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Engineering Failure Analysis 11 (2004) 375-386

ENGINEERING FAILURE ANAL YSIS

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Analysis of the fatigue failure of a mountain bike front shock

Holly Shelton, John Obie Sullivan, Ken Gall* Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO 80309-0427, USA

Received 11 June 2003; accepted 22 June 2003

Abstract

We present an analysis of a mountain bike front shock failure. The failure of the 1-year-old shock occurred cata- strophically as the bike was ridden off of a 1-m drop. The failure was the result of fast fracture through both shock tubes at the location where the tubes were press fit into the shock upper crown. Examination of the fracture surfaces of the tubes revealed regions of fatigue crack growth that nearly penetrated the entire thickness of both tubes. An estimate of the forces" during use, coupled with stress analysis, revealed three stresses near the fracture site--axial compression, bending, an d hoop stresses. During operation, the axial compressive stress is negligible while the hoop and bending stresses are s~gnificant. Based on fracture mechanics, and an estimate of the bending stress from a 1-m drop, it is con- firmed that the fatigue cracks present on the fracture surface were large enough to induce fast fracture. Prior to the existence of the fatigue cracks, the stresses were magnified locally near the fracture site by a significant stress concen- tration caused by the sharp transition from the shock tube to the crown. The fatigue cracks initiated at a circumfer- ential location in the tube commensurate with high tensile bending stress and the stiffest region of the crown (highest stress concentration). Based on the evidence, the most probable cause of the bike shock fatigue failure was the shock design, which facilitated high local stresses during use. © 2003 Elsevier Ltd. All rights reserved.

Keywords: Bicycle failures; Fatigue failure; Fast fracture; Fracture mechanics; Shock absorbers

1. Introduction

1.1. Background

A m o u n t a i n bike shock is designed to par t i a l ly abso rb the kinet ic energy induced f rom riding over and jumping off obstacles. The shock reduces the t ransmiss ion o f force and v ib ra t ion to the r ider and s t ruc tura l components of the bicycle, p rov id ing cri t ical con t ro l on rugged terrain. As is the case with mos t advanced sport ing equipment , m o u n t a i n bike shocks have confl ict ing design requirements . On one hand, the shock needs to be l ightweight to p rov ide the r ider the capac i ty to easily maneuve r the f ront end of the bicycle when r iding technical uphi l l terrain. On the o ther hand, the shock mus t be durab le and safe under the extreme loads exper ienced dur ing downhi l l of f - road riding. I f a shock design t rades weight savings for

* Corresponding author. Tel.: + 1-303-735-2711; fax: + 1-303-492-3498. E-mail address: Kenneth.Gall@colorado.edu (K. Gall).

1350-6307/$ - see front matter © 2003 Elsevier Ltd. All rights reserved. doi:l 0.10 l 6/j .engfailana1.2003.06.002

376 H. Shelton et aI. / Engineering Failure Analysis 11 (2004) 375-386

higher allowable stresses, the probability of component failure increases, and the design may become unsafe. The objective of this paper is to use failure analysis to determine the most probable cause of the failure of a mountain bicycle shock.

1.2. Subject shock design and failure senario

The overall design of the subject shock is typical compared to exemplar shocks from various manu- facturers. A schematic of a typical shock is shown in Fig. 1. The shock was built from two cylinder tubes, one on each side of the bicycle's wheel. One cylinder contains a damper, while the other contains a spring. The shocks' cylinder tubes were located at the bottom of the shock assembly, which attaches to opposite sides of the front wheel axle. Individual piston tubes slide in and out of the cylinders, containing the spring and damper, to create the shock absorption. The piston tubes extend up towards the steering column of the bicycle and are press fit into a crown. The crown has a single stem tube extending from the top, which is slid through the steering column of the bicycle and connected to the handlebars through a rigid clamp.

The piston tubes were constructed of a 7000 series aluminum, a common high strength aluminum alloy used in bicycle components. Due to the shock design and the typical loading configuration, the largest stresses were located at the interface of the piston tube and crown press fit at the point of maximum bending load. The failure occurred as the bicycle operator dropped from a height of approximately one meter onto a hard flat surface. Upon landing, the shock catastrophically failed, shooting the front wheel forward and injuring the rider. The rider weighed 71 kg. Due to the nature of the accident, and pending liabilities, onl1~ nondestructive analysis was permitted on the failed shock, ruling out destructive property testing or scanning electron microscopy (SEM).

D a m p e r - -

i

" - . . )

l I

Fig. 1. Schematic of a front shock with labeled parts.

Stem Tube

Crown Housing

Piston Tube

/ Cylinder Tube

Spring

H. Shelton et al./ Engineering Failure Analysis 11 (2004) 375 386 377

1.3. Visual examination o f the fai led shock

Fig. 2 shows a photograph of the fractured shock. The shock fractured through the piston-tubes where they were press fit into the shock crown as seen in Fig. 1. The fracture surfaces of each tube showed iden- tical features, mirrored across the bike mid-plane. Fig. 3a and b shows the left and right tube fracture surfaces which show a clear region of fatigue crack growth followed by a region of overload fracture (see schematic in Fig. 4). Although SEM analysis was not permitted, the partitioned nature of the fracture surface and the obvious cyclic loading conditions clearly indicate a fatigue failure. The circumferential location of crack initiation in both tubes is identical; both are located in the region where the crown is reinforced and has relatively high stiffness shown in Fig. 4. The strong correlation between the two differ- ent crack initiation sites and the geometric features on the shock overrule the possibility that a material defect was the root cause of the fatigue failure. We note that the cracks initiated near the point of max- imum bending stress in the tubes, however, the initiation point is slightly offset from this point. The aforementioned evidence strongly suggests that the bending stress was a key contributor to the failure in addition to the stress concentration in the shock crown-tube junction.

2. Analysis of the loading on the shock

Here we approximate the applied loads on the bike using two distinct approaches. The first consists of estimating the loads from a dynamic standpoint using the potential energy of the rider and an approximate impact time. The,second approach employs fracture mechanics to estimate the bending stresses required to cause fast fracture of the shock given the observed final fatigue crack sizes on the fracture surface.

Fig. 2. Photograph of the fractured mountain bicycle shock. The failure occurred at the junction between the crown housing and the piston tube.

378 H. Shelton et al. / Engineering Failure Analysis 11 (2004) 375 386

III iilli

(a) 25.4 mm

I II IIIIIIIIIII I I I I

(h) 2 5 . 4 m m

Fig. 3. Fracture surfaces of the failed tubes. Two distinct regions of failure are apparent, fatigue crack growth and fast fracture.

H. Shelton et al. /Engineering Failure Analysis 11 (2004) 375-386

2.1. Approximate dynamic analysis

379

An energy balance of the failure scenario was performed to estimate the forces induced by the biker on the shock. The potential energy from the one-meter drop is converted to kinetic energy, and must be absorbed during the landing. We assume that the kinetic energy contribution due to the horizontal velocity of the bicycle was not absorbed at impact but rather after the fall, and can be ignored. The potential energy, E, of the system is given as:

E = (•person 4- ~gbike)gh (l)

where Wp . . . . . and Wbike are the weight of the rider and bike, respectively, g = 9.8 m/s 2, and h is the drop height. The total impulse force, Ftota], due to dissipation of this potential energy, which is completely con- verted to kinetic energy, is given as:

MV F t o t a l - At (2)

where At is the impulse time required to arrest the motion, M is mass, and V is the vertical velocity com- ponent developed from the conversion of potential to kinetic energy. We also assume the total impact force, Ftotal, is distributed evenly between the front and rear wheel (Fig. 5). The shock rests at approxi- mately a 20 ° angle from vertical as seen in Fig. 5. The total force, Ftotal, acts near the center of the bike. A force of Ftotal/2 is the assumed reaction force from the fall on each wheel. The force on each tube of the bike shock is given by F~otal/4, which is broken into an axial, Fr2,1'a] u~ =gt°talCos20° and a bending

, d r -

stress,~2,1~ ~bo = Ft4t~']XJin20 . onetube Fig. 6 shows the impulse force on each tube, ~L°nebendtUbe, and the bending stress, O'bend , as a function of

drop height, h, With respect to various reasonable impulse times, At. As the drop height increases and the impulse time decreases, the force increases. At the time of the accident, the biker dropped off of a one- meter ridge, as indicated by a vertical line in Fig. 6. Estimating the impulse time is more difficult since the

Region of reinforcement

Region of fatigue crack growth

Crack initiation site

]

Region of fast fracture: v/

Fig. 4. Schematic showing regions of fatigue crack initiation and growth, along with fast fracture.

380 H. Shelton et al. / Engineering Failure Analysis 11 (2004) 375 386

shock absorber and biomechanics of the rider will play a role in dictating the time required to completely stop vertical mot ion of the system center of mass.

If the biker fell 1 m and absorbed this fall over a time of 100 ms, the force on one tube, p~e tube bend would be approximately 0.3 kN. The bending load creates tensile stresses in the location of the fatigue cracks observed on the fracture surface and will load these cracks in Mode I opening. For example, the maximum tensile bending stress caused by a one-meter drop is estimated to be approximately 50 MPa for an impact time of 100 ms, as can be seen in Fig. 6. Based on the geometry of the shock, the fall also induces an axial load on the shock. This axial load, however, acts over a relatively large area and thus the axial compressive stress is about 1% of the bending stress, and is thus negligible.

Shock

Ftotal

' ~ 2 , 'J

Frame

Shock

~" " " ' " ' " "" " ' " - . total

2

F ane tube Ftetal axial /4 F

one tube bend

-\

Fig. 5. Schematic of shock orientation with respect to applied loads and bicycle •frame.

H. She#on et al. / Engineering Failure Analysis l l (2004) 375 386 381

450 2.50

g. v

l u m

e -

" O e -

ll) lll

400 Drop Height = 0.9 rn : ; . 4 , 1 - ' ' / ~

360 TJX 200 300 ~ Time = 15 ms

250 ~

2OO i I

150

100 0,50 m s

. 0 0 0 0.08 0,15 0.23 0.30 0.38 0,46 0.53 0.61 0.69 0.76 0.84 0.91 0.99 1.07 1,14

Drop Height, h (m) Fig. 6. Plot of applied reaction force and bending stress on each tube of the shock as a function of drop height, h.

z ~e

1.50 Z

ou.=

1.00

O u.

2.2. Fracture mechanics approach

The bending stress needed to fast fracture a tube with a fatigue crack of magnitude, a, was calculated using fracture mechanics. The point of instability is given by [1]:

KI C ~ onetube Crbend .,/~f(g) (3)

where K:c is the fracture toughness of the material, O'bend is the applied bending stress, a is the crack length, and f(g) is a factor accounting for the geometry of the loading. Fig. 7 shows the definition of crack length, a, for a part-though crack. The value of K:c, 24 MPa~/m, for 7000 grade aluminum was used, but was varied b y + 10% to account for different material variations [2]. The geometry factor,f(g) was used for a part-through crack on the radial plane of a hollow cylinder [1]. The forces and stresses required to frac- ture the tube, as a function of crack length, a, are shown in Fig. 8.

The crack length at the time of fast fracture is approximately 4.5 mm. This crack length yields a force of about 1.43 kN, or a bending stress of about 245 MPa to initiate fast fracture. This force represents the minimum value that was actually felt during the fall prior to fracture of the shock. The actual force could have been headed towards a higher value, which was never realized, due to the component failure. We note that the forces calculated through a fracture mechanics approach are on par with the forces calculated by the basic dynamic analysis for reasonable impact times from a 1-m drop. Consequently, we feel that the simple dynamic analysis is an appropriate estimation of the applied loads on the bike.

382 H. Shelton et al./ Engineering Failure Analysis l l (2004) 375-386

3. Stress analysis prior to crack initiation

A stress analysis was performed to determine what caused fatigue crack initiation. In a component designed using a "safe-life" or endurance limit approach, premature fatigue failure is often the result of unanticipated local stresses or material conditions. A local deficiency in material properties, particularly the presence of inclusions, voids, or pre-existing cracks due to manufacturing can greatly diminish the high cycle fatigue performance of a component. Similarly, if local stresses exceed the yield strength during operation, constrained plastic flow can result in accelerated crack formation. In both instances, the

Fig. 7. Parameters used to define a partially through the thickness crack in a hollow cylinder.

800

4.5

700 4

Crack length at fast fracture = 4.5 mm i 2 600 Upper Estimate N , " ~ ! 3.5

Average Estimate , / ;

= 3 500 Lower Estimate b ~ ~.

2.5 4OO

2 ~ =

300 °I~'Q c :B 1.5

200 I, 1

100 ; O.5

o ' ~ i ~ ' ' :, . . . . o 0 5 1.5 .5 3 3.5 4.4 4.6 ' 4.8

C r a c k Length, a (ram)

Fig. 8. Plot of the force and bending stress required to initiate fast fracture in a tube with a crack of length a. The figure depicts three different Kic values to allot for different heat treatments of 7000 series A1.

H. Shelton et al./ Engineering Failure Analysis 11 (2004) 375 386 383

decreased component life is a result of a diminished crack initiation lifetime, which is often 85% of total life during high-cycle, low-stress fatigue.

In the subject shock, there were no visible signs of defects or corrosion on the fracture surface, and the same crack was seen in identical locations on both tubes. Furthermore, upon examination of two other "intact" exemplar shocks, fatigue cracks were discovered in precisely the same locations as were found on the fracture surface of the bike shock under investigation. These observations are consistent with pre- mature fatigue failure caused by excessive local stresses driven by the shock design. The probabili ty that detrimental material defects existed in the same exact location in all tubes, and controlled fatigue crack nucleation, is extremely low.

The tubes of the bike shock were joined to the crown using a press fit. Consequently, during use, there will be intrinsic (manufacturing) stresses in addition to extrinsic (operating) stresses near the location of fatigue crack nucleation. The intrinsic stresses are a direct consequence of the press fit and are manifested through a compressive hoop stress. When estimating the stresses due to the press fit, it was assumed the pressure, P, was large enough to keep the shock in place for a force equal to four times the weight of the biker, or 3.0 kN. Fig. 9 shows the forces induced on the tube by the press fit. The friction coefficient, #, was assumed to be 0.2 and the external force from the crown was assumed to be distributed as an even pressure on the tube. Eq. (4) was used to calculate the hoop stress in the tube as a function of the pressure on the tube, P, the diameter of the tube, do, and the thickness of the tube, t:

Pdo O-hoop = 2t (4)

Using Eq. (4), the hoop stress was determined to be approximately 2l MPa. This value is roughly 7% of the bending stresses in the tube during landing. However, it should be understood that both stresses were locally amplifi4d by the presence of a stress-concentration. As previously mentioned, an axial compressive stress exists in:addition to the hoop and bending stress. This compressive stress acts in opposition to the tensile bending stress, and is negligible.

P ~ ~ P

qo0

O-bend

T

,l O-bend

C ~"" LL

('~h o op T Fperson

4

Fig. 9. The stresses in the tube due to the press fit and the bending moment.

384 H. Shelton et al. /Engineering Failure Analysis 11 (2004) 375-386

Table 1 Von Mises stresses for different stress concentration factors and impact absorption times

Kt ffwn, i5 ms Gvm, 50 ms ~vm. I00 ins

1 381.04 122.89 68.48 2 538.88 173.79 96.84 3 659.99 212.84 118.60

The Von Mises stress, ~ .... acting near the crack initiation site is given as:

~/( 2 2 2 ]CtCYhoop ~ k-tO'bend ) -{-ktO'bend -~- kto-fmop

O'V1TI ~ 2 (5)

where Ohoop is the hoop stress and O'bend is the bending stress, which is slightly decreased by the axial compressive stress. The stress concentration factor at the point where the tube joins with the crown, where the crack initiation occurred, is given by kt. The stress concentration resulting from the relatively sharp corner at the press fit junc- tion can significantly amplify the local bending and hoop stresses. It is estimated that the stress concentration is between 1 and 3. Table 1 shows the local Von-mises stresses as a function of kt and assumed impact time.

The slightly offset location of the fatigue cracks, with respect to the point on maximum tensile bending stress due to the applied loading, is an artifact of the different circumferential distribution of the stress concentration. Although the tube being press fit into the crown is axissymmetric, the crown contains a reinforced legion as evident in Fig. 2. The reinforced region possesses a locally high stiffness, and thus is capable of exerting larger local constraining forces against the bike tube during the press fit and during bending. The stiff region of the crown acts to further increase the stress concentration present at the rela- tively Sharp-junction existing at the tube-crown interface.

4. Discussion

In most situations where catastrophic failure occurs, as in this case, a single root cause does not exist. Rather, a series of circumstances and events lead up to the ultimate failure. By itself, the rider dropping off a three-foot ledge would not have caused the shock to fail. However, the aforementioned impact, coupled with a pre-existing fatigue crack, lead to fast-fracture and shock failure. The visual examination revealed the existence of fatigue cracks that nearly penetrated the entire thickness of the tubes. Tl~e cracks were located at a position near the maximum tensile bending stress due to normal operation of the shock. The slightly offset circumferential position of the cracks was caused by the local reinforcement of the crown. This evidence leads to the conclusion that the geometry of the shock, in combination with the loading on the fork, created a situation that led to fatigue in that particular region of the tube.

The purpose of the mechanical analysis was to estimate the applied loads and determine whether or not it was possible for the rider to stress the shock enough to cause failure. From the mechanical analysis, it was determined that the compressive stresses acting on the shock after a one-meter drop were relatively small compared to large bending stresses. An inherent stress of 21 MPa was induce<d by the press fit of the crown.

To understand the premature fatigue failure of the shock, it is imperative to compare the stresses in Table 1 to key fatigue properties in hardened 7000 series aluminum. The yield and tensile strengths of high-

H. She#on et al./ Engineering Failure Analysis 11 (2004) 375-386 385

strength aged 7000 series Al are approximately 500 and 575 MPa, respectively [2]. The alternating stress to cause failure, or the safe-life design limit at 106 cycles, in hardened 7000 series A1, is approximately 150 MPa [3]. Based on the stresses calculated in Table 1, it is clear that the stresses can locally surpass the yield/ tensile strengths for the higher stress concentration factors under reasonable impact times. Locally sur- passing these critical stress values can lead to early crack initiation and premature fatigue failure. In addi- tion, the applied stress amplitude, given by the stress values in Table 1 divided by two assuming a zero minimum stress level, would easily surpass the safe life stress limit. For example, the stress amplitude for kt = 2 and a 15 ms drop is 269 MPa. Note that an impact time between 15 ms and 50 ms results in force levels for a 1 meter drop in reasonable agreement with the overall force levels backed out from fracture mechanics (1.4 kN), which is higher than the minimum 150 MPa limit required for 106 cycles. If a mean stress knockdown factor, such as Goodman [4], is employed, the allowable safe-life stress will decrease below 150 MPa and the material is even more prone to failure under the zero to maximum cyclic loading experience by the shock. In general, a part is not appropriately designed to a "safe-life" if the stresses anywhere can ever surpass the safe-life limit. Clearly, based on the stresses in Table 1 and the material safe- life properties, the shock was not a safe-life component.

It is also possible to examine the crack initiation and growth thresholds for the shock material and compare these to the anticipated loading conditions. In Ref. [3], data are given for the total strain ampli- tude versus the number of cycles to crack initiation for various 7000 series A1 alloys. If the stress locally exceeds the yield strength, the local maximum strains can easily reach values up to 2%. For a local strain amplitude of 1%, crack initiation would occur after approximately 100 cycles in numerous 7000 series alloys [3]. Based on the present shock design, the shock would easily experience 100 loading cycles capable of surpassing the yield strength during normal off-road use. If the local strain amplitude reached 2%, the shock would_ initiate a crack in approximately 10 cycles [3]. Clearly, these values are unacceptable for this component.~ Once a crack is initiated, even mild applied stresses, on a bumpy off-road trail, would be sufficient to propagate the crack since the fatigue crack growth threshold, A K t h , for 7000 series A1, is approximately 3 MPa,Jm [2]. For example, given the present geometry, a 1 mm crack would surpass 3 MPa~/m at- an applied stress range of only 75 MPa. Based on Fig. 6, this stress can be generated at minimal drop heights.

The stress analysis indicates that the fatigue crack initiated during typical operating conditions because of the large stress concentrations near the tube/press fit interface. Apparently, the stresses and stress con- centrations were not fully accounted for in the design of the shock, thus resulting in fatigue crack initiation and propagation followed by subsequent failure.

The overall driving force for this failure is a continual push to provide lighter and more rugged compo- nents on mountain bicycles. The front shock on a mountain bike can compr!se as much as 20% of the weight of the entire bicycle, making it a targeted component for overall bicycle weight reduction. The structural tubes of mountain bike shock are often made from high strength A1 alloys in an effort to save weight. In addition, the tube wall thickness is becoming increasingly thinner in an effort to lower the overall weight of shocks. A decrease in wall thickness amplifies both the intrinsic stresses due to press fit- ting or joining, and the extrinsic stresses due to applied bending loads. Caution must be exercised when designing shock tubes with thinner specifications, as the stresses in the shock can quickly become excessive. In addition, the magnitude of local stress concentrations in high stress regions must be accurately known and accounted for in design.

The present failure could have been avoided by designing the shock to lower local stress values. The redesigned shock could have reduced nominal bending/press-fit stresses in the shock through an increased wall thickness. Alternatively, the redesigned shock could have smaller stress concentrations at the tube- crown interface via more distributed crown reinforcement and/or a more gradual transition between the crown and the tube. Lastly, a tailored tube size could help reduce the bending stress.

386 H. Shelton et al./ Engineering Failure Analysis 11 (2004) 375 386

5. Summary

In summary, the most probable cause o f the premature fatigue failure o f the mounta in bicycle shock was a failure to properly account for elevated local stresses in the shock design. The high local stresses were caused by relatively large bending stresses near the top o f the shock coupled with a stress concentra t ion at the junct ion between the shock tubes and crown. Once initiated, the fatigue cracks progressively grew until they had nearly breached the entire tube thickness. Ultimately, a force resulting f rom a 1-m drop caused a bending overload, which initiated a fast fracture o f the pre-existing fatigue crack and subsequent shock failure.

References

[1] Liu A. Summary of stress intensity factors, 1996, ASM handbook, ASM International, vol. 19, Fatigue and Fracture. p. 980 1000.

[2] Callister WD. Materials science and engineering an introduction. 5th ed. Wiley; 2000. [3] Boyer HE. Atlas of fatigue curves. ASM International; 1986. [4] Shigley JE, Mischke CR. Mechanical engineering design. 5th ed. McGraw-Hill; 1989.