Recent research indicates that accurate material behavior modeling plays an important role in the estimation of residual stresses in the bore of autofrettaged tubes. In this paper, the material behavior under plastic deformation is considered to be a function of the first stress invariant in addition to the second and the third invariants of the deviatoric stress tensor. The yield surface is assumed to depend on the first stress invariant and the Lode angle parameter which is defined as a function of the second and the third invariants of the deviatoric stress tensor. Furthermore for estimating the unloading behavior, the Chaboche's hardening evolution equation is modified. These modifications are implemented by adding new terms that include the effect of the first stress invariant and pervious plastic deformation history. For evaluation of this unloading behavior model a series of loading-unloading tests are conducted on four types of test specimens which are made of the high-strength steel, DIN 1.6959. In addition finite element simulations are implemented and the residual stresses in the bore of a simulated thick-walled tube are estimated under the autofrettage process. In estimating the residual stresses the effect of the tube end condition is also considered.

References

1.
Kendall
,
D. P.
,
2002
, “
A Short History of High Pressure Technology From Bridgman to Division 3
,”
ASME J. Pressure Vessel Technol.
,
122
, pp.
229
233
.10.1115/1.556178
2.
Milligan
,
R. V.
,
Koo
,
W. H.
, and
Davidson
,
T. E.
,
1966
, “
The Bauschinger Effect in a High-Strength Steel
,”
J. Basic Eng.
,
88
, pp.
480
488
. 10.1115/1.3645883
3.
Bauschinger
,
J.
,
1881
, “
Ueber die Veranderung der Elasticitatagrenze und dea Elasticitatamoduls Verschiadener Metalle
,”
Zivilingenieur
,
27
, pp.
289
348
.
4.
Stacey
,
A.
, and
Webster
,
G. A.
,
1988
, “
Determination of Residual Stress Distribution in Autofrettaged Tubing
,”
Int. J. Pressure Vessels Piping
,
31
, pp.
205
220
.10.1016/0308-0161(88)90003-8
5.
Megahed
,
M. M.
, and
Abbas
,
A. T.
,
1991
, “
Influence of Reverse Yielding on Residual Stresses Induced by Autofrettage
,”
Int. J. Mech. Sci.
,
33
, pp.
139
150
.10.1016/0020-7403(91)90063-9
6.
Troiano
,
E.
,
Parker
,
A. P.
,
Underwood
,
J. H.
, and
Mossey
,
C.
,
2003
, “
Experimental Data, Numerical Fit and Fatigue Life Calculations Relating to Bauschinger Effect in High Strength Armament Steels
,”
ASME J. Pressure Vessel Technol.
,
125
, pp.
330
334
.10.1115/1.1593072
7.
Troiano
,
E.
,
Parker
,
A. P.
, and
Underwood
,
J. H.
,
2004
, “
Mechanisms and Modeling Comparing HB7 and A723 High Strength Pressure Vessel Steels
,”
ASME J. Pressure Vessel Technol.
,
126
, pp.
473
477
.10.1115/1.1811108
8.
Parker
,
A. P.
,
Troiano
,
E.
,
Underwood
,
J. H.
, and
Mossey
,
C.
,
2003
, “
Characterization of Steels Using a Revised Kinematic Hardening Model Incorporating Bauschinger Effect
,”
ASME J. Pressure Vessel Technol.
,
125
, pp.
277
281
.10.1115/1.1593071
9.
Jahed
,
H.
, and
Ghanbari
,
G.
,
2003
, “
Actual Unloading Behavior and Its Significance on Residual Stress in Machined Autofrettaged Tubes
,”
ASME J. Pressure Vessel Technol.
,
125
, pp.
321
325
.10.1115/1.1593070
10.
Jahed
,
H.
,
Ahmadi
,
B.
, and
Shambouli
,
M.
,
2006
, “
Re-Autofrettage
,”
ASME J. Pressure Vessel Technol.
,
128
, pp.
223
226
.10.1115/1.2172619
11.
Huang
,
X.
,
2005
, “
A General Autofrettage Model of a Thick-Walled Cylinder Based on Tensile-Compressive Stress-Strain Curve of a Material
,”
J. Strain Anal. Eng. Des.
,
40
, pp.
599
608
.10.1243/030932405X16070
12.
Perry
,
J.
,
Perl
,
M.
,
Shneck
,
R.
, and
Haroush
,
S.
,
2006
, “
The Influence of the Bauschinger Effect on the Yield Stress, Young's Modulus, and Poisson's Ratio of a Gun Barrel Steel
,”
ASME J. Pressure Vessel Technol.
,
128
, pp.
179
184
.10.1115/1.2172962
13.
Farrahi
,
G. H.
,
Hosseinian
,
E.
, and
Assempour
,
A.
,
2009
, “
On the Material Modeling of the Autofrettaged Pressure Vessel Steels
,”
ASME J. Pressure Vessel Technol.
,
131
(
5
), p.
051403
.10.1115/1.3148084
14.
von Mises
,
R.
,
1913
, “
Mechanik der festen Körpern im plastisch-deformablen Zustand. Nachrichten von der königlichen Gesellschaft der Wissenschaften zu Göttingen
,”
Mathematisch-Physikalische Klasse
, pp.
582
592
.
15.
Spitzig
,
W. A.
,
Sober
,
R. J.
, and
Richmond
,
O.
,
1975
, “
Pressure Dependence of Yielding and Associated Volume Expansion in Tempered Martensite
,”
Acta Metall.
,
23
, pp.
885
893
.10.1016/0001-6160(75)90205-9
16.
Spitzig
,
W. A.
,
Sober
,
R. J.
, and
Richmond
,
O.
,
1976
, “
The Effect of Hydrostatic Pressure on the Deformation Behavior of Maraging and HY-80 Steels and Its Implications for Plasticity Theory
,”
Metall. Mater. Trans. A
,
7
, pp.
1703
1710
.10.1007/BF02817888
17.
Spitzig
,
W. A.
, and
Richmond
,
O.
,
1984
, “
The Effect of Pressure on the Flow Stress of Metals
,”
Acta Metall.
,
32
(
3
), pp.
457
463
.10.1016/0001-6160(84)90119-6
18.
Brunig
,
M.
,
1999
, “
Numerical Simulation of the Large Elastic-Plastic Deformation Behavior of Hydrostatic Stress-Sensitive Solids
,”
Int. J. Plast.
,
15
, pp.
1237
1264
.10.1016/S0749-6419(99)00042-X
19.
Brunig
,
M.
,
Berger
,
S.
, and
Obrecht
,
H.
,
2000
, “
Numerical Simulation of the Localization Behavior of Hydrostatic-Stress-Sensitive Metals
,”
Int. J. Mech. Sci.
,
42
, pp.
2147
2166
.10.1016/S0020-7403(00)00002-3
20.
Brunig
,
M.
,
Chyra
,
O.
,
Albrecht
,
D.
,
Driemeier
,
L.
, and
Alves
,
M.
,
2008
, “
A Ductile Damage Criterion at Various Stress Triaxialities
,”
Int. J. Plast.
,
24
, pp.
1731
1755
.10.1016/j.ijplas.2007.12.001
21.
Cazacu
,
O.
,
Plunkett
,
B.
, and
Barlat
,
F.
,
2006
, “
Orthotropic Yield Criterion for Hexagonal Closed Packed Metals
,”
Int. J. Plast.
,
22
(
7
), pp.
1171
1194
.10.1016/j.ijplas.2005.06.001
22.
Cazacu
,
O.
,
Ionescu
,
I. R.
, and
Yoon
,
J. W.
,
2010
, “
Orthotropic Strain Rate Potential for the Description of Anisotropy in Tension and Compression of Metals
,”
Int. J. Plast.
,
26
, pp.
887
904
.10.1016/j.ijplas.2009.11.005
23.
Bai
,
Y.
, and
Wierzbicki
,
T.
,
2008
, “
A New Model of Metal Plasticity and Fracture With Pressure and Lode Dependence
,”
Int. J. Plast.
,
24
, pp.
1071
1096
.10.1016/j.ijplas.2007.09.004
24.
Mirone
,
G.
, and
Corallo
,
D.
,
2010
, “
A Local Viewpoint for Evaluating the Influence of Stress Triaxiality and Lode Angle on Ductile Failure and Hardening
,”
Int. J. Plast.
,
26
, pp.
348
371
.10.1016/j.ijplas.2009.07.006
25.
Gao
,
X.
,
Zhang
,
T.
,
Zhou
,
J.
,
Graham
,
S. M.
,
Hayden
,
M.
, and
Roe
,
C.
,
2011
, “
On Stress-State Dependent Plasticity Modeling: Significance of the Hydrostatic Stress, the Third Invariant of Stress Deviator and the Non-Associated Flow Rule
,”
Int. J. Plast.
,
27
, pp.
217
231
.10.1016/j.ijplas.2010.05.004
26.
Voyiadjis
,
G. Z.
,
Hoseini
,
S. H.
, and
Farrahi
,
G. H.
,
2012
, “
A Plasticity Model for Metals With Dependency on all the Stress Invariants
,”
ASME Journal of Engineering Materials and Technology
(accepted).
27.
Chaboche
,
J.-L.
, and
Rousselier
,
G.
,
1981
, “
On the Plastic and Viscoplastic Constitutive Equations Based on the Internal Variables Concept
,”
SMIRT-6 Post Conference
,
Paris
, T.P. ONERA No. 8–11.
28.
Chaboche
,
J.-L.
, and
Rousselier
,
G.
,
1983
, “
On the Plastic and Viscoplastic Constitutive Equations, Part I: Rules Developed With Internal Variable Concept. Part II: Application of Internal Variable Concepts to the 316 Stainless Steel
,”
ASME J. Pressure Vessel Technol.
,
105
, pp.
153
164
.10.1115/1.3264257
29.
Voyiadjis
,
G. Z.
, and
Abu Al-Rub
,
R. K. A.
,
2003
, “
Thermodynamic Based Model for the Evolution Equation of the Backstress in Cyclic Plasticity
,”
Int. J. Plast.
,
19
, pp.
2121
2147
.10.1016/S0749-6419(03)00062-7
30.
Puskar
,
A.
,
1993
, “
A Correlation Among Elastic Modulus Defect, Plastic Strain and Fatigue Life of Metals
,”
Mater. Sci. Forum
,
119–121
, pp.
455
460
.10.4028/www.scientific.net/MSF.119-121.455
31.
Underwood
,
J. H.
, and
Parker
,
A. P.
,
1997
, “
Fatigue Life Assessment of Steel Pressure Vessels With Varying Stress Concentration, Residual Stress and Initial Cracks
,”
Advances in Fracture Research, Proceedings of ICF9
,
Pergamon, New York
, pp.
215
226
.
32.
Underwood
,
J. H.
, and
Troiano
,
E.
,
2003
, “
Critical Fracture Processes in Army Cannons: A Review
,”
ASME J. Pressure Vessel Technol.
,
125
, pp.
287
292
.10.1115/1.1593075
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