ML18100A895

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Rev a of Critical Crack Sizes. Calculation Estimates Critical Crack Sizes for Growth of Cracks in Alco 251 Diesel Engine Cylinder Liners Due to Mechanical Loads
ML18100A895
Person / Time
Site: Salem  PSEG icon.png
Issue date: 12/17/1993
From:
MPR ASSOCIATES, INC.
To:
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ML18100A891 List:
References
108-32-04, 108-32-4, NUDOCS 9402280238
Download: ML18100A895 (16)
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MPR ASSOCIATES, INC.

320 King Street, Alexandria, VA 22314 CALCULATION TITLE PAGE 1 - - - - - - - - - - - - r - - - - - l PAGE I OF~

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Calculation Title Cr.f,(c.I Cru..c.-1< ~ 1 res REVISION NO.

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320 King Street Alexandria, VA 22314

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    • MPR Calculation No.

/Of-32 1.0 PURPOSE Prepared By

- MPR Associates, Inc.

320 King Street Alexandria, VA 22314 Checked By Page "3 The purpose of this calculation is to estimate the critical crack sizes for growth of cracks in ALCO 251 diesel engine cylinder liners due to mechanical loads. The cracks considered are surface defects in the relief groove radius of the liner flange.

2.0 RESULTS Several cases were evaluated: the nominal configuration along with several other cases to evaluate variations in key parameters. The table below summarizes the calculated criti~al crack sizes for two values of threshold stress intensity factor, 6 ksivin and 10 ksivin.

Critical Crack Size (in)

Case Krn=6 Krn=lO Nominal 0.0135 0.0670 2 Mil Offset 0.0125 0.0540 8 Mil Offset 0.0082 0.0285 Worst Case 0.0073 0.0245 The actual threshold stress intensity factor is likely about 10 ksivin, but could possibly be as low as about 6 ksivin, depending upon environment and actual material resistance, so the critical crack size likely ranges from about slightly less than 10 mils to about 65 mils for the cases considered.

320 King Street Alexandria, VA 22314 Calculation No.

Prepared By Checked By Page +

JDf-32-of-3.0 CALCULATION If a defect exists in a component, crack growth will occur if the defect is of sufficient size.

Crack growth during cyclic loading is a function of the change in stress intensity factor during the cycle. The stress intensity factor is a function of the stresses in the component and the crack size.

Kr = aJTraf(~)

t For shallow edge cracks, f(a/t) is typically equal to about 1.12.

One method for calculating stress intensity factor for a given crack size and stress conditions in a component is that developed in Reference 1. Using this approach, the stresses in the component near the surface are fit to a cubic polynomial using a least squares technique:

a(x) = A0 + A1x + A2x2 + A3x3 Then the stress intensity factor is calculated using the following relationship:

where Fi are geometry factors published in Reference 1 for various configurations. For shallow cracks, these factors tend be independent of component/crack geometry, with F1 ~ 1.12 and Fz

= F3 ~ F 4 =: 1.0. These factors are shown in Figure 1 for an edge cracked plate. In Reference 2, these curves for Fi were fit to cubic polynomials using a least squares technique, with the following results:

F1 = 1.1169 - 0.06906(a/t) + 2.8811(a/t)2 + 8.3332(a/t)3 F2 = 1.0024 - 0.15110(a/t) + 3.0117(a/t)2 + 3.3336(a/t)3 F3 = 1.0041 - 0.04327(a/t) + 0.7501(a/t)2 + 4.4444(a/t)3 F 4 = 0.9974 + 0.33170(a/t) - 0.8333(a/t)2 + 4.4444(a/t)3

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320 King Street Alexandria, VA 22314 Checked By Page (o This approach facilitates calculation of stress intensity factors. For shallow cracks in the relief groove of the cylinder liner, these factors are considered to provide adequate results (aft less than about 0.075 to 0.1).

The stresses in the cylinder were calculated using finite element models in Reference 3.

Stresses were calculated for several configurations of liner fit-up and loading. In this calculation, the stress results from eight cases will be used. These are the engine firing and engine not firing cases for the following configurations:

Nolll.inal - The nominal liner tolerances along with essentially no liner flange/engine block misalignment.

2 Mil Offset - The nominal liner tolerances along with 2 mils of misalignment between the liner flange and engine block.

8 Mil Offset - The nominal liner tolerances along with 8 mils of misalignment between the liner flange and engine block.

Worst Case - The worst case (from a stress point of view) tolerances along with the 8 mils misalignment.

As descnbed in Reference 3, the stresses were calculated conservatively assuming the liner was free to displace axially at the lower seal. In fact, the interference fit at that location would limit movement and reduce the liner stresses.

The maximum stresses in the cylinder liner due to bolt preload forces and the engine firing pressure occur at the relief groove, at a location about 45° from the top of the groove. This location is shown in Figure 2. The stresses which would grow a crack at this location are oriented along an axis rotated 45° from the vertical. Figure 3 shows the crack opening (growing) stress near the relief groove for a typical case. It can be seen that the stresses decrease rapidly into the liner material.

The calculated stresses from the Reference 3 finite element analyses will be fit to cubic polynomials to facilitate calculation of the stress intensity factor. The following tables list the depths/stresses used for this fit.

. mMPR MPR Associates, Inc.

320 King Street Alexandria, VA 22314 Calculation No.

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31117 3293 276 2243 171 119 Prepared By MPR Associates, Inc.

320 King Street Alexandria, VA 22314 Checked By a!:ICI Page g ANSYS 5.0 A DEC 12 1993 01:53:27 PLOT NO.

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0 0.272 0.!145 l.J6l 0.136 0.408 0.681 0.9!14 1.227 DIST ALCO 251 CYLINDER LINER - NOMINAL GJ "'l""lJ s+rt~r~ I" L\\'\\ef Alo"j Cftt-l N~ (~~J ~

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mMPR MPR Associates, Inc.

320 King Street Alexandria, VA 22314 Calculation No.

Prepared By Checked By I Df-3 i-o 'f-Page '1 Depth N orninal Stress Nominal Firing Stress (in)

(psi)

(psi) 0.0 43420.

24424.

0.28396E-1 32446.

18300.

0.56792E-1 21498.

12191.

0.85189E-1 15631.

8915.7 0.11358 12936.

7408.6 0.14198 10382.

5980.1 0.17038 8449.0 4800.2 0.19877 6461.8 3789.1 0.22717 5070.4 -

3014.0 0.25557 3975.3 2404.6 0.28396 2925.5 1820.0 0.31236 2127.8 1379.6 0.34075 1333.7 941.03

mMPR MPR Associates, Inc.

320 King Street Alexandria, VA 22314 Calculation No.

Prepared By Checked By

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Page /0 Depth 2 Mil Offset Stress 2 Mil Offset Firing (in)

(psi)

Stress (psi) 0.0 46516.

27452.

0.28396E-1 34979.

20782.

0.56792E-1 23468.

14128.

0.85189E-1 17229.

10490.

0.11358 14286.

8738.3 0.14198 11481.

7063.l 0.17038 9295.4 5733.2 0.19877 7067.4 4385.6 0.22717 5512.3 3448.9 0.25557 4276.5 2700.4 0.28396 3086.1 1976.7 0.31236 2206.4 1455.3 0.34075 1327.8 933.30

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320 King Street Alexandria, VA 22314 Calculation No.

Prepared By Checked By

/ oe -3 2... -o 'r Page II Depth 8 Mil Offset Stress 8 Mil Offset Firing (in)

(psi)

Stress (psi) 0.0 55425.

32677.

0.28396E-1 42199.

24937.

0.56792E-1 29002.

17213.

0.85189E-1 21678.

12921.

0.11358 18041.

10782.

0.14198 14537.

8718.1 0.17038 11651.

7004.8 0.19877 8754.2 5289.2 0.22717 6741.2 4098.0 0.25557 5114.2 3134.4 0.28396 3533.0 2196.9 0.31236 2421.7 1545.0 0.34075 1305.9 890.40

. mMPR MPR Associates, Inc.

1 320 King Street Alexandria, VA 22314 Calculation No.

Prepared By Checked By

/Df -51.--ot:f-Page IL-Depth Worst Case Stress Worst Case Firing (in)

(psi)

Stress (psi) 0.0 59628.

35258.

0.28276E-1 43766.

25939.

0.56553E~l 28037.

16700.

0.84829E-1 22098.

. 13202.

0.11311 17991.

10780.

0.14138 13990.

8421.7 0.16966 11280.

6816.8 0.19794 8795.3 5344.1 0.22621 6462.1 3963.1 0.25449 4879.9 3023.7 0.28276 3416.6 2152.6 0.31104

. 2128.6 1390.2 0.33932 1072.3 769.70

. mMPR MPR Associates, Inc.

320 King Street Alexandria, VA 22314 Calculation No.

Prepared By Checked By I of-3 L-o"r Page 13 The results of the cubic polynomial least squares fits are shown below:

I I

I Stress I

Case Firing (psi)

No 42773 - 431420x + 11141oax2 - 23s1ooax3 Nominal Yes 24063 - 240730x + 956ooax2 - 1329soax3 No 45839 - 452230x + 176880ax2 - 244510ax3 2 Mil Offset Yes 27062 - 260860x + l00760ax2 - 138420ax3 No 54653 - 514980x + 194410ax2 - 26445oax3 8 Mil Offset Yes 33223 - 301040x + 113220ax2 - 153720ax3 No 58222 - 590060x + 2355100x2 - 331420ax3 Worst Case Yes 34431 - 346500x + 138040ax2 - 194130ax3 The engine firing and not firing cases represent the stress cycle for the liner (neglecting thermal effects, as described in Reference 3). This cycle occurs at a rate of about 450 cycles per minute.

Using these results and the expressions for Fi, the maximum and minimum stress intensity factor are calculated for each case. The maximum stress intensity factor corresponds to the engine not firing case and the minimum stress intensity factor corresponds to the engine firing case.

The mean stress during the stress cycle has an effect on effective stress intensity factor. These effects are included through the use of the Walker Correction Factor (Reference 4). Using this factor, the effective change in stress intensity factor during the stress cycle is calculated from:

AKEFF =

(KMAX - KMIN)

Jl-R R= KMIN K.MAX

..* MPR MPR Associates, Inc.

320 King Street Alexandria, VA 22314 Calculation No.

Prepared By Checked By I vf-3l.-oLf-Page 1'1-The crack growth behavior of cast irons (and other materials) is that for values of AKEFf less than a material threshold value, K'Pi'f essentially no crack growth occurs. Km is matenal and typically environment dependent.

igure 4 (from Reference 5) shows typical crack growth data for cast iron. In this figure, it can be seen that the threshold is about 10 ksivin. However, it is possible that Km could be less, possibly as low as about 6 ksivin in the worst case.

For crack sizes or material defects for which the effective change in stress intensity factor is less than the threshold, no crack growth will occur. Thus, a critical crack size can be calculated for an applied stress profile. This is the critical crack size under which no growth would occur.

Using the stresses in the liner, the following results are calculated:

Case Krn a

KMIN

~

R AKEJ:F (ksivin)

(in)

(ksivin)

(ks1vm) 6 0.0135 5.12 9.10 0.563 6.02 Nominal 10 0.0670 8.57 15.17 0.565 10.01 6

0.0125 5.59 9.46 0.591 6.04 2 Mil Offset 10 0.0540 9.35 15.72 0.595 10.01 6

0.0082 5.53 9.37 0.590 6.00 8 Mil Offset 10 0.0285 9.27 15.70 0.590 10.05 6

0.0073 5.58 9.44 0.592 6.03 Worst Case 10 0.0245 9.28 15.67 0.592 10.01

Calculation No.

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320 King Street Alexandria, VA 22314 Prepared By Checked By Page ( _5 Stress Intensity Factor Range. AK in MPay'ili 10 20 40 60 100 Band for Wrought Ferrite-Pearlite Steels Load Range

  • 2000 lb (910 kg) c 2200 lb (1000 kg)
  • 2500 lb (1130 kg) 0 2500 lb (1130 kg) 6 3000 lb (1360 kg)
  • 3300 lb (1500 kg) 10 20 30 40 150 ao100 Stress Intensity Factor Range. AK in ksi vlnCfi m

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4.0 REFERENCES

Prepared By MPR Associates, Inc.

320 King Street Alexandria, VA 22314 Checked By Page 10

1.

C.B. Buchalet and W.H. Bamford, "Stress Intensity Factor Solutions for Continuous Surface Flaws in Reactor Pressure Vessels", ASTM-590, 1976.

2.

MPR Calculation Dated 3/30/87, "Fracture Mechanics Methodology", by R.N. Coward.

3.

MPR Calculation 108-32-01, "Finite Element Stress Analysis of ALCO 251 Diesel Engine Cylinder Liner", 12/17 /93.

4.

K. Walker, 'The Effect of Stress Ratio During Crack Propagation and Fatigue for 2024-T3 and 7075-T6 Aluminum", ASTM-462, 1970.

5.

Atlas of Fatigue Cuives, American Society for Metals, 1986.

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