The stress–strain response of cast iron under tension or compression is nonlinear. This paper examines how the hyperbolic constitutive law can be applied to characterize nonlinear stress–strain behavior of cast iron used in water supply networks. Procedures are described to obtain parameters of the hyperbolic constitutive law from either the response (data) obtained from simple uniaxial tensile and compressive tests or from bending tests. To demonstrate its applicability, this hyperbolic constitutive law is first applied to data obtained from uniaxial tensile and compressive tests conducted by Schlick and Moore (1936, “Strength and Elastic Properties of Cast Iron in Tension, Compression, Flexure, and Combined Tension and Flexure,” Bulletin 127, Iowa Engineering Experiment Station, Ames, IA). In addition, an approach to extract parameters for the hyperbolic constitutive law from bending (beam and pipe rings) tests is proposed and subsequently applied to tests conducted by Talbot (1908, “Tests of Cast-Iron and Reinforced Concrete Culvert Pipe,” Bulletin No. 22, University of Illinois, Urbana, IL). This latter approach is attractive for practical purposes because the test set up is simple and the test coupons are very easy to prepare. The hyperbolic constitutive law in conjunction with maximum normal strain theory as proposed by St. Venant (Collins, J. A., 1993, Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention, John Wiley, New York, NY) was also used to predict failure loads.

References

References
1.
Fisher
,
V.
,
1999
, “
The History of US Pipe & Foundry Co.—A Centennial Celebration
,” US Pipe Co., Birmingham, AL.
2.
Schlick
,
W. J.
,
1940
, “
Supporting Strength of Cast Iron Pipe for Gas and Water Services
,” Bulletin 146, Iowa Engineering Experimental Station, Ames, IA.
3.
Johnson
,
J. B.
,
1890
, “
Cast-Iron-Strength, Resilience, Tests and Specifications
,”
Trans. Am. Soc. Civil Eng.
,
XXII
(
1
), pp.
91
120
.
4.
Sharp
,
J.
,
1914
, “
Some Considerations Regarding Cast Iron and Steel Pipes
,” Longmans, Green & Co., London, p.
142
.
5.
Shawki
,
G. S. A.
, and
Naga
,
S. A. R.
,
1986
, “
On the Mechanics of Grey Cast Iron Under Pure Bending
,”
ASME J. Eng. Mater. Technol.
,
108
(
2
), pp.
141
146
.10.1115/1.3225851
6.
Makar
,
J. M.
, and
McDonald
,
S. E.
,
2007
, “
Mechanical Behavior of Spun-Cast Gray Iron Pipe
,”
J. Mater. Civil Eng.
,
19
(
10
), pp.
826
833
.10.1061/(ASCE)0899-1561(2007)19:10(826)
7.
Angus
,
H. T.
,
1978
,
Cast Iron: Physical and Engineering Properties
,
2nd ed.
,
Butterworths
,
London
, p.
542
.
8.
Attewell
,
P. B.
,
Yeates
,
J.
, and
Selby
,
A. R.
,
1986
,
Soil Movements Induced by Tunnelling and Their Effects on Pipelines and Structures
,
Chapman & Hall
,
New York
.
9.
Schlick
,
W. J.
, and
Moore
,
B. A.
,
1936
, “
Strength and Elastic Properties of Cast Iron in Tension, Compression, Flexure, and Combined Tension and Flexure
,” Bulletin 127, Iowa Engineering Experiment Station, Ames, IA.
10.
Talbot
,
A. N.
,
1908
, “
Tests of Cast-Iron and Reinforced Concrete Culvert Pipe
,” Bulletin No. 22, University of Illinois, Urbana, IL.
11.
AWWA, 1939, ASA A21.1-1939/AWWA C101-39
, “
American Recommended Practice. Manual for the Computation of Strength and Thickness of Cast Iron Pipe
,” American Water Works Association, New York.
12.
Harris
,
C. W.
, and
O'Rourke
,
T. D.
,
1983
, “
Response of Jointed Cast Iron Pipelines to Parallel Trench Construction
,” Cornell University, Report to New York Gas Group, Report No. 83-5, NY.
13.
Makar
,
J. M.
,
Rogge
,
R.
,
McDonald
,
S.
, and
Tesfamariam
,
S.
,
2005
, “
The Effect of Corrosion Pitting on Circumferential Failures in Grey Cast Iron Pipes
,” Awwa Research Foundation, Denver, CO.
14.
Konder
,
R. L.
,
1963
, “
Hyperbolic Stress–Strain Response: Cohesive Soils
,”
ASCE J. Soil Mech. and Foundations Div.
,
89
(
1
), pp.
115
143
.
15.
Weibull
,
W.
,
1939
, “
A Statistical Theory of the Strength of Materials
,”
Proc. R. Swed. Inst. Eng. Res., Handlingar
,
151
(
3
), pp.
45
55
.
16.
Mayville
,
R. A.
, and
Finnie
,
I.
,
1982
, “
Uniaxial Stress–Strain Curves From a Bending Test
,”
Exp. Mech.
,
22
(
6
), pp.
197
201
.10.1007/BF02326357
17.
Herbert
,
H.
,
1910
, “
Uber den Zusammenhang der Biegungselastizitat des Gusseisens mit seiner Zug- and Druckelastizitat
” (On the connection between bending deformation and tension and compression deformation for cast iron),
Mitt. und Forschungsarb. Ver. deut. Ing.
,
89
, pp.
39
81
.
18.
Crocombe
,
A. D.
,
Richardson
,
G.
, and
Smith
,
P. A.
,
1993
, “
Measuring Hydro-Static Dependent Constitutive Behaviour of Adhesives Using a Bend Specimen
,”
J. Adhesion
,
42
, pp.
209
223
.10.1080/00218469308044648
19.
Jesson
,
D. A.
,
Mohebbi
,
H.
,
Belmonte
,
H. M. S.
,
Mulheron
,
M. J.
, and
Smith
,
P. A.
,
2007
, “
Derivation of Uniaxial Stress–Strain Curves for Cast Iron From Samples Tested in Flexure
,”
Experimental Analysis Nano and Engineering Materials Structures
, Part B, Springer, Dordrecht, The Netherlands, pp.
375
376
.
20.
Schajer
,
G. S.
, and
An
,
Y.
,
2009
, “
Inverse Calculation of Uniaxial Stress–Strain Curves From Bending Test Data
,”
ASME J. Eng. Mater. Technol.
,
131
(
4
), p.
041001
.10.1115/1.3120409
21.
Collins
,
J. A.
,
1993
,
Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention
,
John Wiley
,
New York
.
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