Creator:T.E. Davidson and D.P. Kendall Date Created:October 1960 Place Created:Watervliet, New York Keywords:pressure vessel construction,autofrettaged,jacketed Context:report from Watervliet Arsenal ************************************************** AO- Accession No. Watervliet Arsenal, Watervliet, N. Y. STRENGTH AND ECONOMIC COMPARISON OF AUTOFRETTAGED VERSUS JACKETED PRESSURE VESSEL CONSTRUCTION by T. E. Davidson and D. P. Kendall ires Report WVT-RI-6002-1, October 1960, 28 pages, 5 figur 1 table. Industrial Preparedness Measure 8031-4231-03 46100-01. Report Unclassified The theoretical elastic strength of autofrettaged and jacketed thick-wall cylinders is presented in the form of equations and graphs. The mechanism by which both processes increase the elastic strength of a thick-wall cylinder is discussed and illustrated graphically. The advantages of a combination of jacketing and autofret-tage for very thick-wall, pressure vessel applications are discussed and illustrated by a specific example. The economic advantages of autofrettage over jacketing are presented by a cost analysis of two specific examples namely the 175mm Gun, T256 and the 155mm Howitzer T255. UNCLASSIFIED * AD- Accession No. _ ' Watervliet Arsenal, Watervliet, N. Y. Gun barrels STRENGTH AND ECONOMIC COMPARISON OF AUTOFRETTAGED VERSUS JACKETED PRESSURE VESSEL CONSTRUCTION by T. E. Pressure Davidson and D. P. Kendall vessels Report WVT-RI-6002-I, October 1960, 28 pages, 5 figures, Thick-wall 1 table. Industrial Preparedness Measure 8031-4231-03- cylinders 46100-01. Report Unclassified Industrial The theoretical elastic strength of autofrettaged and production jacketed thick-wall cylinders is presented in the form of equations and graphs. The mechanism by which both Stress processes increase the elastic strength of a thick-wall analysis cylinder is discussed and illustrated graphically. The advantages of a combination of jacketing and autofrettage for very thick-wall, pressure vessel applications Distribution . are discussed and illustrated by a specific example. Unl imited The economic advantages of autofrettage over jacKeting are presented by a cost analysis of two specific examples, namely the 175mm Gun, T256 and the 155mm Howitzer T255. UNCLASSIFIED Gun barrels Pressure vessels Thick-wall cylinders Industrial production Stress analysis Distribution Unlimited AD. Accession No. Watervliet Arsenal, Watervliet, N. Y. STRENGTH AND ECONOMIC COMPARISON OF AUTOFRETTAGED VERSUS JACKETED PRESSURE VESSEL CONSTRUCTION by T. E. Davidson and D. P. Kendall Report WVT-RI-6002-1, October 1960, 28 pages, 5 figures, 1 table. Industrial Preparedness Measure 8031-4231-03-46100-01. Report Unclassified The theoretical elastic strength of autofrettaged and jacketed thick-wall cylinders is presented in the form of equations and graphs. The mechanism by which both processes increase the elastic strength of a thick-wall cylinder is discussed and illustrated graphically. The advantages of a combination of jacketing and autofrettage for very thick-wall, pressure vessel applications are discussed and illustrated by a specific example. The economic advantages of autofrettage over jacketing are presented by a cost analysis of two specific examples, namely the 175mm Gun, T256 and the i55mm Howitzer T255. UNCLASSIFIED Gun barrels Pressure vessels Thick-wall cylinders Industrial production Stress analysis Distribution Unlimited AD. Accession No. Watervliet Arsenal, Watervliet, N. Y. STRENGTH AND ECONOMIC COMPARISON OF AUTOFRETTAGED VERSUS JACKETED PRESSURE VESSEL CONSTRUCTION by T. E. Davidson and D. P. Kendall Report WVT-RI-6002-I, October 1960, 28 pages, 5 figures 1 table. Industrial Preparedness Measure 8031-4231-03-46100-01. Report Unclassified The theoretical elastic strength of autofrettaged and jacketed thick-wall cylinders is presented in the form of equations and graphs. The mechanism by which both processes increase tne elastic strength of a thick-wall cylinder is discussed and illustrated graphically. Tlie advantages of a combination of jacketing and autofrettage for very thick-wall, pressure vessel applications are discussed and illustrated by a specific example. The economic advantages of autofrettage over jacketing are presented by a cost analysis of two specific examples, namely the 175mm Gun, T256 and the 155mm Howitzer T255. UNCLASSIFIED Gun barrels Pressure vessels Thick-wall cylinders Industrial production Stress analysis Distribution Unlimited PB 171679 TECHNICAL REPORT WVT-RI-6002-1 SIR£NGTH AND^ECQjm^COMPARI SOU. Of J\UTOFRETTAGED VERSUS JACKETED PRESSURE VESSEL CONSTRUCTION BY T. E. DAVIDSON D. P. KENDALL OCTOBER-1960 INDUSTRIAL PREPAREDNESS MEASURE 8031-4231-03-46100-01 WATERVLIET ARSENAL WATERVLIET, N. Y. PB 171679 TECHNICAL REPORT WVT-RI-6002-1 STRENGTH AND ECONOMIC COMPARISON OF AUTOFRETTAGED VERSUS JACKETED PRESSURE VESSEL CONSTRUCTION BY T. E. DAVIDSON D. P. KENDALL OCTOBER-1960 INDUSTRI AL PREPAREDNESS MEASURE 8031-4231-03-46100-01 WATERVL1ET ARSENAL WATERVL1ET, N. Y. ASTIA AVAILABILITY NOTICE Qualified requestors may obtain copies of this report from ASTIA. DISPOSITION This report will be destroyed by the holder when no longer required. 2 TABLE OF CONTENTS Page List of Symbols 5 Abstract 6 Conclusions 7 Recommendations 7 Introduction 9 Objective 9 Discussion 9 Jacketing 10 Autofrettage 12 Combination Autofrettage and Jacketing 12 Strength Comparison 15 Economic Comparison 18 Applications 18 175MM Gun T256 19 155MM Howitzer T255 19 References 23 Distribution List 25 Figures 1. Summation of Stresses in Autofrettaged and Jacketed Cylinders 13 2. Pressure Factor Versus Diameter Ratio 16 3. Summation of Stresses in Combination Autofrettaged and Jacketed Cylinder ^ 4. 175MM Gun T256 21 5. 155MM Howitzer T255 22 Table 1* Machining Costs - Autofrettaged and Jacketed Construction 20 3 LIST OF SYMBOLS o Stress in pounds per square inch Oy Yield Stress in pounds per square inch E Modulus of Elasticity W Diameter ratio (|j-) P Pressure in pounds per square inch Pif Interface Pressure in pounds per square inch Pj Internal Pressure in pounds per square inch Pf Firing or Operating Pressure in pounds per square inch p P.F. Pressure Factor, — ( ) t Tangential Radial Longitudinal Jacket Liner Residual 5 STRENGTH AND ECONOMIC COMPARISON OF AUTOFRETTAGED VERSUS JACKETED PRESSURE VESSEL CONSTRUCTION Abstract Cross-Reference Data The theoretical elastic strength of autofrettaged and jacketed thick-wall cylinders is presented in the form of equations and graphs. The mechanism by which both processes increase the elastic strength of a thick-wall cylinder is discussed and illustrated graphically. The advantages of a combination of jacketing and autofrettage for very thick-wall, pressure vessel applications are discussed and illustrated by a specific example. The economic advantages of autofrettage over jacketing are presented by a cost analysis of two specific examples, namely the 175mm Gun, T256 and the 155mm Howitzer T255. Gun barrels Pressure vessels Thick-wall cylinders Industrial production Stress analysis DO NOT REMOVE THIS ABSTRACT FROM THE REPORT 6 CONCLUSIONS Autofrettage is more effective than jacketed construction as a means of increasing the elastic load carrying capacity of pressurized thick-wall cylinders. As a result of this greater effectiveness, pressure vessel design based on the use of autofrettage offers the following significant advantages over a jacketed configuration: 1. Decreased weight - For the same yield strength level and allowable elastic operating pressure, an autofrettaged pressure vessel will weigh substantially less. 2. Increased allowable pressures - For the same yield strength level and configuration, the elastic load carrying capacity is greater. 3. Decreased material strength requirements - For the same operating pressure and configuration, the basic yield strength requirements are reduced. Autofrettage offers a significant economic advantage over jacketed construction by eliminating the additional machining and material required in a construction of two or more pieces. For example, unit savings approaching $2500. are possible in large caliber gun tubes. A combination jacketed and autofrettaged configuration may be utilized to extend elastic breakdown pressures beyond available autofirettage pressure capacity. RECOMMENDATIONS To realize the strength and economic advantages of autofrettage over jacketed construction, it is recommended that: 1. Autofrettage be considered ap a substitute for jacketing as the primary method of manufacture for intermediate diameter ratio, pressure vessel applications such as gun tubes, where the production quantities justify the additional tooling costs. 7 2. A combination of autofrettage and jacketing be considered for thick-wall pressure vessel applications where operating pressures exceed 160,000 pounds per square inch. T. E. DAVIDSON Chief, Metal Working Section D. P. KENDALL Approved: P. K. RUMMEL Chief, Industrial Processes Branch jjLhcAAL VT V^a-CJU^ HAROLD V. MACKEy Lt. Col., Ord. Corps Chief, Research & Engineering Div. 8 INTRODUCTION As a result of the severe weight limitations and extreme mobility requirements placed on cannon by current and proposed warfare concepts, it has become necessary to consider means for substantially increasing the elastic load carrying capacity of gun tubes. The obvious approach is that of increasing the strength of the materials used in tube construction. Current yield strength levels of 160,000 - 190,000 pounds per square inch, however, are already approaching the limit of materials available for configurations such as gun tubes. The alternative is the use of design concepts and processes capable of increasing the elastic load carrying capacity. Two such techniques are autofrettage and jacketing. The desire to increase the load carrying capacity of pressure vessels is not new. In this connection, over the years, such techniques as bore W - 1 1/l + 3W At the inside surface of the liner "tl - Pt S-!-l - 2Pit -i— (6) W2 - 1 Wx 2 - 1 Substituting the value of Pi{ from equation 5 yields [W2 - 1 2W W2 - 1 -2oy (8) Y Vl + 3W The elastic breakdown condition at the bore from equations 7, 8, and 4 is: p.ri + l_LWl -2ov , W . f lL2 1 "Wj * Vl + 3W2 " ^y2 " 3Pi2 (9) Letting Q - 1 + I-±-I and R = W Vl + 3W2 and squaring equation 9 yields a quadratic equation in P^ Solving this yields: P. = 2QR + VQ2 + | - 3R2 (10) a y Q2 + 3 4 A plot of this equation is shown in figure 2 11 Autofrettage The autofrettage process consists of subjecting the cylinder to internal pressure (overstrain pressure) of a large enough magnitude to cause plastic deformation. The residual stresses resulting from this operation are due to the material near the bore being deformed to a greater extent than that near the outside diameter, i.e. a plastic deformation gradient. When the pressure is released the outside material is prevented from returning to its original position by the bore material, which results in the type of residual stress distribution schematically shown in figure 1A. In diameter ratios below approximately 2.2 optimum autofrettage is obtained when the entire wall is plastically deformed, i.e., the 100% overstrain condition. In this case the maximum internal pressure that an autofrettaged cylinder can withstand without further plastic deformation is theoretically equal to the overstrain pressure. In diameter ratios above 2.2, however, the residual stresses resulting from the complete plastic condition are of such a magnitude that reverse yielding occurs. The maximum allowable, elastic pressure in an autofrettaged cylinder thus approaches a maximum. This relationship will be given later. The magnitude of the pressure required to obtain 100% overstrain has been experimentally determined for steel with a 165,000 pound per square inch nominal yield strength (i) and is given by the following empirical relationship: This relationship, along with the following equation for elastic breakdown pressure in an unstressed monobloc cylinder based on the Von Mises yield criterion, is shown in figure 2. Equation (12) has been experimentally substantiated by ths authors. Combination Autofrettage and Jacketing Maximum autofrettage in diameter ratios greater than 2.2 is obtained when the induced residual stress at the bore equals the yield strength of the material. As previously discussed, in diameter ratios above 2.2 maximum autofrettage can be obtained at less than 100% overstrain. Therefore, as the diameter ratio increases, the interface between the plastic and elastic E- = 1.08 log W (11) P_ = w2 - 1 °y Vl + 3W4 (12) 12 (B) FIRING STRESS (C) TOTAL STRESS Figure 1. Summation of stresses in autofrettaged and jacketed cylinders regions required for optimum autofrettage approaches the bore. This means then, that in very thick-wall cylinders, a high yield strength is required only near the bore with a lower value as the outside surface is approached. This phenomenon makes possible the consideration of a combination auto-frettage-jacketing system for thick-wall pressure vessel applications. To demonstrate the merits of a combination of autofrettage and jacketing, consider the hypothetical case of a pressure vessel, with an elastic operating pressure of 245,000 pounds pes? square inch and bore diameter of two inches. To obtain material with a yield strength of 245,000 - 250,000 pounds per square inch in a configuration common to most pressure vessels is difficult due to the hardenability limitations of steel. Even if material of this strength level were available to allow a single or even a two-piece construction, the inherent low ductility of materials at extremely high strength levels would represent a serious safety hazard from the standpoint of catastrophic failure. Applying the phenomenon discussed in the prior paragraph, only the material near the bore needs to be of maximum strength thus permitting the use of a liner of 245,000 - 250,000 pounds per square inch yield strength with a lower strength jacket. In the case considered, the diameter ratio of the liner and jacket are 2.5 and 3.0 respectively with the yield strength of the jacket being 160,000 pounds per square inch. Remembering that optimum autofrettage is obtained when the magnitude of the induced residual stress in the bore of the liner is equal to the yield strength of the material in compression, it is apparent that the 160,000 pound per square inch jacket is not able to induce a residual bore stress of 245,000 pounds per square inch. Also, if autofrettage alone were used, pressure of this magnitude is well beyond the capabilities of current autofrettage equipment which will attain 200,000 pounds per square inch. The required compressive residual stress then is produced by partially autofrettaging the liner to 190,000 pounds per square inch which will result in the residual stress distribution shown in figure 3A. Then the jacket is shrunk onto the liner with an interface pressure necessary to produce the difference between the required and the autofrettage residual stress i.e. 245,000 - 170,000 pounds per square inch. The final combined residual stress distribution is shown in figure 3B. Figure 3C depicts the algebraic summation of the residual and elastic stresses associated with a 245,000 pounds per square inch internal pressure. 14 In cylinders with a diameter ratio of greater than 2.2 where full autofrettage has been attained i.e., otr = oy the maximum elastic operating pressure is, from equation (l) assuming a = 0 P_ = 5W4 - 2W2 - 1 . . oy 3W4 + 1 U3j The sample configuration considered then, will remain elastic up to a pressure of 245,000 pounds per square inch. If one slightly increases the overstrain pressure for the liner and/or the jacket interface pressure, the resulting residual stress at the bore will exceed the yield strength of the liner material and reverse yielding will occur. However, it is possible to operate such a vessel slightly above the optimum autofrettage pressures i.e., up to the new overstrain pressure, if a small amount of recoverable plastic deformation during operation is not harmful. Strength Comparison Figure 1 shows a comparison of the mechanism by which the residual stresses produced by jacketing and autofrettage increase the elastic strength. For simplicity it is based on the maximum shear stress (Tresca) theory of yielding which is slightly on the conservative side. The same analysis based on the Von Mises yield criterion would give similar results. Figure 1A shows the residual stress distributions which would be produced in a cylinder with a total diameter ratio of 2.0 for both optimum autofrettaged and two-component jacketed construction. Figure IB shows the elastic stress which would be produced by internal firing pressures of 80,000 and 111,000 pounds per square inch if the material was considered to remain elastic at these pressures. Actually, both of these pressures would produce plastic flow if the tube was of unstressed, monobloc construction. By applying the principle of superposition and adding the residual and firing or operating stresses algebraically, figure 1C is obtained. From this it can be seen that the jacketed configuration cylinder will yield simultaneously at the bore of the jacket and the liner at a pressure of 80,000 pounds per square inch. In the autofrettaged cylinder, yielding will occur throughout the wall at a pressure of 111,000 pounds per square inch. Figure 2 represents a plot of pressure factor (P.F.) versus diameter ratio for jacketed, autofrettaged and monobloc construction from equations (10), (11) and (12) respectively. As can be noted and as was shown in figure 1 for a specific diameter ratio, autofrettage offers a significant strength advantage over a two-component jacketed configuration. It should be noted 15 Autofrettaged Jacketed Monobloc Figure 2. Pressure factor vs diameter ratio Figure 3. Summation of stresses in combination autofrettaged and jacketed cylinder however, that as the number of jackets increases, the residual stress magnitude also increases and approaches that for autofrettage. Thus, for a multi-jacketed configuration the difference between the autofrettage and jacketed curve will decrease. It can be shown in fact, that an infinite number of jackets will yield the same results as autofrettage for any given diameter ratio, Economic Comparison The manufacture of pressure vessels, particularly gun tubes, based on the use of autofrettage is generally much less expensive than that associated with jacketed construction. This is due to autofrettage not requiring a separate liner and jacket thus eliminating the machining associated with the jacket. This cost is usually considerable since very close tolerances must be maintained in the bore of the jacket to insure the correct amount of interference between the jacket and liner and thus the correct interface pressure. Another saving that could be realized by using autofrettage is a reduction in forging costs. This is due to only one forging being required instead of two and, if the configuration remains the same, the material strength requirements being reduced. The actual jacketing operation on a small and relatively short pressure vessel is not difficult. However, as the length increases, as in a gun tube, difficulties may arise due to distortion of the jacket which may inhibit the placing of the jacket onto the liner thus increasing the cost. For the purpose of cost estimates, however, it is assumed that the costs of the actual autofrettage and jacketing operations are effectively equal and therefore only the major manufacturing items will be considered. A factor which tends to increase the cost of using the autofrettage process is the requirement for restraining containers and pressure closures and seals. Although this comprises a considerable initial investment, over a reasonably large number of tubes it becomes an insignificant part of the unit manufacturing cost. A new process known as the swaging method of autofrettage(2) is now under development. It will -eliminate the need for restraining containers and also the critical machining of the exterior surface prior to autofrettage. This will result in further cost reductions. Applications To demonstrate both the strength and economic advantage of autofrettage over jacketed construction, two examples will be discussed. In 18 both cases, the configuration will be fixed to that common to a jacketed construction. 175MM Gun T256 This gun tube, as schematically shown in figure 4, is designed as a two-piece construction with both jacket and liner having a yield strength of 160,000 - 190,000 pounds per square inch. Table I depicts the relative costs of this tube for both the jacketed and autofrettaged configuration. As can be seen, the total savings per tube, due primarily to the elimination of the jacket, is $2454.00. Although not included, there may be further savings in basic material cost, as a result of having only a single forging instead of two. As a result of having the configuration fixed, the autofrettaged tube may be fabricated of a lower strength material. Incorporating current autofrettage design factors, the material yield strength requirements may be reduced from 160,000 - 190,000 pounds per square inch to 120,000 pounds per square inch. This reduced material strength will not only enhance forging manufacture but may make possible substantial savings in machining costs as compared to that for higher strength materials. 155 MM Howitzer T255 This gun, as can be seen from figure 5, is substantially smaller than the prior example. In this case, also as shown in table I, savings of $542. 00 per tube due to the elimination of the jacket are possible. 19 OPERATION AUTOFRETTAGED 175MM T256 155MM T255 Machining Tube Before Autofrettage $3,784.00 $ 616.00 Machining Tube After Autofrettage $6,732.00 $1,694.00 Autofrettage Tooling Cost $ 40.00 $ 50.00 (Unit cost based on 200 tubes) ___ $10,556.00 $2,360.00 JACKETED Machining Liner Before Jacketing $3,784.00 $ 616.00 Machining Jacket Before Jacketing $2,494.00 $ 592.00 Machining Tube After Jacketing $6,732.00 $1,694.00 $13,010.00 $2,902.00 TOTAL SAVINGS $2,454.00 $ 542.00 TABLE I. MACHINING COSTS - AUTOFRETTAGED AND JACKETED CONSTRUCTION ^Jacket Length 210. Figure 4. 175mm gun T256 Figure 5. 155mm Howitzer T255 REFERENCES 1. Davidson, T. E., Barton, C. S., Reiner, A. N., and Kendall, D. P., "The Autofrettage Principle as Applied to High Strength Light Weight Gun Tubes", Watervliet Arsenal, Technical Report No. RI 5907, October 1959. 2. Davidson, T. E., Barton, C. S., Reiner, A. N., and Kendall, D. P., "A New Approach to The Autofrettage of High Strength Cylinders", presented at the National Meeting of the Society for Experimental Stress Analysis , Indianapolis, Indiana; May 1960. 3. Timoshenko, S., "Strength of Materials", Part II, D. Von Nostrand Inc., New York, N. Y., 1942. 23 DISTRIBUTION LIST Copies Office of the Chief of Ordnance Department of the Army Attn: ORDIX 2 ORDIR 2 ORDTB 2 Washington 25, D. C. Commander 10 Armed Services Technical Information Agency Attn: TIPDR Arlington Hall Station Arlington 12, Virginia Director 1 National Bureau of Standards Washington 25, D. C. U. S. Atomic Energy Commission 1 Technical Information Service 1901 Constitution Avenue Washington 25, D. C. Applied Mechanics Reviews 1 Southwest Research Institute 8500 Culebra Road San Antonio 6, Texas Commander 1 Air Materiel Command Wright-Patterson Air Force Base, Ohio Director Ballistics Research Laboratory 1 Aberdeen Proving Ground Aberdeen, Maryland Commanding Officer 1 Office of Ordnance Research Duke Station Durham, North Carolina Commanding Officer 1 Redstone Arsenal Huntsville, Alabama Commanding Officer 1 White Sands Proving Grounds Las Cruces, New Mexico 25 Commander Air Force Office of Scientific Research Air Research and Development Command Attn: Directorate of Research Information Washington 25, D. C. Chief of Naval Research Department of the Navy Attn: Mechanics Branch Washington 25, D. C. Director U. S. Naval Research Laboratory Attn: Mechanics Division Washington 25, D. C. Chief, Bureau of Ordnance Department of the Navy Attn: Research and Development Division Washington 25, D. C. Commander Naval Ordnance Laboratory White Oak Silver Spring, Maryland Commander David Taylor Model Basin Washington 7, D. C. Armour Research Foundation Illinois Institute of Technology Chicago, Illinois Library Massachusetts Institute of Technology Cambridge 39, Massachusetts Director of Research Rensselaer Polytechnic Institute Troy, New York Commanding Officer Picatinny Arsenal Attn: Technical Information Section Dover, New Jersey Commanding Officer Detroit Arsenal Center Line, Michigan 26 Commanding Officer Watertovm Arsenal Laboratories Attn: Technical Information Section Watertovm 72, Mass. Commanding Officer Diamond Ordnance Fuze Laboratories Attn: Technical Reference Section Connecticut Ave & Van Ness St., N.W. Washington 25, D. C. Commanding Officer Frankford Arsenal f Philadelphia 37, Pa. Commanding Officer Ordnance Weapons Command Rock Island Arsenal Rock Island, Illinois Commanding Officer Springfield Armory Springfield, Mass. The Ramo-Wooldridge Corporation Attn: Chief Librarian 5730 Arbor Vitae Los Angeles 45, Calif. The University of Texas Defense Research Laboratory P.O. Box 8029 Austin 12, Texas Ohio State University Research Foundation Columbus 10, Ohio Director of Research California Institute of Technology Pasadena, Calif. Convair San Diego Division Attn: Chief, Applied Research San Diego, Calif. University of Southern California Engineering Center 3518 University Avenue Los Angeles 7, Calif. 27 United Aircraft Corporation Research Department 362 Main Street East Hartford 8, Conn. The Pennsylvania State University Department of Engineering Mechanic University Park, Pa. The General Electric Company Research Laboratories Cincinnati 15, Ohio Harwood Engineering Co. Walpole, Mass. National Bureau of Standards Mechanical Instruments Section Washington 25, D. C. Battelle Memorial Research Inst. 505 King Avenue Columbus, Ohio Director of Research Brigham Young University Provo, Utah Office of Technical Services U. S. Department of Commerce Washington 25, D. C. 75377