Rail Base Corrosion Detection and Prevention (2007)

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17 CHAPTER 4: NUMERICAL SIMULATIONS 4.1 Finite Element Analysis Simulations Based on the survey results, 100- and 115-lb rails are the most common rails used in transit systems. The first numerical simulation was conducted using a 115-lb rail provided by the Toronto Transit Commission (TTC). Figure 8 shows a section of the rail sample with severe corrosion. These images make it obvious that the structural integrity of the corroded rail is drastically compromised. The images also help to define the challenges associated with the detection of the corrosion because it occurs at the base, most likely over the tie, hiding the corrosion from visual detection. Several of the transit authorities reported that rail corrosion was not detected sometimes until the rail was removed from the tracks because the corrosion was hidden at the base of the rail (7,9). Figure 8. Pictures of the 115-lb rail used for the simulation. Pictures a-d show different angles and details of the effects of corrosion on the base of the rail. This rail was provided by TTC- Toronto, Canada. The arrow shows the location with the sharpest edge (stress concentrator). The other simulation was conducted on a 136-lb rail donated by Amtrak. This rail sample was chosen for the second simulation because it contained common corrosion characteristics produced by the contact of the tie plate with the rail in the presence of stray currents. In this particular case, the rail base eroded leaving behind only a thin section of rail, which, in some cases, was as thin as a razor blade (9). Figure 9 shows several images of the rail base and (b) (d) (a) (c)

18 detailed images of the thin section. Contrary to the previously mentioned corrosion, this type of corrosion is easily detected by visual inspection. Each transit system has specific safety standards to prevent break failure for this corrosion condition, but most of them agree that the rail needs immediate replacement when 1/8 in. to 1/4 in. of the base has been removed (8-10). (a) (b) (c) Figure 9. Pictures of the 136-lb rail donated from Amtrak for the rail base corrosion project showing a clear reduction from the base of the rail. Note: each transit authority has its own safety standard. However, most of them agree that a reduction in rail base between 1/8” to 1/4” is the maximum permissible allowance for immediate replacement of the rail.

19 4.1.1 Two Approaches for Dimensions and Size Determination Two procedures were used to closely approximate the effects of corrosion from the base of the 115- and 136-lb rails. The first procedure used a mold of the rail base to copy the detail and determine the rough dimensions of the corrosion effects. Figure 10 shows the mold created during the first procedure. (a) (b) (c) (d) Figure 10. Pictures of the clay molds used to copy the detail and main features of the base of the rails for the numerical simulations. (a,b) 115-lb rail and (c,d) 136-lb rail.

20 The mold for the 136-lb rail was sufficient for defining the corrosion characteristics and effects. The mold from the 115-lb rail did not provide the necessary information, so a second approach was used. The second approach used the FARRO-Silver ARM digitizer to make an electronic digitalization of the rail. The FARRO-Silver ARM and electronic image are shown in Figure 11. The FARRO-Silver ARM produces a precise three-dimensional digitalization of the exposed surfaces. The digital data were directly used in ANSYS® to build a highly reliable model that represents the characteristics of the corroded rail. Figure 11. (a,b) Pictures of the FERRO-Silver ARM surface digitizer and (c,d) 3-D images of the corrosion effects at the base of the rail. (a) b (c) (d)

21 4.1.2 Finite Element Analysis 115-lb Rail For the FEA of the 115-lb rail, the digitized image of the corroded section was imposed onto the base of a 115-lb AREMA rail profile taken from AREMA Chapter 4 (11). The simulation conditions for tie and tie plate dimensions and loads were provided by TTC-Toronto. The conditions used to conduct the numerical simulation are as reported by the TTC-Toronto transit system (see Appendix C). Figure 12 shows the results of the FEA simulations. The maximum stress due to the stress concentration effects of corrosion was approximately 120 ksi, which is close to the yield strength of the steel used for this rail type. These data indicate that for this rail type, under these corrosion conditions, catastrophic failure can occur at any time. Figure 12 also shows that areas of high stress concentration occur more often near the sharp edges than the areas where extensive corrosion has occurred, which directly correlates to the stress concentration theory (12). Figure 12. Results of the FEA analysis for the 115-lb rail. Notice the very high level of stresses reaching values as high as the yield strength (120 ksi) of rail steel.

22 4.1.3 Finite Element Analysis 136-lb Rail Figure 13 shows the results of the FEA simulations for a 136-lb rail with base reduction of 1.5 mm. This simulation used a thickness value of 1.5 mm because it was the thinnest rail base found among the donated rails. The maximum stress of 22 ksi was located along the radius formed by the tie plate and perpendicular to the sharp edge and extended along the width of the rail. Comparing these results with the results of the 115-lb rail concludes that this type of corrosion provides less stress concentration than the sharp angles produced in the previous case. Figure 13. Results of the FEA analysis for the 136-lb rail. Notice that the highest stress is approximately 22.3 ksi and is found distributed along the sharp edge formed by the tie plate. c d a b

23 4.1.4 Conclusions of the Finite Element Analysis The stress concentration at the base of the rail is considerably higher in the 115-lb rail than in the 136-lb rail and is dependent on the defect shape rather than the geometry of the rail and the load at which each rail is subjected by the respective transit systems. The equations shown in Figure 14 show the relationship between the size and shape of defects and their effect on stress concentration. ⎟⎠ ⎞⎜⎝ ⎛ += = b a K MAX NOM MAX t 21σσ σ σ (1) where: Kt is the stress concentration factor, a and b are the geometry parameters of cracks, σMAX is the maximum stress that results from the stress concentration, σNOM is the nominal stress or stress applied Figure 14. Stress distribution due to (a) spherical and (b) elliptical holes, respectively, along a component(12). Equation 1 expresses the effect of geometry on stress concentration and stress distribution. Equation 1 can be used for holes of any shape along a component; the sharper the hole, the higher the concentration of stresses, which can be seen in Figure 14, where the stresses are y a σθ σr θ b σmax σnom a b x y

24 concentrated along the tips of the holes. The formula shows that as the a/b factor increases, a linear enlargement of the concentration of stresses is observed (e.g., for a circular hole Kt = 3). This confirms that locations with sharp edges correspond to the maximum stresses as confirmed by the numerical simulations shown in Figures 12(b-d) and 13(c). The results from the FEA showed that the stress concentrations were considerably higher for the 115-lb rail than for the 136-lb rail. This is due to the shape of the corrosion induced geometry that is present in both rails, which helps to conclude that the size of defect plays an important role, even though in some cases the shape of the defect is more important. For instance, Figure 12(b) shows that at the tip of the defect, the stress levels reach intensities between 120 ksi and 140 ksi. In contrast, long defects distributed along the tie-tie plate location build up stresses of approximately 7 times lower. Therefore, the effect of evenly distributed corrosion along the base of the rail also builds up stresses, but this type of stress concentrator is not as efficient as sharp edges (see Figure 13). As a result, the stress intensity in this region is considerably lower (between 15 and 24 ksi) than the stresses observed in the 115-lb rail. The presence of sharp edges produced by corrosion is very detrimental to the analysis of defects under the flange for two main reasons: (1) the defects are usually outside of visual inspection capabilities and (2) the corrosion typically causes very intricate defect shapes. The previous discussion directed the analysis to a numerical simulation for the determination of the effect of defects on fatigue, performance, and structural integrity of the rail. • The analysis of the 115-lb rail proved that the level of stresses is high enough to easily cause a catastrophic failure at any time during regular traffic conditions. The cyclic stresses on this rail are equivalent to the yield strength (which is between 80 ksi and 120 ksi for standard and high strength rail steels, respectively). • The analysis of the 136-lb rail showed that the stresses were considerably below yield. A high cycle fatigue analysis was conducted for the 136-lb rail because the stresses indicated by the numerical simulation can be detrimental under high cycle fatigue and corrosion. Section 4.2 provides the conditions and results of the fatigue simulations. 4.2 High Cycle Fatigue Analysis The following parameters were used for the high cycle fatigue analysis. The values for the analysis were in accordance to the data provided by Amtrak (9), except where indicated and properly referred. 4.2.1 Load/Stress Environment • 216 passenger trains per day • Each train contained eight passenger cars and two locomotives • Each locomotive weighed 146,000 lb and each car weighed 78,500 lb • Wheel loads estimated as 12,500 lb for locomotives and 10,000 lb for cars • FEA was used to calculate maximum stress in corroded areas due to wheel loads. Maximum stresses of 7,771 psi and 6,220 psi for locomotive and passenger car wheel loads were used, respectively. The resulting stress cycle environment used per train consisted of 12 cycles of zero to 7,771 psi and 32 cycles of zero to 6,200 psi.

25 4.2.2 Rail Material Properties • A section the width of a tie corroded away on the bottom surface of the rail. • Material is considered to be quenched and tempered Ni/Cr/Mo wrought steel with a yield of 110 ksi and a tensile strength of about 180 ksi. • S-N curve for the material is estimated to have stress range intercept of about 94.3 ksi and a life cycle of 1.0E6 of 43.5 ksi. The S-N curve has a constant slope on a Log- Log plot, and the slope remains constant to a life cycle of 1.0E10 (Figure 15). • The S-N curve is considered to be produced from small test samples or coupons — not from full-scale rail samples. • The S-N curve used is Stress Range versus Life Curve. 4.2.3 Fatigue Analysis Parameters • The Goodman mean stress correction factor was used to account for all cycles having only positive stress. • A correction factor accounting for a corrosive environment was used to modify the material S-N curve. • The Miner’s constant was reduced from 1.0 to 0.90 to account for the rough surface produced by the corrosion. 4.2.4 Results of the High Cycle Fatigue Analysis Estimated life (for 50% of the locations) until crack initiation with this type of base corrosion is approximately 1.39E7 to 1.87E7 “load blocks” or “trains.” This is equivalent to 176 to 237 years, if there are 216 trains passing through the location each day. This implies that this type of situation is not as dangerous for rail’s integrity as the presence of sharp edges. However, it is very important to notice that the “razor sharp” effect (9) was not found in any of the rails provided for the current research. Therefore, by introducing this effect on the numerical simulation, the rail’s life can be reduced considerably.

26 Figure 15. S-N curve for 136-lb rail steel. 136-lb Rail S-N Data Plot