The paper presents a method for modeling and measuring the residual stress (RS) field in axisymmetric autofrettaged elements. The method is based on the assumption that an Initial Strain Distribution (ISD), originated by the plastic strain previously induced during the autofrettage process, is the source of RSs. The ISD is the quantity to be evaluated and, after being determined, it can be used, by means of a dedicated finite element (FE) model, to evaluate the RS field in the component or in any part extracted from it. The ISD is obtained by elaborating the relaxed strains produced by cutting the autofrettaged component in incremental steps. The elaboration is based on solving a set of Fredholm's integral equations in which the unknown function is the ISD and the kernel is an Influence Function (IF) correlating the measured relaxed strain to the ISD. After a general discussion of the RS induced by the autofrettage and the effect of the plastic properties of the material under process, the methods for obtaining the relaxed strains by a rational experimental setup and the procedures for obtaining the IFs are presented and discussed. The whole methodology is applied to evaluate the RS field in a hollow cylinder for which the autofrettage was modeled by a FE simulation. The consistency of the method is verified and useful indications for the experimental activities were obtained.

References

1.
Chen
,
P. C. T.
,
1986
, “
The Bauschinger and Hardening Effect on Residual Stresses in an Autofrettaged Thick-Walled Cylinder
,”
ASME J. Pressure Vessel Technol.
,
108
(
1
), pp.
108
112
.
2.
Parker
,
A. P.
,
Troiano
,
E.
,
Underwood
,
J. H.
, and
Mossey
,
C.
,
2003
, “
Characterization of Steels Using a Revised Kinematic Hardening Model Incorporating the Bauschinger Effect
,”
ASME J. Pressure Vessel Technol.
,
125
(
3
), pp.
277
281
.
3.
Livieri
,
P.
, and
Lazzarin
,
P.
,
2001
, “
Autofrettaged Cylindrical Vessels and Bauschinger Effect: An Analytical Frame for Evaluating Residual Stress Distributions
,”
ASME J. Pressure Vessel Technol.
,
124
(
1
), pp.
38
46
.
4.
ASME,
1997
, “
Correction for Reverse Yielding (Bauschinger Effect), Pressure Vessel and Piping Design Code
,” Division 3, Section KD-522.2, American Society of Mechanical Engineers, New York, p. 71.
5.
Gibson
,
M. C.
,
Hameed
,
A.
,
Parker
,
A. P.
, and
Hetherington
,
J. G.
,
2005
, “
A Comparison of Methods for Predicting Residual Stresses in Strain-Hardening, Autofrettaged Thick Cylinders, Including the Bauschinger Effect
,”
ASME J. Pressure Vessel Technol.
,
128
(
2
), pp.
217
222
.
6.
Jahed
,
H.
, and
Dubey
,
R. N.
,
1997
, “
An Axisymmetric Method of Elastic-Plastic Analysis Capable of Predicting Residual Stress Field
,”
ASME J. Pressure Vessel Technol.
,
119
(
3
), pp.
264
273
.
7.
Parker
,
A. P.
,
Hara
,
G. P. O.
, and
Underwood
,
J. H.
,
2003
, “
Hydraulic Versus Swage Autofrettage and Implications of the Bauschinger Effect
,”
ASME J. Pressure Vessel Technol.
,
125
(
3
), pp.
309
314
.
8.
Parker
,
A. P.
,
2001
, “
Autofrettage of Open-End Tubes-Pressures, Stresses, Strains, and Code Comparisons
,”
ASME J. Pressure Vessel Technol.
,
123
(
3
), pp.
271
281
.
9.
Parker
,
A. P.
,
Underwood
,
J. H.
, and
Kendalll
,
D. P.
,
1998
, “
The Bauschinger Effect in Autofrettaged Tubes—A Comparison of Models Including the ASME Code
,” Watervliet Arsenal, Watervliet, NY, Report No.
ARCCB-TR-98010
.
10.
Troiano
,
E.
,
Underwood
,
J. H.
, and
Parker
,
A. P.
,
2006
, “
Finite Element Investigation of Bauschinger Effect in High-Strength A723 Pressure Vessel Steel
,”
ASME J. Pressure Vessel Technol.
,
128
(
2
), pp.
185
189
.
11.
Troiano
,
E.
,
Underwood
,
J. H.
,
Venter
,
A. M.
,
Izzo
,
J. H.
, and
Norray
,
J. M.
,
2012
, “
Improved Finite Element Model to Predict the Reverse Loading Behavior of Autofrettaged A723 and HB7 Cylinders
,”
ASME J. Pressure Vessel Technol.
,
134
(
4
), p.
041012
.
12.
Schajer
,
G. S.
,
2013
,
Practical Residual Stress Measurement Methods
,
Wiley
,
Chichester, UK
.
13.
Jahed
,
Z.
,
Jahed
,
H.
, and
Faritus
,
M. R.
,
2012
, “
Residual Stress Measurements in an Autofrettage Tube Using Hole Drilling Method
,”
ASME J. Pressure Vessel Technol.
,
134
(
5
), p.
051501
.
14.
Prime
,
M. B.
,
2011
, “
Contour Method Advanced Applications: Hoop Stresses in Cylinders and Discontinuities
,”
Engineering Applications of Residual Stress (Conference Proceedings of the Society for Experimental Mechanics Series)
, Vol.
8
, Springer, New York, pp.
13
28
.
15.
Prime
,
M. B.
,
1999
, “
Residual Stress Measurement by Successive Extension of a Slot: The Crack Compliance Method
,”
ASME Appl. Mech. Rev.
,
52
(
2
), pp.
75
96
.
16.
de Swardt
,
R. R.
,
2003
, “
Finite Element Simulation of the Sachs Boring Method of Measuring Residual Stresses in Thick-Walled Cylinders
,”
ASME J. Pressure Vessel Technol.
,
125
(
3
), pp.
274
276
.
17.
Parker
,
A. P.
,
2004
, “
A Critical Examination of Sachs' Material-Removal Method for Determination of Residual Stress
,”
ASME J. Pressure Vessel Technol.
,
126
(
2
), pp.
234
236
.
18.
Prime
,
M. B.
,
2003
, “
Experimental Procedure for Crack Compliance (Slitting) Measurements of Residual Stress
,” Los Alamos National Laboratory, Los Alamos, NM, Report No.
LA-UR-03-8629
.
19.
de Swardt
,
R. R.
,
2003
, “
Finite Element Simulation of Crack Compliance Experiments to Measure Residual Stresses in Thick-Walled Cylinders
,”
ASME J. Pressure Vessel Technol.
,
125
(
3
), pp.
305
308
.
20.
Parker
,
A. P.
,
Underwood
,
J. H.
, and
Kendall
,
D. P.
,
1999
, “
Bauschinger Effect Design Procedures for Autofrettaged Tubes Including Material Removal and Sachs' Method
,”
ASME J. Pressure Vessel Technol.
,
121
(
4
), pp.
430
437
.
21.
Perl
,
M.
,
1998
, “
An Improved Split-Ring Method for Measuring the Level of Autofrettage in Thick-Walled Cylinders
,”
ASME J. Pressure Vessel Technol.
,
120
(
1
), pp.
69
73
.
22.
Perl
,
M.
, and
Aroné
,
R.
,
1994
, “
An Axisymmetric Stress Release Method for Measuring the Autofrettage Level in Thick-Walled Cylinders—Part I: Basic Concept and Numerical Simulation
,”
ASME J. Pressure Vessel Technol.
,
116
(
4
), pp.
384
388
.
23.
Perl
,
M.
, and
Aroné
,
R.
,
1994
, “
An Axisymmetric Stress Release Method for Measuring the Autofrettage Level in Thick-Walled Cylinders—Part II: Experimental Validation
,”
ASME J. Pressure Vessel Technol.
,
116
(
4
), pp.
389
395
.
24.
Taylor
,
D. J.
,
Watkins
,
T. R.
,
Hubbard
,
C. R.
,
Hill
,
M. R.
, and
Meith
,
W. A.
,
2011
, “
Residual Stress Measurements of Explosively Clad Cylindrical Pressure Vessels
,”
ASME J. Pressure Vessel Technol.
,
134
(
1
), p.
011501
.
25.
Cheng
,
W.
, and
Finnie
,
L.
,
1986
, “
Measurement of Residual Hoop Stresses in Cylinders Using the Compliance Method
,”
ASME J. Eng. Mater. Technol.
,
108
(
2
), pp.
87
92
.
26.
Schajer
,
G. S.
, and
Prime
,
M. B.
,
2006
, “
Use of Inverse Solutions for Residual Stress Measurements
,”
ASME J. Eng. Mater. Technol.
,
128
(
3
), pp.
375
382
.
27.
Prime
,
M. B.
, and
Hill
,
M. R.
,
2006
, “
Uncertainty, Model Error, and Order Selection for Series-Expanded, Residual-Stress Inverse Solutions
,”
ASME J. Eng. Mater. Technol.
,
128
(
2
), pp.
175
185
.
28.
Beghini
,
M.
, and
Bertini
,
L.
,
2004
, “
Residual Stress Measurement and Modeling by the Initial Strain Distribution Method—Part II-Application to Cladded Plates With Different Heat Treatments
,”
J. Test. Eval.
,
32
(
3
), pp.
177
183
.
29.
Beghini
,
M.
, and
Bertini
,
L.
,
2004
, “
Residual Stress Measurement and Modeling by the Initial Strain Distribution Method—Part I: Theory
,”
J. Test. Eval.
,
32
(3), pp.
167
176
.
30.
Beghini
,
M.
, and
Bertini
,
L.
,
1990
, “
Residual Stress Modelling by Experimental Measurements and Finite Element Analysis
,”
J. Strain Anal. Eng. Des.
,
25
(
2
), pp. 103–108.
31.
Nakacho
,
K.
,
Ogawa
,
N.
,
Ohta
,
T.
, and
Nayama
,
M.
,
2014
, “
Inherent-Strain-Based Theory of Measurement of Three-Dimensional Residual Stress Distribution and Its Application to a Welded Joint in a Reactor Vessel
,”
ASME J. Pressure Vessel Technol.
,
136
(
3
), p.
031401
.
32.
Hill
,
M. R.
, and
Nelson
,
D. V.
,
1995
, “
The Inherent Strain Method for Residual Stress Determination and Its Application to a Long Welded Joint
,”
Joint American Society of Mechanical Engineers (ASME)/Japan Society of Mechanical Engineers (JSME) Pressure Vessels and Piping Conference
, Honolulu, HI, July 23–27.
33.
Ueda
,
Y.
,
Fukuda
,
K.
, and
Kim
,
Y. C.
,
1986
, “
New Measuring Method of Axisymmetric Three-Dimensional Residual Stresses Using Inherent Strains as Parameters
,”
ASME J. Eng. Mater. Technol.
,
108
(
4
), pp.
328
334
.
34.
Korsunsky
,
A. M.
,
2009
, “
Eigenstrain Analysis of Residual Strains and Stresses
,”
J. Strain Anal. Eng. Des.
,
44
(
1
), pp. 29–43.
35.
Faghidian
,
S. A.
,
2016
, “
Analytical Inverse Solution of Eigenstrains and Residual Fields in Autofrettaged Thick-Walled Tubes
,”
ASME J. Pressure Vessel Technol.
,
139
(
3
), p.
031205
.
36.
Loffredo
,
M.
,
2017
, “
Measurement and Modelling of Bauschinger Effect for Low-Level Plastic Strains on AISI 4140 Steel
,” American Institute of Architecture Students Conference, Pisa, Italy, Paper No. 786.
37.
Hill
,
R.
,
1950
,
The Mathematical Theory of Plasticity
,
Oxford University Press, New York
.
38.
Hosseinzadeh
,
F.
,
Toparli
,
M. B.
, and
Bouchard
,
P. J.
,
2011
, “
Slitting and Contour Method Residual Stress Measurements in an Edge Welded Beam
,”
ASME J. Pressure Vessel Technol.
,
134
(
1
), p.
011402
.
39.
Prime
,
M. B.
,
1997
, “
Residual Stresses in a Bi-Material Laser Clad Measured Using Compliance
,”
Fifth International Conference on Residual Stresses
, Linköping, Sweden, June 16–18, Paper No.
LA-UR-97-1495
.
40.
Lee
,
M. J.
, and
Hill
,
M. R.
,
2006
, “
Effect of Strain Gage Length When Determining Residual Stress by Slitting
,”
ASME J. Eng. Mater. Technol.
,
129
(
1
), pp.
143
150
.
41.
Timoshenko
,
S.
, and
Goodier
,
J. N.
,
1951
,
Theory of Elasticity
,
McGraw-Hill
, New York.
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