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Fatigue life prediction of a heavy vehicle steel wheel under radial loads by using finite element analysis
Engineering Failure Analysis 20 (2012) 67–79
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Fatigue life prediction of a heavy vehicle steel wheel under radial loads by using finite element analysis M.M. Topaç a,⇑, S. Ercan b, N.S. Kuralay a a b
Department of Mechanical Engineering, Dokuz Eylül University, Faculty of Engineering, 35100 Bornova, Izmir, Turkey Hayes Lemmerz Jantasß Jant Sanayi ve Ticaret A.Sß., Organize Sanayi Bölgesi 4. Yol, No. 1, 45030 Manisa, Turkey
a r t i c l e
i n f o
Article history: Received 7 March 2011 Received in revised form 10 October 2011 Accepted 18 October 2011 Available online 25 October 2011 Keywords: Steel wheel Dynamic radial fatigue test Stress concentration Fatigue life prediction Finite element analysis
a b s t r a c t The origin of fatigue failure that occurs on the air ventilation holes of a newly designed heavy commercial vehicle steel wheel in dynamic radial fatigue tests is studied. In these tests, all of the test samples failed in the same regions. The cause of this damage was studied via finite element analysis. In order to determine the reason of the fatigue failure, stress analysis was performed via the finite element method. In this way, stress concentrated regions, where fatigue failure is expected, were determined. Mechanical properties of the wheel material were determined by tensile tests and hardness measurements. The fatigue life of the damaged wheel was estimated using the stress–life (S–N) approach, utilising the ultimate tensile strength of the processed wheel material and the Marin factors determined for the critical regions. To extend the life of the wheel disc and delay the onset of fatigue, design enhancement solutions were applied. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The steel wheel, which is one of the basic structural elements of motor vehicle tyre assemblies, connects the vehicle body and the tyre and enables the wheel rotation. It also transmits vertical and lateral tyre forces to the axle housing or the axle beam [1,2]. Because of the position and function in vehicle suspensions, they are categorised as safety components [3]. Therefore, it is necessary to guarantee a predicted durability of this component that should not fail under service loads. Location of a steel wheel in the rear axle assembly of a heavy commercial vehicle is seen in Fig. 1. The load capacity and fatigue behaviour of a steel wheel under a certain dynamic load is determined by dynamic radial fatigue tests shown in Fig. 2. In these tests, the tyre-wheel assembly is positioned on a rotating drum. The predicted radial test load is applied to the tyre producing contact pressure between the tyre and the drum. In this way, cyclic loading, that may occur during service is simulated. According to the standards predicted by EUWA – The Association of European Wheel Manufacturers and SAE – The Society of Automotive Engineers, steel wheels should not fail during Nw = 5 105 wheel turns in these tests [4,5]. On the other hand, in some cases an enhanced fatigue life may be required by the vehicle manufacturers. In the design process of a newly designed 22.5 8.25 steel wheel, although the component satisfies EUWA and SAE standards, vehicle manufacturers demanded an enhanced fatigue life about Nw = 1 106 wheel turns. During the radial fatigue tests, it was observed that, fatigue failure took place at the air ventilation holes of the wheel disc at about Nw = 5.3 105 wheel turns. In these tests, samples were controlled per 2 104 wheel turns. This means that the minimum number of wheel turns before fatigue failure initiation is in the range of Nw = 5.1 105–5.3 105 turns. An example of failure location is seen
⇑ Corresponding author. Tel.: +90 232 388 31 38; fax: +90 232 388 78 68. E-mail address: [email protected] (M.M. Topaç). 1350-6307/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2011.10.007
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Fig. 1. A typical rear axle assembly of a heavy commercial vehicle.
Fig. 2. General view of the wheel dynamic radial fatigue test.
in Fig. 3. This kind of a failure may result in dangerous consequences such as separation of the wheel from the axle as shown in Fig. 4. In literature there are a number of published works on the failure of steel and aluminium alloy wheels under radial and/or lateral forces [3,6–11]. Carboni et al. investigated the fatigue behaviour of the steel wheel material, in terms of S–N and the crack propagation curves. They also assessed the acceptability of the defects due to the hole punching procedure of the air ventilation hole where in-service premature failures took place [3]. Carvalho et al. proposed a key method to predict the fatigue life of steel wheels that is based on finite element analysis. In their work, they predicted the ultimate tensile strength of the processed wheel disc material via Vickers and Brinell hardness tests [6]. Grubisic and Fischer described a method for optimal wheel design [7]. Hsu and Hsu introduced a sequential neural-network approximation method (the SNA method) to handle the structural optimisation problem of aluminium disc wheels under cornering fatigue constraints [8]. Firat and Kocabicak proposed a fatigue life prediction methodology that is based on the local strain-life approach [9]. Raju et al. presented an evaluation of the fatigue life of aluminium alloy wheels under radial loads by using finite element analysis. In order to obtain the S–N curve they used the results of the rotary bending fatigue tests in which test specimens extracted from the spokes of alloy wheels were used [10]. A computational methodology that was proposed for fatigue damage assessment of steel wheels along with a detailed theoretical background was given by Firat et al. [11]. This paper presents the computer-aided fatigue life prediction of a failed truck wheel prototype. In order to analyse this failure, a full scale CAD model of the wheel was prepared. Loading conditions of the bench tests were simulated on this
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Fig. 3. Fatigue failure at the air ventilation hole after 6.4 105 wheel turns.
Fig. 4. Failure of tyre-axle connection of a test sample.
model by using the finite element analysis. Stress analysis of the steel wheel was performed via ANSYSÒ Workbench V12.0 commercial finite element software. As a result, stress distribution and possible failure initiation regions that are under stress concentration on the damaged wheel disc were obtained. The mechanical properties of the non-processed wheel disc material were obtained via tensile tests. Moreover, in order to determine the effects of the manufacturing process on the ultimate tensile strength of the wheel disc material, hardness test samples were extracted from steel wheel samples and Vickers hardness measurements were carried out as proposed by Carvalho et al. [6]. Through the use of this data, the estimated S–N diagram was constructed by means of a simple method that uses the ultimate tensile strength of the processed material and endurance-limit modifying factors, also known as Marin factors. This diagram was utilised in fatigue analyses and fatigue life estimation of the wheel disc. In order to reduce the stress concentration and obtain an extended fatigue life, a design enhancement solution was also applied to the wheel disc.
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2. Stress analysis of the wheel 2.1. Finite element model A tubeless steel wheel basically consists of two parts: The rim flange and the wheel disc. These two components are joined via gas shielded arc welding or submerged arc welding. From literature it is known that a steel wheel may fail at the air ventilation holes of the wheel disc due to stress concentration [3,11]. In order to predict the stress magnitude at the damaged regions of the wheel disc, a full scale solid model of the wheel, shown in Fig. 3, was built using SolidWorksÒ, a commercial software. In order to build the finite element model, shown in Fig. 5, the CAD model was imported into ANSYSÒ Workbench V12.0 preprocessing environment. The finite element model consisting of 196,200 elements and 335,738 nodes, was meshed using SOLID187, a higher order three dimensional solid element, which has a quadratic displacement behaviour and is well suited to modelling irregular meshes. The element is defined by 10 nodes having three translational DOF at each node [12,13]. In this model, in order to find out whether there are other critical areas on the wheel disc in addition to the damaged regions, the mesh density was kept as intense as permitted by the computer hardware capacity. To model the contact between the structural parts of the steel wheel, CONTA174 and TARGE170 elements were used. A completely bonded contact was chosen as the contact condition for all welded surfaces. 2.2. Load model Wheel radial fatigue tests were performed in accordance with EUWA (Association of European Wheel Manufacturers) – E S 3.11 and SAE (Society of Automotive Engineers) – J267 standards. Test conditions can be found in Table 1. The schematic view of these tests is also given in Fig. 6. In these tests, a wheel-tyre assembly was positioned on the driven drum under a radial load Fr with a predicted tyre inflation air pressure pi. The radial test load Fr is determined as:
Fr ¼ Fv k
ð1Þ
where Fv is the nominal design load of the wheel, as specified by the vehicle or wheel manufacturer. The accelerated test load factor k is given as 2.2 by EUWA and SAE [4,5]. The nominal design load of the wheel is Fv = 3650 kg. Hence, the radial test load Fr was computed as 8030 kg or P = 78 kN. The drum has a rotational speed of 237 rpm which corresponds to ca. 45 km/h speed of a vehicle. Finite element analysis was performed considering the radial test load P and the effect of the tyre inflation pressure pi. The boundary conditions used in the finite element analysis is shown in Fig. 7. Here, the actual configuration of wheel-tyre assembly that is identical to the mounting of the wheel and the test device was taken into account. Fixed support condition was applied on the nut–wheel disc (F1) and wheel disc–brake drum (F2) contact surfaces. The vertical load model of the wheel is also given in Fig. 8 where, the radial load P was exerted on tyre bead seat–rim contacts. In order to take the effects of the air pressure into account, a uniform pressure of pi = 10 bar = 1 MPa was also applied along the outer circumference of the rim flange. Any effect of centrifugal force is ignored.
Fig. 5. Finite element model of the steel wheel (cutaway view).
Table 1 Test conditions. Nominal wheel load, Fv (kg)
Radial test load, Fr (kg)
Accelerated test load factor, k
Tyre pressure, pi (bar)
Camber angle, rw (°)
Rotational wheel speed, nw (rpm)
3650
8030
2.2
10
0
237
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Fig. 6. Schematic view of the wheel dynamic radial fatigue test (according to [4]).
Fig. 7. Fixed surfaces on the finite element model.
Fig. 8. Load model of the steel wheel.
2.3. Determination of the mechanical properties of wheel disc material The wheel disc is manufactured using the flow forming process from 13 mm thick sheets made from hot rolled, high strength steel S355MC (Material number 1.0976 according to DIN EN 10149). Because of its high elongation characteristic,
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steel is suitable to cold forming and flow forming. The chemical composition of the material obtained from the supplier is given in Table 2 [14]. In order to determine the exact mechanical properties of the non-processed wheel disc material, samples were extracted from S355MC steel sheet in pursuance of DIN 50125 and tensile tests were carried out in accordance with DIN EN 10002-1 [15,16]. Tests were conducted at room temperature. Average mechanical properties obtained from these tests are given in Table 3. On the other hand the flow forming process increases hardness and enhances ultimate tensile strength of steel [17,18], resulting in the improvement of fatigue life [6]. However, the geometry of the failure region means it is not possible to extract tensile test samples. It is also known from literature that the hardness of the material gives an approximation of the ultimate tensile strength [19,20]. In order to take the effects of the manufacturing process on the ultimate tensile strength into account in the finite element analysis, Vickers hardness tests were also carried out on the specimens extracted from the failure region as shown in Fig. 9. Hardness was measured at ten points in each specimen. All of the measurements were performed in accordance with DIN ISO 6507-1 [21]. Average Vickers hardness was obtained as 225 HV that corresponds to ca. Sut = 720 MPa. 2.4. Finite element analysis A total nominal test load of P = 78 kN and a tyre pressure of pi = 1 MPa were exerted on the finite element model statically in accordance with Fig. 8. Stress analysis was carried out using ANSYSÒ Workbench V12.0 commercial finite element analysis software. The analysis pointed out that there are stress concentrated regions on the chamfer surfaces of the air ventilation holes, which are well-matched with the location of the fatigue failure as seen in Fig. 10. Circumferential stress distribution on the outer and inner chamfer surfaces of the air ventilation holes for the most stressed position is also shown in Fig. 11. The location of the maximum stress concentrated region is detected on the outer surface at ca. u = 233° with respect to Fig. 11. Equivalent von Mises stress distribution on the full model and stress alteration at the critical regions computed for various positions of an air ventilation hole during one turn of the wheel are presented in Fig. 12. Here, h is the angular position of Table 2 Chemical composition of disc material. Component
C (max)
Mn (max)
P (max)
S (max)
Si (max)
Al (min)
Nb (max)
Ti (max)
V (max)
wt.%
0.12
1.50
0.025
0.020
0.50
0.015
0.09
0.15
0.20
Table 3 Mechanical properties of non-processed disc material (S355MC). Modulus of elasticity, E (GPa)
Poisson’s ratio, t
Yielding strength, Sy (MPa)
Ultimate tensile strength, Sut (MPa)
Maximum elongation, emax (%)
210
0.3
374.51
522.57
24.75
Fig. 9. Hardness test samples extracted from the failure regions.
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Fig. 10. Comparison of analysis and test results.
Fig. 11. Stress distribution on the surfaces of the air ventilation hole chamfers along the circumference for the critical loading position.
the air ventilation hole with respect to the acting direction of the vertical load in X–Z plane. Maximum value of von Mises stress at the critical failure region was calculated as rmax = 295.8 MPa, where h 108°. 3. Fatigue life prediction In order to predict the fatigue life of the wheel disc in the range of 105–106 cycles, the estimated S–N diagram of the processed wheel disc material was composed by means of a simple method given in Ref. [22] that uses the ultimate tensile
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Fig. 12. Stress alteration at the maximum stressed region during one turn of the wheel.
strength, Sut and the mean stress, rm. It is known from literature that fatigue analyses that use this method and the static equivalent von Mises stresses distribution obtained from finite element analyses provide a reasonable estimation of the fatigue life of steel-based mechanical parts [23]. Stress life endurance limit S0e of steels having a tensile strength Sut 6 1400 MPa is given as:
S0e ¼ 0:504 Sut
ð2Þ
6
at 10 cycles for the ideal rotating-beam specimen [20,24]. In order to estimate the true fatigue strength Se, five factors called Marin factors were taken into account with respect to Shigley and Mischke [24]. Se can be written in term of these parameters and S0e as:
Se ¼ ka kb kc kd ke S0e
ð3Þ
Here, the surface factor ka which depends on the surface finish, can be determined by using the average surface roughness, Ra and the tensile strength, Sut. Fig. 13 shows the relation between ka and Sut for various Ra values [22]. In order to determine this factor for the wheel disc, Ra was measured at the critical regions of twenty different steel wheel samples. The average surface roughness Ra was obtained as 2.29 lm. For Sut = 720 MPa, ka was determined as 0.85. Deformation of the wheel disc under vertical load and tyre pressure is given in Fig. 14. Here, detail C shows one of the most stressed angular position of an air ventilation hole. In this position, the air ventilation hole is subjected to bending in both g–e and n–e planes. In order to determine the size factor, the air ventilation hole surface was taken into account as the section that is subjected to bending. The size factor kb is given as:
kb ¼
de 7:62
0:1133
Fig. 13. Surface factor ka for steel as a function of average surface roughness, Ra and the ultimate tensile strength, Sut (according to [22]).
ð4Þ
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Fig. 14. A simple approach to predict the stress-concentration factor around the air ventilation hole (deformation is exaggerated).
where de, the effective dimension can be written as [24]:
de ¼ 0:808ðhbÞ0:5
ð5Þ
The average depth of the hole, h which is also the thickness of the wheel disc at this region was measured as t = 6.5 mm. The width of the section was calculated as the circumference of the air ventilation hole as b = 251.327 mm by using r = 40 mm. Hence, the effective dimension de was obtained as 32.658 mm and kb was computed as 0.848. The load factor kc is given as 1 for bending and the temperature factor kd is also 1 for the range of the ambient temperature of T = 0–250 °C [24]. By means of static finite element analysis, it is observed that there are stress concentrated regions at the failure locations. Therefore, in addition to the modifying factors mentioned, a fatigue-strength-reduction factor ke must be taken into account by means of the fatigue stress-concentration factor kf that is related to the static stress-concentration factor kt [24]. Hence ke is calculated as:
ke ¼
1 kf
ð6Þ
In order to determine the stress-concentration factor, the deformation at the critical loading position (detail C) was taken into account. It was idealised that the air ventilation hole is located on a planar surface that is subjected to out-of-plane bending by means of the bending moments M1 and M2, as shown in Fig. 14. Because of the complex shape of the wheel disc, it is difficult to compute the exact values of M1 and M2 under the loads P and pi. On the other hand, if either M1 or M2 is equal to zero, which portrays the case of simple bending, kt is given as [25]:
kt ¼ 1:79 þ
0:25 0:81 0:26 þ 2 3 0:39 þ 2rt 1 þ 2r 1 þ 2r t
ð7Þ
t
The proportion r/t was computed as 6.154. Hence, kt was calculated as 1.817. The maximum value of kt is also given as 2.0, where M1 = M2. In this case kt is independent from the r/t proportion. Thus, it can be assumed that the static stress-concentration factor kt for this geometry should be in the range of 1.817–2.0. By taking the effect of the notch sensitivity q into account, fatigue stress-concentration factor kf can be written as:
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kf ¼ 1 þ qðkt 1Þ
ð8Þ
According to research q is given as a function of the notch radius r, and the ultimate tensile strength Sut. For Sut 720 (MPa) and the value of the notch radius r, which is greater than r = 4.0 mm, q was obtained as ca. 0.862 [22,24,26]. Hence, the range of kf was calculated as 1.704–1.862. By using these values, the fatigue-strength-reduction factor was computed in the range of ke = 0.537–0.587. On the other hand, at the critical loading position, when the maximum stress concentration occurs at the failure region, the air ventilation hole is subjected to bending in both g–e and n–e planes as seen in Fig. 14. It can be concluded that for this position, the moments M1 or M2 cannot be equal to zero. Hence, ke should be less than the maximum value of 0.587. By using the Marin factors, the true fatigue strength Se was calculated in the range of 140.46–153.54 MPa, for the variation range of kf. So far, the effect of the mean stress rm on the true fatigue strength Se has been ignored. Therefore, the Se range must be corrected by means of a failure criteria. Since the loading has fluctuating characteristic (rm > 0) as seen in Fig. 12, modified Goodman and Gerber approaches can be applied [22]. On the other hand, because of the ductile characteristic of the wheel disc material, the Gerber approach is preferable [6,22,24,27]. The corrected fatigue limit for the Gerber approach is given as [22,24,28]:
" Sfk ¼ Se 1
rm
2 # ð9Þ
Sut
here, the mean stress rm can be expressed as:
rm ¼
rmax þ rmin
ð10Þ
2
It must be noted that, rmin = 14.74 MPa is the minimum value of the stress concentration at the critical regions as shown in Fig. 12. rm was assumed as constant. The corrected fatigue limit range was calculated as Sfk = 133.93–146.4 MPa. According to the Basquin relation, the characteristic of the estimated S–N diagrams was assumed as being linear between 102 and 106 load cycles [22] as shown in Fig. 15. The S–N diagrams plotted by taking the modifying factors and the mean stress into account were defined in the ANSYSÒ Workbench V12.0 user interface. The parameters used in the fatigue analyses are given in Table 4. Von Mises stress distribution obtained from finite element analysis was utilised in fatigue life calculations. Stress–life approach was used to determine the fatigue life of the processed wheel disc material. All fatigue analyses were performed according to infinite life criteria (N = 107 cycles).
Fig. 15. Estimated S–N diagram for the critical region of the wheel disc.
Table 4 Parameters used in the fatigue analyses. Parameter
Modulus of elasticity Poisson’s ratio Ultimate tensile strength Surface factor Size factor Load factor Temperature factor Fatigue-strength-reduction factor
Symbol
E
t Sut ka kb kc kd ke
S355MC (1.0976) Condition
Value
Cold formed carbon steel Cold formed carbon steel Cold formed carbon steel Sut = 720 MPa, Ra = 2.29 lm de = 32.658 mm Bending Ambient temperature, T < 250 °C kf = 1.704–1.862
210 GPa 0.3 720 MPa 0.85 0.848 1.0 1.0 0.587–0.537
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4. Results and discussion Finite element analysis showed that the critical regions, where fatigue failure was initiated during wheel radial fatigue tests, are under stress concentration. Failure that took place during the tests is one of three typical problems of the disc wheels that are caused by the maximum circumferential stress as reported by Carboni et al. and Firat et al. [3,11]. In the light of the results obtained from fatigue analyses, it was estimated that crack initiation may occur at the critical region of the outer chamfer surface in the range of N = 6.45 105–8.75 105 load cycles for the minimum value of ke = 0.537. On the other hand, it must be noted that one turn of the wheel corresponds to two load cycles at the critical regions of the air ventilation holes as shown in Fig. 12. Thus, it can be said that the wheel may fail in the range of Nw = 3.23 105–4.37 105 turns. This means that by using finite element analysis, fatigue life of the wheel disc may be estimated with an average approximation of 73% when assuming the average number of the wheel turns before crack initiation at the radial fatigue tests as Nw = 5.2 105 turns. As an example, the fatigue life N estimations at the critical region for ke = 0.537 are shown in Fig. 16. With the exception of the predicted critical regions, the steel wheel satisfies the infinite life criteria. Results of the fatigue analyses for various ke values are given in Table 5. A comparison of radial fatigue tests and the results obtained from fatigue analyses can also be found in Fig. 17 for these ke values. In order to enhance the fatigue life of the steel wheel, it is necessary to decrease the stress concentration at the critical regions. The simplest way to reduce the stress concentration and improve the fatigue life is to increase the thickness of the wheel disc. On the other hand, an increase of sheet metal thickness along the radial cross section causes an unnecessary
Fig. 16. Fatigue life estimations at the critical region of the air ventilation hole for ke = 0.537.
Table 5 Results of the fatigue analyses for various ke values. Fatigue strength-reduction factor ke ()
Corrected fatigue limit Sfk (MPa)
Estimated failure initiation cycles, N (load cycles)
Estimated wheel turns before failure initiation, Nw (turns)
0.587 0.575 0.562 0.550 0.537
146.4 143.28 140.14 137.044 133.93
837,830 783,630 733,350 687,590 645,050
418,915 391,815 366,675 343,795 322,525
Fig. 17. Comparison of the test results and the estimated fatigue life of the wheel disc as a function of ke.
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Fig. 18. Design enhancement at the critical regions of wheel disc.
weight increase. Since light weight wheels regain contact with the ground quicker than heavier wheels after a lift due to poor road surface [29], a total thickness increase is not a preferred solution. In order to solve the problem, a form enhancement solution was also carried out, given in Fig. 18. In order to strengthen the critical regions, the local thickness, tc and the crosssectional radius, rc was increased. Because of the nature of flow forming, it is not necessary to increase the thickness along the whole section. The computer aided flow forming process enables the thickness to be increased only at the critical regions along the radial cross section. Finite element analyses also showed that by using this solution, it is possible to decrease the maximum equivalent stress at these regions without any weight increase. The proposed design enhancement was applied to five new steel wheel prototypes which were also subjected to wheel radial fatigue tests. In these tests Nw = 1.26 106– 1.39 106 wheel turns range was obtained without any fatigue failure which is more than the desired 1 106 load cycles. 5. Conclusion The premature failure of a truck steel wheel prototype that occurs during the course of radial fatigue tests is studied using finite element analysis. Finite element-based stress analysis showed that the crack initiation regions on the wheel disc are subjected to stress concentration. Crack initiation occurs at the most stress concentrated regions of the air ventilation holes which are the critical regions of the wheel. The predicted failure locations are quite close to the actual crack initiation regions. In order to predict the minimum number of wheel turns before fatigue crack initiation, the stress life (S–N) approach was utilised. The estimated S–N diagram was constructed using the ultimate tensile strength of the processed wheel disc material which was determined via Vickers hardness tests. The effects of factors such as surface roughness, size and stress concentration were also taken into account using endurance-limit modifying factors also known as Marin factors. The Gerber approach was used to predict the fatigue life of the wheel disc. The results obtained correspond to the results of radial fatigue tests. In order to obtain an extended fatigue life, a design enhancement solution, including both increasing the local thickness, tc and the cross-sectional radius, rc at the critical regions was applied. Stress analyses showed that by using this solution, it is possible to decrease the equivalent von Mises stress at these regions. Wheel radial fatigue tests also proved that the proposed design enhancement is a suitable solution to obtain the desired fatigue life. It can be concluded that the fatigue analysis based on the static stress analysis and the stress life approach gives a reasonable estimate of the fatigue life of the steel wheel. By using the procedure which is used in this study, the number of prototypes produced before mass production may be considerably reduced. On the other hand, during the design process and the durability enhancement studies of vital structural elements such as automotive wheels, the numerical results obtained must necessarily be verified by bench tests or road tests. Acknowledgements This study was carried out with the support of Hayes Lemmerz Jantasß Jant Sanayi ve Ticaret A.S ß . in Manisa, Turkey. The authors are grateful for the suggestions of Mr. Ö. Öztürk, the R&D director at Hayes Lemmerz Jantasß Jant Sanayi ve Ticaret A.Sß . The considerable efforts of Mr. G.M. Gencer, M.Sc. of Dokuz Eylül University Department of Mechanical Engineering on the performance of the tensile tests and the hardness measurements are acknowledged. The contributions of Mr. C. Cengiz and Mr. H.E. Enginar during the preparation of CAD models are also appreciated.
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Contents lists available at SciVerse ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Fatigue life prediction of a heavy vehicle steel wheel under radial loads by using finite element analysis M.M. Topaç a,⇑, S. Ercan b, N.S. Kuralay a a b
Department of Mechanical Engineering, Dokuz Eylül University, Faculty of Engineering, 35100 Bornova, Izmir, Turkey Hayes Lemmerz Jantasß Jant Sanayi ve Ticaret A.Sß., Organize Sanayi Bölgesi 4. Yol, No. 1, 45030 Manisa, Turkey
a r t i c l e
i n f o
Article history: Received 7 March 2011 Received in revised form 10 October 2011 Accepted 18 October 2011 Available online 25 October 2011 Keywords: Steel wheel Dynamic radial fatigue test Stress concentration Fatigue life prediction Finite element analysis
a b s t r a c t The origin of fatigue failure that occurs on the air ventilation holes of a newly designed heavy commercial vehicle steel wheel in dynamic radial fatigue tests is studied. In these tests, all of the test samples failed in the same regions. The cause of this damage was studied via finite element analysis. In order to determine the reason of the fatigue failure, stress analysis was performed via the finite element method. In this way, stress concentrated regions, where fatigue failure is expected, were determined. Mechanical properties of the wheel material were determined by tensile tests and hardness measurements. The fatigue life of the damaged wheel was estimated using the stress–life (S–N) approach, utilising the ultimate tensile strength of the processed wheel material and the Marin factors determined for the critical regions. To extend the life of the wheel disc and delay the onset of fatigue, design enhancement solutions were applied. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The steel wheel, which is one of the basic structural elements of motor vehicle tyre assemblies, connects the vehicle body and the tyre and enables the wheel rotation. It also transmits vertical and lateral tyre forces to the axle housing or the axle beam [1,2]. Because of the position and function in vehicle suspensions, they are categorised as safety components [3]. Therefore, it is necessary to guarantee a predicted durability of this component that should not fail under service loads. Location of a steel wheel in the rear axle assembly of a heavy commercial vehicle is seen in Fig. 1. The load capacity and fatigue behaviour of a steel wheel under a certain dynamic load is determined by dynamic radial fatigue tests shown in Fig. 2. In these tests, the tyre-wheel assembly is positioned on a rotating drum. The predicted radial test load is applied to the tyre producing contact pressure between the tyre and the drum. In this way, cyclic loading, that may occur during service is simulated. According to the standards predicted by EUWA – The Association of European Wheel Manufacturers and SAE – The Society of Automotive Engineers, steel wheels should not fail during Nw = 5 105 wheel turns in these tests [4,5]. On the other hand, in some cases an enhanced fatigue life may be required by the vehicle manufacturers. In the design process of a newly designed 22.5 8.25 steel wheel, although the component satisfies EUWA and SAE standards, vehicle manufacturers demanded an enhanced fatigue life about Nw = 1 106 wheel turns. During the radial fatigue tests, it was observed that, fatigue failure took place at the air ventilation holes of the wheel disc at about Nw = 5.3 105 wheel turns. In these tests, samples were controlled per 2 104 wheel turns. This means that the minimum number of wheel turns before fatigue failure initiation is in the range of Nw = 5.1 105–5.3 105 turns. An example of failure location is seen
⇑ Corresponding author. Tel.: +90 232 388 31 38; fax: +90 232 388 78 68. E-mail address: [email protected] (M.M. Topaç). 1350-6307/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2011.10.007
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Fig. 1. A typical rear axle assembly of a heavy commercial vehicle.
Fig. 2. General view of the wheel dynamic radial fatigue test.
in Fig. 3. This kind of a failure may result in dangerous consequences such as separation of the wheel from the axle as shown in Fig. 4. In literature there are a number of published works on the failure of steel and aluminium alloy wheels under radial and/or lateral forces [3,6–11]. Carboni et al. investigated the fatigue behaviour of the steel wheel material, in terms of S–N and the crack propagation curves. They also assessed the acceptability of the defects due to the hole punching procedure of the air ventilation hole where in-service premature failures took place [3]. Carvalho et al. proposed a key method to predict the fatigue life of steel wheels that is based on finite element analysis. In their work, they predicted the ultimate tensile strength of the processed wheel disc material via Vickers and Brinell hardness tests [6]. Grubisic and Fischer described a method for optimal wheel design [7]. Hsu and Hsu introduced a sequential neural-network approximation method (the SNA method) to handle the structural optimisation problem of aluminium disc wheels under cornering fatigue constraints [8]. Firat and Kocabicak proposed a fatigue life prediction methodology that is based on the local strain-life approach [9]. Raju et al. presented an evaluation of the fatigue life of aluminium alloy wheels under radial loads by using finite element analysis. In order to obtain the S–N curve they used the results of the rotary bending fatigue tests in which test specimens extracted from the spokes of alloy wheels were used [10]. A computational methodology that was proposed for fatigue damage assessment of steel wheels along with a detailed theoretical background was given by Firat et al. [11]. This paper presents the computer-aided fatigue life prediction of a failed truck wheel prototype. In order to analyse this failure, a full scale CAD model of the wheel was prepared. Loading conditions of the bench tests were simulated on this
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Fig. 3. Fatigue failure at the air ventilation hole after 6.4 105 wheel turns.
Fig. 4. Failure of tyre-axle connection of a test sample.
model by using the finite element analysis. Stress analysis of the steel wheel was performed via ANSYSÒ Workbench V12.0 commercial finite element software. As a result, stress distribution and possible failure initiation regions that are under stress concentration on the damaged wheel disc were obtained. The mechanical properties of the non-processed wheel disc material were obtained via tensile tests. Moreover, in order to determine the effects of the manufacturing process on the ultimate tensile strength of the wheel disc material, hardness test samples were extracted from steel wheel samples and Vickers hardness measurements were carried out as proposed by Carvalho et al. [6]. Through the use of this data, the estimated S–N diagram was constructed by means of a simple method that uses the ultimate tensile strength of the processed material and endurance-limit modifying factors, also known as Marin factors. This diagram was utilised in fatigue analyses and fatigue life estimation of the wheel disc. In order to reduce the stress concentration and obtain an extended fatigue life, a design enhancement solution was also applied to the wheel disc.
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2. Stress analysis of the wheel 2.1. Finite element model A tubeless steel wheel basically consists of two parts: The rim flange and the wheel disc. These two components are joined via gas shielded arc welding or submerged arc welding. From literature it is known that a steel wheel may fail at the air ventilation holes of the wheel disc due to stress concentration [3,11]. In order to predict the stress magnitude at the damaged regions of the wheel disc, a full scale solid model of the wheel, shown in Fig. 3, was built using SolidWorksÒ, a commercial software. In order to build the finite element model, shown in Fig. 5, the CAD model was imported into ANSYSÒ Workbench V12.0 preprocessing environment. The finite element model consisting of 196,200 elements and 335,738 nodes, was meshed using SOLID187, a higher order three dimensional solid element, which has a quadratic displacement behaviour and is well suited to modelling irregular meshes. The element is defined by 10 nodes having three translational DOF at each node [12,13]. In this model, in order to find out whether there are other critical areas on the wheel disc in addition to the damaged regions, the mesh density was kept as intense as permitted by the computer hardware capacity. To model the contact between the structural parts of the steel wheel, CONTA174 and TARGE170 elements were used. A completely bonded contact was chosen as the contact condition for all welded surfaces. 2.2. Load model Wheel radial fatigue tests were performed in accordance with EUWA (Association of European Wheel Manufacturers) – E S 3.11 and SAE (Society of Automotive Engineers) – J267 standards. Test conditions can be found in Table 1. The schematic view of these tests is also given in Fig. 6. In these tests, a wheel-tyre assembly was positioned on the driven drum under a radial load Fr with a predicted tyre inflation air pressure pi. The radial test load Fr is determined as:
Fr ¼ Fv k
ð1Þ
where Fv is the nominal design load of the wheel, as specified by the vehicle or wheel manufacturer. The accelerated test load factor k is given as 2.2 by EUWA and SAE [4,5]. The nominal design load of the wheel is Fv = 3650 kg. Hence, the radial test load Fr was computed as 8030 kg or P = 78 kN. The drum has a rotational speed of 237 rpm which corresponds to ca. 45 km/h speed of a vehicle. Finite element analysis was performed considering the radial test load P and the effect of the tyre inflation pressure pi. The boundary conditions used in the finite element analysis is shown in Fig. 7. Here, the actual configuration of wheel-tyre assembly that is identical to the mounting of the wheel and the test device was taken into account. Fixed support condition was applied on the nut–wheel disc (F1) and wheel disc–brake drum (F2) contact surfaces. The vertical load model of the wheel is also given in Fig. 8 where, the radial load P was exerted on tyre bead seat–rim contacts. In order to take the effects of the air pressure into account, a uniform pressure of pi = 10 bar = 1 MPa was also applied along the outer circumference of the rim flange. Any effect of centrifugal force is ignored.
Fig. 5. Finite element model of the steel wheel (cutaway view).
Table 1 Test conditions. Nominal wheel load, Fv (kg)
Radial test load, Fr (kg)
Accelerated test load factor, k
Tyre pressure, pi (bar)
Camber angle, rw (°)
Rotational wheel speed, nw (rpm)
3650
8030
2.2
10
0
237
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Fig. 6. Schematic view of the wheel dynamic radial fatigue test (according to [4]).
Fig. 7. Fixed surfaces on the finite element model.
Fig. 8. Load model of the steel wheel.
2.3. Determination of the mechanical properties of wheel disc material The wheel disc is manufactured using the flow forming process from 13 mm thick sheets made from hot rolled, high strength steel S355MC (Material number 1.0976 according to DIN EN 10149). Because of its high elongation characteristic,
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steel is suitable to cold forming and flow forming. The chemical composition of the material obtained from the supplier is given in Table 2 [14]. In order to determine the exact mechanical properties of the non-processed wheel disc material, samples were extracted from S355MC steel sheet in pursuance of DIN 50125 and tensile tests were carried out in accordance with DIN EN 10002-1 [15,16]. Tests were conducted at room temperature. Average mechanical properties obtained from these tests are given in Table 3. On the other hand the flow forming process increases hardness and enhances ultimate tensile strength of steel [17,18], resulting in the improvement of fatigue life [6]. However, the geometry of the failure region means it is not possible to extract tensile test samples. It is also known from literature that the hardness of the material gives an approximation of the ultimate tensile strength [19,20]. In order to take the effects of the manufacturing process on the ultimate tensile strength into account in the finite element analysis, Vickers hardness tests were also carried out on the specimens extracted from the failure region as shown in Fig. 9. Hardness was measured at ten points in each specimen. All of the measurements were performed in accordance with DIN ISO 6507-1 [21]. Average Vickers hardness was obtained as 225 HV that corresponds to ca. Sut = 720 MPa. 2.4. Finite element analysis A total nominal test load of P = 78 kN and a tyre pressure of pi = 1 MPa were exerted on the finite element model statically in accordance with Fig. 8. Stress analysis was carried out using ANSYSÒ Workbench V12.0 commercial finite element analysis software. The analysis pointed out that there are stress concentrated regions on the chamfer surfaces of the air ventilation holes, which are well-matched with the location of the fatigue failure as seen in Fig. 10. Circumferential stress distribution on the outer and inner chamfer surfaces of the air ventilation holes for the most stressed position is also shown in Fig. 11. The location of the maximum stress concentrated region is detected on the outer surface at ca. u = 233° with respect to Fig. 11. Equivalent von Mises stress distribution on the full model and stress alteration at the critical regions computed for various positions of an air ventilation hole during one turn of the wheel are presented in Fig. 12. Here, h is the angular position of Table 2 Chemical composition of disc material. Component
C (max)
Mn (max)
P (max)
S (max)
Si (max)
Al (min)
Nb (max)
Ti (max)
V (max)
wt.%
0.12
1.50
0.025
0.020
0.50
0.015
0.09
0.15
0.20
Table 3 Mechanical properties of non-processed disc material (S355MC). Modulus of elasticity, E (GPa)
Poisson’s ratio, t
Yielding strength, Sy (MPa)
Ultimate tensile strength, Sut (MPa)
Maximum elongation, emax (%)
210
0.3
374.51
522.57
24.75
Fig. 9. Hardness test samples extracted from the failure regions.
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Fig. 10. Comparison of analysis and test results.
Fig. 11. Stress distribution on the surfaces of the air ventilation hole chamfers along the circumference for the critical loading position.
the air ventilation hole with respect to the acting direction of the vertical load in X–Z plane. Maximum value of von Mises stress at the critical failure region was calculated as rmax = 295.8 MPa, where h 108°. 3. Fatigue life prediction In order to predict the fatigue life of the wheel disc in the range of 105–106 cycles, the estimated S–N diagram of the processed wheel disc material was composed by means of a simple method given in Ref. [22] that uses the ultimate tensile
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Fig. 12. Stress alteration at the maximum stressed region during one turn of the wheel.
strength, Sut and the mean stress, rm. It is known from literature that fatigue analyses that use this method and the static equivalent von Mises stresses distribution obtained from finite element analyses provide a reasonable estimation of the fatigue life of steel-based mechanical parts [23]. Stress life endurance limit S0e of steels having a tensile strength Sut 6 1400 MPa is given as:
S0e ¼ 0:504 Sut
ð2Þ
6
at 10 cycles for the ideal rotating-beam specimen [20,24]. In order to estimate the true fatigue strength Se, five factors called Marin factors were taken into account with respect to Shigley and Mischke [24]. Se can be written in term of these parameters and S0e as:
Se ¼ ka kb kc kd ke S0e
ð3Þ
Here, the surface factor ka which depends on the surface finish, can be determined by using the average surface roughness, Ra and the tensile strength, Sut. Fig. 13 shows the relation between ka and Sut for various Ra values [22]. In order to determine this factor for the wheel disc, Ra was measured at the critical regions of twenty different steel wheel samples. The average surface roughness Ra was obtained as 2.29 lm. For Sut = 720 MPa, ka was determined as 0.85. Deformation of the wheel disc under vertical load and tyre pressure is given in Fig. 14. Here, detail C shows one of the most stressed angular position of an air ventilation hole. In this position, the air ventilation hole is subjected to bending in both g–e and n–e planes. In order to determine the size factor, the air ventilation hole surface was taken into account as the section that is subjected to bending. The size factor kb is given as:
kb ¼
de 7:62
0:1133
Fig. 13. Surface factor ka for steel as a function of average surface roughness, Ra and the ultimate tensile strength, Sut (according to [22]).
ð4Þ
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Fig. 14. A simple approach to predict the stress-concentration factor around the air ventilation hole (deformation is exaggerated).
where de, the effective dimension can be written as [24]:
de ¼ 0:808ðhbÞ0:5
ð5Þ
The average depth of the hole, h which is also the thickness of the wheel disc at this region was measured as t = 6.5 mm. The width of the section was calculated as the circumference of the air ventilation hole as b = 251.327 mm by using r = 40 mm. Hence, the effective dimension de was obtained as 32.658 mm and kb was computed as 0.848. The load factor kc is given as 1 for bending and the temperature factor kd is also 1 for the range of the ambient temperature of T = 0–250 °C [24]. By means of static finite element analysis, it is observed that there are stress concentrated regions at the failure locations. Therefore, in addition to the modifying factors mentioned, a fatigue-strength-reduction factor ke must be taken into account by means of the fatigue stress-concentration factor kf that is related to the static stress-concentration factor kt [24]. Hence ke is calculated as:
ke ¼
1 kf
ð6Þ
In order to determine the stress-concentration factor, the deformation at the critical loading position (detail C) was taken into account. It was idealised that the air ventilation hole is located on a planar surface that is subjected to out-of-plane bending by means of the bending moments M1 and M2, as shown in Fig. 14. Because of the complex shape of the wheel disc, it is difficult to compute the exact values of M1 and M2 under the loads P and pi. On the other hand, if either M1 or M2 is equal to zero, which portrays the case of simple bending, kt is given as [25]:
kt ¼ 1:79 þ
0:25 0:81 0:26 þ 2 3 0:39 þ 2rt 1 þ 2r 1 þ 2r t
ð7Þ
t
The proportion r/t was computed as 6.154. Hence, kt was calculated as 1.817. The maximum value of kt is also given as 2.0, where M1 = M2. In this case kt is independent from the r/t proportion. Thus, it can be assumed that the static stress-concentration factor kt for this geometry should be in the range of 1.817–2.0. By taking the effect of the notch sensitivity q into account, fatigue stress-concentration factor kf can be written as:
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kf ¼ 1 þ qðkt 1Þ
ð8Þ
According to research q is given as a function of the notch radius r, and the ultimate tensile strength Sut. For Sut 720 (MPa) and the value of the notch radius r, which is greater than r = 4.0 mm, q was obtained as ca. 0.862 [22,24,26]. Hence, the range of kf was calculated as 1.704–1.862. By using these values, the fatigue-strength-reduction factor was computed in the range of ke = 0.537–0.587. On the other hand, at the critical loading position, when the maximum stress concentration occurs at the failure region, the air ventilation hole is subjected to bending in both g–e and n–e planes as seen in Fig. 14. It can be concluded that for this position, the moments M1 or M2 cannot be equal to zero. Hence, ke should be less than the maximum value of 0.587. By using the Marin factors, the true fatigue strength Se was calculated in the range of 140.46–153.54 MPa, for the variation range of kf. So far, the effect of the mean stress rm on the true fatigue strength Se has been ignored. Therefore, the Se range must be corrected by means of a failure criteria. Since the loading has fluctuating characteristic (rm > 0) as seen in Fig. 12, modified Goodman and Gerber approaches can be applied [22]. On the other hand, because of the ductile characteristic of the wheel disc material, the Gerber approach is preferable [6,22,24,27]. The corrected fatigue limit for the Gerber approach is given as [22,24,28]:
" Sfk ¼ Se 1
rm
2 # ð9Þ
Sut
here, the mean stress rm can be expressed as:
rm ¼
rmax þ rmin
ð10Þ
2
It must be noted that, rmin = 14.74 MPa is the minimum value of the stress concentration at the critical regions as shown in Fig. 12. rm was assumed as constant. The corrected fatigue limit range was calculated as Sfk = 133.93–146.4 MPa. According to the Basquin relation, the characteristic of the estimated S–N diagrams was assumed as being linear between 102 and 106 load cycles [22] as shown in Fig. 15. The S–N diagrams plotted by taking the modifying factors and the mean stress into account were defined in the ANSYSÒ Workbench V12.0 user interface. The parameters used in the fatigue analyses are given in Table 4. Von Mises stress distribution obtained from finite element analysis was utilised in fatigue life calculations. Stress–life approach was used to determine the fatigue life of the processed wheel disc material. All fatigue analyses were performed according to infinite life criteria (N = 107 cycles).
Fig. 15. Estimated S–N diagram for the critical region of the wheel disc.
Table 4 Parameters used in the fatigue analyses. Parameter
Modulus of elasticity Poisson’s ratio Ultimate tensile strength Surface factor Size factor Load factor Temperature factor Fatigue-strength-reduction factor
Symbol
E
t Sut ka kb kc kd ke
S355MC (1.0976) Condition
Value
Cold formed carbon steel Cold formed carbon steel Cold formed carbon steel Sut = 720 MPa, Ra = 2.29 lm de = 32.658 mm Bending Ambient temperature, T < 250 °C kf = 1.704–1.862
210 GPa 0.3 720 MPa 0.85 0.848 1.0 1.0 0.587–0.537
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4. Results and discussion Finite element analysis showed that the critical regions, where fatigue failure was initiated during wheel radial fatigue tests, are under stress concentration. Failure that took place during the tests is one of three typical problems of the disc wheels that are caused by the maximum circumferential stress as reported by Carboni et al. and Firat et al. [3,11]. In the light of the results obtained from fatigue analyses, it was estimated that crack initiation may occur at the critical region of the outer chamfer surface in the range of N = 6.45 105–8.75 105 load cycles for the minimum value of ke = 0.537. On the other hand, it must be noted that one turn of the wheel corresponds to two load cycles at the critical regions of the air ventilation holes as shown in Fig. 12. Thus, it can be said that the wheel may fail in the range of Nw = 3.23 105–4.37 105 turns. This means that by using finite element analysis, fatigue life of the wheel disc may be estimated with an average approximation of 73% when assuming the average number of the wheel turns before crack initiation at the radial fatigue tests as Nw = 5.2 105 turns. As an example, the fatigue life N estimations at the critical region for ke = 0.537 are shown in Fig. 16. With the exception of the predicted critical regions, the steel wheel satisfies the infinite life criteria. Results of the fatigue analyses for various ke values are given in Table 5. A comparison of radial fatigue tests and the results obtained from fatigue analyses can also be found in Fig. 17 for these ke values. In order to enhance the fatigue life of the steel wheel, it is necessary to decrease the stress concentration at the critical regions. The simplest way to reduce the stress concentration and improve the fatigue life is to increase the thickness of the wheel disc. On the other hand, an increase of sheet metal thickness along the radial cross section causes an unnecessary
Fig. 16. Fatigue life estimations at the critical region of the air ventilation hole for ke = 0.537.
Table 5 Results of the fatigue analyses for various ke values. Fatigue strength-reduction factor ke ()
Corrected fatigue limit Sfk (MPa)
Estimated failure initiation cycles, N (load cycles)
Estimated wheel turns before failure initiation, Nw (turns)
0.587 0.575 0.562 0.550 0.537
146.4 143.28 140.14 137.044 133.93
837,830 783,630 733,350 687,590 645,050
418,915 391,815 366,675 343,795 322,525
Fig. 17. Comparison of the test results and the estimated fatigue life of the wheel disc as a function of ke.
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Fig. 18. Design enhancement at the critical regions of wheel disc.
weight increase. Since light weight wheels regain contact with the ground quicker than heavier wheels after a lift due to poor road surface [29], a total thickness increase is not a preferred solution. In order to solve the problem, a form enhancement solution was also carried out, given in Fig. 18. In order to strengthen the critical regions, the local thickness, tc and the crosssectional radius, rc was increased. Because of the nature of flow forming, it is not necessary to increase the thickness along the whole section. The computer aided flow forming process enables the thickness to be increased only at the critical regions along the radial cross section. Finite element analyses also showed that by using this solution, it is possible to decrease the maximum equivalent stress at these regions without any weight increase. The proposed design enhancement was applied to five new steel wheel prototypes which were also subjected to wheel radial fatigue tests. In these tests Nw = 1.26 106– 1.39 106 wheel turns range was obtained without any fatigue failure which is more than the desired 1 106 load cycles. 5. Conclusion The premature failure of a truck steel wheel prototype that occurs during the course of radial fatigue tests is studied using finite element analysis. Finite element-based stress analysis showed that the crack initiation regions on the wheel disc are subjected to stress concentration. Crack initiation occurs at the most stress concentrated regions of the air ventilation holes which are the critical regions of the wheel. The predicted failure locations are quite close to the actual crack initiation regions. In order to predict the minimum number of wheel turns before fatigue crack initiation, the stress life (S–N) approach was utilised. The estimated S–N diagram was constructed using the ultimate tensile strength of the processed wheel disc material which was determined via Vickers hardness tests. The effects of factors such as surface roughness, size and stress concentration were also taken into account using endurance-limit modifying factors also known as Marin factors. The Gerber approach was used to predict the fatigue life of the wheel disc. The results obtained correspond to the results of radial fatigue tests. In order to obtain an extended fatigue life, a design enhancement solution, including both increasing the local thickness, tc and the cross-sectional radius, rc at the critical regions was applied. Stress analyses showed that by using this solution, it is possible to decrease the equivalent von Mises stress at these regions. Wheel radial fatigue tests also proved that the proposed design enhancement is a suitable solution to obtain the desired fatigue life. It can be concluded that the fatigue analysis based on the static stress analysis and the stress life approach gives a reasonable estimate of the fatigue life of the steel wheel. By using the procedure which is used in this study, the number of prototypes produced before mass production may be considerably reduced. On the other hand, during the design process and the durability enhancement studies of vital structural elements such as automotive wheels, the numerical results obtained must necessarily be verified by bench tests or road tests. Acknowledgements This study was carried out with the support of Hayes Lemmerz Jantasß Jant Sanayi ve Ticaret A.S ß . in Manisa, Turkey. The authors are grateful for the suggestions of Mr. Ö. Öztürk, the R&D director at Hayes Lemmerz Jantasß Jant Sanayi ve Ticaret A.Sß . The considerable efforts of Mr. G.M. Gencer, M.Sc. of Dokuz Eylül University Department of Mechanical Engineering on the performance of the tensile tests and the hardness measurements are acknowledged. The contributions of Mr. C. Cengiz and Mr. H.E. Enginar during the preparation of CAD models are also appreciated.
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