In order to study the mechanical properties of defect-free thin walled elbows (TWE), and evaluate impacts of the intermediate principal stress effect, tension/compression ratio, and strain-hardening of materials into logical consideration, this research, in the framework of finite deformation theory, derived the computational formula of burst pressure for defect-free TWE according to unified strength theory (UST). In addition, influences of various factors on burst pressure were analyzed, which include strength disparity (SD) effect of materials, intermediate principal stress, curvature influence coefficient, strain-hardening exponent, yield to tensile (Y/T) and thickness/radius ratio. The results show that the greater the tension/compression ratio is, the higher the burst pressure is. The influence of the SD effect of materials is more obvious with the increase of elbow curvature and intermediate principal stress. The intermediate principal stress effect can bring the self-bearing capacities and strength potential of materials into a full play, which can achieve certain economic benefits for projects. Moreover, the burst pressure of defect-free TWE increases with the growth of yield ratio and thickness/radius ratio, while decreases with the rise of curvature influence coefficient and strain-hardening exponent. It is also concluded that the Tresca-based and Mohr–Coulomb-based solutions of TWE are the lower bounds of the burst pressure, the twin shear stress (TSS)-based solution is the upper bound of the burst pressure, and the solutions based on the other yield criteria are between the above two. The unified solution in this paper is suitable for all kinds of isotropous materials which have the SD effect and intermediate principal stress effect. As the deduced formula has unified various burst pressure expressions proposed on the basis of different yield criteria for elbows of any curvature (including straight pipelines), and has established the quantitative relationships among them, its applicability is broader. Therefore, the unified solution is of great significance in security design and integrity assessment of defect-free TWE.

References

References
1.
Jin
,
C. W.
,
Wang
,
L. Z.
, and
Zhang
,
Y. Q.
,
2012
, “
Strength Differential Effect and Influence of Strength Criterion on Burst Pressure of Thin-Walled Pipelines
,”
Appl. Math. Mech. (Engl. Ed.)
,
33
(
11
), pp.
1361
1370
.10.1007/s10483-012-1628-7
2.
Zhu
,
X. K.
, and
Leis
,
B. N.
,
2012
, “
Evaluation of Burst Pressure Prediction Models for Line Pipes
,”
Int. J. Pressure Vessels Piping
,
89
, pp.
85
97
.10.1016/j.ijpvp.2011.09.007
3.
Zhu
,
X. K.
, and
Leis
,
B. N.
,
2006
, “
Average Shear Stress Yield Criterion and Its Application to Plastic Collapse Analysis of Pipelines
,”
Int. J. Pressure Vessels Piping
,
83
(
9
), pp.
663
671
.10.1016/j.ijpvp.2006.06.001
4.
Zhu
,
X. K.
, and
Leis
,
B. N.
,
2004
, “
Strength Criteria and Analytic Predictions of Failure Pressures in Line Pipes
,”
Int. J. Offshore Polar Eng.
,
14
(
2
), pp.
125
131
.
5.
Law
,
M.
, and
Bowie
,
G.
,
2007
, “
Prediction of Failure Strain and Burst Pressure in High Yield-to-Tensile Strength Ratio Linepipe
,”
Int. J. Pressure Vessels Piping
,
84
(
8
), pp.
487
492
.10.1016/j.ijpvp.2007.04.002
6.
Zhu
,
X. H.
,
Pang
,
M.
, and
Zhang
,
Y. Q.
,
2011
, “
Estimation of Burst Pressure of Pipeline Using Twin-Shear Stress Yield Criterion
,”
ASME Chin. J. Appl. Mech.
,
28
(
2
), pp.
135
138
.
7.
Li
,
C. M.
,
Zhao
,
D. W.
,
Zhang
,
S. H.
, and
Zhou
,
P.
,
2011
, “
Analysis of Burst Pressure for X80 Steel Pipeline With MY Criterion
,”
J. Northeast. Univ. (Nat. Sci.)
,
32
(
7
), pp.
964
967
.
8.
Duan
,
Z. X.
, and
Shen
,
S. M.
,
2004
, “
Analysis and Experiments on the Plastic Limit Load of Elbows Under Internal Pressure
,”
Pressure Vessel Technol.
,
21
(
8
), pp.
1
4
.
9.
Chaix
,
R.
,
1972
, “
Factors Influencing the Strength Differential of High-Strength Steels
,”
Metall. Trans.
,
3
(
2
), pp.
369
375
.10.1007/BF02642040
10.
Drucker
,
D. C.
,
1973
, “
Plasticity Theory, Strength–Differential (SD) Phenomenon, and Volume Expansion in Metals and Plastics
,”
Metall. Trans.
,
4
(
3
), pp.
667
673
.10.1007/BF02643073
11.
Rauch
,
G. C.
, and
Leslie
,
W. C.
,
1972
, “
The Extant and Nature of the Strength–Differential Effect in Steels
,”
Metall. Trans.
,
3
(
2
), pp.
377
389
.10.1007/BF02642041
12.
Yu
,
M. H.
,
2004
,
Unified Strength Theory and Its Applications
,
Springer, Berlin
,
Germany
.
13.
Zhao
,
J. H.
,
Li
,
Y.
,
Liang
,
W. B.
, and
Zhu
,
Q.
,
2012
, “
Unified Solution to Ultimate Bearing Capacity of Dumbbell Shaped Concrete-Filled Steel Tube Arch Rib With Initial Stress
,”
China J. Highw. Transp.
,
25
(
5
), pp.
58
66
.
14.
Li
,
Y.
,
Zhao
,
J. H.
,
Liang
,
W. B.
, and
Wang
,
S.
,
2013
, “
Unified Solution of Bearing Capacity for Concrete-Filled Steel Tube Column With Initial Stress Under Axial Compression
,”
J. Civ. Archit. Environ. Eng.
,
35
(
3
), pp.
63
69
.10.11835/j.issn.1674-4764.2013.03.010
15.
Zhao
,
J. H.
,
Liang
,
W. B.
,
Zhang
,
C. G.
, and
Li
,
Y.
,
2013
, “
Unified Solution of Coulomb's Active Earth Pressure for Unsaturated Soils
,”
Rock Soil Mech.
,
34
(
3
), pp.
609
614
.
16.
Zhang
,
C. G.
,
Zhao
,
J. H.
,
Zhang
,
Q. H.
, and
Hu
,
X. D.
,
2012
, “
A New Closed-Form Solution for Circular Openings Modeled by the Unified Strength Theory and Radius-Dependent Young's Modulus
,”
Comput. Geotech.
,
42
, pp.
118
128
.10.1016/j.compgeo.2012.01.005
17.
Zhang
,
C. G.
,
Wang
,
J. F.
, and
Zhao
,
J. H.
,
2010
, “
Unified Solutions for Stresses and Displacements Around Circular Tunnels Using the Unified Strength Theory
,”
Sci. China Technol. Sci.
,
53
(
6
), pp.
1694
1699
.10.1007/s11431-010-3224-0
18.
Zhao
,
J. H.
,
Li
,
Y.
,
Zhang
,
C. G.
,
Xu
,
J. F.
, and
Wu
,
P.
,
2013
, “
Collapsing Strength for Petroleum Casing String Based on Unified Strength Theory
,”
Acta Pet. Sin.
,
34
(
5
), pp.
969
976
.10.1038/aps.2013.9
19.
Wang
,
L. Z.
, and
Zhang
,
Y. Q.
,
2011
, “
Plastic Collapse Analysis of Thin-Walled Pipes Based on Unified Yield Criterion
,”
Int. J. Mech. Sci.
,
53
(
5
), pp.
348
354
.10.1016/j.ijmecsci.2011.02.004
20.
Zhao
,
J. H.
,
Zhang
,
Y. Q.
,
Liao
,
H. J.
, and
Yin
,
Z. N.
,
2000
, “
Unified Limit Solutions of Thick Wall Cylinder and Thick Wall Spherical Shell With Unified Strength Theory
,”
ASME Chin. J. Appl. Mech.
,
17
(
1
), pp.
157
161
.
21.
Qiang
,
H. F.
,
Cao
,
D. Z.
, and
Zhang
,
Y.
,
2008
, “
Modified M-Criterion Based on Unified Strength Theory and Its Application to Grain Crack Prediction
,”
J. Solid Rocket Technol.
,
31
(
4
), pp.
340
343
.
22.
Zhu
,
X. K.
, and
Leis
,
B. N.
,
2005
, “
Influence of Yield-to-Tensile Strength Ratio on Failure Assessment of Corroded Pipelines
,”
ASME J. Pressure Vessel Technol.
,
127
(
4
), pp.
436
442
.10.1115/1.2042481
23.
Zhang
,
S. H.
,
Gao
,
C. R.
,
Zhao
,
D. W.
, and
Wang
,
G. D.
,
2013
, “
Limit Analysis of Defect-Free Pipe Elbow Under Internal Pressure With Mean Yield Criterion
,”
J. Iron Steel Res. Int.
,
20
(
4
), pp.
11
15
.10.1016/S1006-706X(13)60075-8
24.
Hill
,
R.
,
1950
,
The Mathematical Theory of Plasticity
,
Oxford University
,
Oxford, UK
.
25.
Yu
,
M. H.
,
2011
,
A New System of Strength Theory: Theory, Application and Development
,
Xi'an Jiao Tong University
,
Xi'an, China
.
26.
Zheng
,
C. X.
, and
Wen
,
Q.
,
2002
, “
Rectification of the Pressure Explosion Formula of Low Carbon Steel Pressure Vessels
,”
Chem. Mach.
,
29
(
5
), pp.
275
278
.
You do not currently have access to this content.