Existing experimental lifetime measurements are shown to require the inclusion ..... hoop residual stress at the bore may serve to maximise initiation lifetime in.
AD
TECHNICAL REPORT ARCCB-TR-97020
INFLUENCE OF THE BAUSCHINGER EFFECT ON RESIDUAL STRESS AND FATIGUE LIFETIMES IN AUTOFRETTAGED THICK-WALLED CYLINDERS
ANTHONY P. PARKER JOHN H. UNDERWOOD
SEPTEMBER 1997
US ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER CLOSE COMBAT ARMAMENTS CENTER BENET LABORATORIES WATERVLIET, N.Y. 12189-4050
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2. REPORT DATE September 1997
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JEäaaL
4. TITLE AND SUBTITLE
INFLUENCE OF THE BAUSCHTNGER EFFECT ON RESIDUAL STRESS AND FATIGUE LIFETIMES IN AUTOFRETTAGED THICK-WALLED CYLINDERS
5. FUNDING NUMBERS
AMCMS No. 6226.24.H180.0 PRON No. TU6A6F361ABJ
6. AUTHOR(S)
Anthony P. Parker (Royal Military College of Science, Cranfield University, Swindon, UK) and John H. Underwood 8. PERFORMING ORGANIZATION REPORT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
U.S. Army ARDEC Benet Laboratories, AMSTA-AR-CCB-O Watervliet, NY 12189-4050
ARCCB-TR-97020
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9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
U.S. Army ARDEC Close Combat Armaments Center Picatinny Arsenal, NJ 07806-5000
11. SUPPLEMENTARY NOTES
Presented at the 29th National Fatigue and Fracture Symposium, Stanford University, CA, 24-26 June 1997. Published in ASTM STP Proceedings of the NFFM Symposium. 12b. DISTRIBUTION CODE
12a. DISTRIBUTION /AVAILABILITY STATEMENT Approved for public release; distribution unlimited.
13. ABSTRACT (Maximum 200 words) . .- . ,-, . ■ A . «. » A c This work addresses the influence of Bauschinger effect upon residual stresses and associated fatigue lifetimes for pressurized, autofrettaged thick cylinders. The model employed allows for the variation with radius of Bauschinger Effect Factor (BEF) throughout the autofrettaged tube since the percentage plastic strain, which determines BEF, will vary from a maximum value at the bore to zero at the elastic-plastic interface. Accounting for BEF variability, it is demonstrated that the residual compressive hoop stress at the inner radius of the tube Teaches a maximum value at the percentage overstrain level below which reversed yielding does not occur. Existing experimental residual stress measurements from a variety of sources are shown to support this thesis. This value of overstrain may serve to maximize crack initiation lifetime in autofrettaged thick cylinders. For a tube with significant heat-checking and associated initial crack-like defects, it is necessary to consider fatigue crack growth rates governed by a crack growth law such as Paris's Law. For a tube of radius ratio 2.0 and at a value of approximately 40% overstrain, slightly in excess of that for the onset of reversed yielding, the fatigue lifetime exhibits a maximum value. Fatigue lifetimes achieve a maximum value at overstrain levels in which yielding reaches 1.4 times bore radius and are almost constant thereafter. Furthermore, such extended overstrain leads to a small increase in residual stress at the outside diameter (OD), thus increasing R ratio at that location and reducing fatigue lifetime for crack growth originating at the OD. Existing experimental lifetime measurements are shown to require the inclusion of BEF to properly account for these observed lifetimes. 15. NUMBER OF PAGES
14. SUBJECT TERMS
Bauschinger Effect, Crack Growth, Fatigue Cracks, Fatigue Lifetimes, Cylinders, Fracture (Materials), Fracture Mechanics, Residual Stress, Stress Intensity Factor 17. SECURITY CLASSIFICATION
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NSN 7540-01-280-5500
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UL Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std Z39-18 298-102
TABLE OF CONTENTS
Page 1
INTRODUCTION
3
ANALYSIS PROCEDURE INFLUENCE OF BAUSCHINGER EFFECT ON RESIDUAL STRESSES
8
INFLUENCE OF BAUSCHINGER EFFECT ON FATIGUE LIFETIME
10
EXPERIMENTAL LIFETIME DATA
10
A NOTE ON YIELD STRENGTH MODIFICATION
12
SUMMARY AND CONCLUSIONS
12
FOOTNOTE
• • •
13
ACKNOWLEDGMENTS
13
REFERENCES
14
TABLES 1.
Summary of Hydraulic Fatigue Tests of 188 mm Inner Diameter A723 Steel Thick Walled Cylinders with 0 and 50% Overstrain
11
| |RT OF II I MRTRATIONS
1.
Bauschinger Effect: (a) Stress-Strain Curve for Typical Gun Steel; (b) Variation of BEF with Percentage Plastic Strain; (c) Form of Residual Hoop Stress Predictions; (d) Form of Residual Hoop Stress Measurements . 16
2.
Tube Geometry
3.
Plastic Strain, Bauschinger Effect Factor, and Residual Hoop Stress as a Function of Radius
18
4.
Comparison of Predicted Stresses with Experimental Data
19
5.
Plastic Strain, Bauschinger Effect Factor, and Residual Hoop Stress at the Bore
20
17
i
DTIC QUALITY INSPECTED S
6.
Residual Stress at the Bore - Bauschinger Model and Experimental Evidence
21
7.
Predicted Lifetimes as a Function of Percentage Overstrain
22
8.
Effect of Overstrain and BEF on Measured Fatigue Lifetime of Pressurized Cylinders
23
INTRODUCTION The use of autofrettage to enhance fatigue lifetimes of thick cylinders subjected to internal cyclic pressurization is well known and relatively well understood. The determination of residual stresses arising from the autofrettage process is important for fatigue life estimation [1]. The residual stress and strain distribution in a thick cylinder which has been pressurized until yielding spreads outwards from the bore to a known radius and which then has the internal pressure removed has been analyzed by Hill [2]. Hill's analysis is based upon ideal elastic-perfectly plastic assumptions and standard yield criteria, normally those due to Tresca or Von Mises, with identical magnitude of yield strength in tension and compression. For many years workers have acknowledged the probable influence of the Bauschinger effect [3] which serves to reduce the yield strength in compression as a result of prior tensile plastic overload. This phenomenon is illustrated in Fig. 1(a) wherein the yield strength in tension is Y and the yield strength in compression is -fY; the data in Fig. 1(a) are based upon work by Clark [4]. f is sometimes termed the Bauschinger Effect Factor (BEF); work by Milligan et al [5] provides a relationship between tensile plastic overstrain and the BEF; the latter varies from unity at zero plastic strain, drops rapidly with increasing plastic strain and saturates at around 2% plastic strain, being effectively constant thereafter. This saturation value of BEF is designated f*. The variation of BEF, based upon [5], is illustrated in Fig. 1(b). Fig. 1: Bauschinger Effect, Relevant Earlier Work: (a) Stress-Strain Curve for Typical Gun Steel (after[4]) (b) Variation of BEF with Percentage Plastic Strain (after[5]) (c) Form of Residual hoop Stress Predictions (after[8,9]) (d) Form of Residual Hoop Stress Measurements(after[6])
The reduction of compressive yield strength within the yielded zone of an autofrettaged tube is of importance because, on removal of the autofrettage pressure, the region near the bore experiences high values of compressive hoop stress, approaching the normal tensile yield strength of the material if the unloading is totally elastic. If the combination of hoop and radial stresses exceeds some yield criterion the tube will re-yield from the bore thus losing much of the potential benefits of autofrettage. There is convincing experimental evidence, based upon X-ray and other residual stress measurements, for this effect [6,7]. A cruder measure of this effect is obtained by radial slitting of tubes to release the locked-in bending moment created by the autofrettage stresses; any level of opening angle below the 'ideal' value predicted by the elastic-perfectly plastic analysis is an indication of Bauschinger effect [1].
Most prior work on the stress analysis of autofrettaged tubes which encompasses the Bauschinger effect has assumed a constant value of BEF thoughout the autofrettaged tube [4,8]. This is clearly incorrect as a general assumption, since the percentage plastic strain will vary from a maximum value at the bore of the autofrettaged tube to zero at the elastic-plastic interface. The most striking feature of residual hoop stress predictions based upon such modelling is an abrupt change of slope at the reversed yielding interface with a subsequent decrease in the magnitude of compressive hoop stress towards the bore; the value at the bore being -fY, as required by the yield criterion. This is illustrated in Fig. 1(c). In one case Chen [9] has selected a constant value of f as a function of plastic strain at the bore (based upon data in [5]) and the continued 'compressive strain hardening' slope (also illustrated in Fig. 1(c)). Chen employed a constant value for the slope, m', of 0.3. The most obvious impact of incorporating this quasi-strain hardening effect is that the abrupt change of slope at the elastic plastic reversed yielding interface is dramatically reduced and that the magnitude of compressive hoop stress continues to increase all the way to the bore. At this stage it is hypothesized that much of this predicted shift is caused by the selection of a model of unbounded strain hardening which does not match the experimental evidence for a given value of plastic strain; furthermore, by adopting a single constant value for m' there is an implicit assumption that the slope (even if it were an adequate proxy for the non-linear process) is constant for all values of prior tensile plastic strain. Whilst there is a reasonable body of experimental work on measuring residual hoop stresses via X-ray [4,6], neutron-diffraction [7] and hardness/acoustoelasticity [10] very few have sufficient data points to investigate the critical, near-bore, reversed yielding zone arising from the Bauschinger effect. Only two such have been located, the most useful of which is due to Lee et al [6]; these results consistently show a significant change of slope at the reversed yield interface and a significant subsequent decrease in hoop residual compressive stress as the bore is approached, Fig. 1(d). The other work which contains a significant number of data points near the bore is due to Frankel et al [10]; these measurements relate to hardness but may be interpreted in terms of residual stress. Reference [10] consistently demonstrates the same form of slope change and reduced residual stress as [6]. The objectives of the work presented herein are to: a. Develop a simple analysis procedure to include variations in plastic strain and hence BEF through the wall thickness which conforms with experimentally observed residual stress distributions, particularly in the near-bore region. b. Conduct a parameter study to identify optimum values of percentage overstrain in order to maximize fatigue lifetimes of tubes having different diameter ratios.
c. Comment upon the implications for fatigue lifetime of increases in material yield strength.
ANALYSIS PROCEDURE References [3, 4, 8 and 9] provide all necessary analyses required to develop a model for the autofrettage process with a yield strength in tension of Y and a yield strength in compression of -fY. The equations required for this analysis are summarized below. Note that the various references have been assembled adopting a consistent set of definitions, and presenting only those details required for this particular analysis.
Fig. 2: Tube Geometry
The following definitions apply (see Figure 2): Tube inner radius, a; tube outer radius, b; radius of plastic zone at peak of autofrettage cycle, c; maximum radius of reversed plasticity, d; general radius location, r: Tube with internal pressure p, hoop (oe) and radial (ar) stresses are: 2 crp •>
[1+4]
(1)
(2)
b~-a-
b ~i_ r2_
ö - ,2
a2p
The pressure, p*, to cause yielding out to radius r = c is :
p*^Y\n(c/a) + ^(b2-c2)
0)
Pressure for initial yielding at the bore, p*:
P*=^Ab2-a2) Pressure p * for complete yielding out to radius b:
(4)
pi = Y)n(b/a)
(5)
If tube is pressurized to p* (p* < p* < py*) there is partial yielding to radius c, with associated stresses:
ao = -jp* + K(l+ln(r/flf))
a! L
bl~>-dy
2b2 J + \n(d/a)
(23)
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