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Critical evaluation of mountain bike front shock failure analysis Fabris, Janna; Gubbels, Wade; Gadala, Ibrahim M.; Bromley, Darren Michael Oct 2, 2012

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           CRITICAL EVALUATION OF MOUNTAIN BIKE FRONT SHOCK FAILURE ANALYSIS  MTRL 585 Case Study 2  Prepared By: GROUP 7  Janna Fabris   Wade Gubbels  Ibrahim Gadala  Darren Bromley   Submitted 2 October 2012                J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 2  Contents List of Figures ............................................................................................................................................................. 3 List of Tables ............................................................................................................................................................... 3 1.0 INTRODUCTION .......................................................................................................................................... 4 2.0 FACTS AND EVENTS ................................................................................................................................. 4 3.0 ENGINEERING ANALYSIS ....................................................................................................................... 5 3.1 Visual analysis of the failed shock .................................................................................................. 5 3.2 Approximate dynamic analysis ....................................................................................................... 6 3.3 Fracture mechanics analysis.......................................................................................................... 10 3.4 Stress (Von Mises) analysis ............................................................................................................ 12 4.0 CRITICAL EVALUATION ....................................................................................................................... 15 4.1 Facts presented and missing information ....................................................................................... 15 4.1.1 Material .............................................................................................................................................. 15 4.1.2 Background ...................................................................................................................................... 15 4.1.3 Fatigue analysis .............................................................................................................................. 16 4.2 Assumptions, simplifications, and analysis .................................................................................... 16 4.2.1 Simplifications ................................................................................................................................ 16 4.2.2 Assumptions .................................................................................................................................... 17 4.2.3 Analysis .............................................................................................................................................. 17 4.3 Results ............................................................................................................................................................ 18 4.4 Failure prevention .................................................................................................................................... 18 4.4.1 Stress analysis ................................................................................................................................. 18 4.4.2 Material selection .......................................................................................................................... 19 4.4.3 Design ................................................................................................................................................. 19 4.4.4 Physical testing ............................................................................................................................... 20 5.0 CONCLUSION ............................................................................................................................................. 21 REFERENCES ........................................................................................................................................................... 21          J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 3  List of Figures Figure 1: Schematic drawing of front shock ................................................................................. 5 Figure 2: Image analysis of tube A fracture surface .................................................................. 6 Figure 3: Bike and front shock tube free body diagram .......................................................... 8 Figure 4: Applied reaction force and bending stress versus drop height ......................... 8 Figure 5: Allowable bending stress and corresponding forces versus crack length . 12 Figure 6: The stresses in the tube due to the press fit, bending moment, and axial force .......................................................................................................................................................... 13 Figure 7: Original cross-section (a) and modified cross-section (b) ............................... 19 Figure 8: Extension of crown mating surface ........................................................................... 20  List of Tables Table 1: Missing and/or additional data required for analysis ............................................ 7 Table 2: Applied reaction force and bending stress calculations (dynamic analysis) . 9 Table 3: Missing and/or additional data required for analysis ......................................... 11 Table 4: Bending stress and corresponding force required to initiate crack growth 11 Table 5: VM stresses for different   and impact absorption times (using equation 3) ................................................................................................................................................................ 14 Table 6: VM stresses for different   and impact absorption times (using equation 4) ................................................................................................................................................................ 14     J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 4  1.0 INTRODUCTION  In a journal article, authors Holly Shelton, John Obie Sullivan, and Ken Gall present their investigation into the failure of a mountain bike front shock [1]. The approach taken by the failure analyst was critically evaluated to develop alternate methods of analyzing and portraying the findings.   2.0 FACTS AND EVENTS  A cyclist using a mountain bike with 1-year old shocks encountered a catastrophic failure of the front forks.  The final fracture occurred as a result of riding off a 1-m drop and landing onto a hard flat surface. The front wheel and forks were liberated from the bike frame, and the rider was injured.  Due to pending liabilities, the investigation was limited to only non-destructive testing.  A schematic of the component and location of the fracture is shown in Figure 1.  Like other standard shocks, two cylinder tubes are located on either side of the wheel and couple with the wheel?s axle.  One tube contains a damper while the other contains a spring, providing shock absorption as the individual piston tubes slide in and out.    The opposite ends of the piston tubes are press fit into the crown housing, which in turn is coupled to the steering column.  As shown in Figure 1, fracture occurred in both piston tubes at the junction of the crown housing.   The following is a list of relevant background information provided: ? Piston tubes were constructed from 7000 series aluminum alloy ? Rider?s weight was 71 kg ? Age of the shock was 1 year ? Drop height was 1 meter  J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 5   Figure 1: Schematic drawing of front shock 3.0 ENGINEERING ANALYSIS 3.1 Visual analysis of the failed shock  Fracture surfaces exhibited the same features mirrored across the bike?s mid-plane, which suggests that fracture did not initiate as a result of a material defect or anomaly.  Each fracture surface had a smooth thumbnail shaped region, which is indicative of fatigue failure.  In both pistons, the fatigue region was located in an area of high stiffness in which the crown is reinforced.  The location, shape, and orientation of the fatigue crack suggest that bending stress and stress concentration at the junction between crown and tube were key contributors to the failure.  Images of the two fracture surfaces were provided, including a scale bar for dimensional reference.  It was noticed that the reported crack depth of 4.5 mm does not match the dimensions in the pictures.  This means that the author either reported the wrong crack depth or the scale is incorrect.  If the crack was 4.5 mm Crown Housing Cylinder Tube Spring Stem Tube Piston Tube Damper Fracture Planes  J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 6  deep, the tube would have to be greater than 50 mm in outer diameter.  This seemed excessively large to our group, so it was assumed that the reported crack dimensions were incorrect.  Other dimensions pertinent to the analysis were not reported by the author.  Hence, Quartz PCI image analysis software was calibrated according to the provided scale bar, and used to measure the dimensions of both the tube and the fatigue crack.  Since calibration for image analysis is most accurate at the focal plane, and the authors? Figure 3b was out of focus, the fracture surface in Figure 3a was used for dimension measurements.  Shown in Figure 2, the following dimensions were measured: ? Outside diameter, do = 29.77 mm ? Inside diameter, di = 23.60 mm ? Wall thickness, t = 3.09 mm ? Crack depth, a = 2.51 mm ? Crack breadth, 2C = 12.42 mm   Figure 2: Image analysis of tube A fracture surface  3.2 Approximate dynamic analysis  The purpose of this analysis was to estimate an applied bending stress due to the impact force induced by the rider.  The total impact force is the dissipation of potential energy (conversion to kinetic energy) due to a vertical drop:                   ?                    (            )?       J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 7   Load distribution (refer also to Figure 3): ? the total impact force is considered a point load applied near the center of the bike (at the rider?s seat) ? the impact force is reacted equally at the front and rear bike wheels ? the reaction force at the front wheel is equally split between the two front shock tubes ? this load is considered in axial and bending components                                                                       Impulse times are assumed rather than estimated; the authors claim it is difficult to compute this value given the dependencies the rider?s biomechanics and the shock?s ability to completely arrest the vertical fall.  Computation of the applied bending stresses requires the geometry of the shock tube to be defined.  These dimensions were not explicitly mentioned in the authors? report and have been estimated in order to reproduce the analysis, refer to table Table 1.                (                  )(   )   Table 1: Missing and/or additional data required for analysis mass of bike + rider m 86 kg outer shock tube diameter Do 2.98E-02 m inner shock tube diameter Di 2.36E-02 m shock tube wall thickness t 3.09E-03 m shock tube length l 2.79E-01 m second moment of inertia I 2.33E-08 m4    J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 8   Figure 3: Bike and front shock tube free body diagram  Figure 4: Applied reaction force and bending stress versus drop height 0501001502002503003504004500.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.200.000.501.001.502.002.50Bending Stress   b-per tube (MPa) Drop Height (m) Bending Force Fb-per tube (kN) Applied reaction force and bending stress (per each shock tube) v drop height Fb-100ms Fb-50ms Fb-15ms sb-100ms sb-50ms sb-15ms J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 9  Table 2: Applied reaction force and bending stress calculations (dynamic analysis)  Bending force and stress calculations100ms50ms15ms0.100.050.02NNkNMPaNNNkNMPaNNNkNMPaNNNkNMPahFtFaxial-cFbendingFb-100ms b-100msFtFaxial-cFbendingFb-50ms b-50msFtFaxial-cFbendingFb-15ms b-15ms0.000.00.000.000.000.000.00.000.000.000.000.00.000.000.000.000.05851.8200.1172.830.0712.981703.6400.21145.660.1525.975678.61334.04485.550.4986.560.101204.6282.99103.000.1018.362409.2565.98206.000.2136.738030.81886.61686.670.69122.420.151475.3346.59126.150.1322.492950.7693.19252.300.2544.989835.62310.62841.000.84149.930.201703.6400.21145.660.1525.973407.2800.42291.330.2951.9411357.22668.07971.100.97173.120.251904.7447.45162.860.1629.033809.3894.90325.720.3358.0712697.72982.991085.721.09193.560.302086.5490.16178.400.1831.804172.9980.31356.800.3663.6113909.73267.711189.351.19212.030.352253.6529.43192.700.1934.354507.31058.86385.390.3968.7115024.23529.531284.641.28229.020.402409.2565.98206.000.2136.734818.51131.97412.000.4173.4516061.53773.221373.341.37244.830.452555.4600.32218.500.2238.955110.71200.63436.990.4477.9117035.84002.111456.651.46259.690.502693.6632.79230.320.2341.065387.21265.58460.630.4682.1217957.34218.591535.441.54273.730.552825.1663.67241.560.2443.065650.11327.35483.120.4886.1318833.84424.501610.391.61287.090.602950.7693.19252.300.2544.985901.41386.37504.600.5089.9619671.34621.241681.991.68299.860.653071.2721.49262.600.2646.826142.41442.98525.200.5393.6320474.54809.931750.671.75312.100.703187.1748.73272.510.2748.586374.21497.45545.030.5597.1721247.44991.511816.761.82323.880.753299.0775.00282.080.2850.296597.91550.01564.160.56100.5821993.15166.701880.521.88335.250.803407.2800.42291.330.2951.946814.31600.84582.660.58103.8722714.45336.141942.201.94346.250.853512.0825.06300.300.3053.547024.01650.11600.590.60107.0723413.55500.372001.972.00356.900.903613.8848.98309.000.3155.097227.71697.95618.000.62110.1824092.35659.842060.012.06367.250.953712.9872.24317.470.3256.607425.71744.48634.940.63113.1924752.55814.932116.462.12377.311.003809.3894.90325.720.3358.077618.61789.80651.430.65116.1325395.55965.992171.442.17387.121.053903.4917.00333.760.3359.507806.81834.00667.520.67119.0026022.66113.322225.072.23396.681.103995.3938.58341.610.3460.907990.51877.15683.230.68121.8026635.06257.182277.432.28406.011.154085.0959.67349.290.3562.278170.11919.34698.580.70124.5427233.66397.812328.612.33415.14 J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 10  Table 2 summarizes the total impact force and applied bending stress induced by the rider.  As shown in Figure 4, given a one meter drop and an assumed 100ms impulse time, the reacted force and applied bending stress per shock tube is 0.33kN and 58MPa respectively.  Sample hand calculations are provided for this particular example, as shown:         (     )?                                          (        )                              (         )  (         )(         ) (         )        Axial compressive stresses are neglected since they are reported to be approximately 1% of the bending induced stresses  3.3 Fracture mechanics analysis  An alternate analysis method was employed by the authors to validate the applied bending stresses computed by approximate dynamic analysis.  The allowable stress required to advance an existing (partial through-thickness) crack, of known length, in a hollow tube can be calculated with a fracture mechanics based approach using the following relationship:                   ?(  ) ( )   In order to reproduce the fracture mechanics analysis, the geometry of the crack needs to be defined in order to determine the appropriate geometry factor f(g), refer to Table 3.    J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 11  Table 3: Missing and/or additional data required for analysis fracture toughness (7000-series AL) (nominal) KIC 24 MPa?  crack length a 2.51E-03 m crack arc length 2c 1.24E-02 m geometry factor (external part through crack) f(g) 1.014   The geometry factor was obtained from ASM Handbook Volume 19.  The nominal fracture toughness is assumed from the authors? report, given that the particular Al-alloy used in the shock tube design has not been explicitly specified.  The allowable bending stresses and corresponding forces required to grow an existing part through thickness crack for a nominal fracture toughness with respect to crack length are summarized in Table 4.  Table 4: Bending stress and corresponding force required to initiate crack growth   It can be seen from Figure 5 that the allowable stress and corresponding force required to initiate further crack growth in an existing 2.5mm crack is 270MPa and 1.5kN respectively.  This figure only shows a trend for a ?nominal? fracture toughness value.  Taking into account the authors ?material variation? of ?10%, this allowable stress is approximately 240MPa, as shown:               (         )            ?(  (         ))               Fracture MechanicsKIC24 MPamm Mpa kNa  b-KIC=24MPaFb-KIC=24MPa0.000.25 844.56 4.740.50 597.19 3.350.75 487.60 2.741.00 422.28 2.371.25 377.70 2.121.50 344.79 1.931.75 319.21 1.792.00 298.60 1.672.25 281.52 1.582.50 267.07 1.502.75 254.64 1.433.00 243.80 1.373.25 234.24 1.31 J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 12  These allowable values appear to corroborate the approximate dynamic analysis applied bending stress figures, as the authors seem to suggest in their report.   Figure 5: Allowable bending stress and corresponding forces versus crack length  3.4 Stress (Von Mises) analysis  The authors? stress analysis in the paper was reproduced in two ways.  A reproduction of Table 1 in the paper is done using the authors? Von-Mises (VM) equation.  Using this equation provided by the authors does not reproduce the values reported in their analysis.  Since the parameters used in finding the table values are taken directly from the paper, we suspect that the authors? reported values are incorrectly calculated.  Furthermore, we disagree with the VM equation (and diagram) the authors use.  Table 1 is again recreated using a corrected equation.  We consider this a serious error in the paper which should have been identified through their internal editing or the journal?s peer review process.  In describing the stress state of the critical location in the tube, the author discusses the compressive hoop stress as a result of the press fit.  From thin-walled pressure vessel theory it is known that there is also a longitudinal stress and a radial stress, in addition to the hoop stress.  The radial stress is indeed negligible compared to the other stresses, thus is rightly neglected by the author.  However, the longitudinal stress is half of the hoop stress and should have at least been mentioned as such.   01002003004005006007008000.00 0.50 1.00 1.50 2.00 2.50 3.000.00.51.01.52.02.53.03.54.04.5Bending Stress   b-per tube (MPa) Crack Length a (mm) Bending Force Fb-per tube (kN) Allowable force and bending stress required to initiate fast fracture (per shock tube) v crack length [f(g)_c-tip = 1.014] Fb-KIC=24MPa sb-KIC=24MPa J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 13  Numerically, as shown in the Tables 1 and 2, this longitudinal stress does not greatly affect the VM stress.  There is also a compressive axial stress due to the axial force of the impact.  This is also negligible and aptly neglected by the author.  Thus, what remains is the bending and hoop stresses, which are both significant.  At the critical location in the tube, the bending moment creates a maximum tensile bending stress (at the outer circumference of the tube) in the axial direction.  The hoop stress created by the press fit is a compressive stress since pressure is applied on the outer surface of the tube.  This compressive stress is in the circumferential direction and not the radial direction as indicated in the authors? diagram.  Figure 6 below indicates the correct orientation of the hoop stress along with all other stresses in the tube, whether significant or not.   To find the VM stress at the critical location, the value for       and       are required. To reproduce the VM analysis, these stresses were read from Figure 6 in the paper, and were as follows:                  MPa                MPa                MPa            MPa (compressive) regardless of impact time  The VM stress equation using principal stresses is:           ?(     )  (     )  (     )   (1)                                                                                            ? Figure 6: The stresses in the tube due to the press fit, bending moment, and axial force  J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 14  Since              ,                                        ?              (           )   ?              (|     |      )   (2)  With the stress concentration due to the sharp corner at the press fit junction, each principal stress is concentrated then inserted into the VM equation (2).  Each stress is concentrated by the same factor  , so                               .  Inserting this into (2) yields:           ?(       )  (       )  (  |     |        )   (3)  However, in the paper, two of the stresses in the authors?    equation are multiplied by    after they are squared, which essentially means that the effect of the stress concentration is greatly reduced. The authors?   equation is shown in (4) below.   From paper:          ?                  (  |     |        )   (4)  We believe the VM stress equation (4) is incorrect since two of the stress concentrations factors have a reduced effect.  Comparing our method to the authors? method, the VM stress for the three different impact times using equation (3) are calculated in the Table 5 and compared to the VM stress values resulting from equation (4) in Table 6.  In both tables, the VM stress taking in consideration the compressive longitudinal stress is also calculated.  Table 5: VM stresses for different   and impact absorption times (using equation 3)   Table 6: VM stresses for different   and impact absorption times (using equation 4)  Kt sigma_vm, 15 ms sigma_vm, 15 ms (with sigma_long) sigma_vm, 50 ms sigma_vm, 50 ms (with sigma_long) sigma_vm, 100 ms sigma_vm, 100 ms (with sigma_long)1 380.9 369.9 121.9 111.0 68.0 57.52 761.9 739.9 243.7 222.0 136.0 114.93 1142.8 1109.8 365.6 333.0 203.9 172.4sigma_bend 370.0 359.0 110.0 99.0 55.0 44.0sigma_vm author with Kt=2 538.9 \ 173.8 \ 96.8 \sigma_bend needed using modified VM equation 258.3 \ 74.5 \ 34.4 \sigma_vm author with Kt=3 660.0 \ 212.8 \ 118.6 \sigma_bend needed using modified VM equation 208.7 \ 58.1 \ 24.6 \Kt sigma_vm, 15 ms sigma_vm, 15 ms (with sigma_long) sigma_vm, 50 ms sigma_vm, 50 ms (with sigma_long) sigma_vm, 100 ms sigma_vm, 100 ms (with sigma_long)1 380. 369.9 121.9 111.0 68.0 57.52 665.7 646.6 216.5 197.6 122.5 104.13 945.5 918.6 309.9 283.1 176.6 150.3si 370.0 359.0 110.0 99.0 55.0 44.0sigma_vm author with Kt=2 538.9 \ 173.8 \ 96.8 \sigma_bend needed using equation 5 from paper 296.7 \ 85.1 \ 39.7 \sigma_vm author with Kt=3 660.0 \ 212.8 \ 118.6 \sigma_bend needed using equation 5 from paper 253.3 \ 70.0 \ 30.6 \ J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 15  As expected, it can be seen that the VM stress values of Table 5 are considerably higher than those in Table 6 (for stress concentration factors other than 1).  Also, as mentioned earlier, even when using the authors? VM equation (4) the results are different than those they reported in the paper for stress concentrations other than 1.  To confirm that this is a mistake in the authors? calculations, we solved for the bending stress value that would be required to arrive at the values the author reported using both equation (3) and equation (4) (equation 5 from the paper is the same as equation 4 in this report).  This was done using Excel?s solver feature, although it can also be done ?manually? by solving the following quadratic equation:               where        (         )    (                   ) We found that the bending stress values which give the VM stress numbers the authors reported are significantly lower than the bending stress values which can be read directly off Figure 6 in the paper. This confirms that the authors reported incorrect values, even if their VM equation is assumed to be correct.  4.0 CRITICAL EVALUATION  4.1 Facts presented and missing information 4.1.1 Material The authors initially describe the material of the failed part as ?7000 series aluminum? and in a latter section as ?hardened 7000 series aluminium?.  This description of the material is vague and does not provide enough information for anyone to critically assess the analyses performed, particularly when key material property data used in their analysis is not provided in the report.  Additionally, there is also no mention of the residual stresses which may exist in the part.  Many 6000 and 7000 series aluminum bike frames have a T6 temper designation (which is not stress-relieved) whereas a T651 is mechanically stretched for stress relief (2).  It could be possible that residual tensile hoop stress is present within the material which would counteract the compressive hoop stress induced by the press fit.  This may lower the effective or VM stress within the forks. 4.1.2 Background The authors neglect to provide some basic context of the failure situation. Without being given these values or more detailed descriptions, recreating the authors? analysis is difficult.  ? Background   J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 16  o Previous use of the shock. This information could be used to draw direct comparisons to the fatigue life calculations presented in the discussions sections of the paper.  o Similar shocks. It is mentioned that two other similar shocks were visually investigated and appeared to have cracks initiated at approximately the same location as the failed shock. While this information does offer more evidence that the crown design had created a local stress concentration, a more detailed investigation of these components should have been completed. For example, these shocks could have been fatigue tested or investigated using and SEM.   ? Bicycle Dimensions  o Fork length (needed for moment and stress calculations). o Cylinder dimensions (wall thickness and diameter). o Mass of the bicycle (needed for energy and force equations). ? Failure Surface  o The crack length is given but is not equal to the value depicted using the authors scale in figures 3a and 3b.  o The ?c? dimension of the crack surface needed for the shape function is not referenced. o The actual shape function used for the analysis is not presented to the reader. 4.1.3 Fatigue analysis The data and examples covering fatigue cycles and limits of safe life stress should have been presented in the analysis section of the paper.  It is made apparent that the component was drastically under designed and lacked any proper thought towards being a safe-life part.  The fatigue analysis offered should have been presented with the rest of the failure analysis.  The stress states prior to crack initiation and eventual fast fracture are central to the failure of the component and should have been addressed earlier, and in more detail.  Further analysis of the similar shocks could have provided evidence of crack initiation and propagation.  Finally the fatigue analysis could have been presented visually in some way to help the reader better absorb the information.  For instance, the Goodman relation is used quite extensively in fatigue life prediction, but is mentioned only briefly in the report. 4.2 Assumptions, simplifications, and analysis In any analysis, proper assumptions and simplifications can be made to aid in finding a set of plausible solutions. The author is consistent in his assumptions throughout, using the lowest possible energy and stress scenarios. Much higher stresses would most likely be encountered in actual use but this is never explicitly stated by the author.   4.2.1 Simplifications It is believed that the actual fork in question had some sort of additional threaded feature which would have carried some of the applied load. The stress analysis in a  J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 17  threaded component would have been much more complex. The simplification is justified if the goal of the paper is simply to show that the effective stresses encountered were high enough to bring about early crack initiation.  In solving for the cylindrical stresses induced by the press fit the authors make a gross underestimation.  It is stated that the press fit should create a pressure high enough so that one tube could support a force 4 times that of the rider?s weight.  In diagram 9 though, this force is represented as one quarter of the force which the rider?s weight would impose.  As mentioned earlier this value does represent the lowest pressure possible in which the bike would still hold the rider up and therefore represents the lowest hoop stress. So, while a more accurate value for the press fit pressure could have been used, the simplification is an underestimation and does not detract from the conclusions of the analysis.  Finally, the author mentions that due to the complexity of the energy absorption of the rider during impact the fall scenario is simplified as a one meter drop. In most cases, the rider would be descending along a trail and have some initial velocity in the downward direction. It should at least be mentioned that while the drop was approximately 1 meter, the kinetic energy at impact in the vertical direction was probably much higher than the value used in the energy equations.   4.2.2 Assumptions From the data presented in figure 8 it shows that the author assumes a constant shape factor for the entire propagation of the crack. While this is not necessarily false, it should be mentioned that this is an assumption because further investigation of the crack propagation was not completed.   Quite possibly the authors? largest assumption (and an incorrect assumption) is that the piston/shock fall under the radius and thickness ratio of a ?thin-walled? cylinder.  Vessels are considered thin-walled when the radius is greater than ten times the wall thickness (3).  As evident from the fracture pictures, the radius is roughly 4 times the wall thickness.  Therefore, calculation of hoop stress cannot be simplified as it has been in equation 4 of the paper. The proper thick-walled equations should have been used.  4.2.3 Analysis ? Force and Stress Analysis o The author refers to the fall height as 1 meter or 3 feet throughout the entire paper and without mention places a dotted line at .90 m for the actual fall scenario.  o It is also interesting that the authors chose to assume an impulse time rather than calculate a value.  The data required to estimate it are given in the report.  There is no mention if the assumed impulse times fall within a reasonable range.  J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 18  o The stress state acting near the crack initiation site was simplified to a 2-dimensional Von Mises equivalent stress in equation 5.  Unfortunately, the equation was incorrectly stated.  The application of stress concentration factor was used incorrectly the equation.  ? Energy and Impact Analysis o The potential energy equation on page 379 indicates that             This should actually be            ? Fracture Surface o As previously mentioned, the scale provided suggests that the authors stated crack length of 4.5 mm is incorrect. o A proper sample should have been taken from one of the similar forks and analyzed using a SEM to provide more information on crack propagation. 4.3 Results  The authors take a simplified approach involving fracture mechanics and impact forces to ascertain whether the rider could have stressed the shock enough to cause failure. Both analyses agree it was quite easy for rider to stress the shock above safe-life design limits. Whilst the analysis does have its errors the concluding results seem to be relevant and correct.  4.4 Failure prevention  There are several approaches designers may take to mitigate fatigue crack initiation.  These can generally be described as follows: ? Stress analysis ? Material selection ? Design ? Physical testing 4.4.1 Stress analysis Simple stress analyses must be performed to avoid premature failure of components, similar to that which has been performed in this failure analysis.  Using a thorough evaluation of static and dynamic stresses with consideration of stress concentrations, a safe-life design should be easily achieved.  Finite element analysis software is an essential tool in design when many different design factors must be adjusted and balanced.    J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 19  4.4.2 Material selection A 7000 series high strength aluminum alloy was selected for the piston tubes because of its favorable strength-to-weight ratio.  Unfortunately, aluminum alloys are more susceptible to fatigue failure than alloy steel.  It is acknowledged that weight savings is an important design factor, but if fatigue issues persist, a material with higher fatigue strength can be selected.  A steel alloy may be implemented only in areas of high local stresses.  Aside from weight savings, the cost of the material must also be considered.  For example, fatigue life and strength may be improved without sacrificing weight if a titanium alloy was selected, but the part would be extremely expensive.   4.4.3 Design The most critical stress has been identified as longitudinal tension due to bending loads on the tubes.  One method that may be used to reduce stress is an increased wall thickness at problem locations.  Increasing wall thickness of the tube will provide a proportional reduction in axial tension.  The additional weight may be minimized by using specialized extrusion profiles such as an asymmetric tube having greater thickness on the tension side, as depicted in Figure 7.   Figure 7: Original cross-section (a) and modified cross-section (b) It was also identified in the failure analysis that the point at which the piston tube meets the crown creates a high stress concentration.  Since this region has been made quite stiff from reinforcement, the loads are not effectively distributed.  A reduction in stress concentration may be achieved by extending the crown mating surface away from the reinforcement, as depicted in Figure 8.    Other features to be avoided when considering stress concentration are: ? Poor surface roughness, gouges, or notches ? Sharp sectional transitions ? Unblended radii or corners  (a) (b) Tension side  J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 20   Figure 8: Extension of crown mating surface The rake (angle) of the front forks is directly related to the magnitude of bending stress in the piston tubes.  Again, selection of rake requires a compromise of design factors.  In reducing the angle of rake, the stresses may be reduced, but steering performance and ?feel? may be sacrificed.   4.4.4 Physical testing Bench scale material tests can provide important material properties such as tensile strength, fracture toughness, or fatigue strength, but literature values will provide a reliable basis for stress analysis.  On the other hand, full scale physical testing will always be required to qualify engineering analysis. Ultimately, a manufacturer must prevent distribution of a flawed product.    In a controlled lab setting, a fatigue test frame can be used to apply a large number of cycles at anticipated load levels.  Any oversights in the design stage (e.g. incorrect stress analysis) should be revealed via premature failure.  Any premature failures encountered can be analyzed and corrective measures can be implemented.   Field testing should also be conducted to account for factors not controlled in the lab.  For instance, the response or ?feel? of the bike can be compromised and cannot be measured with instrumentation.  A rider?s feedback is very important in establishing a balance of all design considerations.   Field testing may also be useful in obtaining estimates of loading and impact values.  A mountain bike instrumented with accelerometers would provide data that would be useful in developing control parameters for laboratory tests.   Crown reinforcement Piston tube Extension  J. Fabris, W. Gubbels, I. Gadala, D. Bromley / MTRL 585 (2012) 21  5.0 CONCLUSION  The key engineering analysis of front bike shock tube failure has been reproduced, including: ? an approximate dynamic analysis; ? a fracture mechanics based analysis ? Von Mises stress based analysis  Critical data required to reproduce these analyses was omitted from the authors? report.  Mostly this data related to the geometry of the tube.  The group agrees with analysis approaches and methods used in the analysis.  However, as discussed in the previous section, we believe that some assumptions made over-simplified or misrepresented the problem being investigated.  Furthermore, the group believes that there were several errors in the authors? report relating to the Von Mises analysis.  The authors rightly concluded that the front shock failed due to a combination of poor geometric design and excessive applied bending stresses.  This case study clearly highlighted that the failed component was not designed to meet ?safe-life? design requirements.  It would appear that the front shock design did not take into consideration stress concentrations factors.  It is recognized that there continues to be a trade-off in the cost and weight in mountain bike design, a ?safe-life? design philosophy lends itself to mitigating the likelihood of component failure during its expected lifetime.  Techniques, as described in the previous section could be implemented to ensure component failure, as examined in this case study, is prevented in future. REFERENCES  [1] Holly Shelton, John Obie Sullivan, and Ken Gall. ?Analysis of the fatigue failure of a mountain bike front shock?. Engineering Failure Analysis 11 (2004) 375-386.  [2] Joseph C. Bededyk (Editor).  ?International Temper Designation Systems for Wrought Aluminum Alloys: Part II ? Thermally Treated (T Temper) Aluminum Alloys?.  Light Metal Age (August 2010) 16-22.  [3] Richard W. Hertzberg.  ?Deformation and Fracture Mechanics of Engineering Materials? Fourth Edition. Toronto: John Wiley & Sons, Inc (1996). 

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