Influence of Bauschinger Effect on Residual Stress and Fatigue Lifetimes in Autofrettaged Thick-Walled Cylinders

Autofrettage is a practical method for increasing the elastic carrying capacity and the fatigue life of thick-walled cylinders such as cannon and high-pressure tubular reactor. Many analytical and numerical solutions for determining the residual stress distribution in an autofrettaged tube have been reported. It is still difficult to model the Bauchinger effect, which is dependent on the prior plasticity in an analytical solution. The reduced Young’s modulus during unloading affects residual stress distribution. However, until now this effect has not been considered in any analytical model. In this paper, an autofrettage analytical solution considering Young’s modulus and the reverse yield stress dependent on the prior plasticity, based on the actual tensile-compressive curve of the material and the von Mises yield criterion, has been proposed. New model incorporates the Bauschinger effect factor and the unloading modulus variation as a function of prior plastic strain, and hence of the radius. Thereafter it assumes a fixed nonlinear unloading profile. The comparison of predicted residual stress distribution by the present solution with that of fixed unloading curve model, and test results shows that the present solution gives accurate prediction of residual stress distribution of an autofrettaged tube. This analytical procedure for the cylinder permits an excellent representation of various pressure vessel steels.

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Use of A True Material Constitutive Model for Stress Analysis of A Swage Autofrettaged Tube Including Asme Code Comparison

Journal of Pressure Vessel Technology ◽

10.1115/1.4051688 ◽

2021 ◽

Author(s):

Zhong Hu ◽

Anthony P Parker

Keyword(s):

Residual Stress ◽

Constitutive Model ◽

Stress Analysis ◽

Bauschinger Effect ◽

Kinematic Hardening ◽

Pressure Vessels ◽

Material Behavior ◽

Elastoplastic Material ◽

Material Constitutive Model ◽

Deformation Mechanics

Abstract This work reports a new finite element analysis (FEA)-based user programmable function (UPF) featuring true material constitutive behavior with proper algorithms for accurate stress analysis of swage autofrettage of high-strength thick-walled cylinders. The material constitutive model replicates an existing Bauschinger-effect characterization (BEC). This incorporates elastoplastic material behavior during loading. Reversed loading includes a reduced elastic modulus and nonlinear plasticity resulting from the Bauschinger effect (BE), both depend upon the maximum level of loading plastic strain. Swage autofrettage case studies identify the difference in stress distributions based on different material models: a bilinear isotropic material model, a bilinear kinematic hardening model, and the user defined model that features the BEC. Development and integration of such a UPF into a standard FEA package is a crucial unresolved and fundamental modeling issue relating to re-yield, fatigue and fracture of modern swaged cylinders and pressure vessels. It will not only provide a fundamental understanding of the deformation mechanics of the tube during the swage autofrettage process and ensure optimal process parameters are achieved, but also provide guidance for material selection, design and optimization of the manufacturing processes for high intensity cylindrical parts, a potential multibillion-dollar market. Near-bore residual stresses for the BEC case are noteworthy and reported in detail, e.g., axial residual stress is tensile and hoop residual stress exhibits a distinct slope reversal, unlike hydraulic autofrettage, indicating the possible need to re-assess the ASME Pressure Vessel Code (correction for BE) regarding swage autofrettage.

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Influence of the Bauschinger Effect on Residual Stress and Fatigue Lifetimes in Autofrettaged Thick-Walled Cylinders

10.21236/ada330071 ◽

1997 ◽

Cited By ~ 10

Author(s):

Anthony P. Parker ◽

John H. Underwood

Keyword(s):

Residual Stress ◽

Bauschinger Effect

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The influence of Bauschinger effect on overstrained spring strip

The Journal of Strain Analysis for Engineering Design ◽

10.1243/03093247v113168 ◽

1976 ◽

Vol 11 (3) ◽

pp. 168-176

Author(s):

W A C Swift

Keyword(s):

Residual Stress ◽

Stress Distribution ◽

Bauschinger Effect ◽

Residual Stress Distribution ◽

Experimental Results ◽

Layer Removal ◽

Spring Strip ◽

Removal Technique

A theoretical Bauschinger chart has been constructed, the data being based on experimental results. This chart is used to predict the resisting moment of the strip whilst determining the residual-stress distribution using a layer-removal technique.

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Prediction of Residual Stresses in an Autofrettaged Thick–Walled Cylinder

MRS Proceedings ◽

10.1557/proc-22-235 ◽

1983 ◽

Vol 22 ◽

Author(s):

Peter C. T. Chen

Keyword(s):

Residual Stress ◽

Residual Stresses ◽

Bauschinger Effect ◽

Residual Stress Distribution ◽

Effect Factor ◽

Hardening Effect ◽

Loading And Unloading ◽

Reverse Yielding ◽

Walled Cylinder ◽

Elastic Unloading

ABSTRACTMost of the earlier results for residual stresses are based on the assumption of elastic unloading. In this paper, the prediction of residual stresses for the case of reverse yielding including the combined Bauschinger and hardening effect will be reported for an autofrettaged thick-walled cylinder. The Bauschinger effect factor is varying as a function of overstrain. The strain-hardening effect is considered with different parameters used for loading and unloading process. The new results indicate that the influence of the combined Bauschinger and hardening effect on residual stress distribution is significant.

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Impact of Intensity of Residual Stress Field Upon Re-Yielding and Re-Autofrettage of an Autofrettaged Thick Cylinder

ASME 2010 Pressure Vessels and Piping Conference: Volume 5 ◽

10.1115/pvp2010-25020 ◽

2010 ◽

Cited By ~ 1

Author(s):

Anthony P. Parker ◽

John H. Underwood ◽

Edward Troiano

Keyword(s):

Residual Stress ◽

Stress Field ◽

Hoop Stress ◽

Bauschinger Effect ◽

Numerical Study ◽

Fatigue Cracks ◽

Maximum Pressure ◽

Residual Stress Field ◽

Intensity Effect ◽

Elastic Plastic

Re-autofrettage has been identified as a significant, cost-effective method to achieve higher re-yield pressure (RYP) and/or weight reduction in large caliber gun tubes. For a given overstrain, residual stress profiles for hydraulic and for swage autofrettage may differ significantly in their intensity. The simplest representation of this ‘intensity’ effect is the magnitude of the bending moment ‘locked in’ via the residual hoop stress. Hill’s analytical, plane strain, Von Mises, analysis predicts a larger ‘locked-in’ moment than does the equivalent open-end condition. By assuming a range of stress-field intensities (f) scaleing from 1.0 to 1.4 times that produced by open-end hydraulic autofrettage, it was possible to assess re-yield behavior following initial autofrettage via a generic numerical study. In cases where Bauschinger effect is absent, re-yield initiates at the original elastic plastic interface. This includes the ideal Hill distribution. When Bauschinger effect is present, re-yield for f ≤ 1.1 initiates at the bore and after further pressurization at the original elastic plastic interface within two zones. For f ≥ 1.2 the reverse is the case, with initial yield at the original elastic plastic interface and subsequently at the bore. RYP increases with increasing f up to f = 1.175 and then decreases significantly. This loss of RYP may be mitigated by hydraulic re-autofrettage. At f = 1.0 re-autofrettage increases RYP by 4%. At f = 1.4 RYP is increased by 19%. There are modest increases in safe maximum pressure as a result of re-autofrettage. RYP closely approaching re-autofrettage pressure is achievable for f ≥ 1.3. Within this range, re-autofrettage offers a significant benefit. Re-autofrettage also produces beneficial effects via increased bore hoop compressive stress, this increase varying from 20% for f = 1 to zero for f = 1.4. Such increased compression will benefit fatigue lifetime for fatigue cracks initiating at the bore. Conversely, tensile OD hoop stress increases, with increasing f, by a maximum of 6%.

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Autofrettaged Cylindrical Vessels and Bauschinger Effect: An Analytical Frame for Evaluating Residual Stress Distributions

Journal of Pressure Vessel Technology ◽

10.1115/1.1425809 ◽

2001 ◽

Vol 124 (1) ◽

pp. 38-46 ◽

Cited By ~ 30

Author(s):

Paolo Livieri ◽

Paolo Lazzarin

Keyword(s):

Residual Stress ◽

Residual Stresses ◽

Explicit Form ◽

Analytical Solutions ◽

Bauschinger Effect ◽

Superposition Principle ◽

Pressure Vessels ◽

Material Behavior ◽

Stress Distributions ◽

Hardening Law

The paper reports analytical solutions valid for residual stresses in cylindrical pressure vessels subjected to autofrettage. The material behavior is thought of as obeying a generic monotonic σ−ε curve and exhibiting the Bauschinger effect during the unloading phase. Under linear and power-hardening conditions, the solution is given in an explicit form. The circumstances under which it is possible to apply the superposition principle also in the presence of localized plasticity are clearly identified. When possible, the final stresses can be obtained by using in an appropriate manner the stress expressions related to the loading phase. Finally, the influence on residual stresses, both of the hardening law and of the shape of the unloading σ−ε curve, is discussed.

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Assessment and Extension of an Analytical Formulation for Prediction of Residual Stress in Autofrettaged Thick Cylinders

Volume 5: High Pressure Technology, Nondestructive Evaluation, Pipeline Systems, Student Paper Competition ◽

10.1115/pvp2005-71368 ◽

2005 ◽

Cited By ~ 4

Author(s):

Anthony P. Parker

Keyword(s):

Residual Stress ◽

Plane Strain ◽

Bauschinger Effect ◽

Incompressible Material ◽

Simple Modification ◽

Linear Behavior ◽

Wide Range ◽

End Conditions ◽

Von Mises ◽

Recent Formulation

A recent formulation due to Huang and Cui provides an analytic method for calculating residual stresses in autofrettaged tubes exhibiting non-linear behavior (including Bauschinger effect) during manufacture. The formulation incorporates Von Mises criterion but is limited in its application to plane strain end conditions and an incompressible material (i.e. Poisson’s ratio 0.5) with a fixed unloading behavior. Comparisons indicate that, by selecting unloading behavior typical of that at the bore, the method produces reliable results for both A723 type steels and for steels which exhibit significant strain hardening and/or more dramatic Bauschinger effect. Numerical comparisons show that open-end, compressible conditions produce results which differ from the plane strain, incompressible case, but that these differences may be accurately corrected using a straightforward, pragmatic process. It is concluded that a simple modification of the Huang & Cui procedure may be used to perform extremely accurate straightforward spreadsheet calculations of residual stress in autofrettaged tubes manufactured from a wide range of steels under various end conditions. The Huang & Cui formulation also provides a reliable and highly accurate means for validating numerical formulations including Finite Element methods.

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Consideration of damage in the analysis of autofrettage of thick-walled pressure vessels

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406215615908 ◽

2016 ◽

Vol 230 (20) ◽

pp. 3585-3593 ◽

Cited By ~ 2

Author(s):

H Altenbach ◽

GI Lvov ◽

K Naumenko ◽

V Okorokov

Keyword(s):

Residual Stress ◽

Plastic Deformation ◽

Bauschinger Effect ◽

Pressure Vessels ◽

Stress Fields ◽

Constant Thickness ◽

Process Conditions ◽

Material Damage ◽

Damage Processes ◽

Walled Cylinder

In this study, the influence of material damage and the Bauschinger effect on the autofrettage of thick-walled pressure vessels is investigated. Constitutive equations for the elasto-plastic deformation and damage processes are presented. Boundary value problems for a thick-walled cylinder and for a thick-walled sphere of constant thickness are formulated. Computations are preformed to find the optimum autofrettage pressure, for which the equivalent stresses in the vessel take the minimum value under process conditions. Furthermore, residual stress fields after the autofrettage are analyzed. The results show that the Bauschinger effect and damage lead to essential reduction of favorable residual stresses.

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