Creator:T.E. Davidson, R. Eisenstadt, and A.N. Reiner Date Created:August 1962 Place Created:Watervliet, New York Keywords:open-end thick-walled cylinders Context:technical report from the U.S. Army Weapons Command Research Division ************************************************** TECHNICAL REPORT WVT-RI-6216 FATIGUE CHARACTERISTICS OF OPEN-END THICK-WALLED CYLINDERS UNDER CYCLIC INTERNAL PRESSURE 9Y T. E. DAVIDSON R. EISENSTADT A. N. REINER AUGUST 1962 U.S. ARMY WEAPONS COMMAND WATERVLIET ARSENAL RESEARCH 8 ENGINEERING DIVISION WATERVLIET NEW YORK JICAL REPORT WVT-RI-6216 CHARACTERI STI CS OF OPEN-END THI CK-WALLED NDERS UNDER CYCLIC INTERNAL PRESSURE BY T. E. DAVIDSON R. EISENSTADT A. N. REINER AUGUST 1962 ARMY WEAPONS COMMAND ERVLIET ARSENAL •,RCH 8 ENGINEERING DIVISION ATERVLIET NEW YORK DISPOSITION This report will be destroyed by the holder when no longer required. ADDITIONAL COPIES Qualified requesters may obtain copies of this report from ASTIA. Copies available at Office of Technical Services $1.25. The findings in this report are not to be construed as an official Department of the Army position. FATIGUE CHARACTERISTICS OF OPEN-END THICK-WALLED CYLINDERS UNDER CYCLIC INTERNAL PRESSURE Abstract Cross-Reference Data Thick-walled cylinder fatigue data due to cyclic internal pressure for open-end cylinders in the range of 10^ to 105 cycles to failure and having a diameter ratio of 1.4 to 2.0 at a nominal yield strength of 160,000 pounds per square inch is presented. Discussed and also presented are the effects of autofrettage on the fatigue characteristics of thick-walled cylinders. Autofrettage substantially enhances fatigue characteristics at stress levels below the corresponding overstrain pressure; the degree of improvement increasing with decreasing stress levels. The rate of improvement in fatigue characteristics increases significantly with diameter ratio in autofrettaged cylinders up to a diameter ratio of 1.8 - 2.0 and to a much smaller degree in the non-autofrettaged condition. The rate of improvement of fatigue characteristics above 2.0 is the same for both the autofrettaged and non-autofrettaged cases. Fatigue Fracture Gun Barrels Pressure Vessel Thick-Walled Cylinders It is shown that thermal treatment of 675°F for 6 hours after autofrettage does not affect fatigue characteristics and that there is a correlation between the cyclic stress level and the area and depth of the fatigue crack to the point of ductile rupture. The depth of the fatigue crack decreases with increasing cyclic stress level. A means for using data from a uni-directional tensile fatigue test to predict the fatigue characteristics of thick-walled cylinders is discussed. IX) NOT REMOVE THIS ABSTRACT FROM THE REPORT 1 CONCLUSIONS Data for the hydrostatic fatigue characteristics of high-strength, thick-walled cylinders in the range of 103 to 105 cycles to failure are presented. Based on this investigation, the following points have been established: 1. Autofrettage significantly improves the fatigue characteristics of thick-walled cylinders at stress levels lower than those associated with the overstrain pressure. The degree of improvement increases as the cyclic stress level decreases. 2. Using the difference in principal bore stress as the cyclic parama-ter, the fatigue characteristics improve with increasing diameter ratio. This increase with diameter ratio is small in the case of the non-autofrettaged condition. In the case of autofrettaged cylinders, the increase in fatigue life with diameter ratio is substantial. The rate of improvement in the autofrettaged cylinders approaches that for the non-autofrettaged condition beyond a diameter ratio of 2.0. 3. The slope of the difference in principal bore stress versus cycles to failure curve appears to approach zero below 103 cycles to failure. 4. Based on the similarity in the correlation coefficient, no single cyclic stress or strain parameter evaluated for the presentation of thick-walled cylinder fatigue data offered significant advantage over the others. 5. Thermal treatment of the overstrained cylinders at 675°F for 6 hours did not affect fatigue characteristics. 6. There is a correlation between the cyclic stress level and the area and depth of the fatigue crack to the point of ductile rupture; the depth of the crack decreasing with increasing stress level. 7. Internal diameter surface finishes varying from 16 to .125 micro-inches RMS did not show a consistent pattern in affecting the fatigue life. T. E. DAVIDSON R. EISENSTADT A. N. REINER Approved: L. J. Wooge Capt., Ord Corps Chief, Research and Engineering Division 2 R. E. WeigZe Chief Scientist TABLE OF CONTENTS Page Abstract 1 Conclusions 2 List of Symbols 5 Subscripts 6 Introduction Procedure Test Specimens 7 Test Apparatus 8 Instrumentation 9 Pressure Control and Recording 9 Strain Measurement and Recording 9 Theory 9 Results and Discussion Analysis of Various Cyclic Parameters for Use in 11 Presenting Fatigue Data Effects of Autofrettage on Fatigue Life 14 Effect of Thermal Treatment After Autofrettage 16 Effect of Surface Finish and Tensile Strength Variations 17 Comparison of Results with Other Investigations 17 Fracture Analysis 18 Acknowledgement 18 References 19 Distribution List 50 FIGURES 1. Pressure Source for 80,000 Pounds per Square Inch Fatigue 27 System 2. Holding Press and Specimens for 80,000 Pounds per Square 28 Inch Fatigue System 3. Schematic of the 80,000 Pounds per Square Inch Fatigue 29 System 4. 150,000 Pounds per Square Inch Fatigue System 30 5. Schematic of the 150,000 Pounds per Square Inch Fatigue 31 System 3 6. Controls and Instrumentation for 150,000 Pounds per Square 32 Inch Fatigue System 7. Residual Stress Distribution for a 2.0 Diameter Ratio 100 33 Percent Overstrained Cylinder 8. Pressure vs. Cycles to Failure 34 9. Tangential Bore Stress vs. Cycles to Failure 35 10. Difference in Principal Bore Stress vs. Cycles to Failure 36 11. Octahedral Stress Parameter vs. Cycles to Failure 37 12. Strain Parameter vs. Cycles to Failure 38 13. Difference in Principal Bore Stress vs. Cycles to Failure 39 for 1.4 Diameter Ratio 14. Difference in Principal Bore Stress vs. Cycles to Failure 40 for 1.6 Diameter Ratio 15. Difference in Principal Bore Stress vs. Cycles to Failure 41 for 1.8 Diameter Ratio 16. Difference in Principal Bore Stress vs. Cycles to Failure 42 for 2.0 Diameter Ratio 17. Difference in Principal Bore Stress vs. Cycles to Failure 43 for 1.4 - 2.0 Diameter Ratios 18. Pressure vs. Cycles to Failure for 1.4 t 2.0 Diameter Ratios 44 19. Ratio of Autofrettaged to Non-Autofrettaged Cycles to 45 Failure vs. Diameter Ratio 20. Diameter Ratio vs. Cycles to Failure at Various Differences 46 in Principal Bore Stress Levels 21. Differences in Principal Bore Stress vs. Cycles to Failure for 47 Autofrettaged Cylinders Showing the Effect of Thermal Treatment 22. Typical Fatigue Fractures 48 23. Difference in Principal Bore Stress vs. Crack Depth/Thickness 49 TABLE 1. Compilation of Data 20 4 LIST OF SYMBOLS P Plastic Hrp Tangential residual plastic )rrp Radial residual plastic )c Confidence level Least squares value of function 6 INTRODUCTION The current trend is towards the design of pressure vessels for use at higher operating stress levels. One of the most common techniques for extending the elastic load carrying capacity is by autofrettage. For example, the operating pressure to weight ratio for cannon type weapons has been substantially increased in recent years by the combined use of high-strength materials and autofrettage. Similar advances have been made in other areas where the requirement exists for vessels capable of operating at very high pressures. In many instances, the operation of highly stressed pressure vessels is cyclic in nature. In these instances, it is not enough to consider the yielding characteristics alone, but one must also take into account the problem of fatigure life and the manner in which it is affected by such techniques as autofrettage for increasing elastic load carrying capacity. This report summarizes the results of an experimental program aimed at the study of the fatigue characteristics of high-strength open-end cylinders of intermediate diameter ratio. The fatigue characteristics of closed-end cylinder cyclically stressed in the region of the endurance limit has been reported by Morrison^1). He has found that, in the region of the endurance limit, the residual stresses associated with overstrain substantially enhances fatigue life. Similar results were found by Newhall and Kosting(2) for several rifled sections of cannon tubes, at somewhat higher stress levels. In light of the current interest in the use of highly stressed pressure vessels, the investigation to be described herein involves a study of fatigue characteristics of thick-walled cylinders in what is commonly referred to as the low cycle fatigue range, that is, up to approximately 10^ cycles to failure. Presented are data for open-end cylinders in the diameter ratio range of 1.4 to 2.0 at a nominal yield strength level of 160,000 pounds per square inch. Data is also presented on the effects of autofrettage on fatigue characteristics as a function of diameter ratio and cyclic stress level. The possibility of utilizing a simple tensile fatigue test to predict the life of thick-walled cylinders, and the mode of fatigue fracture for cylinders exposed to cyclic internal pressures is discussed. PROCEDURE Test Specimens The specimens utilized in this program consisted of a common one-inch internal diameter and diameter ratios of 1.4, 1.6, 1.8 and 2.0. The specimen material was of a 4340 type composition with the following nominal chemical analysis in percent: 7 Carbon 0.37 Nickel 2.39 Manganese 0.72 Chromium 0.98 Silicon 0.28 Molybdenum 0.38 Sulphur 0.035 Phosphorous 0.016 Specimens were heat-treated to a nominal yield strength of 160,000 pounds per square inch by austenizing at 1525°F; oil quenching, and tempering at 1075°F + 25°. Tensile and Charpy test specimens were taken from each group of three specimens which were heat-treated in 40-inch lengths. After heat treatment, sufficient material was removed from the bore to eliminate any decarburization. The final surface finish on the internal diameter ranged from 16 to 125 RMS. The autofrettaged specimens were overstrained 100 percent in the manner described in reference (3). Those specimens that were thermally treated after autofrettage to reduce anelastic effects were subjected to a temperature of 675°F for 6 hours. Test Apparatus The pressure systems used in this program consisted of two basic types. The first type is a Harwood Engineering Company system of 80,000 pounds per square inch capacity with a cyclic rate of up to 20 cycles/minute. As shown in figure (1), the pressure source consists of an intensifier-type pump which feeds high-pressure fluid into the specimens through a manifold shown in figure (2). As can be noted, four specimens may be tested simultaneously. The holding press serves to support the pressure packings which effectively eliminates longitudinal forces in the specimen; thus, resulting in the open-end condition for the specimens. Upon attaining the peak pressure, a valve is opened and the pressure dropped to near atmospheric level. The high-pressure fluid is an instrument oil. A schematic of this system is shown in figure (3). The second type is a Harwood Engineering Company system of 150,000 pounds per square inch capacity with a cyclic rate of up to 10 cycles/ minute. As shown in figure (4), it also consists of an intensifier-type pumping system which feeds pressure into the specimens. In contrast to the former system, the pressure is released by removing the drive pressure in the intensifier instead of venting to atmosphere; thus, resulting in a closed system. This results in the pressure not returning to zero between cycles, but to a value of approximately 2,500 pounds per square inch. However, since this system is used primarily above 80,000 pounds per square inch, a small residual pressure will have little effect, and the comparative results from both systems are in the range of anticipated experimental error. A schematic of this system is shown in figure (5). 8 Instrumentation Pressure Control and Recording In the 80,000 pounds per square inch system, pressure measurement is by means of Manganin wire-type pressure transducers. Two sucli transducers are used. One serves as input to the "Rotax" control unit which regulates the automatic cycling of the pressure system through a self-balancing "servo" system equipped with electrical contacts and recording pen. The setting of control contacts relative to the desired indicated pressure determines the point of opening and closing of the dump valve as well as stopping the main intensifier at the end of each pressure peak. The second transducer is used to monitor and record the total pressure cycle on an oscillographic recorder. The second basic type of pressure transducer, known as a bulk modulus cell, is used in the 150,000 pounds per square inch system. It is a mechanical device designed to sense the linear motion produced by a cylinder with one end closed and exposed to the pressure being measured. This particular system uses a low-pressure air transmitter and receiver unit to remotely record and control peak and minimum specimen pressure. The error in the measurement and recording of pressure is estimated to be approximately one percent in the calibration of the pressure transducer and two percent in the recording system due to the cyclic conditions. Strain Measurement and Recording To insure that each specimen is at the anticipated test pressure, two strain gages are mounted diametrically opposite each otiier at the mid-length of each specimen. The output of one gage on each specimen is monitored on an oscillographic recorder. In normal operation the instruments are set to record the full elastic strain cycle. The recording system, along with the control panel for the 150,000 pounds per square inch system, is shown in figure (6). THEORY Fatigue failure can be divided into two phases. The first phase consists of the microscopic initiation of the crack. The second stage consists of the propagation of the fatigue crack to the point where the specimen or component can no longer support the applied cyclic load and failure occurs. To a great extent, this second stage is dependent upon the applied tensile stress and; therefore, would be affected by superimposed mean or residual stresses and stress gradients. It is this second stage that will be of primary concern in this paper. o It is well-known that a compressive mean stress increases the allowable cyclic stress amplitude for a given fatigue life. Conversely, a mean tensile stress decreases the allowable amplitude stress as shown in the following diagram from H. Sigwart(4) where & m is the mean and ff the cyclic stress. 9 In an overstrained thick-walled cylinder, the tangential and radial residual stress distribution is described by the relationshipsbased on the Tresca yield criterion: trp = and & rrp = [b2 + R2 2 lOg n" R b2 ( ~2--+2 log (1) i 2 D2 b - R + 2 log ,2 - a2 V ? ? b - R „ , R -jl— . 2 log - ■x ■ i (2) For the 100 percent overstrain condition, i.e., R = b, these relationships become: 10 * trp - V ^ ♦ 2 log £ - (2 loS 0 0 + £)]......(3) and * rrp-^1 £ (2 log^) ......(4) Equations (3) and (4) arc shown in figure (7) for a 2.0 diameter ratio in the 100 percent overstrain condition. As can be seen, the tangential residual stress is compressive at the bore. In view of the compressive residual stress, it would be expected that the overstrained, or autofrettaged, cylinder will withstand a higher cyclic pressure for a given life or a longer life for a given stress level than the non-autofrettaged cylinder. Since, for the 100 percent overstrain condition, the magnitude of the residual stresses increases with diameter ratio, it would also be expected that the increased life due to autofrettage would also increase with diameter ratio. By equating the tangential residual stress to the yield strength of the material in compression, it is found for the 100 percent overstrain condition; assuming the simplified maximum shear stress yield criterion, that beyond a diameter ratio of approximately 2.2, the cylinder will reverse yield upon the release of the overstrain pressure. Theoretically then, the increase in fatigue characteristics due to autofrettage will approach a maximum at the 2.2 diameter ratio level. As will be shown however, due to what appears to be the Bauschinger effect, this critical diameter ratio appears to be in the range of 1.8 - 2.0 instead of 2.2. RESULTS AND DISCUSSION Analysis of Various Cyclic Parameters for Use in Presenting Fatigue Data In the presentation of fatigue data for thick-walled cylinders, several cyclic parameters may be plotted against life in terms of number of cycles of failure. How the fatigue data for the non-autofrettaged cylinders appears when plotted in terms of various cyclic parameters is shown in figures 8 through 12. For simplicity in comparing the various cyclic parameters, only the least squares line for each diameter ratio corresponding to the regression of the cycles to failure on the pressure or stress level along with the correlation coefficient (equation 6) for all of the data in terms of the pertinent cyclic parameter will be shown in this series of figures. Based on conventional statistical theory, the general relationship describing the least squares line for the regression of x on y is: 11 x = a + b (y - y) ....................(5) where for the purposes of this investigation y = log (cyclic parameter) a = y = ~~—Z log (No. cycles to failure) and n Ix I n n b = (x - x) (y - y) £Cy - y)2 The correlation coefficient (r) is defined by r = E (x - x) (y - y) ...........• • (6) NXlx - ly - and is a measure of the effectiveness or probability of the data being described by the defined least squares line and, as will be shown, is an indication of the relative data spread for the various cyclic parameters. The data could also be statistically analyzed in terms of the regression of y on x. However, because of the high correlation coefficients of the experimental results, varying from .91 to .986, there are only minor variations between the regressions, and only one will be shown. For the purpose of minimizing the effects of minor property variations in the test specimens, and to enable comparison of the results of this work with those of other investigators, all cyclic parameters and the data presented herein will be normalized with respect to the ultimate tensile strength, except where otherwise specified. In the simplest form, the data may be plotted as cyclic pressure versus cycles to failure, as shown in figure 8, for a series of non-autofrettaged cylinders. As can be noted, there are distinctive lines corresponding to each individual diameter ratio. This would be expected since the maximum tangential stress for any given pressure decreases with increased diameter ratio. Figure 9 for the same data shows normalized maximum tangential stress at the bore which is defined as ll JL w2 + 1 ................... (?) UTS = UTS w2 - 1 as a function of cycles to failure. As would be expected, a large amount of the diameter ratio dependence has been removed. It should be noted; however, that the least squares line for the smaller diameter ratio is at 12 a higher value than the larger diameter ratio. This is opposite to what would be expected. The actual initiation of the fatigue crack can probably be predicted by some cyclic stress or strain parameter independent of diameter ratio. The crack, however, must propagate over a larger area in the larger diameter. Intuitively then, the larger diameter ratio should be at a higher stress and life level. Based on this, fatigue failure is probably some function of a combined stress condition instead of a single principal stress. Figure 10 shows the difference in the principal stresses at the bore as defined by ct - &r _ 2 PIV2 j UTS UTS (w2 - l) as a function of the number of cycles to failure. As can be noted, the diameter ratio dependency is again small with the larger diameter ratio logically exhibiting the higher fatigue strength characteristics. Figure 11 shows the data in terms of the normalized octahedral stress as defined by UTS |[«Tt - 2 - -