The main purpose of the present paper is to investigate the effect of crack depth on the plastic load (collapse load) of miter pipe bends (MPB) under in-plane bending moment. The experimental work is conducted to investigate multimiter pipe bends, with a bend angle 90 deg, pipe bend factor h = 0.844, standard dimension ratio (SDR) = 11, and number of welding junctions m = 3 under a crosshead speed 500 mm/min. The material of the investigated pipe is a high-density polyethylene (HDPE), which is used in natural gas (NG) piping systems. The welds in the miter pipe bends are produced by butt-fusion method. The crack depth varies from intrados to extrados location according to the in-plane opening/closing bending moment, respectively. For each in-plane bending moment, the plastic load is obtained by the tangent intersection (TI) method from the load–deflection curves produced by the testing machine specially designed and constructed in the laboratory.5 The study reveals that increasing the crack depth leads to a decrease in the stiffness and plastic load of MPB for both in-plane closing and opening bending moment. Higher values of the plastic load are reached in case of opening bending moment. This behavior is true for all investigated crack depths. A circumferential external crack has an obvious effect on the behavior of load–deflection curve. The linear elastic region in both mode of loading decreases with increasing crack depth.

References

References
1.
Watanabe
,
O.
, and
Ohtsubo
,
H.
,
1984
, “
Stress Analysis of Mitred Bends by Ring Elements
,”
Trans. ASME J. Pressure Vessel Technol.
,
106
(
1
), pp.
54
62
.10.1115/1.3264309
2.
Bantlin
,
A.
,
1910
, “
Formanderung und Beansprüchung federnder Ausgleichrohre
,”
Z. Ver. Deutsch. Ingen.
,
54
, pp.
43
49
.
3.
Von Karman
,
Th.
,
1911
, “
Uber die Formanderung dunnwandiger Rohre, insbesondere federnder Ausgleichrohre
,”
Z. Ver. Dtsch. Ing.
,
55
, pp.
1889
1895
.
4.
Vigness
,
I.
,
1943
, “
Elastic Properties of Curved Tubes
,”
Trans. ASME
,
65
, pp.
105
120
.
5.
Gross
,
N.
,
1952
1953
, “
Experiments on Short-Radius Pipe Bends
,”
Proc. Inst. Mech. Eng.
,
1
(
B
), pp.
465
479
.
6.
Marcal
,
P. V.
, and
Turner
,
C. E.
,
1961
, “
Elastic Solution in the Limit Analysis of Shells of Revolution With Special Reference to Expansion Bellows
,”
J. Mech. Eng. Sci.
,
3
(
3
), pp.
252
257
.10.1243/JMES_JOUR_1961_003_032_02
7.
Marcal
,
P. V.
,
1967
, “
Elastic-Plastic Behaviour of Pipe Bends With In-Plane Bending
,”
J. Strain Anal.
,
2
(
1
), pp.
84
90
.10.1243/03093247V021084
8.
Calladine
,
C. R.
,
1974
, “
Limit Analysis of Curved Tubes
,”
J. Mech. Eng. Sci.
,
16
, pp.
85
87
.10.1243/JMES_JOUR_1974_016_016_02
9.
Dowling
,
A. R.
, and
Townley
,
C. H. A.
,
1975
, “
The Effect of Defects on Structural Failure: A Two-Criterion Approach
,”
Int. J. Pressure Vessel Piping
,
3
, pp.
77
107
.10.1016/0308-0161(75)90014-9
10.
Griffiths
,
J. E.
,
1979
, “
The Effect of Cracks on the Limit Load of Pipe Bends Under In-Plane Bending: Experimental Study
,”
Int. J. Mech. Sci.
,
21
, pp.
119
130
.10.1016/0020-7403(79)90038-9
11.
Zahoor
,
A.
,
1991
,
Ductile Fracture Handbook
, Vol.
3
,
Electric Power Research Institute
,
Palo Alto, CA
, EPRI-NP-6301-D, N14-1, Research Project 1757–69.
12.
Kitching
,
R.
,
Zarrabi
,
K.
, and
Moore
,
M. A.
,
1979
, “
Limit Moment for a Smooth Pipe Bend Under In-Plane Bending
,”
Int. J. Mech. Sci.
,
21
, pp.
731
738
.10.1016/0020-7403(79)90053-5
13.
Chan
,
K. L. C.
,
Boyle
,
J. T.
, and
Spence
,
J.
,
1986
, “
An Approximate Limit Load Analysis of Pipe Bends With End Constraints
,”
Applied Solid Mechanics-1
,
A. S.
Tooth
and
J.
Spence
, eds.,
Elsevier Applied Science
, London, pp.
275
285
.
14.
Miller
,
A. G.
,
1986
, “
The Plastic TES Plastic of Cracked Pipe Bends Under Internal Pressure or In-Plane Bending
,”
Central Electrical Generating Board
, CEGB Report No. TPRD/B/0806/R86.
15.
Miller
,
A. G.
,
1988
, “
Review of Limit Loads of Structures Containing Defects
,”
Int. J. Pressure Vessels Piping
,
32
, pp.
191
327
.10.1016/0308-0161(88)90073-7
16.
Hilsenkopf
,
P.
,
Boneh
,
B.
, and
Sollogoub
,
P.
,
1988
, “
Experimental Study of Behavior and Functional Capability of Ferritic Steel Elbows and Austenitic Stainless Steel Thin-Walled Elbows
,”
Int. J. Pressure Vessels Piping
,
33
, pp.
111
128
.10.1016/0308-0161(88)90065-8
17.
Shalaby
,
M. A.
,
1996
, “
Elastic-Plastic Behavior and Limit Load Analysis of Pipe Elbows Under In-Plane Bending and Internal Pressure
,”
American University in Cairo
,
Cairo, Egypt
.
18.
Shalaby
,
M. A.
, and
Younan
,
M. Y. A.
,
1998
, “
Limit Loads for Pipe Elbows With Internal Pressure Under In-Plane Closing Bending Moments
,”
ASME J. Pressure Vessel Technol.
,
120
, pp.
35
42
.10.1115/1.2841882
19.
Shalaby
,
M. A.
, and
Younan
,
M. Y. A.
,
1999
, “
Limit Loads for Pipe Elbows Subjected to In-Plane Opening Moments and Internal Pressure
,”
ASME J. Pressure Vessel Technol.
,
121
, pp.
17
23
.10.1115/1.2883661
20.
Chattopadhyay
,
J.
,
Nathani
,
D. K.
,
Dutta
,
B. K.
, and
Kushwaha
,
H. S.
,
2000
, “
Closed-Form Collapse Moment Equations of Elbows Under Combined Internal Pressure and In-Plane Bending Moment
,”
ASME J. Pressure Vessel Technol.
,
122
, pp.
431
436
.10.1115/1.1285988
21.
Chattopadhyay
,
J.
,
2002
, “
The Effect of Internal Pressure on In-Plane Collapse Moment of Elbows
,”
Nucl. Eng. Des.
,
212
, pp.
133
144
.10.1016/S0029-5493(01)00468-X
22.
Chattopadhyay
,
J.
,
Tomar
,
A. K. S.
,
Dutta
,
B. K.
, and
Kushwaha
,
H. S.
,
2004
, “
Closed-Form TES Plastic Moment Equations of Through Wall Circumferentially Cracked Elbows Subject to In-Plane Bending Moment
,”
ASME J. Pressure Vessel Technol.
,
126
, pp.
307
317
.10.1115/1.1767177
23.
Kim
,
Y. J.
, and
Oh
,
C. S.
,
2006
, “
Limit Loads for Pipe Bends Under Combined Pressure and In-Plane Bending Based on Finite Element Limit Analysis
,”
Int. J. Pressure Vessels Piping
,
83
, pp.
148
153
.10.1016/j.ijpvp.2005.11.001
24.
Kim
,
Y. J.
, and
Oh
,
C. S.
,
2006
, “
Closed-Form Plastic Collapse Loads of Pipe Bends Under Combined Pressure and In-Plane Bending
,”
Eng. Fract. Mech.
,
73
(
11
), pp.
1437
1454
.10.1016/j.engfracmech.2006.02.001
25.
Kim
,
Y. J.
,
Kim
,
Y.-I.
, and
Song
,
T.-K.
,
2007
, “
Finite Element Plastic Loads for Circumferential Cracked Pipe Bends Under In-Plane Bending
,”
Eng. Fract. Mech.
,
74
, pp.
643
668
.10.1016/j.engfracmech.2006.07.001
26.
Song
,
T. K.
,
Kim
,
Y. J.
,
Oh
,
C. K.
,
Jin
,
T. E.
, and
Kim
,
J. S.
,
2009
, “
Net-Section Limit Moments and Approximate J Estimates for Circumferential Cracks at the Interface Between Elbows and Pipes
,”
Int. J. Pressure Vessels Piping
,
86
, pp.
495
507
.10.1016/j.ijpvp.2009.03.008
27.
Owen
,
B. S.
, and
Emmerson
,
W. C.
,
1963
, “
Elastic Stresses in Single Mitred Bends
,”
J. Mech. Eng. Sci.
,
5
(
4
), pp.
303
324
.10.1243/JMES_JOUR_1963_005_042_02
28.
Green
,
A. E.
, and
Emmerrson
,
W. C.
,
1961
, “
Stresses in a Pipe With Discontinuous Bend
,”
J. Mech. Phys. Solids
,
9
, pp.
91
104
.10.1016/0022-5096(61)90027-8
29.
Kitching
,
R.
,
1965
, “
Mitre Bends Subjected to In-Plane Bending Moments
,”
Int. J. Mech. Sci.
,
7
, pp.
551
575
.10.1016/0020-7403(65)90012-3
30.
Kitching
,
R.
,
1965
, “
In-Plane Bending of A 180 deg Mitred Pipe Bend
,”
Int. J. Mech. Sci.
,
7
, pp.
721
736
.10.1016/0020-7403(65)90001-9
31.
Kitching
,
R.
, and
Bond
,
M. P.
,
1970
, “
Flexibility and Stress Factors for Mitred Bends Under In-Plane Bending
,”
Int. J. Mech. Sci.
,
12
, pp.
267
285
.10.1016/0020-7403(70)90044-5
32.
Kitching
,
R.
,
Rahimi
,
G. H.
, and
So
,
H. S.
,
1989
, “
Plastic Collapse of Single Mitred Pipe Bends
,”
Int. J. Pressure Vessel Piping
,
38
, pp.
129
145
.10.1016/0308-0161(89)90009-4
33.
Kitching
,
R.
, and
Thompson
,
W. J.
,
1970
, “
In-Plane Bending of Single Unreinforced Mitred Pipe Bends
,”
J. Strain Anal.
,
5
, pp.
12
24
.10.1243/03093247V051014
34.
DIN 8074-1975
, “
Pipes of High-Density Polyethylene (High-Density PE), Type 1 Dimensions
,” 1975, pp.
99
102
.
35.
DIN 8074 Type 2
, “
Pipes of High-Density Polyethylene (High-Density PE), Type 2 Dimensions
,” 1980, pp.
103
105
.
36.
DIN 8075-1987
, “
High-Density Polyethylene (HDPE), General Quality Requirements Testing
,” 1987, pp.
1
5
.
37.
ASTM D2122-98
, “
Standard Test Method for Determining Dimensions of Thermoplastic Pipe and Fittings
” Annual Book of ASTM Standards, 98 (2012), Part 8.04, Plastic Pipe and Building Products.
38.
British Standard
,
1998
, “
Methods of Testing Plastics
,” BS2782.
39.
British Gas Transco
,
1998
, “
Technical Specification for Polyethylene Pipes and Fittings for Natural Gas and Suitable Manufactured Gas
,” PL2: Part 8-Pipes for Use at Pressure up to 7 bars.
40.
ASTM Standard D638M-99
, “
Standard Test Method for Tensile Properties of Plastics (Metric)
,” Annual Book of ASTM Standards, Part 08.01, Plastics-General Test Method, pp.
59
67
.
41.
El-Bagory
,
T. M. A.
,
2010
, “
Failure Analysis of Polymeric Miter Pipe Bends Under Combined Loading
,” Ph.D., thesis, Faculty of Engineering Mattaria, Helwan University, Cairo, Egypt.
42.
DVS 2207-1
,
2005–2009
, “
Welding Thermoplastic Plastics, Hard PE (Hard Polyethylene) Pipes and Elements for Gas Water Pipelines
.”
43.
ASTM D3261-03
,
2001e1
, “
Standard Test Method for Butt Fusion Polyethylene (PE) Plastic Fittings for Polyethylene (PE) Plastic pipe and Tubing
” Annual Book of ASTM Standards, Part 8.04, Plastic Pipe and Building Products.
44.
DIN 16963
,
1980
, Part 1 “
Pipe Joints and Elements for High Density Polyethylene (HDPE) Pressure Pipelines, Types 1 and 2 Pipe Bends of Segments for Butt-Welding Dimensions
.”
45.
ASTM F 1473-97
,
2012
, “
Standard Test Method for Notch Tensile Test to Measure the Resistance to Slow Crack Growth of Polyethylene Pipes and Resins
” Annual Book of ASTM Standards, Part 8.04, Plastic Pipe and Building Products.
46.
The American Society for Mechanical Engineers
, ASME, Boiler and Pressure Vessel Code,
2004
, Section VIII, Division 2, Appendix 6, pp.
6
153
.
47.
EN 13445-3
,
2002
, “
European Standard for Unfired Pressure Vessels—Part 3: Design
,” European Committee for Standardization (CEN).
48.
Robertson
,
A.
,
Li
,
H.
, and
Mackenzie
,
D.
,
2005
, “
Plastic Collapse of Pipe Bends Under Combined Internal Pressure and In-Plane Bending
,”
Int. J. Pressure Vessels Piping
,
82
, pp.
407
416
.10.1016/j.ijpvp.2004.09.005
49.
Moffat
,
D. G.
,
Hsieh
,
M. F.
, and
Lynch
,
M.
,
2001
, “
An Assessment of ASME III and CEN TC54 Methods of Determining Plastic and Limit Loads for Pressure System Components
,”
J. Strain Anal. Eng. Des.
,
36
(
3
), pp.
301
312
.10.1243/0309324011514485
50.
Wood
,
J.
,
2008
, “
A Review of Literature for the Structural Assessment of Mitred Bends
,”
Int. J. Pressure Vessels Piping
,
82
, pp.
275
294
.10.1016/j.ijpvp.2007.11.003
51.
Neilson
,
R.
,
Wood
,
J.
,
Hamilton
,
R.
, and
Li
,
H.
,
2010
, “
A Comparison of Plastic Collapse and Limit Loads for Single Mitred Pipe Bends Under In-Plane Bending
,”
Int. J. Pressure Vessels Piping
,
87
, pp.
550
558
.10.1016/j.ijpvp.2010.08.015
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