

Contents lists available at ScienceDirect

Materials and Design

journal homepage: www.elsevier .com/locate /matdes

Simulation of fatigue failure in composite axial compressor blades

Qubo Li a,⇑, Janusz Piechna b, Norbert Müeller a

a Turbomachinery Laboratory, Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226, USAb Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Warsaw, Poland

a r t i c l e i n f o

Article history:Received 3 August 2010Accepted 23 November 2010Available online 2 December 2010

Keywords:Composite axial impellerFatigueFinite element methodDamage accumulation

0261-3069/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.matdes.2010.11.051

⇑ Corresponding author.E-mail address: [email protected] (Q. Li).

a b s t r a c t

Centrifugal forces are generated by a spinning impeller, of magnitudes that create large stresses. Aerody-namic forces are also imparted on an impeller blade, which varies with time and position. These twoforces play different roles during compressor events. Damage accumulated from these events results inthe fatigue failure of impeller material and structure. Therefore, it is important to design an impelleragainst dynamic and fatigue failure. The finite element method has been used in the study of impellerfracture mechanics and is regarded as an important tool in the design and analysis of material and struc-tures.

Novel axial composite impellers, manufactured through filament winding technology, were inventedand studied at Michigan State University. These impellers will be used to compress water vapor so asto use it as a refrigerant. In this study dynamic and fatigue behavior of two types of composite impellers8B and 8C, were analyzed using commercial code ANSYS. Firstly, load cases were identified calculated andevaluated. Static analysis was then performed with a full 3-D finite element model. The critical zonewhere fatigue failure begins was extracted and used to determine life assessment positions. Secondly,aerodynamic forces imparted on the blade were obtained from FLUENT, so that damage from dynamicstresses could be calculated. Finally, based on the FEM and FLUENT simulation results, a linear damageaccumulation model was employed as a damage estimation rule to predict life of the two compositeimpellers. A conservative life of 6498 h for 8B was calculated by this method, as was a life of 5435 h of8C. Based on the method, safe fatigue life reduces for about 32% in case of 8B and 40% in case of 8C com-pared with conventional approaches where aerodynamic forces are omitted.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Of all the statistical data regarding fracture failure, the study ofthese events in rotating parts and structures account for more than80% of the cases [1]. This relates to the high degree of interest inthe failure of complicated rotating and moving systems. The rootcauses behind these failures vary a lot based on different operatingconditions, such as high rotational speed and elevated tempera-ture. In general, compressor blade failures can be grouped intotwo categories: (a) fatigue, including both high-cycle fatigue(HCF) and low-cycle fatigue (LCF) [2–6] and (b) creep rupture [7].Blade fatigue failures are often related to anomalies in mechanicalbehaviors and manufacturing defects. Because the mechanical per-formance requirements of compressor blades have high theoreticalsignificance and application value, a precise life prediction is veryimportant. Fig. 1 shows a comparison between different industrialcomponents and their expected life cycles.

Considering centrifugal stresses for the life prediction of impel-ler blade components, we examine the non-steady-state usage.

ll rights reserved.

Typically there is a high accelerating stage during every start-up,where low-cycle fatigue problems exist. The same problem hap-pens at every shut-down period where the deceleration effectscause large LCF problems. In this case, because of large loadingchanges from centrifugal forces within a short time, low-cycle fati-gue approaches are suitable to calculate damage in these twoperiods.

From an aerodynamic viewpoint, when rotor blades rotate, thepressure difference from the suction side and pressure sidechanges periodically due to the aerodynamic impact from stator.These pressure differences change periodically which produce cyc-lic loads on rotor blades. Since this aerodynamic force is typicallysmall compared with centrifugal force, it is usually neglected byinvestigators [8]. A relative small pressure stress coming fromblade’s suction side and pressure side would generate dynamicpressure force changes along the blade’s rotating angle. This forceis far less than many materials’ elastic force limit, and investigationof damage accumulation in this period can be done via high-cyclefatigue approaches. Under high temperature and high rpm condi-tions, this relatively small oscillating force coupled with a highcentrifugal force would impact the impeller blades fatigue life,and possibly shorten the service life significantly. In published

Fig. 1. Schematic S–N curve for different industrial components.

Q. Li et al. / Materials and Design 32 (2011) 2058–2065 2059

research, aerodynamic force has been obtained from calculation[9], yet its discussion is typically just limited to the case of stea-dy-state. Dynamic forces from the oscillating pressure forces werenot included to evaluate fatigue behavior of impeller blades. To theauthor’s knowledge, there are few studies that have been con-ducted considering influence of both oscillating aerodynamicforces and centrifugal forces on a compressor blade’s fatigue lifestudy.

At Michigan State University, a novel method has been devel-oped to manufacture a composite impeller using filament windingtechnology for water chillers [10]. A schematic structure for thechiller is shown in Fig. 2. Here impeller wheels can be actuatedfrom an external shaft, or from a magnetic force between polesin the outer shroud and coil poles on a stationary device surround-ing the impeller and housing. Through this approach to wheel pro-duction, several threads such as Kevlar and carbon fibers can beused to weave a composite impeller impregnated with epoxythrough an automated process. A myriad of patterns have alsobeen developed by Eyler [11]. Of these patterns, two patterns withthe greatest potential of structure stability and aerodynamic per-formance have been selected for compressing water vapor asrefrigerant [12].

In order to evaluate fatigue life to these two novel axial com-posite impellers, an investigation was conducted to calculate dam-

Air Handling Ducts

Cold Water Loop

Counter-rotating

Compressor

Cooling Tower Fan

Cooling Water Loop

Condenser

Recycled Water

Cooled Air

Rotor wrapped with stator

Fig. 2. Turbo chiller employing R718 refrigeration cycle [13].

age accumulated from an impeller during different workingperiods. During the first and last period, which are startup andshut-down period respectively, large angular acceleration anddeceleration caused the centrifugal force to dominate in the struc-ture loadings. Crack initiation or growth is mainly from this stressand it is calculated from ANSYS static analysis. During the standbyperiod, centrifugal force does not significantly vary with time,however oscillating aerodynamic stresses at the critical zone actas the main damage source. These oscillating stresses act to in-crease damage propagation and crack size; this force is calculatedfrom FLUENT analysis. During these periods, the S–N curve ap-proach is used to calculate fatigue resistance and the accumulationof them is then used to evaluate fatigue life of composite impellerblades.

2. Modeling

Impeller geometric patterns have significant influence on theperformance of both compressing capacity and structural stability.Fig. 3 presents two impeller patterns with the same shroud andhub diameters: 8B and 8C. These two impeller patterns can bemanufactured in the same mandrel; thus they share the sameblade angles at the shroud. Angle at the leading edge is set at25�, and 90� at trailing edge (relative to the radial direction). Sincethe wheel is weaved by crossing slots, different patterns mean dif-ferent weaving routes for manufacturing. Therefore, blade anglesat shroud tip for different patterns are the same, though the distri-bution of angles on the blade in radial direction is different for dif-ferent patterns. Considering that there are eight points on the outershroud, and from manufacturing view, when the second point ofweaving is going to surpass two points, it is named B; and if it isgoing to surpass three points, it is named C. Interested readerscan refer to detailed manufacturing process and naming methodin related publications [10–12].

To make these 3D impeller geometries, IGES data was modeledin Unigraphics NX and the data was then imported into ANSYS tocreate the finite element model required in the analyses. In themeshing process, a higher order three dimensional solid elementSOLID187 was employed to increase accuracy of the modeling.The element is defined by 10 nodes having 3� of freedom at eachnode: translations in the nodal x, y and z directions [13]. In orderto accurately evaluate the results, convergence analysis was per-formed. A suitable number of elements were obtained after step-by-step improving mesh density. The stabilization of deflectionat a location from the applied loads will be the criteria ofconvergence.

In Fig. 4, the results of convergence analysis are shown and fromthis figure it is evident that at least 140,000 elements are requiredfor the convergence. Similar trends are also found for case of 8Cwhere at least 240,000 elements are needed considering conver-gence issue.

3. Material characterization

The required properties for analyzing the structure are mate-rial’s mechanical properties used for stress analysis, and strengthproperties used for failure analysis [14]. Through work done byMichigan State University [10] it has been verified that 30% of fibervolume fraction have been obtained through filament windingsimilar approach and material’s mechanical properties barelymatch with ones calculated through classic laminate theory withintolerated difference. In this work, carbon fiber AS-4 from HexcelInc. (tensile modulus 231 GPa, transverse modulus 15 GPa, Poissonratio 0.2) and epoxy SC-15 made by Applied Poleramic Inc. (tensilemodulus 26.2 GPa, shear modulus 9.17 GPa, Poisson ratio 0.35)

Fig. 3. Rotor 3D 8B(left) and 8C(right) patterns.

Convergence Based on Deflection

0.20.40.60.8

11.21.41.61.8

2

Number of elements

Shro

ud d

efle

ctio

n

Convergence Based on Stress

8.0E+07

1.0E+08

1.2E+08

1.4E+08

1.6E+08

1.8E+08

2.0E+08

2.2E+08

0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 180,000 200,000

0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 180,000 200,000

Number of elements

Max

Von

s M

isse

s St

ress

Fig. 4. Convergence graphs of FE model.

Table 1Material mechanical properties (GPa).

Material E11 E22 = E33 G12 = G13 G23 m12 = m13 = m23

Carbon fiber 231 15 15 7 0.2Epoxy 26.2 26.2 9.17 9.17 0.35U-D composite 87.64 22.84 14.52 8.52 0.31

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were used as composite constituents; a similar fiber volume frac-tion of 30% can be obtained using this novel manufacturing meth-od. According to mechanics of composite materials [15],unidirectional (U-D) composites mechanical properties can bedetermined from micromechanics model from:

E1 ¼ Ef 1Vf þ EmVm ð1Þ

E2 ¼Vf

Efþ Vm

Em

� ��1

ð2Þ

v12 ¼ v f V f þ vmVm ð3Þ

G12 ¼Vf

Gfþ Vm

Gm

� ��1

ð4Þ

Calculated mechanical properties are listed in Table 1. Theseorthotropic material properties will be used as input for a furtherANSYS simulation. With a fiber volume fraction 30% obtainedthrough the filament winding method, composite density canreach about 1.31 g/cm3 with tensile strength of 1.40 GPa.

Centrifugal force

Aerodynamic force blade

Fracture blade root 1

Fracture blade root 2

shroud

hub

Fig. 5. Forces acting on a 2D blade.

Table 2Static analysis of blade under different events 8B.

Events Shrouddeflection(mm)

Maximumlongitudinalstress (MPa)(safety factor)

Maximumtransversestress (MPa)(safety factor)

Maximum in-plane shearstress (MPa)(safety factor)

Start-up 1.95 240 (5.85) 51.3 (1.17) 22 (3.64)Compression 1.84 208 (6.75) 48.1 (1.25) 20.3 (3.94)Shut down 2.10 253 (5.55) 53.2 (1.13) 24.5 (3.27)

Table 3Static analysis of blade under different events 8C.

Events Shrouddeflection(mm)

Maximumlongitudinalstress (MPa)(safety factor)

Maximumtransversestress (MPa)(safety factor)

Maximum in-plane shearstress (MPa)(safety factor)

Start-up 1.23 320 (4.38) 52.3 1.19) 28.7 (4.75)Compression 0.87 281 (4.99) 51.2 (1.33) 25 (4.85)Shut down 1.35 341 (4.11) 54.8 (1.16) 30.3 (4.04)

Fig. 6. Von Mises equivalent stres

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4. Loading

The loading cases were determined by inspection of the differ-ent operating conditions. There are four main operating conditionsaccording to different impeller working periods: (1) start-up, (2)steady-state, (3) standby compression, and (4) shut down. Theseloading cases were used for fatigue analysis and were treated in-ter-connectedly since damage accumulated from a previous work-ing period is able to initiate or enlarge crack growth rate for thenext one. All of the load cases that occur during the aforemen-tioned events can be categorized as follows:

(1) Aerodynamic loads on the blade.(2) Weight of the blade.(3) Centrifugal forces.(4) Forces that arise from start/stop angular acceleration.(5) Thermal effects.

All of the above forces were considered as main load eventswhich supposedly influence the impeller blade’s fatigue life. How-ever, because temperature changes along the flow channel wouldvary within 10 �C, force coming from thermal effect can be ne-glected. Gravity’s effect can also be neglected considering thatthe blade is made from composite material and the whole struc-ture is light, and axis of rotation is positioned vertically duringoperation. Thus loading considered in the study can be illustratedin Fig. 5.

5. Static strength analysis under centrifugal force

The purpose of this section is to discover the weak position ofthe structure under centrifugal force loading only. Therefore, thetemperature field is not considered here and the computations

s distribution for pattern 8B.

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were performed under a temperature of 50 �C, which is the testingrig’s average testing temperature.

With the start of the compressor, surfaces connecting theshroud and blade body come into steady contact state very quickly.Therefore the FE problem is a nonlinear problem and surface tosurface contact elements are used for this purpose. The results ofthese analyses are summarized in Table 2 for 8B and Table 3 for8C; here the rated loads correspond to the speed of 9000 rpm(steady-state operation speed). The safety factor results show thatin all cases both structures are in a safe condition under rpm of

11

119

120

121

122

124123

Fig. 7. Keypoint location i

Fig. 8. Von Mises equivalent stres

9000. When the tip clearance is 4 mm, for the maximum shrouddeflection case the impeller shroud will not hit the cylinder wall.

Fig. 6 shows that the Von Mises stress distribution on the impel-ler blade 8B and it is shown that maximum Von Mises stress existsat the fracture blade root 1 between blade body and shroud whichis supposed to be the critical zone. In addition, considering vibra-tions of blades, the connection root between blade body andshroud is also a dangerous area where an interaction of low cycleand high-cycle fatigue exists. This critical surface results in mostfracture failure in service mainly due to the influence of stress con-

111

112

113

114

115

1167

118

n the critical section.

s distribution for pattern 8C.

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centration factors. As it is illustrated in Fig. 7, positions at key-points 114 and 121 have equal, and the largest, stress concentra-

Fig. 9. FLUENT static pressure distribution on the blade for 8B.

Fig. 10. FLUENT static pressure distribution on the blade for 8C.

Aerodynamic pr

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

0 30 60 90 120 150 180

Rotating a

Stat

ic p

ress

ure,

Pas

cal

Fig. 11. Transient static pressure trend at

tion factors. These positions are supposed to be weak points,where during start-up and shut-down periods centrifugal force isonly considered. Changes of aerodynamic force are negligible com-pared with changes of centrifugal force’s change during these twoperiods. Similar phenomenon can also be observed for 8C patternin Fig. 8. It can be seen that the critical zone locates at the cornerwhere blades meet together, and it will be the area where maxi-mum damage accumulation occurs when centrifugal force is onlyconsidered as the main oscillating stress source.

6. Strength analysis under peak aerodynamic flow

The fluid analysis was carried out to estimate the aerodynamicforce exerted on the blade. Simulation was made using the com-mercial fluid dynamic software FLUENT. One stationery wheelwhich is similar to the 8C pattern and one rotating wheel (8B or8C pattern) were considered in the model. In the fluid calculation,a moving mesh was used so that the rotor impeller’s movementwas relative to the rotating fluid’s reference frame. The centralpart, which is mainly connected with a shaft to convert torque,has been ignored for aerodynamic performance calculation. Theblade velocity was set to be rx, where x is the rotating speed(9000 rpm) and r is the tip distance of the blade from wheel center.The fluid was assumed to be an ideal gas and viscous. The k–eequation was used to model the turbulence where enhanced walltreatment was set up to make sure the y+ value near the wallwas between 20 and 500 [16].

The static pressure distributions around the rotor blade for 8Bwere calculated and are shown in Fig. 9. The maximum static pres-sure locations are found at the corner between trailing edge of theblade and shroud. This is where the blade imparts kinetic energythe most into pressure energy thus the highest static pressure. Asimilar phenomenon for 8C pattern can be shown in Fig. 10. Whenthe impeller wheel rotates, transient static pressure at both pres-sure and suction sides, were also traced and it was found thatmean aerodynamic static pressure was about 4000 Pascal; as seenin Fig. 11. A linear distribution of aerodynamic force can be as-sumed on the blade based on the observation in Fig. 9, and thismean stress loading is also the pressure difference between suctionand pressure sides. Mean aerodynamic stress from the bending ef-fect at keypoint 114 is 27 MPa which is nearly 10 times less thancentrifugal stress (200 MPa). The critical zone of the structure fromaerodynamic stress only is located at the fracture blade root 2 be-tween blade body and hub.

essure on blade tip

210 240 270 300 330 360 390

ngle, Degree

weak point under 9000 rpm for 8B.

Table 4Linear elastic FEM analysis results for 8B.

Key positions Linear elastic analysis

A. Centrifugalstress (MPa)

B. Aerodynamic meanbending stress (MPa)

A + B

Key point 114 atfracture blade root1

200 9.3 209.3

Key point at fractureblade root 2

158 27 185

Table 5Linear elastic FEM analysis results for 8C.

Key positions Linear elastic analysis

A. Centrifugalstress (MPa)

B. Aerodynamic meanbending stress (MPa)

A + B

Key point 114 atfracture blade root1

278 1.1 279.1

Key point at fractureblade root 2

162 5.3 167.3

0

0.2

0.4

0.6

0.8

1

0 3 6 9 12 15 18 21 24 27Log (Nf), Cycles

S=St

ress

/Str

engt

h

Fig. 12. S–N for unidirectional carbon/epoxy composite material under longitudinalloading [19].

2064 Q. Li et al. / Materials and Design 32 (2011) 2058–2065

Linear elastic FEM results based on ANSYS calculation for 8B arelisted in Table 4 for several critical zones. Where keypoint 114 isthe critical zone during the start-up period and the keypoint atfracture blade root 2 is the other critical zone when aerodynamicstress is the only load during compression stage.

By summing aerodynamic stress and centrifugal stress together,combined stress during compressor standby period which will beimportant for fatigue life investigation next can be expressed suchas:

r ¼ rcentrifugal þ raerodynamic ð5Þ

From values listed in Table 4, it is readily found that keypoint114 would be the critical zone during standby stage since it hasthe biggest stress than other locations. Similar procedures werealso taken for 8C pattern where FEM results are listed in Table 5.

During standby periods, centrifugal force acts as constant meanstress while aerodynamic bending stress acts in an oscillating man-ner. Since both weak points in these two patterns locate at theplace around keypoint 114, and difference between maximumand minimum oscillating stress from bending effect is small com-paring with the mean centrifugal stress, it is thus reasonable tohave an R ratio in these two patterns equal to one. The value of thisR ratio is considered an important influence factor for crack growthrates [17]. Interestingly in the pattern 8C where centrifugal stressas mean stress is higher than 8B, the magnitude of oscillating stressfrom aerodynamic mean bending effect is smaller; still distancebetween this pattern’s maximum stress intensity factor and itsmaterial’s critical stress state is smaller than 8B, and it is foundthat crack growth rate in 8C during this period will be higher than8B. By comparing these two patterns, it is obvious that weak posi-tions locate at the same place, where blades intercross withshroud, and the 8C pattern has higher stress intensity factor than8B, even though a better aerodynamic performance has been foundin this pattern [12].

7. Accumulated fatigue damage

To model damage accumulated for fatigue mechanics of com-posite material, Ye [18] proposed stiffness degradation techniqueas a single criteria and based Ye’s model, Shookrieh improved itwith several practical parameters which make the model moreclosed with experimental data [19].

Based on the model, a normalized S–N curve in a unidirectionalcarbon/epoxy composite material under longitudinal fatigue load-ing has been obtained in Fig. 12. The figure is also validatedthrough available experimental data related with fatigue damagemodeling of composite materials [20–22]. In order to model accu-mulated damage during different stages in this study, this figure isused to calculate fatigue cycles at specific stress condition.

8. Life prediction results and discussions

As it is mentioned at the beginning of this work, the main pur-pose of this research is to evaluate fatigue life of two patterns ofcomposite impeller’s. This is done by calculating damage accumu-lated during different impeller working stages. Since centrifugaland aerodynamic stresses are the main loadings considered, loadprocedures can be simplified as in Fig. 11. From stress analysis inprevious sections, we have known that there exist stress concen-tration factors on the fracture blade roots and the critical zone infacture blade root 1 has the biggest dynamic stress changes. It isnecessary to consider points such as keypoint 114 as the weakpoints for structural life prediction. Similar conclusions have beenreached by authors to investigate impeller blade’s fatigue life[9,19].

During compressor start-up period, Dtstart, keypoint 114 in frac-ture blade root 1 is subjected to the heaviest tensile stress. Herethis point also has the largest stress concentration factor comparedto all other keypoints. Local damaging occurs as micro-crack nucle-ation occurs. Damage caused by the centrifugal stress is reciprocalto the fatigue resistance of the material at the same load range, Nf,i

according to Miner’s linear rule [23]:

di ¼1

Nf ;ið6Þ

The damage due to ni load cycles of the load rang i during differentworking range, is given by

di;n ¼ ni � di ¼ni

Nf ;ið7Þ

And the total damage caused to the detail by the load cycles of dif-ferent load levels is thus:

Dtot ¼X

i

di;n ¼X ni

Nf ;ið8Þ

In this case, the total fatigue life the impeller blade can be cal-culated through:

1Nf¼ Dtot ¼

X ni

Nf ;i¼ nstart

Nf ;startþ ncomp

Nf ;compþ nshut-down

Nf ;shut-downð9Þ

Taking Miner’s linear law as above, this composite impeller canrotate 3.2 � 105 cycles with a converted 9455 h before its cata-strophic failure (for 8B) and 7390 h for 8C. Since Miner’s law isbased on linear assumption, the law itself is overly conservative

t

p

Δtc

Δtstart

ΔtshutΔ

Fig. 13. Loadings for blade life determination.

Table 6Life prediction results of patterns.

Patterns Lifecycles

Lifeinhour

Modified life in hour(centrifugal + aeroloads)

Modified life in hour(only centrifugalload)

8B 3.2 � 105 9455 6498 95008C 2.5 � 105 7390 5077 8500

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in fatigue life predictions, especially in the compression stagewhere stress change is low and variable amplitude loading in thisstudy is considered. To improve the reliability of the predicted life,effects of vibrations and load variations should be considered.Here, we adopt a modified coefficient of 1.455 for the fractureblade root 1. The number of is based on a scatter factor of loads.From this consideration, we can draw a conclusion that fatigue lifetime of 6498 h for 8B and 5077 for 8C is a safe and conservativevalue.

Following the same procedure, except omitting aerodynamicstress in conventional approaches where only start and stop proce-dures exist in Fig. 13, calculated results in Table 6 show that safefatigue life time for 8B is about 9500 h, for 8C is 8500 h. It thereforeindicates that by taking into account of the high frequency aerody-namic load with small amplitude, a prediction of safe fatigue lifereduces about 32% for 8B and 40% for 8C. Presented results showthe importance of proposed methodology taking account termsomitted in conventional approaches; in order to predict a better fa-tigue life in such complicated geometry, more sophisticated andexact method integrated with aerodynamic and centrifugal loadsshould be proposed and applied.

9. Conclusion

The aim of this study was to numerically simulate two types ofaxial composite impellers’ fatigue life using both finite elementanalysis (FEA) and computational fluid dynamic (CFD) method.This paper presents first time the consideration of simultaneousinfluence on the predicted safe life of specific impeller, of two typesof load having different features. The low frequency load compo-nent is characterized by high load amplitude in contrary to a highfrequency aerodynamic load of small amplitude.

In this work, carbon fiber/epoxy composites with fiber volumefraction of 30% were used for blade structure. To simplify the mod-eling process, linear elastic stress strain relationship was assumed

for finite element analysis and composite micromechanical model-ing theory was used to predict composite’s physical and mechani-cal properties. Convergence issues were discussed and addressedbefore various loading to the blade, and all load cases, were iden-tified calculated and evaluated and negligible cases were ignored.By performing finite element modeling, the critical zone of theblade can be obtained at the tip of blade. The impeller rotates atthe designed rpm of 7000 and safety factors for fatigue life havebeen calculated based on FE analysis results. In order to betterevaluate impeller’s fatigue life, this work considered aerodynamicforce’s effect to the blade beam. From FLUENT calculation, a tran-sient static pressure trend was obtained which provided informa-tion for a further calculation of aerodynamic stress bending effectin ANSYS. Methodology of combining centrifugal stress and aero-dynamic stress from bending effect would improve fatigue life’sinvestigation accuracy. Based on this methodology and by usingMiner’s linear law, fatigue life evaluation was conducted basedon the detailed simulation results. Considering vibration and loadvariation effects, the fatigue life was modified. 8B pattern has a fa-tigue life of 6498 h and 8C pattern has shorter one 5077 h. Com-pared with conventional approaches where aerodynamic loadsare omitted, safe fatigue life has been reduced for 32% in case of8B and 40% in case of 8C. It is thus concluded that aerodynamicloads is important especially when fatigue life is predicted insophisticated impeller geometry.

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