basis of the fatigue capacities, stress intensification

Basis of the Fatigue Capacities, Stress Intensification Factors, and Flexibility Factors for High Density Polyethylene Pipe in the ASME Boiler

and Pressure Vessel Code, Section III, Division 1

Timothy M. Adams Senior Consulting Enginneer

Stevenson and Associates FCSU Corporate Center

6611 Rockside Road, Ste. 110 Independence, Ohio 44131

Douglas Munson Project Manager

EPRI 3420 Hillview Ave

Palo Alto, CA 94304-1395

ABSTRACT

For corroded piping in low temperature systems, such as service water systems in nuclear power plants, replacement of carbon steel pipe with high density polyethylene (HDPE) pipe is a cost-effective solution. Polyethylene pipe can be installed at much lower labor costs than carbon steel pipe and HDPE pipe has a much greater resistance to corrosion. HDPE pipe has been successfully used in non-safety related systems in nuclear power facilities and is commonly used in other industries such as water mains and natural gas pipelines. Via Code Case N-755-1, the ASME Boiler and Pressure Vessel Code (BPVC), Section III, Division 1, currently permits the use of non-metallic HDPE piping in buried safety Class 3 piping systems. This paper presents the basis for the fatigue stress values to be used for HDPE in the ASME BPVC Section III, Division 1, Class 3 Construction. This information was developed based on testing support by the Electric Power Research Institute. Stress Intensification Factors (SIF) and flexibility factors for use in the design and analysis of HDPE piping systems in nuclear safety-related applications will be provided in the Code and the basis of these stress intensification and flexibility factors is provided. This data may also be useful for applications of HDPE pipe in commercial electric power generation facilities and chemical, process, and waste water plants via its possible use in the B31 series piping codes.

NOMENCLATURE

A0 = Constant relating fatigue stress to failure cycles Do = Nominal outside diameter, in (mm)

h = Flexibility characteristic i = Stress Intensification Factor (SIF) k = Exponent on cycles at failure to relating cycles at

failure to fatigue stress N = Total equivalent full range

of stress cycles. NE = Number of cycles for highest temperature range. N1, N2,…,Nn = Number of cycles for each of the NE lesser

temperatures ranges. n = Cycles to failure R = Nominal bend radius of elbow or pipe bend, in (mm) r = Mean radius of pipe (in) (mm) (matching pipe for

elbows and tees) r’m = Mean radius of branch pipe, in (mm) Rm = Mean radius of run pipe, in (mm) S = Based fatigue failure stress s = Miter spacing at center line, in (mm) SA = Allowable Code cyclic fatigue stress SDR = HDPE Pipe Standard Diameter Ratio = Do/tn T = Temperature T’b = Nominal wall thickness of branch pipe tb = Thickness in reinforcement zone of branch, in (mm) tn = Nominal wall thickness of pipe, in (mm) (matching

pipe for elbows and tees) Tr = Nominal wall thickness of run pipe ΔTE = The highest temperature range. ΔT1, ΔT2,…,ΔTn = Lesser temperature ranges. σ = Standard deviation θ = One-half angle between adjacent miter axes, deg

1 Copyright © 2012 by ASME

Proceedings of the 2012 20th International Conference on Nuclear Engineering collocated with the

ASME 2012 Power Conference ICONE20-POWER2012

July 30 - August 3, 2012, Anaheim, California, USA

ICONE20-POWER2012-54244

DETERMINATION OF THE BASIC ALLOWABLE FATIGUE STRESS, SA

The base fatigue curves for butt fusion joints were developed in EPRI report 1015062 [1] and reported in PVP 2008 -61907 [6]. Cycles to failure testing of fusion butt joints at 50°F (10°C), 70°F (21°C), 140°F (60°C) and 160°F (71°C) was conducted and the base S-N curves for those temperatures were developed from the test data. The resulting Stress Intensification Factor (SIF) for a butt fusion joint was set equal to 1.0. This approach is similar to that used by Markl in the original fatigue testing of steel piping components [2]. With this approach, butt fusion joints can be located anywhere in the piping system without the need to track and evaluate their locations. The Markl approach for SIF development has been formalized and is stipulated in Appendix II of Section III of the ASME BPVC [8]. The requirements of Appendix II were applied and used in this test program.

The S-N curves resulting from the fatigue test data were used as the base curves for piping manufactured from PE 4710 cell classification 445474C material and were used to develop SIFs for other piping components by establishing ratios [6] from the base curve. For simplified Class 3 design as used in Code Case N-755-1 [4], a simplified equation is required to determine the value of SA, the allowable secondary stress as is done for steel piping in ND-3600. This task was accomplished as follows:

• The test data was reviewed and a consolidated equation for SA that considers temperature was developed.

• The following four cases were considered:

Case 1 - Linear in temperature considering all four SA versus cycles to failure curves at four temperatures (50°F, 70°F, 140°F, and 160°F).

Case 2 -Linear in temperature combining the 140°F and 160°F curves into one curve and considering the resulting three SA versus cycles to failure curves (50°F, 70°F and combined 140°F/160°F curves).

Case 3 - Converging (Power Law Based) in temperature considering SA versus cycles to failure curves at four temperatures (50°F, 70°F, 140°F, and 160°F).

Case 4 - Converging (Power Law Based) in temperature combining the 140°F and 160°F curves into one curve and considering the resulting three SA versus cycles to failure curves (50°F, 70°F and combined 140°F/160°F curves).

• Four relationships were then developed for the number of equivalent cycles similar to the relationship currently in the NC/ND-3600 of the Code for steel piping.

• The resulting SA values were then calculated by first determining the number of equivalent cycles and then using this value in conjunction with the highest temperature to enter the developed stress versus cycles to failure equation.

• After the relationships for SA were determined, the points obtained from these relationships were plotted against the original curves for each temperature. This approach was taken so the responsible ASME Code Committees can review the data and determine by consensus the best relationship to use for HDPE piping.

In EPRI report 1015062 [1] and PVP 2008-61907 [6] an alternating stress versus cycles to failure mean curve was developed for each test temperature (50°F, 70°F, 140°F and 160°F) by plotting the stress versus cycle data points and then applying a power fit to it. The four curves developed provided the stress (S) and cycles to failure (n) relationships for the fusion joints. The curves follow the function:

Input Data

knAS 0=

where A0 and k are both a function of temperature. The curves are based on the amplitude of stress which is half the range of stress. Code Case N-755-1 requires the thermal and other secondary stresses be determined as the maximum range of stress. Therefore the use of the amplitude capacity curves and relationships as developed in the EPRI report with the full range of stress provides a minimum margin of 2 on stress.

Four formulas were developed based on different assumptions. Four subsets of curves were developed for each of the four equations consisting of:

• Mean • Mean – 1 Standard Deviation • Mean – 2 Standard Deviations • Lower Bound

This data was then used to develop one consolidated set of curves considering cycles to failure and temperature.

The range of the fatigue testing cycles to failures was from less than 100 to over 500,000 cycles. The great majority of the results fell between 100 to 100,000 cycles. This range of cycles was used for the calculations that follow. The Markl approach for SIF development has been formalized and is stipulated in Appendix II of Section III of the ASME BPVC, Section III [8]. The requirements of Appendix II were applied and used in this test program. Figure 1 shows the data sets for the four test temperatures with the power curve fit applied. The curves in Figure 1 are the base curves that are used to develop the mean base curve relationships.

Case 1 – Parallel Graphs Calculated from Four Temperatures

The assumption is that the curves follow the same shape (parallel) and are linearly displaced due to temperature. This means that at any temperature, stress change is effected by the same amount due to fatigue (number of cycles). This assumption means the k exponent for n has to be determined and A0 has to be calculated as a function of temperature (T).


Because it is assumed that all the curves are parallel, k will be constant for the different temperature curves. To calculate a k that is representative of all the different temperature curves, all the data points from Figure 1 were combined into one data set.

All four data sets combined were used to generate one single curve called the ‘master curve’. This is shown in Figure 2. The exponent k of the master equation that determines the shape of the curve can be taken as representative of all the resultant curves. The equation of the line was calculated as

1800 14378 .−== nnA

Sk

as shown in Figure 2. The exponent k is

therefore -0.18.

The A0 values from Table 1 were plotted against temperature and a linear curve fit was applied to them. The equation of this curve is taken as A0 as shown in Figure 3. A0 is calculated to be:

A0 = 24016 - 96.39T

A0 and k were then used to create a formula that can calculate the stress given the temperature of the pipe and the number of cycles:

18.00 39.9624016

nT

nA

S k

−==

The mean curves are compared to the master curve in Figure 4.

As shown in Figure 1, the curves for 140°F and 160°F cross each other which does not match the assumptions of parallel curves. Because the 140°F and 160°F curves are very close to each other, they were combined into a single curve to help generate a more accurate k and A0 value for the equation over all temperatures. When the formulated data was plotted, the curves used the average temperature of 150°F. The 50°F, 70°F and 140°F/160°F combined curves are shown in Figure 5. The master curve equation remains unchanged at S=A0/nk =14378/n0.18 because the combined data points have not changed.

Case 2 – Parallel Graphs Calculated From Three Temperatures

To find A0 the individual stress versus cycles to failure data from EPRI report 1015062 [1] was plotted and a power fit was applied to develop the curve equations. The equations are listed in Table 2 and the individual stress versus cycles to failure curves can be viewed in Figure 5.

The three A0 values are then plotted against temperature and a linear curve was developed. The equation of this curve was taken as A0 as shown in Figure 6.

A0 = 23719 – 91.41T A0 and k were then used to create a formula that can calculate the stress given the temperature of the pipe and the number of fatigue cycles (Figure 7).

18.00 41.9123719

nT

nA

S k−

==

The assumption is that the curves converge as more cycles are completed; the graphs show this is representative of a power function. This assumption means that the temperature has a greater effect on stress at high cycle fatigue than at low cycle fatigue. Not only does A0 have to be calculated as a linear function of temperature but the n power value (k) also has to be calculated as a function of temperature which provides the power relationship.

Case 3 - Converging Power Law Based Curves Calculated From Four Temperatures

To find both k and A0, all the individual temperature lines were plotted from the test data and the equations calculated. These graphs and power trends are shown in Figure 1. The resulting equations are repeated in Table 3.

The A0 values were then plotted against temperature and a linear curve fit was applied. The equation of this curve is taken as A0; this is shown in Figure 8. A0 was calculated as:

A0 = 24016 - 96.39T The k values were then plotted against temperature and a linear curve fit was applied. The equation of this curve is taken as k; this is shown in Figure 9. k was calculated as:

k = 0.1991 – 0.0003T

A0 and k were then placed in the equation to create a formula that can calculate the stress given the temperature of the pipe and the number of cycles (Figure 10).

)0003.01991.0(0 39.9624016

Tk nT

nA

S −

−==

Case 4 is the same as Case 3 except that data for 140°F and 160°F were combined as the temperature curves cross each other as shown in Figure 1. Because the 140°F and 160°F curves are very close to each other they were combined to make a single curve to help generate a more accurate k and A0 value for the equation over all temperatures. A combined curve was developed using the data points from both the 140°F and 160°F data. When the formulated data was plotted, the curve used the average temperature of 150°F. The 50°F, 70°F and 140°F/160°F combined curves were previously illustrated in Figure 5.

Case 4 – Converging Power Law Based Curves Calculated From Three Temperatures

To find both k and A0, all the individual temperature lines were plotted and the equations were calculated. The equations are provided in Table 4.

The A0 values were then plotted against temperature and a linear curve fit was applied. The equation of this curve was taken as A0 as shown in Figure 11. A0 was calculated to be:


A0 = 23719 – 91.41T

The k values were then plotted against temperature and a linear curve fit was applied. The equation of this curve is taken as k, this is shown in Figure 12. k was calculated to be:

k = 0.1960 – 0.0002T

A0 and k are now used in the equation to create a formula that can calculate the stress given the temperature of the pipe and the cycle number (Figure 13).

)0002.01960.0(0 41.9123719

Tk nT

nA

S−

−==

EQUIVALENT NUMBER OF FULL RANGE CYCLES

ASME Section III Section ND-3600 for Class 3 [8] piping uses the following equation to determine an equivalent full range of cycles to establish the allowable fatigue stress SA. In this manner, only one full range thermal analysis is required for piping.

552

2

51

1 ...,

∆∆

++

∆∆

+

∆∆

+=E

nn

EEE T

TN

TT

NTT

NNN

The basis of this equation will be explained so a similar equation can be developed for HDPE.

Per Section III, Mandatory Appendix II the base fatigue curve used in Class 3 design is:

2.0

245000n

iS =

This equation is rewritten as 2.0nAS = assuming i will be a

constant for any component under review and letting 245,000 be represented by A. The resulting curve is shown in Figure 3-14.

Let S1 be the stress range associated with the largest ΔT then:

151

55

1

55

112.1

1 NSAS

ASAN

NASi

=⇒

=

=⇒=

−

Let S2 be the stress range associated with the second highest ΔT then:

522

55

2

52

1 SNAS

AN =⇒

=

Setting the A5 equal yields:

5

1

2212

521

51

=⇒=

SSNNNSNS

Since the thermal analysis conducted for class 2 and 3 piping is linear elastic: 11 TS ∆∝ and 22 TS ∆∝ . Therefore:

5

1

221

∆∆

=TTNN

Therefore the number of equivalent full range cycles of the second highest thermal stress range is:

5

1

22

∆∆

TTN

Similarly the number of equivalent stress cycles for the third thermal stress range is:

5

1

33

∆∆

TT

N

Therefore, the equivalent cycle equation in the Code is based on the temperature ranges raised to the one over the exponent on the fatigue curve relationship. Therefore, for a relationship

of kNAiS = the equivalent thermal stress range equation is

now:

k

E

nn

k

E

k

EE T

TN

TTN

TTNNN

11

22

1

11 ...,

∆∆

++

∆∆

+

∆∆

+=

A full range equivalent cycle equation can be developed for HDPE using this base equation. The temperature effect is used to establish the base range and it does not need to be considered if the allowable stress, SA, is based on the highest temperature range. This is true for both the A0 values and the k exponent. In that case, the exponents that would be used in the four cases developed in the previous section are:

Case 1 and Case 2: 1/k = 1/0.18 = 5.6

Case 3: 1/0.1991 = 5.0

Case 4: 1/0.1960 = 5.1

For case 3 and 4, the effect of temperature, being very small, was neglected for simplicity and ease of use as discussed above.

The resulting equivalent cycle equations for each of the three cases considered in the previous section are:

Case 1 6.56.5

22

6.5

11 ...,

∆∆

++

∆∆

+

∆∆

+=E

nn

EEE T

TN

TTN

TTNNN


Case 2 6.56.5

22

6.5

11 ...,

∆∆

++

∆∆

+

∆∆

+=E

nn

EEE T

TN

TTN

TTNNN

Case 3 0.50.5

22

0.5

11 ...,

∆∆

++

∆∆

+

∆∆

+=E

nn

EEE T

TN

TTN

TTNNN

Case 4 1.51.5

22

1.5

11 ...,

∆∆

++

∆∆

+

∆∆

+=E

nn

EEE T

TN

TTN

TTNNN

OTHER DEVELOPED RELATIONSHIPS

In addition, mean minus one standard deviation , mean minus two standard deviations, and lower bound curves were developed for each case. The details of the development of these curves is beyond the scope of this paper. It is presented in detail in EPRI Report 1020439 [3]. The resulting relationships for SA are provided in Table 5.

STRESS INTENSIFICATION FACTOR RECOMMENDATIONS

The test data acquired from the fatigue testing reported in EPRI Report 1020439 [3] and PVP2012-78775 [7] was used to develop empirical SIF equations for the components tested. Based on that testing equations for SIF for various components were developed. The resulting relationships are summarized in the following paragraphs.

Mitered Bends

The following SIF is recommended for mitered bends:

32

h

71i .=

where: 1SDR)cot1(

r2)cot1(t

h n

−θ+

=θ+

=

In addition, the bend needs to satisfy the criteria from [1] for widely spaced miters

)tan1(rs θ+≥

Molded Elbows

The following equation is recommended for molded elbows:

3225.1

hi =

where 2n

rRt

h =

Equal Outlet Fabricated Tees

The following SIFs are recommended for fabricated, 3-segment tees:

Run leg:

3221.2

hir =

Branch leg:

3245.4

hib =

Where rt4.4

h n= or 1SDR

8.8h−

=

Equal Outlet Molded Tees

The following SIFs are recommended for equal outlet molded tees:

Run leg:

3217.1

hir =

Branch leg:

3273.1

hib =

Where n

nn

tDt8.8

rt4.4

h−

==

The tee thickness must be 1.4 times the run pipe thickness.

Electrofusion Branch Saddles

It is recommended that the SIFs for both the run pipe and the branch pipe of electrofusion branch saddles be taken as 1.0.

Sidewall Fusion Branch Connections

The following SIFs are recommended for sidewall fusion branch connections:

Run leg: 5.1R

'rTR

54.1im

p32

r

mr ≥

=

Branch leg: 5.1r'r

T'T

TR

74.1ip

m

r

b32

r

mb ≥

=

45° Fabricated Wyes

The following equations are recommended for 45° fabricated wyes:

Run leg: 3271.1

hir =


Branch leg: 3275.2

hib =

Where rt4.4

h n= or 1SDR

8.8h−

=

The above equations are limited to 45° wyes.

Electrofusion Coupling

The electrofusion joint was consistently stronger than the fusion joints. It is recommended that the SIF for electrofusion couplings be taken as 1.0.

Monolithic Reducers

The following SIF is recommended for use with monolithic reducers

5.2tD

DD32.05.0i

21

2

2

2

1 ≤

+=

Fabricated Reducers

The following SIF is recommended for use with fabricated reducers:

0.3tD

DD40.05.0i

21

2

2

2

1 ≤

+=

HDPE to HDPE Bolted Flanged Connections

It is recommended that the SIF for HDPE to HDPE bolted flanged connections be taken as 1.0 under cyclic bending moment loading provided the joint is accessible for periodic inspection and retightening of the flange bolts if seepage should occur. If the joints are not accessible, their use should be limited to 100 thermal cycles.

FLEXIBILITY FACTOR RECOMMENDATIONS

Mitered Bends

It is recommended that mitered bends be assigned the following in-plane flexibility factor:

65

h

1.1k =

where h is defined as

1SDR)cot1(

r2)cot1(t

h n

−θ+

=θ+

=

An out-of-plane flexibility factor could not be developed at this time because of the considerable torsion effects.

Molded Elbows

Even though it was possible to calculate individual flexibility factors based on the geometry of the test specimens and the test data, an empirical flexibility factor equation could not be developed at this time. Based on the test results, the in-plane flexibility factors are affected by the overall geometry of the molded elbows, not just the parameters R, r and tn that were used to calculate the flexibility characteristic, h. The outside radii of the two types of molded elbows tested differed substantially. Not enough test data was available to establish a relationship between the outside radii and the flexibility factors. It is recommended to develop an industry standard for the design of molded HDPE elbows and then conduct some additional testing.

Equal Outlet Fabricated Tees

It is recommended that the flexibility factor for equal outlet fabricated tees be set at 1.0.

Equal Outlet Molded Tees

It is recommended that the flexibility factor for equal outlet molded tees be set at 1.0. Molded tees contain a section that is thicker than the run pipe, essentially stiffening the pipe and providing resistance to ovalization.

Electrofusion Branch Saddles

It is recommended that electrofusion branch saddles be assigned a flexibility factor of 1.0. The branch saddle will stiffen the run pipe and result in less ovalization.

Sidewall Fusion Branch Connections

It is recommended that sidewall fusion branch connections be assigned a flexibility factor of 1.0. The branch connection contains a section that is thicker than the run pipe, essentially stiffening the pipe and providing resistance to ovalization.

45° Fabricated Wyes

It is recommended that 45° fabricated wyes be assigned a flexibility factor of 1.0. Lateral wyes are usually one or two SDR values lower than the run pipe to maintain the pressure rating.

Electrofusion Couplings

It is recommended that electrofusion couplings be assigned a flexibility factor of 1.0. The couplings act to thicken and stiffen the run pipe, resulting in less flexibility than a straight pipe segment.

Monolithic and Fabricated Reducers

It is recommended that monolithic and fabricated reducers be assigned a flexibility factor of 1.0. The reducers contain sections that are thicker and stiffer than the run pipe, resulting in less flexibility than a straight pipe.


SUMMARY AND CONCLUSIONS

Four equations for SA and the number of equivalent secondary cycles were developed in this report:

Case 1: Fatigue curves as a function of temperature are parallel to each other. The design curves were derived from S-N data curves at four temperatures.

Case 2: Fatigue curves as a function of temperature are parallel to each other. The design curves were derived from S-N data curves at 3 temperatures (the 140°F and 160°F data were combined into 1 data curve).

Case 3: Converging (Power Law) in temperature. The curves were derived from S-N data at four temperatures.

Case 4: Converging (Power Law) in temperature. The curves were derived from S-N data at 3 temperatures (the 140°F and 160°F data were combined into 1 data curve).

Additionally, mean, mean - 1σ, and mean - 2σ curves were developed.

It is recommended to select the base curve from the available Mean-1σ curves. This recommendation is based on the following considerations:

• This represents an 84% probability of non-exceedance with a margin of 2. This is consistent with the approach used to set other allowables in the ASME Code.

• This results in approximately a 25% capacity reduction below the mean values which provides margin to address unspecific items not considered in the piping analysis such as through-the-wall thermal gradients.

• This is a relatively new and unique material relative to steel. Therefore, the additional margin is warranted until additional operating history is obtained.

It should be noted that the equations above are for cell classification 445474C unimodal resins. Additional testing is planned for 2012 using 445574C bimodal resins with a 2000 hour PENT value which is consistent with the material requirements of revision 1 to Code Case N-755, issued in July 2011, [4]. Figure 15 provides a summary of recommend SIFs and flexibility factors of fittings for use in Code Case N-755-1. It is equivalent to Figure ND-3673.2(b)-1 of the ASME Section III Code.

REFERENCES

[1] Adams, T. M., et. al., “Fatigue and Capacity Testing of High Density Polyethylene Pipe and Pipe Components Fabricated from PE 4710”, EPRI, Palo Alto, CA December 2007. EPRI Report 1015062

[2] Markl, A.R.C., “Fatigue Tests of Piping Components”, Transactions of the ASME, April 1952, pp 287 – 303.

[3] Adams, T. M., et. al., “Stress Intensification and Flexibility Factors of High Density Polyethylene Pipe Fittings,” EPRI Palo Alto, CA, Report 1020439, June 2010.

[4] ASME Code Case CC N-755 Rev. 1 (N-755-1), “High Density Polyethylene (HDPE) Buried Pipe, Section III, Division 1, Class 3,” July 2011

[6] Adams, T. M., et. al., “Bending Fatigue of Piping and Piping Components Fabricated from High Density Polyethylene Materials,” 2008 ASME PVP Conference, July 2008; PVP2008-61907

[7] Adams, T. M., et. al., “Bending Fatigue Testing of Pipe and Piping Components Fabricated from High Density Poly Ethylene Materials, “Proceedings of PVP-2012, PVP2012-78775, July 2012.

[8] ASME Boiler and Pressure Vessel Code, Section III, Division 1, 2004 edition up to and including the 2006 Addenda.


Table 1 – A0 Values for Case 1

Temperature (°F) Equation A0 Value

50 S = 17382n-0.17 17382

70 S = 19528n-0.20 19528

140 S = 10335n-0.17 10335

160 S = 8335n-0.15 8335


Temperature (°F) Equation A0 Value

50 S = 17382n-0.17 17382

70 S = 19528n-0.20 19528

140/160 S = 9566n-0.16 9566


Temperature (°F) Equation A0 Value k Value

50 17382n-0.17 17382 0.17

70 19528n-0.20 19528 0.20

140 10335n-0.17 10335 0.17

160 8335n-0.15 8335 0.15


Temperature (°F) Equation A0 Value k Value

50 17382n-0.17 17382 0.17

70 19528n-0.20 19528 0.20

140/160 9566n-0.16 9566 0.16


Table 5 – Result SA and Equivalent Cycle Equations

Case Number Curve CurveFormula Equivalent Full Range Cycles

1

Mean 18.00 39.9624016

nT

nA

S k

−==

6.56.5

22

6.5

11 ...,

∆∆

++

∆∆

+

∆∆

+=E

nn

EEE T

TN

TTN

TTNNN

Mean - 1σ 18.0

1 03.78190971n

TnA

S k

−==− σσ

Mean - 2σ 18.0

2 68.59141772n

TnA

S k

−==− σσ

Lower Bound 18.0

86.4315282n

TnA

LB kLB −

==

2

Mean 18.00 40.9123719

nT

nA

S k

−==

6.56.5

22

6.5

11 ...,

∆∆

++

∆∆

+

∆∆

+=E

nn

EEE T

TN

TTN

TTNNN

Mean - 1σ 18.0

1 10.69185441n

TnA

S k

−==− σσ

Mean - 2σ 18.0

2 80.46133692n

TnA

S k

−==− σσ

Lower Bound

18.0

86.4315282n

TnALB k

LB −==

3

Mean )0003.01991.0(0 39.9624016

Tk nT

nA

S −

−==

0.50.5

22

0.5

11 ...,

∆∆

++

∆∆

+

∆∆

+=E

nn

EEE T

TN

TTN

TTNNN

Mean - 1σ 0.0003T - 0.1991

1 27.65181211n

TnA

S k

−==− σσ

Mean - 2σ 0.0003T - 0.1991

2 16.34122252n

TnA

S k

−==− σσ

Lower Bound

0.0003T - 0.1991

72.6516748n

TnALB k

LB −==

4

Mean )0002.01960.0(0 40.9123719

Tk nT

nA

S −

−==

1.51.5

22

1.5

11 ...,

∆∆

++

∆∆

+

∆∆

+=E

nn

EEE T

TN

TTN

TTNNN

Mean - 1σ 0.0002T - 0.1960

1 84.54174921n

TnA

S k

−==− σσ

Mean - 2σ 0.0002T - 0.196

2 64.26116352n

TnA

S k

−==− σσ

Lower Bound 0.0002T -0.196

71.5816506n

TnALB k

LB −==


Figure 1 – Base Curves Based on Test Data

Figure 2 – Stress Versus Cycles to Failure Master Curve

y = 17382x-0.1696

y = 19528x-0.2013

y = 10335x-0.1726

y = 8335.7x-0.1507

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

100 1000 10000 100000Cycles to Failure, n

Am

plitu

de o

f Alte

rnat

ing

Stre

ss, p

si50 F 70 F 140 F 160 FPower (50 F) Power (70 F) Power (140 F) Power (160 F)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000


Ampl

itude

of A

ltina

ting

Stre

ss, p

si

Equation of the Master Line

y = 14378x-0.18


A0

Temperature (°F)

Figure 3 – A0 Calculation – Case 1 Mean

Figure 4 – Stress Versus Cycles to Failures Case 1 – Mean Equations

y = -96.393x + 24016

0

5000

10000

15000

20000

25000

0 20 40 60 80 100 120 140 160 180

Ao Variation Linear (Ao Variation)

A0 = 24016 - 96.39t T = Temperature (F)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

100 1000 10000 100000

Cycles to Failure, n

Ampl

itude

of A

ltern

atin

g St

ress

, psi

Formula Calculated 50F




Power (50F)

Power (70F)

Power (140F)

Power (160F)

Power (Master)


Figure 5 – Mean Base Curves Based on Test Data with a 140°F/160° Combined Curve

A0

Temperature (°F)

Figure 6 – A0 Constant Variation Due to Temperature – Case 2

y = 17382x-0.1696

y = 19528x-0.2013

y = 9566.5x-0.1647

y = 14378x-0.1859

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000


Ampl

itude

of A

ltern

atin

g St

ress

, psi

Power (50F)

Power (70F)

Power (140F160F)

Power (Master)

y = -91.407x + 23719

0

5000

10000

15000

20000

25000

0 20 40 60 80 100 120 140 160


A0 = 23719 - 91.40t


Figure 7 – Stress Versus Cycles to Failure Curves – Case 2 – Mean Equations

A0

Temperature (°F)

Figure 8 – A0 Variation Due to Temperature – Case 3

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000


Ampl

itude

of A

ltern

atin

g St

ress

, psi





Power (50F)

Power (70F)

Power (140F)

Power (160F)

Power (Master)

y = -96.393x + 24016

0

5000

10000

15000

20000

25000

0 50 100 150 200

Ao Linear (Ao)

A0 = 24016 - 96.39T T = Temperature


k

Temperature (°F)

Figure 9– k Variation Due to Temperature – Case 3

Figure 10 – Stress Versus Cycles to Failure Curves Case 3 – Mean Equations

y = -0.0003x + 0.1991

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150 200

n^ Linear (n^)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

100 1000 10000 100000Cycle to Failure, n

Ampli

tude

of A

ltern

ating

Stre

ss, ps

i





Power (50F)

Power (70F)

Power (140F)

Power (160F)


A0

Temperature (°F)

Figure 11 – A0 Variation Due to Temperature

k

Temperature (°F)

Figure 12 – k Variation Due to Temperature

y = -91.407x + 23719

0

5000

10000

15000

20000

25000

0 50 100 150 200


y = -0.0002x + 0.1960

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150 200

n Power equation Linear (n Power equation)

Eq = n(0.1960 - 0.002t)

t = Temperature


Figure 13 – Stress versus Cycles to Failure Case 4 – Mean Equations

Cod

e A

llow

able

Stre

ss, S

A

Figure 14 – Allowable Stress curve

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000


Ampl

itude

of A

ltern

atin

g St

ress

, psi





Power (50F)

Power (70F)

Power (160F)

Power (140F160F)

Power (140F)


Figure 15- STRESS INDICES, FLEXIBILITY, AND STRESS INTENSIFICATION FACTORS FOR HDPE PIPING COMPONENTS [NOTE (1), (2)]

Description

Primary Stress Index [Note (10)] Flexibility Characteristic h Flexibility

factor k Stress Intensification Factors i Sketch

B1 B2

Molded Elbow

2rRtn TBD

32

251

h

.

tnr

R

Miter Bend

)tan( θ+≥ 1rs

[Note (3) and (4)]

1

1−θ+

SDR)cot(

or

rtn

21 )cot( θ+

In-plane Loading:

65

11

h.

3

2

71

h

.

S

S/2θ

rtn

Equal Outlet Molded Tee

[Note (5)]

rt n44.

1.0

32

731

hib

.=

r tnD

32

17.1

hir =

Equal Outlet Mitered Tee

rt n44.

or 1

88−SDR

. 1.0

32

454

hib

.= r tnD

32

212

hi r

.=

2θ

=cotsR


Description



B1 B2

Sidewall Fusion Branch Connection

[Note (6)]

N/A 1.0

5174132

.''. ≥

=

p

m

r

b

r

mb r

rTT

TRi

5154132

.'

. ≥

=

m

p

r

mr R

rTR

i Rm

Tr

T'b

r'm

rp

Electrofusion

Saddle Branch Connection

[Note (7)]

N/A 1.0 1.0

45° Equal Outlet Lateral Wye

[Note (8)]

rt n44.

or 1

88−SDR

. 1.0

32

752

hib

.= r

tn

3

2

711

hi r

.=

Concentric Monolithic Reducers N/A 1.0 5232050

21

2

2

2

1 ... ≤

+

tD

DD

D1

t1

t2

D2

Concentric Fabricated Reducers N/A 1.0 0340050

21

2

2

2

1 ... ≤

+

tD

DD

D2

t2

D1

t1

Electrofusion Coupling

N/A 1.0 1.0


Description



B1 B2

HDPE to HDPE Bolted Flanged Connection

[Note (9)] N/A 1.0 1.0

Notes to Figure: (1) The following nomenclature applies:

Do = Nominal outside diameter, in (mm) r = Mean radius of pipe (in) (mm) (matching pipe for elbows and tees) r’m = Mean radius of branch pipe, in (mm) R = Nominal bend radius of elbow or pipe bend, in (mm) Rm = Mean radius of run pipe, in (mm) θ = One-half angle between adjacent miter axes, deg s = Miter spacing at center line, in (mm) tb = Thickness in reinforcement zone of branch, in (mm) tn = Nominal wall thickness of pipe, in (mm) (matching pipe for elbows and tees) T’b = Nominal wall thickness of branch pipe Tr = Nominal wall thickness of run pipe SDR = HDPE Pipe Standard Diameter Ratio = Do/tn

(2) The stress intensification factors, i, and the flexibility factors, k, shall not be taken as less than 1.0. They are applicable to moments in any plane for fittings

except as noted. (3) Miter angle θ is limited to ≤ 11.25°. (4) The flexibility factor k is only applicably for in-plane bending moment loading. (5) The tee thickness tn has to be 1.4* the pipe thickness Tr. (6) The ratio ODBranch/ODRun has to be ≤ 0.4. (7) The ratio ODBranch/ODRun has to be ≤ 0.6. (8) The Stress Intensification Factor equation is limited to 45° lateral wyes. (9) The Stress Intensification Factor of 1.0 is limited to 100 thermal cycles if the flange is not periodically inspected and retorqued should seepage occur. (10) B1, B2 indices were not developed as part of this program. These two columns are provided so the table format matches the format of the table in the Code.


basis of the fatigue capacities, stress intensification

Documents