Assessment of bending fatigue limit for crankshaft sections with inclusion of residual stresses

International

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International Journal of Fatigue 29 (2007) 318–329

JournalofFatigue

Assessment of bending fatigue limit for crankshaft sectionswith inclusion of residual stresses

Paul Spiteri a, Simon Ho b, Yung-Li Lee a,*

a Stress Lab and Durability Development, DaimlerChrysler, CIMS 484-05-20, 800 Chrysler Drive, Auburn Hills, MI 48326, United Statesb Powertrain CAE, DaimlerChrysler, United States

Received 2 August 2005; received in revised form 2 February 2006; accepted 2 March 2006Available online 5 May 2006

Abstract

The fatigue limit of rolled, ductile cast iron crankshaft sections under bending was investigated experimentally and analytically. Therelationship of different failure criteria – specifically, surface crack initiation, resonant shifts, and two-piece failures – on the fatigue limitof the crankshafts was explored from testing. A comparison showed that using the surface crack failure criterion decreased the apparentfatigue limit of the crankshaft significantly. This result supported the theory of crack arrest in the fillet area of crankshafts and raises asignificant challenge to the use of the surface crack failure criterion due to its inconsistent correlation to two-piece failure. Also an engi-neering practice for residual stress simulation and fatigue limit estimation due to a fillet rolling process on a crankshaft was explored. Thecomplete analytical process was validated by the resonant bending fatigue test results. The normal stress distribution from the fillet sur-face-to-depth of a crankshaft section under bending was first obtained by a three-dimensional elastic finite element analysis. The residualstress distribution near the crankshaft fillet induced by a fillet rolling process was then determined by a three-dimensional elastic–plasticfinite element analysis. A resultant normal stress distribution along any possible crack growth plane originating from the fillet surfaceand extending into the component was defined by superimposing the normal stress components due to the bending moment and the roll-ing load. Based on these calculated normal stresses, two fatigue models (such as the SWT equivalent stress and the effective stress inten-sity factor range) used to estimate the fatigue limits on surface cracks and in-depth cracks were examined by the experimental data. Theresults showed that the SWT equivalent stress was not a good fatigue damage parameter for surface cracks and the effective stress inten-sity factor range derived on the technique of crack modeling did correlate reasonably to the experimental data.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Fatigue limit; Ductile cast iron crankshaft; Fillet rolling; Residual stress; SWT equivalent stress; Effective stress intensity factor range; Surfacecracks; Finite element analysis; Threshold; Fatigue testing

1. Introduction

Experimental and analytical determinations of the bend-ing fatigue limit for a rolled, ductile cast iron crankshaftare the two challenging tasks in an engineering community.Crankshafts in the automotive engines are usually designedfor infinite life because a typical engine will operate for sev-eral 100 h at full load over the life of a vehicle. In the caseof automotive crankshafts, the number of cycles under

0142-1123/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijfatigue.2006.03.009

* Corresponding author. Fax: +1 248 944 2005.E-mail address: [email protected] (Y.-L. Lee).

maximum load can easily exceed 10 millions cycles asreported by Lee and Morrissey [7]. A fatigue limit isdefined as the fatigue strength at 10 millions. Also, sincefatigue damage always initiates at the cheek fillets underbending, a typical fillet rolling process has been used foryears to introduce compressive residual stress in that regionand, subsequently, to improve the fatigue strength. Fromthe testing perspective, there is a need to explore the empir-ical relationship of different failure criteria – specifically,surface crack initiation, resonant shifts, and two-piece fail-ures – with the bending fatigue limit of rolled, ductile castiron crankshaft sections. From the analytical point of view,

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P. Spiteri et al. / International Journal of Fatigue 29 (2007) 318–329 319

there is a need to determine an engineering practice forresidual stress simulation and fatigue limit determinationbased on long in-depth cracks.

Crankshaft failures take place when the crankshaft canno longer transmit torque. Therefore, running bench test-ing until a two-piece failure occurs would best matchengine failures. However, this failure mode becomes lim-ited in practical testing operations since component frac-ture failures can damage the resonant bending fixture rig.Therefore, users of resonant bending fixture rigs in crank-shaft testing have adopted different criteria to detect theimminent two-piece failure: surface crack initiation andresonant shifts.

Users of surface crack failure criteria such as Love andWaistall [10] attempted to identify crack initiation. Crackinitiation is often employed as a failure criterion in con-stant stress amplitude, high cycle fatigue tests. However,since the post-stressed surface of cast-iron componentscan be beset with non-propagating cracks, the essentialquestion becomes defining a significant crack. Watmoughand Malatesa [18] followed the logic that any macroscopiccrack visible with Magnaglow was considered to be a fail-ure. The pervasive use of Magnaglow inspection in thecrankshaft industry followed this logic – if a crack couldbe seen, it was a failure.

Users of resonant shift failure criteria track resonanceshifts. These shifts correlate to stiffness drops that, in turn,correlate to crack formations. Feng and Li [4] mathemati-cally demonstrated the link between stiffness, resonance,and cracks. Yu et al. [19] empirically demonstrated this phe-nomenon and compared their results to finite element pre-dictions. Both studies concurred that resonance shiftscould be used to identify developed cracks. And neitherstudy showed how resonance shifts correlated to two-piecefailure or to small surface cracks. Watmough and Malatesa[18] showed that a 0.5–1.0 Hz resonance shift was alwaysaccompanied by a significant 12 mm circumferential filletcrack. However, they did not examine suspended sampleswith Magnaglow or go into any detail of the correlationof surface cracks to resonant shifts. Therefore, despite theseimportant studies, the correlations between surface cracks,resonant shifts, and two-piece failures remain unexplained.

In an attempt to determine the behavior of fillet cracks,Chien et al. [1] studied crankshafts using finite elementsanalysis and linear elastic fracture mechanics. Throughthese approaches, the crankshaft fillet stress intensity factorwas calculated by combining the predicted bending stressesand residual stresses. The stress intensity factor wasmapped against the depth of the fillet. This mapping tech-nique showed the possibility of crack arrest as subsurfacecompressive residual stresses increase. Chien et al. con-cluded that surface crack initiation did not indicatewhether crankshaft fillet cracks would propagate throughor arrest in the sub-surface compressive residual zone.

An empirical study was conducted in this paper to qual-ify the crack arrest theory proposed by Chien et al. [1]using physical crankshaft fatigue testing. Samples of rolled,

ductile cast iron crankshaft were tested. This crankshafthad been tested already for fatigue strength using a surfacecrack failure criterion. In the first part of the study, reso-nance shifts were recorded and compared to final crack sizeto determine how frequency shifts compared to two-piecefailure. In the second part of this study, a two-piece failurecriterion based on resonant shifts was used to determinefatigue strengths of these crankshafts. A comparison wasthen made between the two different failure criteria (surfacecrack failure criterion and two-piece failure criterion). Thefatigue limit based on the surface crack failure criterionwas much lower than that based on two-piece failure. Over-all, this study showed that crack arrest was a significantfactor in crankshaft bending fatigue.

An analytical study was conducted to explore an engi-neering practice for residual stress simulation due to a filletrolling process on a ductile, cast iron crankshaft. The nor-mal stress distributions due to bending on potential crackpropagation planes originating from the fillet surface andextending to the crankshaft section were first obtained bya three-dimensional elastic finite element analysis. Theresidual stress distributions induced by a fillet rolling pro-cess near the crankshaft fillet were then determined by athree-dimensional elastic–plastic finite element analysis.Although many advanced experimental techniques suchas X-ray diffraction, neutron diffraction, and hole drillingwith interferometer strain/slope rosette [12] were availablefor determination of residual stress distribution, they weredifficult to use in our validation study due to the complex-ity of surface shapes and the small fillet radius. Therefore,it was our ultimate objective to validate the whole analyti-cal process by correlating the simulation results to the mea-sured fatigue limit data based on the surface crack failurecriterion and the two-piece failure criterion.

Subsequently, a fully reversed equivalent stress derivedon the Smith–Watson–Topper (SWT) damage parameter[13] which combined the in-depth normal stress compo-nents due to bending and rolling loading was used to definethe fatigue limit for surface cracks. An effective stress inten-sity factor range derived by the technique of crack model-ing developed by Taylor et al. [17] was used to determinethe fatigue limit for long cracks. The validity of the twomodels was examined in this paper.

2. Experimental fatigue limit assessment

The focus of this study was on a rolled, ductile cast ironcrankshaft. Crankshaft test samples were coupons cut frommain to main, as shown in Fig. 1. The symmetry of themains allowed for resonant bending fatigue testing sincethe masses that would be in resonance could be centeredto each main. The orientation of the bending moment tocrankshaft sections was across the cheek from main topin journals. This resulted in the highest stress concentra-tion points in the fillet region.

Fig. 2 showed a crankshaft resonant bending fatiguetest fixture for testing. This was the same fixture used in

Fig. 1. Test sample cut from a crankshaft.

Fig. 2. Crankshaft resonant bending fatigue test apparatus.

320 P. Spiteri et al. / International Journal of Fatigue 29 (2007) 318–329

previous fatigue strength studies [1] using the surfacecrack failure criterion. This fixture had an adjustablefunction generator for a drive load and a pair of heavytines attached to the crankshaft section and instrumentedwith a bending load cell for a feedback. The assembly wasexcited at its resonant frequency through the functiongenerator attached to one of the tines. The resonant fre-quency of the assembly would continue to decreasebecause of the change in stiffness from cracks. The con-stant supervision of a technician was needed to overseethe resonance frequency of the assembly, the drive loads,and the feedback loads during testing so that bendingfatigue testing could be preserved at a resonant frequency

and at the targeted load. An updated bending resonanceof the assembly was determined by the peak feedbackload after sweeping through the frequencies of+/�0.5 Hz from the previous resonant frequency. Afterthe new resonance was attained, the function generatorwould be adjusted until the feedback load matched thetargeted load.

Fatigue test results using a surface crack failure criterionwere available on these crankshafts at the start of thisstudy. The surface crack failure criterion used was a�6 mm crack known internally as a ‘‘four-bubble failure’’[10]. A magnified look at such a crack can be found inthe report by Chien et al. [1]. To gather statistical fatigue

Fig. 3. Frequency versus cycle plot for the six samples tested.


strength results of these crankshafts using the surface crackfailure criterion, a ray projection method described by Leeand Morissey [7] was used. This followed the assessment byLin et al. [9] that the median ray projections result wascomparable to the median fatigue limit using the staircasemethod. Also, a linear approximation of hardness usingthe Brinell scale was used. The fatigue limit was multipliedby the ratio of the minimum print hardness to the averagesample hardness to acquire the final fatigue limit. Thehardness corrected median bending fatigue limit was foundto be 414 N-m.

The first objective was to prove a two-piece failure waspossible with the current resonant bending fixture rig andif the could be tracked using resonant shifts. Two sampleswere tested at high loads of 700 N-m and tested as long aspossible to ascertain feasibility of attaining two-piece fail-ures on the available fixture. The results of these two testedsamples were found in Fig. 3. Surface cracks were observedearly in testing within 100,000 cycles. Yet, very little changewas found in the resonance of these crankshaft samplesuntil 100,000 cycles. Around this point, there was anabrupt and accelerating shift. After a negative shift of

Fig. 4. A 14 mm crack on a tested samp

12 Hz (from 68 to 56 Hz), the acceleration of the resonanceshifts became unmanageable for the operator to compen-sate. Nevertheless, an acceptable level of crack propagationwas found in the post-test examination (14 mm crackdepth, see Fig. 4) to demonstrate two-piece failure wasimminent. Four more tests were conducted and the col-lected results were shown in Fig. 3. It should be noted thatthe discrepancy of two frequencies 63 and 68 Hz in Fig. 3was due to different weight of the tines used in the resonantbending fatigue test fixture. Each test had the same results:apparent surface cracking and period with an insufficientchange in resonant frequency followed by an abrupt andaccelerating resonant shift to an unmanageable level witha post-test examination showing significant crack depthranging from 8 to 15 mm. These results in Fig. 5 showedthe frequency rate change versus percent of total cyclestested. Note here that the accelerations continued toincrease as the test progresses. Several small accelerationspikes were negligible for most of the test and then spikedsignificantly – an apparent indication of failure. With thisin mind, Table 1 showed frequency shifts and cycle infor-mation at the first acceleration spike in these samples. Thistable showed that a 2.0 Hz or 3.0% resonant shift failurecriterion would capture 90% of the total cycles accumu-lated. It should also be noted that no frequency shift accel-eration spikes were found in any suspended test conductedthroughout this study.

To determine crack depth of samples with a 2.0 Hz res-onant shift, one more test was conducted and suspended ata 2.0 Hz shift. The sample showed a significant crack of9.5 mm. Therefore, it was concluded that resonant shiftdecreases of 2.0 Hz or 3.0% would adequately approximatetwo-piece failures for the crankshaft tested.

The second objective was to determine the fatigue limitof the crankshaft using this two-piece failure criterion.Testing was planned with a staircase methodology to 10million cycles. The staircase technique was chosen overthe ray projection to better match industry practice.

le that had a 12 Hz resonance shift.

Table 1Spike frequency shift rates versus cycle information for crankshaft sectionstested at 150% fatigue limit as determined by the surface crack initiationcriterion

Sample no. Percent oftotal cycles(%)

Resonantfrequencyshift (Hz)

Resonantfrequencyshift (%)

1 96.6 1.98 2.902 93.8 2.05 3.003 96.4 2.15 3.204 90.0 1.38 2.205 98.5 1.70 2.506 96.0 3.01 4.80

550

650

750

1 4 7 10 13 16 19 22 25

Ben

ding

Loa

d (N

-m)

- failure

- suspension

Fig. 6. Staircase fatigue limit test results using a % resonant shift failurecriterion.

Fig. 5. Frequency rate change versus the percent of total cycles tested.


The staircase test method and its data analysis procedurecan be found elsewhere [8,14,15]. The test method requiresa bending load increment (targeted as half to twice thestandard deviation of the fatigue limit) and an initial load-ing before beginning. The standard deviation of the fatiguelimit for previously tested crankshafts using surface crackfailure modes was used for the bending moment increment.The initial loading condition was arbitrarily chosen at ahigh bending moment level as 728 N-m.

Twenty-two samples were tested. All crankshafts com-pleted fatigue strength testing using the resonance dropfailure criterion. Fig. 6 shows the data collected. The med-ian bending fatigue limit of the crankshaft section was thencalculated as 642 N-m. Therefore, the fatigue limit testmethod based on the surface failure criterion underesti-mated the strength based on the two-piece failure criterionby 36%.

Fillet surface cracks, as determined by the four-bubblecrack, were present during every test, including samplesthat suspended. Since the ‘‘four-bubble’’ criterion is notan industry standard, Magnaglow inspection was com-pleted on three failed samples and eight suspended samples.All of the failed samples had 30 mm surface cracks thatwere identified on the fillet surface. Also, the eight sus-pended samples showed surface cracks of comparablelengths. One suspended part was checked for crack depth;the depth was 0.8 mm. The appearance of these macro-

scopic but shallow and non-propagating cracks on sus-pended samples supports the existence of crack arrest incrankshaft fillets.

3. Finite element analysis for residual and bending stresses

The focus of this section was to explore an engineeringapproach to stress analyses of a rolled, ductile cast ironcrankshaft section under bending fatigue testing. In a typ-ical crankshaft fillet rolling process, a roller is often used toapply compressive force onto the crankshaft fillet regionfor improvement of fatigue strength. The force is graduallyincreased from a pre-defined state as the crankshaft isrotating (ramping up stage). After a specified amount ofcrankshaft revolutions, the rolling force reaches the fullload. The full load will be maintained for a fixed amountof revolutions (full load stage). As the full load stage iscompleted, the roller load is gradually brought down tothe pre-defined state within a specified amount of revolu-tions. Fig. 7 depicted the roller loading scheme exampleof a fillet rolling process. The rolling load was zero at thebeginning of the process. After three revolutions, the rollerload was maintained at the full load for another eight rev-olutions. Then, it took another three revolutions to bringdown the roller load to zero. For the crankshafts of inter-est, the maximum roller load of 6000 N along the rollingdirection at 32� normal to the crankshaft axis was usedthroughout this paper.

The prediction of residual stresses in the crankshaft filletregion was essential to the fatigue assessment of a crank-shaft. However, it was challenging to determine the resid-ual stress distribution experimentally and analytically.Although many advanced experimental techniques wereavailable for determination of residual stress distribution,it was difficult to use in our validation study due to thecomplexity of surface shapes and the small fillet radius. Athree-dimensional elastic–plastic finite element analysis

Fig. 7. Roller loading scheme example of a fillet rolling process.

Table 2Chemical compositions of the crankshaft tested

Chemistry data % Weight

Carbon, C 3.60Silicon, Si 2.40Manganese, Mn 0.50Phosphorus, P 0.02Sulfur, S 0.001Copper, Cu 0.13Magnesium, Mg 0.04

0

200

400

600

800

1000

1200

1400

1600

0 0.05 0.1 0.15 0.2

Plastic strain

Str

ess

(MP

a)Monotonic tension

Cyclic tension

Cyclic compression

Fig. 8. Monotonic and cyclic stress versus plastic strain curves for theductile cast iron with 244 HB.


would be the perfect solution to the residual stress simula-tion of a rolled, ductile cast iron crankshaft section, but itwas limited to the modeling techniques and large CPU timeconsumption. Certain assumptions needed to be consideredfor such an analysis. For example, Chien et al. [1] investi-gated the effect of residual stress distribution on the bend-ing fatigue limit of a crankshaft section by a plane-strainelastic–plastic finite element analysis. Their analysis wascarried out under a deformation-controlled numerical pro-cedure. The rolling depth of the fillet surface measured bythe shadowgraphs taken before and after the fillet rollingprocess was used as the input to the two-dimensional FEanalysis. A ductile iron crankshaft would exhibit differentmaterial behavior under tension and compression. But,for simplicity, Chien et al. assumed the ductile cast ironexhibited identical material behavior under tension/com-pression and adopted the von Mises criterion to describethe post-yield behavior of ductile cast iron under multiaxialstates of stress.

In this paper, a load-controlled finite element analysiswas performed to simulate the actual fillet rolling processon the crankshaft radius. The ductile cast-iron materialproperties with the Brinell hardness of 244 BHN was con-sidered in the analyses. Table 2 listed the chemical compo-sitions of the crankshaft tested. The mechanical materialproperties of ductile cast irons can be found from the workby Tartaglia et al. [16]. The ductile cast iron has the mod-ulus of elasticity, (E = 165 GPa), ultimate tensile strength,(Su = 754 MPa), 0.2% offset yield strength (Sy = 447 MPa),and Poisson’s ratio (m = 0.275). Fig. 8 showed the mono-tonic and cyclic stress versus plastic strain curves for theductile cast iron with 244 BHN. Since this ductile cast ironshowed a cyclically stable material response in tension, itwas reasonable to assume the material in compression fol-

lowed the same cyclically stable behavior. Then, the mono-tonic stress–plastic strain curve in compression that wasnot available in [16] could be extracted form the cyclicone in compression.

The cast iron plasticity model in a commercial finite ele-ment program ABAQUS [6] was used to describe mechan-ical behavior of cast iron having different yield strength intension and compression with the yield stress in compres-sion being higher than the yield stress in tension. Thismodel was intended for the simulation of cast iron materialresponse only under monotonic loading conditions, whichwere the loading conditions for rolling in this study. Thismodel provided elastic–plastic behavior with differentstrengths, flow, and hardening in tension and compression.Also, this model was based on a yield function thatdepended on the maximum principal stress under tensionand the von Mises yield criterion under compression. Themonotonic tension hardening and compression hardeningdata shown in Fig. 8 were used for the plasticity model.

A three-dimensional elastic–plastic finite element analy-sis was performed to simulate the ramping loading/unload-ing rolling process (as described in Fig. 7) in the fillet regionof a crankshaft section. But intense CPU time consumptionfrom the numerical computations prohibited the authors topursue any further analysis. Thus, there was a need to sim-plify the rolling load process for our three-dimensional sim-ulations. It was assumed that the induced residual stresswas greatly affected by the rolling force in the rampingup and down stage and additional operation in the full load


stage increased the magnitude and the distribution of theresidual stress very little. In this case, two-dimensionalplane-strain finite element analyses were conducted toinvestigate the residual stress distribution for a cylindershaft subjected to a roller under both single loading/unloading (SL/U) and ramping loading/unloading (RL/U).

In the simulations, the contact surface between the twocylinders was defined. Applying the rolling force automat-ically induces the normal stress at the contact area. Thetangential traction was subsequently generated based onthe use of the Coulomb’s friction law in ABAQUS with afriction coefficient of 0.05. The relative movement was con-trolled by specifying the relative rotation of the two cylin-ders. Consequently, there was very little slippage betweenthe two cylinders. Fig. 9 showed that even there were dis-crepancies in the profiles of the applied roller loads androller center displacements, the model with SL/U providedreasonable residual stress patterns as compared with thosewith RL/U. The noted difference in magnitudes could beimproved by using finer element size in the contact regionsuch as 1.5–1.0 lm as reported by Guo and Barkey [5].Therefore, a three-dimensional model with SL/U wasdecided for use in assessing the residual stresses of a ductilecast iron crankshaft under a typical RL/U process.

Three different finite element models were used in thisstudy:

Fig. 9. Comparisons of residual stress, roller load, and roller displace

1. Model A – a three-dimensional local fillet model forresidual stress predictions.

2. Model B – a three-dimensional full crank-throw modelto predict the stresses due to a specified bendingmoment.

3. Model C – a three-dimensional zoom-in model to deriveoperating stress components.

Second, order elements were used for Model B and first-order elements were used for Model A and Model C. ModelA and Model C were identical in terms of geometric dimen-sioning. However, Model A had finer meshes than Model Caround the area where the roller load was applied. This wasto ensure that reasonable residual stress results could beobtained with a less amount of CPU time. On the symmetricplanes of the local fillet models, Model A and Model C,mesh patterns were identical so that the derived stressesfrom these models could be easily combined. ABAQUSsoftware was used to derive the residual stresses and thezoom-in operating stresses on Model A and Model C, whileMSC-NASTRAN software [11] was used to calculate theoperating stresses on Model B. The number of grids, num-ber of elements, element types, meshing method, and size ofthe element were summarized as in Table 3.

For residual stress simulations, Model A was usedunder a specified rolling load from the roller. As shownin Fig. 10, the roller was assumed to be rigid and was

ment for two cylinder shafts under single and ramping contacts.

Table 3Summary and description of finite element models

Model A Model B Model C

Number of grids 56,567 3,39,942 92,317Type and number of elements C3D8R – 76944 CPENTA – 2444 C3D8R – 85180

CTETRA – 226318RBE2 – 2

Meshing method Hand Auto HandElement size Critical region: 0.186 · 0.096 · 0.067 Critical region: �0.5 for all edges Critical region: 0.744 · 0.096 · 0.067

Fig. 10. Description of Model A, 3-D local fillet model for residual stresspredictions.

Fig. 11. Description of Model B, 3-D full crank-throw model foroperating stress predictions.

Fig. 12. Description of Model C, 3-D zoom-in local model for operatingstress predictions.


modeled with a rigid surface. Maximal rolling load of6000 N along the rolling direction was applied at a refer-ence point of the roller and, then, was unloaded toderive the residual stresses. This model was restrainedat those cutting surfaces. For operating bending stresssimulations, Model B, a three-dimensional full crank-throw model, was used to calculate the stresses under aspecified operating moment. Fig. 11 depicted the FEmodel, loads, and boundary conditions that were usedto predict the operating stresses of a crankshaft section.Load was applied on the pin end and the rigidly fixedboundary conditions were applied to the main end.Finally, Model C, a 3-D zoom-in local model shown inFig. 12, was constructed around the high stress regionof Model B. Boundary conditions along the boundarysurfaces in Model C were retrieved from Model B. Oper-ating stresses of Model C were then calculated.

4. Analytical fatigue limit assessment

For fatigue limit assessment, there was a need to defineseveral possible crack propagation planes, originating fromthe fillet surface and extending into the component. Theseplanes were chosen to represent the expected directions offatigue crack propagation dominated by the Mode-I open-ing stress. Therefore, the normal stress distribution on each

plane was the subject of interest and a global-to-local coor-dinate transformation was needed during this stress opera-tion. During fully reversed resonant fatigue testing, the


applied operating stress in the fillet region varied from+rn,op to �rn,op. In the presence of the residual stress,the maximum normal stresses could be obtained by a linearsuperposition of the derived residual (rn,res) and operating(rn,op) stresses from Model A and Model C, respectively.This was a valid assumption for our fatigue limit studywhere little plastic strain occurred. Fig. 13 showed the nor-mal stress distributions on the fillet surface S and the in-depth planes (A, B, and C) for a crankshaft under a rollingload of 6000 N and an operating bending moment ampli-tude of 1000 N-m. Note that the angle associated withPlane B or C was measured counterclockwise with respectto Plane A.

4.1. A stress-based SWT damage parameter

For fatigue assessment based on a surface crack crite-rion, an equivalent reversed stress amplitude ðDrn;ar

2Þ normal

to the crack propagation plane and on the fillet surface wasdefined by the Smith–Watson–Topper (SWT) model [13].This SWT model has been successfully applied to grey cast

Fig. 13. Normal stress distributions acting on planes (A, B, C) and the fillet su1000 N-m.

irons as reported by Fash and Socie [3]. The SWT stress isexpressed as follows:

Drn;ar

2¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirn;max

Drn

2

� �sð1Þ

where rn,max(=rn,res + rn,op) and Drn

2ð¼ rn;opÞ are the max-

imum normal surface stress and stress amplitude in a cycle,respectively.

Simulation studies were performed to examine the effectof four different operating bending moment levels (1150,1000, 850, and 700 N-m) on the SWT equivalent stress dis-tribution along the fillet surface of the crankshaft under agiven rolling load of 6000 N. Fig. 14 showed the calculatedSWT equivalent stresses on the fillet surface S, where thematerial fatigue limit of 260 MPa was depicted in a dotline. It was noted that based on the peaks of the SWTequivalent stress distribution there were two possible crackinitiation sites: 45� and 80� counterclockwise with respectto Plane A. For applied moment amplitudes exceeding1150 N-m, the first surface crack would appear at the side

rface S under rolling load of 6000 N and operating moment amplitude of

SW

T e

quiv

alen

t str

ess

(M

Pa)

Angle from line A (degree)30 0 30 60 90

0

100

200

300

400

500

6001150 N m1000 N m850 N m700 N m

Material fatigue limit (260 MPa)

Fig. 14. SWT equivalent stress distribution along the fillet surface S underfour operating bending levels (1150, 1000, 850, and 700 N-m) and a givenrolling load of 6000 N.


of 45�. Otherwise, for moment amplitudes from 850 to1150 N-m, the first surface crack would be observedaround the angle of 80�. There would be no surface crackinitiated at bending moment amplitudes below 850 N-mbecause the corresponding peak SWT equivalent stresswas below the material fatigue limit as 260 MPa. However,the scanning electron microscope (SEM) technique indi-cated that two surface crack sites were observed at 35�and at 75� when the crankshaft sections were tested at abending fatigue limit of 414 N-m. The finite element simu-lation with the SWR equivalent stress had a qualitative cor-relation to the surface crack locations, but did not producecomparable results to what applied bending moment to ini-tiate the surface cracks.

4.2. An effective stress intensity factor range

For subsequent fatigue assessment based on a two-piecefailure criterion, the bending fatigue limit of the crankshafttested could be obtained when the effective stress intensityfactor range (D(KI)eff) of a crankshaft was equal to athreshold effective stress intensity factor range (DKth).For the case of ferrite nodular graphite cast iron, Clementet al. [2] reported the value of DKth as 8:5MPa

ffiffiffiffimp

. Theeffective stress intensity factor range (D(KI)eff) was esti-mated by the technique of crack modeling developed byTaylor et al. [17]. This technique has been able to predictthe fatigue limit of an unrolled, spheroidal graphite castiron crankshaft with a very high degree of accuracy. Itassumed that the effective stress intensity range of a crank-shaft could be obtained from an equivalent center-crackedinfinite plate in tension, which had the similar maximumstress distribution near the crack tip to the in-depth maxi-mum stress distribution normal to the possible crack prop-agation plane. Since this study assumed that only tensilestress causes crack extension, the effective crack face stressrange was identical to the maximum crack face tensile

stress. The theoretical stress distribution for the standardcenter-cracked infinite plate developed by Westgaard ascited in [17] is:

r ¼ rwffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� aw

awþr

� �2r ð2Þ

where rw is the remote stress; 2aw is the crack length, and r

is the crack extension measured from the crack tip. Thebest fit between the Westgaard equation and the maximumnormal stress distribution could be found by varying rw

and aw. The effective stress intensity factor range was thendetermined as follows:

DðKIÞeff ¼ rw

ffiffiffiffiffiffiffiffipaw

p ð3Þ

Subsequent simulations were performed to examine themaximum stress distribution normal to the two crackgrowth planes (Planes B and C) for the crankshaft testedunder various bending moment amplitudes (1150, 1000,850, and 700 N-m) and a rolling force of 6000 N. Theseresults were illustrated in Fig. 15 for Plane B and Fig. 16for Plane C. Both planes were the potential crack propaga-tion planes because of the experimental and analytical evi-dence – the observed surface crack sites and the highestSWT equivalent stress values on the fillet surface.

It was our objective to determine the predicted bendingfatigue limit of the tested crankshaft section with a longcrack propagating along Planes B and C. Crack propaga-tion due to a bending fatigue limit would occur if the effec-tive stress intensity factor range of a crankshaft exceeded orwas equal to the reported threshold value of 8:5MPa

ffiffiffiffimp

.Fig. 15 indicated that surface cracks would occur on PlaneB but they were unlikely to propagate along the plane dueto the rapid reduction of the maximum normal stress distri-bution. On the other hand, due to the gradual decrease inmaximum normal stress values along Plane C as shownin Fig. 16, the surface cracks would have a higher possibil-ity to propagate.

To investigate what bending moments would cause acrack to propagate along Plane C, the in-depth maximumnormal stress distribution under the operating bendingmoment of 850 N-m was chosen. The corresponding stressfield matched very well with the one for the center-crackedinfinite plate in tension, in which rw = 110 MPa and aw =2.60 mm. Fig. 17 showed the correlation between the FEdata and the best fit Westergaard equation for an equiva-lent crack. Therefore, the corresponding effective stressintensity factor range was calculated as 9:94MPa

ffiffiffiffimp

. Sim-ilarly, the effective stress intensity range for 700 N-m wasfound to be 7:40MPa

ffiffiffiffimp

. Because of the elastic analysisof bending stress superimposed on a given residual stresses,the above two calculated K values for the two bendingmoment amplitudes could be linearly extrapolated toobtain the K value for any other bending moment. There-fore, it was predicted that the reported threshold effectivestress intensity of 8:5MPa

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would occur in the crank-shaft subjected to a bending moment of 765 N-m, which

Depth from the surface along line B (mm)

Max

imum

nor

mal

str

ess

(M

Pa)

0 0.5 1 1.5 2 2.5 3400

300

200

100

0

100

200

300

400

1150 N m1000 N m850 N m700 N m

Fig. 15. Maximum normal stress distributions normal to Plane B underfour operating bending moments (1150, 1000, 850, and 700 N-m) and agiven rolling load of 6000 N.

Depth from the surface along line C (mm)

Max

imum

nor

mal

str

ess

(M

Pa)

0 0.5 1 1.5 2 2.5 30

50

100

150

200

250

300

350

4001150 N m1000 N m850 N m700 N m

Fig. 16. Maximum normal stress distributions normal to Plane C underfour operating bending moments (1150, 1000, 850, and 700 N-m) and agiven rolling load of 6000 N.

0

50

100

150

200

250

300

350

400

450

0 3Depth from the surface along line C (mm)

Max

imu

m n

orm

al s

tres

s (M

Pa)

FEA Data Equivalent_Crack

1 2 4

Fig. 17. Stress versus distance curves from FE data and the best-fitWestergaard equation for the equivalent crack.


overestimated the experimental data (642 N-m). The 16.1%discrepancy between the predicted and experimental resultscould be attributable to the fact that the cast iron we con-sidered was different from the one studied by Clement et al.[2]. A new threshold value of D(KI)eff for the grade of ourcast iron was required for future engineering applications.Thus, a back calculation based on the bending fatigue limit(642 N-m) of the tested crankshaft on a two-piece failurecriterion led to a new D(KI)eff as 6:42MPa

ffiffiffiffimp

. This was areasonable threshold value of D(KI)eff since the tensile yieldstrength of our cast iron (511 MPa) was higher than theone in the reported cast iron (270 MPa) from Ref. [2], thevalue of D(KI)eff was expected to be lower than the valueof 8:5MPa

ffiffiffiffimp

.

5. Conclusions

The following conclusions were drawn from experimen-tal results of resonant bending fatigue testing on rolled,ductile cast iron crankshaft sections.

1. An accelerating resonant shift was a valid failure crite-rion that correlated well with two-piece failure.

2. Fatigue limits derived using the surface crack failure cri-terion would be significantly lower than those derivedusing a two-piece failure criterion.

3. Cracks, as defined by the four-bubble criterion or thosefound in post-process Magnaglow inspection, could beform in the fillet surface and not propagate to failure.

4. The analytical hypothesis made by Chien et al. [1] ofcrack arrest due to increasing subsurface compressiveresidual stresses was supported empirically by this study.

The following conclusions were drawn based on simula-tion data from the three-dimensional finite element analysisand the fatigue limit assessment:

1. The fatigue limit based on the surface crack failure cri-terion was assessed by the SWT equivalent stress onthe crankshaft fillet surface. The surface crack would ini-tiate if the SWT stress value exceeded the reported mate-rial fatigue limit of 260 MPa. When compared to the testresults, the SWT equivalent stress had a qualitative cor-relation to the crack initiation sites, but failed to pro-duce comparable bending fatigue limit prediction.

2. The fatigue limit based on the in-depth cracks was eval-uated by the effective stress intensity factor range thatcould be estimated by the technique of crack modelingdeveloped by Taylor et al. [17]. This approach assumedthat the effective stress intensity factor range of a crank-shaft could be identical to that for a standard center-cracked plate if the combined normal stress distributionin the crankshaft fillet region is similar to that in thatstandard plate. The fatigue limit of the crankshaft wasassumed to occur when the threshold stress intensity fac-tor is reached in the corresponding cracked plate. Theresults showed that the fatigue limit of the crankshaft


could be linked to the value of a given threshold stressintensity factor range. For future engineering applica-tions, the threshold stress intensity factor for long cracksin the tested ductile cast iron crankshafts was found tobe 6:42MPa

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.

References

[1] Chien WY, Pan J, Close D, Ho S. Crankshaft fatigue crackpropagation analysis with consideration of residual stresses. Int JFatigue 2005;27:1–19.

[2] Clement P, Angeli JP, Pineau A. Short crack behavior in nodular castiron. Fatigue Fract Eng Mater Struct 1984;7:251–65.

[3] Fash J, Socie DF. Fatigue behavior of micro alloyed steels for hotforged mechanical components. Int J Fatigue 1982;4(3):137–42.

[4] Feng M, Li M. Development of a Computerized ElectrodynamicResonant Fatigue Test Machine and Its Applications to AutomotiveComponents. SAE Technical Paper 2003-01-0951, 2003.

[5] Guo YB, Barkey ME. FE-Simulation of the effects of machining-induced residual stress profile on rolling contact of hard machinedcomponents. Int J Mech Sci 2004;46:371–88.

[6] Hibbitt HD, Karlsson BI, Sorensen EP. ABAQUS Theory Manual,Version 6.3, 2001.

[7] Lee YL, Morrissey W. Uncertainties of experimental crankshaftfatigue strength assessment. Int J Mater Prod Tech 2001;16:379–92.

[8] Lee YL, Pan J, Hathaway R, Barkey M. Fatigue Testing and Analysis:Theory and Practice. Elsevier Butterworth-Heinemann, Burlington,MA, USA; Jordan Hill, Oxford, UK; 2005 [Chapter 4.2.3] of FatigueStrength Testing, p. 119–26.

[9] Lin SK, Lee YL, Lu MW. Evaluation of the staircase and theaccelerated test methods for fatigue limit distributions. Int J Fatigue2001;23:75–83.

[10] Love RJ, Waistall DN. The Improvement in the Bending FatigueStrength of Production Crankshafts by Cold Rolling. M.I.R.A.Report No. 1954/5; 1954. p. 1–8.

[11] MacNeal RH. The NASTRAN Theoretical Manual, Level 15.5; 1972.[12] Ren W, Li K, Lee Y. Optical measurement of residaul stress at the

deep-rolled crankshaft fillet. SAE Technical Paper Number 2004-01-1500, SAE 2004 World Congress, Detroit, Michigan; 2004.

[13] Smith KN, Watson P, Topper TH. A stress–strain function for thefatigue of metals. J Mater 1970;5(4):767–78.

[14] Snyder PM, Lu MW, Lee YL. Reliability-based fatigue strengthtesting by the staircase method. SAE Technical Paper Number 2004-01-1288, SAE 2004 World Congress, Detroit, Michigan; 2004.

[15] Spiteri PV, Lee YL, Segar R. An exploration of failure modes inrolled, ductile, cast-iron crankshafts using a resonant bending testingrig. SAE Technical Paper Number 2005-01-1906, SAE 2005 WorldCongress, Detroit, Michigan; 2005.

[16] Tartaglia JM, Paige ER, Gundlach RB, Jenkins L. Monotonic andcyclic property design data for ductile iron castings. SAE TechnicalPaper Number 2000-01-0758, SAE 2000 World Congress, Detroit,Michigan; 2000.

[17] Taylor D, Ciepalowicz AJ, Rogers P, Devlukia J. Prediction offatigue failure in a crankshaft using the technique of crack modelling.Fatigue Fract Eng Mater Struct 1997;20(1):13–21.

[18] Watmough T, Malatesta MJ. Strengthening of ductile iron forcrankshaft applications. In: Proceedings of Expendable PatternCasting: Managing the Technology. AFS; 1993. p. 83–99.

[19] Yu V, Chien WY, Choi K, Pan J, Close D. Testing and modeling ofresonant shifts in resonance bending fatigue tests of notchedcrankshaft sections. SAE Technical Paper 2004-01-1501; 2004.

Assessment of bending fatigue limit for crankshaft sections with inclusion of residual stresses

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