Defects and in-service fatigue life of truck wheels

Defects and in-service fatigue life of truck wheels

M. Carbonia,*, S. Berettaa, A. Finzib

aDipartimento di Meccanica, Politecnico di Milano, Via La Masa 34, 20158 Milan, ItalybGianetti Ruote S.p.A., Via Stabilimenti 1, 20020 Ceriano Laghetto (MI), Italy

Received 6 June 2002; accepted 26 June 2002

Abstract

Truck wheels are usually assessed against fatigue by experimental tests based on standardised load sequences(CARLOS load spectra) which reproduce a typical service life of the real component. The present paper deals with the

effect of defects, caused by the manufacturing process, on the fatigue life of wheels subjected to block loading tests. Theresearch was prompted by premature service failures of a batch of truck wheels. The investigation firstly dealt withfatigue and crack growth tests for the quality control of the material and then with the detection of defects at the origin

of the unexpected failures. The data have been used to assess the acceptability of defects and to estimate life underproof tests using current crack propagation models.# 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Defects; Wheels; Fatigue strength; Automotive failures

1. Introduction

Truck wheels are classified as ‘‘safety components’’ and, for this reason, they are subjected to particularattention during fatigue design in order to guarantee an appropriate in-service durability together with theneed of a light-weight design. In fatigue assessment of wheels, the commonly accepted procedure by man-ufacturers is to pass two durability tests, namely the ‘‘radial fatigue test’’ and the ‘‘cornering fatigue test’’[1–3]. These tests are conventionally defined and are based on simple load conditions not representing thereal in-service behaviour of components.Another widely used type of test is based on standardised load spectra (grouped under the name

‘‘CARLOS’’: CAR LOading Spectra) consisting of a preset sequence of lateral and vertical forces obtainedby extrapolation of loads measured directly on components during typical manoeuvrings (straight driving,braking, cornering, parking,. . .) both on-road and off-road. In the special case of truck wheels, LBF(Germany) has developed ‘‘Eurocycle’’ [4,5], an accelerated test spectrum able to represent, in a 65 kmroute, 2032 km of typical exercise of truck wheels on European roads. Load spectra are applied to the realcomponent, during fatigue tests, by a special Biaxial Test Facility [5,6]. Particularly, in this machine the

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* Corresponding author. Tel.: +39-02-2399-8253; fax: +39-02-2399-8202.

E-mail address: [email protected] (M. Carboni).

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wheel, fully assembled with hub, spindle, bearings and tire, turns inside a slightly larger steel cylinder, thatrotates by means of an electric motor, and is simntaneously loaded by two servo-hydraulic actuators (ver-tical and horizontal) according to the load sequence included in ‘‘Eurocycle’’. Proceeding in this way, theexperimental durability check of a given wheel is carried out subjecting, by the biaxial test facility, aminimum lot of three components that have to survive to at least 246 ‘‘Eurocycle’’ blocks, correspondingto about 500 000 km of service.The typical problems of the components, in terms of fatigue strength, are essentially three: i) disk failure

caused by fretting-fatigue in the attachment face zone; ii) crack nucleation and propagation at the edge ofthe ventilation holes where the maximum circumferential stress exists (at 45� to the axial direction); iii)fatigue failure of the welded joint between disk and rim. The design approach to these different problems,from the point of view of the test based on simple load conditions, is based on FEM analyses with the aimof defining the linear damage [7] or the elasto-plastic behaviour of the component [8] under the simple loadconditions.Considering load spectra, a simple approach to design [4–6] can be directly exploited with experimental

tests: after a design verification with strain-gauge measurements of the maximum stresses under simpleload conditions, fatigue strength of the component is essentially assessed by durability tests based on‘‘Eurocycle’’ load spectra using the biaxial facility. In order to obtain wheel prototypes ‘‘designed againstload spectra’’, a computational model has been recently developed by Gianetti Ruote [9]. It consists of aFEM analysis of the 52 load sequences constituting ‘‘Eurocycle’’ in order to achieve from them a simula-tion of the stress histories of the critical points of the wheel. Based on these analyses it is then possible toestimate the fatigue damage and to design the wheel for the proof tests using a critical Miner indexobtained from data on previous wheel and specimen fatigue test spectra. Such a procedure permits one torefine the design procedure to a life evaluation of the prototypes, which will be subjected to ‘‘Eurocycle’’under the biaxial test facility, very close to the experimental evidence [10,11].It is necessary to remark that both these approaches (direct experiments or FEM calculations) are not

fully able to account for the process variability and the influence of defects (of any origin: metallurgical,technological, etc. . .) on fatigue strength of wheels during the design procedure [12]. From this point ofview, some in-service premature failures (Fig. 1) of a 34.8 kN wheel have prompted the present research.

Fig. 1. Introduction to the wheel problem: (a) solid model of the wheel; (b) particulars of the premature failures.

46 S. Beretta et al. / Engineering Failure Analysis 10 (2003) 45–57

First of all, the fatigue behaviour of two lots of material (the first coming from the batch of prematurefailures and the other from a standard batch) has been investigated in terms of S–N and crack propagationcurves with the aim to verify the homogeneity of the material properties between the batches. The typicaldefects present in different lots of the component have then been evaluated. Since fractographic observa-tion has shown that the fractures could be ascribed to the presence of defects due to the hole punchingprocedure of the ventilation hole, the research addressed the analysis of the acceptability of these defects.The material data have eventually allowed us to define of criteria to assess defect acceptability.

2. Investigation of the causes of premature service failures

The wheels under investigation have a nominal capacity of 34.8 kN with a rim diameter of 57.15 mm.Wheels are produced in a Fe430D steel whose mechanical properties are: ultimate tensile strength 450MPa, yield stress 320 MPa and rotating bending (R=�1) fatigue limit 225 MPa [11].

2.1. Fatigue experiments

Fatigue tests have been carried out on two different lots of wheels in order to investigate the presence ofsignificant differences in fatigue properties. To this aim, fatigue specimens are similar to the ‘‘key-hole’’type and have been extracted from the attachment face of the wheels by machining (Fig. 2). FEM analyses

Fig. 2. Dimensions of the ‘‘key-hole’’ specimens obtained from the wheels.

S. Beretta et al. / Engineering Failure Analysis 10 (2003) 45–57 47

have permitted us to determine the relation between the applied load and the maximum stress at the notchroot [13].Two series of specimens (one extracted from the batch of wheels which failed in service and the other

from a standard production batch) have been subjected to fatigue tests (stress ratio R=0.1) in order todetermine the S–N diagrams of the two wheel batches. The fatigue limits of the two specimen series havebeen investigated using ‘‘Short Stair-case’’ sequences. The finite life region has been investigated usingequally spaced stress levels between 280 and 320 MPa, which corresponds to the monotonic yield strength.Fatigue tests have been carried out on a servo-hydraulic testing machine at a frequency of 30 Hz. Thespecimens have been gripped by universal joints to avoid any secondary bending.The results of the fatigue tests are shown in Fig. 3 in terms of the maximum stress applied to the speci-

men. The tests have substantially shown that the fatigue behaviour of the two lots is very similar and thatthe fatigue limit, at R=0.1, is �SR=0.1=264 MPa (Fig. 3). The fatigue life scatter can be ascribed to thepresence of non-metallic Ca inclusions with dimensions up to 100 mm [13].

2.2. Crack growth tests

In order to evaluate the crack propagation curve of the Fe430D steel and to check the material homo-geneity of the two wheel batches, crack growth tests have been performed using two small CT specimensper wheel batch. Specimens, whose dimensions were 50�50�10 mm (precrack 25 mm), have beenmachined from the wheels. Test were carried out at constant �P with R=0.1 at an operating frequency of20 Hz. Crack propagation was measured on both the specimen faces using plastic replicas that were even-tually observed under an optical microscope at 100� magnification. Growth rate was then obtained with

Fig. 3. S–N curve of the ‘‘key-hole’’ specimens obtained from the wheels (R=0.1).


the secant method [14]. During propagation tests, closure measurements have been carried out using twodifferent methods of ‘‘global compliance’’: by an extensometer at the notch edge and by a ‘‘BackFace’’strain gauge. A further test series has been carried out on another CT specimen, coming from the standardbatch, in order to determine the �Kth value using the �K-decreasing technique [14].The relevant results obtained from the tests are shown in Fig. 4: the results show that also from the

propagation point of view there is no differences between the two different lots of material. Closure mea-surements gave an average �Keff/�K of 0.64 for �K<15 MPa

pm. The crack propagation threshold at

R=0.1 was found to be �Kth=6.9 MPapm.

2.3. Defect analysis

In order to analyse the causes of the premature in-service failures, some fractographic observations havebeen firstly carried out. These observations have evidenced the presence of tearings, presumably due tohole punching, at the fracture origin.To measure the entity of the found defects, polished sections have been extracted from the two different

lots of wheels already examined. The polished sections have been extracted in a radial direction withrespect to the ventilation hole, in the same position where the failures took place (see Fig. 5a). Particularly,polished sections revealed the presence of narrow defects (Fig. 5b) whose typical sections are shown inFig. 5c and d. Because of the elongated shape, defect size was measured in terms of depth.The defect data have then been analysed using Weibull distributions (Fig. 6): the result is that the data

coming from the lot of the premature failures are described by a defect population different from that of thestandard production wheels. The characteristic value of the defect depth is about 60 mm for the standard

Fig. 4. Propagation properties of the material: crack propagation curves of the analysed lots.


production wheels and about 200 mm for the wheels of the batch with premature failures. The same ana-lysis was carried out on the wheels that suffered premature in-service failures. In this case the averagedimension of defects at ventilation holes (excluding fractured holes) was about 600 mm.

3. Defect size and fatigue strength of Fe430D steel

The first step for the defect acceptability analysis has been the establishment of a relationship betweendefect size and fatigue strength for the Fe430D steel at R=�1, which is the typical stress ratio of stressspectrum at wheel ventilation holes [10]. This has been done by analysing material data and by carrying outfatigue tests on micronotched specimens.The analysis of the effect of defects on fatigue strength can be done by treating defects as small cracks:

the fatigue limit is then the threshold cyclic stress for the non-propagation of these small cracks [15].Considering irregular defects, the maximum stress intensity factor at the tip can be calculated with Mur-akami’s equation [15]:

�KI ¼ 0:65��

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi��

ffiffiffiffiffiffiffiffiffiarea

pq

ð1Þ

whereparea (root square of the defect section in a direction perpendicular to the applied stress) is the

geometric parameter defined by Murakami.

Fig. 5. Typical defect aspect (a and b) due to punching operations as observed (c and d) by an optical microscope from lapped

sections.


By using steel data obtained at R=0.1, namely the fatigue limit and the �Kth, together with Eq. (1)it is possible to depict the so-called ‘‘Kitagawa–Takahashi diagram’’ [15] and to obtain the ‘‘El-Had-dad parameter’’ [16] (or alternatively ‘‘fictitious crack size’’)

pareao equal to 450 mm (Fig. 7). Since

the shape of the Kitagawa diagram does not change with stress ratio [17] and thepareao parameter

is expected to remain the same also at a stress ratio R=�1, the relationship between fatigue strengthat R=�1 and crack size (expressed in terms of

parea) could be described by the El-Haddad equation

[16]:

��w ¼ ��wo �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiareao

pffiffiffiffiffiffiffiffiffiffiffiareao

pþ

ffiffiffiffiffiffiffiffiffiarea

p

sparea <10�

pareao ð2Þ

where ��wo (fatigue limit on smooth specimens at R=�1) is equal to 225 MPa [11]. Eq. (2) is valid only inthe short crack region, that is

parea <10.

pareao [16].

3.1. Experiments on micro-notched specimens

In order to verify the validity of Eq. (2) we decided to carry out fatigue test series on micro-notchedspecimens. Particularly, two series of ‘‘dog-bone’’ specimens were micro-notched by means of a pair ofmicro-drills equivalent to defects with

parea of 143 and 443 mm (Fig. 8). Successively, two series of fatigue

limit tests with short ‘‘stair-case’’ sequences were carried out on a resonant bending machine. Fatigue testswere interrupted if a specimen had survived 107 cycles.

Fig. 6. Analysis by Weibull distribution of the defects obtained from the lapped sections.


Fig. 9 shows a details of experimental tests: in particular can be seen a non-propagating crack at the tipof a run-out specimen. The presence of these non-propagating cracks confirms that micro-notches can betreated as small cracks.The fatigue limit of 143 mm and 443 mm defects were respectively 392 and 348.8 MPa. These results are in

good accordance with the predictions of Eq. (2) (Fig. 7), that was eventually adopted for analysing thedetrimental influence of defects on the service life of wheels.

4. Effect of defects on wheel life

The final phase of the research consisted of estimating the effect of defects on the life of a wheel subjectedto the ‘‘Eurocycle’’ load spectrum. The analysis was carried out in terms of fatigue damage calculation andcrack propagation.

4.1. Fatigue damage

First of all, how can the defects measured with the lapped sections be drawn in the determined Kitagawadiagram? As we said earlier, for the particular shape of these defects, it is more opportune to consider, as acharacteristic parameter, the depth than the

parea. But to apply Eqs. (1) and (2) it is necessary to find out

a good way to characterize defects geometry also by the second parameter. Murakami [15] suggested thatfor narrow and lengthy defects the best characterization in terms of

parea is to assume, for the defect

itself, a rectangular shape presenting dimensions ‘‘a’’ and 10a (Fig. 10), where ‘‘a’’ is the depth of the givendefect.

Fig. 7. Influence of the defect dimension on the fatigue limit of Fe430D steel.


Proceeding in this way, the standard production batch (characteristic depth equal to 60 mm) presentsparea=189 mm corresponding, using the obtained Kitagawa Diagram, to a fatigue limit (R=�1) of 198

MPa, while the batch of premature failures (characteristic depth equal to 200 mm) presentsparea=632 mm

corresponding to a fatigue limit (always R=�1) of 152 MPa.The edge of the ventilation hole is subjected, during the ‘‘Eurocycle’’ test on the wheel, to a stress time

history with a stress ratio of approximately �1 [11]. In Fig. 11a the stress history measured by a strain gageglued near the edge of the ventilation hole is reported. Considering that fatigue design of wheels is based onfatigue damage whose critical value has been obtained by wheel biaxial fatigue tests, it is then possible toevaluate approximately the effect of defects in terms of increment of damage due to the variation of thefatigue limit (Fig. 10b).

4.2. Propagation of defects

The analysis of defect propagation has been carried out by means of dedicated software: ‘‘NASGRO’’developed by different International Research Institutes [18]. NASGRO has been chosen because, untilnow, it has shown the best correlations of experimental results and because it includes a powerful versionof the ‘‘Yield Strip’’ model proposed by Newman [19].The experimental tests of crack propagation have been executed at R=0.1, while the ‘‘Eurocycle’’ spec-

trum is mainly at R=�1. This problem is solved by NASGRO by the application, to describe the propa-gation law, of the following expression:

Fig. 8. Geometry of the micronotched ‘‘dog-bone’’ specimens used to validate the obtained Kitagawa Diagram and particulars of the

introduced artificial defects.


da

dN¼ C

1� f

1� R

� ��K

� �n 1��Kth

�K

� �p

1�Kmax

Kcrit

� �q ð3Þ

where the ‘‘f ’’ parameter represents a measure of the closure effect on propagation and it is used to gen-eralise the crack propagation curve to different R values. ‘‘f ’’ depends on the constraint factor ‘‘�’’ thatcurrently is well defined for aluminium alloys, but not yet for steels [19,20], even if its value, for theFe430D, has been recently [21] found to be equal to 2.5.The difficulties of the analysis of the system wheel by means of NASGRO come principally from two

considerations: i) the system geometry is too complicated; ii) the ventilation hole during use is subjected toa combination of axial and bending stresses [4]. Recent research [22] has shown the possibility of repre-senting the ventilation hole by a ‘‘companion specimen’’. Particularly, it has been seen that a holed plate,subjected at the edge of the hole to the strain history of the ventilation hole, presents a durability similar to

Fig. 9. Details of experimental results on micronotched specimens: (a) crack surface for aparea=443 mm micronotch (broken during

the test); (b) particular of the same starting defect; (c) starting micronotch for aparea=143 mm (run-out); (d) particular of the non-

propagating crack for the same specimen.

Fig. 10. Assumption of the characteristic parameterparea for the particular morphology of the defects found from the lapped sections.


Fig. 11. Effect of defects on wheel life: (a) stress history measured by a strain gauge glued near the edge of the ventilation hole; (b)

evaluation in terms of increment of damage due to the variation of the fatigue limit; (c) assumption of the geometry of the system for

the defect propagation approach.


that of the wheels. On the basis of these results, the analysis has been carried out modelling holed plates,subjected to the Eurocycle load history measured at the ventilation hole, with different dimensions ofstarting defects (Fig. 11c).

4.3. Life predictions and comparison with experiments

Fig. 12 shows the results, in terms of normalised life and depth of the starting defect, of the damagecalculation and of the defect propagation. From this figure, it is possible to see that the two methods yieldquite different results. In order to define which of the two is the best at describing the behaviour of thebatch of the premature failures, it is necessary to know that the in-service life of this batch (characterisedby an average maximum defect of 600–700 mm) has been about one tenth of the design life (the ‘‘In-service’’dash in Fig. 12). Assuming ‘‘1’’ the life of the wheels of standard production (characterised by a maximumdefect of 100 mm), it is evident that the NASGRO analysis is very near to the one tenth of life shown by thebatch of premature failures. However, the damage calculation leads to a conservative design, suggesting alife, for the maximum defects, of about one thousandth.As a further comparison, some wheels of the batch of premature failures have been tested on the biaxial

machine. These wheels have shown a defects distribution at the ventilation hole characterised by a max-imum defect of about 150–200 mm and a life half of the design one. The ‘‘Biaxial’’ dash in Fig. 12 shows theregion covered by the wheels which failed during biaxial tests and in this case the NASGRO analysis seemsto be nearer to experimental evidences.

Fig. 12. Obtained results in terms of damage calculation and defect propagation.


5. Conclusions

The analysis has been presented of a component subjected to random fatigue in the presence of defectscoming from the production procedure. First of all has been characterised the fatigue and crack propaga-tion behaviour of the material, then typical defects have been inserted and their influence on the fatiguelimit, strength and crack propagation speed has been investigated, thus defining the limit of acceptability ofthe defects and the residual life of the component subjected to random fatigue.

References

[1] ISO 3006 Road vehicles—passenger car wheels—fatigue testing methods, vol. 2. Switzerland: 1976.

[2] Richard C, Rice M. SAE fatigue design book. 2nd ed. SAE Publication; 1988.

[3] Wright DH. Testing automotive materials and components. SAE Publication; 1993.

[4] Grubisic V, Fischer G. Procedure for optimal lightweight design and durability testin of wheels. Int J Vehicle Des. 1984; 6.

[5] Grubisic V, Fischer G. Automotive wheels, methods and procedure optimal design and testing. SAE Technical Paper 1983;

830135.

[6] Grubisic V, Fischer G, Heinritz M. Design optimisation of forged wheel hubs for commercial vehicles. SAE Technical Paper

1984; 841706.

[7] Landgraf RW, Thangjitham S, Ridder RL. Automotive wheel assembly: a case study in durability design. Case studies for fatigue

education ASTM STP 1250 1994.

[8] Kocabicak U, Firat M. Numerical analysis of wheel cornering fatigue tests. Eng. Fail. Anal. 2001; 8.

[9] Finzi A, Piazza L. Fatigue life prediction in wheels design. Marc Users Scientific Technical Conference, Genova, 1999.

[10] Carboni M, Beretta S, Clerici P, Finzi A, Piazza L. A fatigue design procedure for truck wheels. ATA 2000; 53 (9/10).

[11] Carboni M. Analisi dell’affaticamento di ruote per autocarri. MSc thesis, Politecnico di Milano 1997.

[12] McGrath PJ, Hattingh DG, James MN, Els-Botes A. Effects of forming process on fatigue performance of wheel centre discs.

Proceedings ECF13, San Sebastian, 2000.

[13] Beretta S, Carboni M, Clerici P. Caratterizzazione a fatica di diverse forniture di lamiere per la costruzione di ruote. Report of

research contract between Politecnico di Milano and Gianetti Ruote no. 8/99, Milano, 2000.

[14] ASTM E647-95a. Standard test method for measurement of fatigue crack growth rates. Philadelphia: ASTM; 1994.

[15] Murakami Y, Endo M. Effect of defects, inclusions and inhomogeneities on fatigue strength. Int. J. Fatigue 1994; 16.

[16] El-Haddad MH, Smith KN, Topper TH. Fatigue crack propagation of short cracks. J Eng Mater Struct ASME Trans 1979; 101.

[17] Hertzberg RW. Deformation and fractures mechanics of engineering materials. New York: J. Wiley & Sons; 1995.

[18] AAVV NASGRO. Developed by different research institutes: NASA, ESA, NLR and Lockheed; 2000.

[19] Newman Jr JC. A crack closure model for predicting fatigue crack growth under aircraft spectrum loading ASTM STP 748.

Philadelphia: ASTM; 1981.

[20] Skorupa M. Empirical trends and prediction models for fatigue crack growth under variable amplitude loading. ECN-R-96–

0071996. The Netherlands: Petten: Netherlands Energy Research Foundation ECN.

[21] Beretta S, Carboni M, Machniewicz T, Skorupa M. Correlation between experiments and Strip Yield results on fatigue crack

growth in a structural steel. Proceedings ECF14, Krakow, 2002.

[22] Cantini S, Cerini G. Danneggiamento a fatica di ruote per autocarro. MSc thesis, Politecnico di Milano, 1998.


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Defects and in-service fatigue life of truck wheels