I
EDWARD SAIBEL Rensselaer Polytechnic Institute, Troy,
N. Y.
Failure of Thick-Walled Pressure Vessels Simple tests do not provide adequate data for autoclave design
THE
NEEDS of research and industry in the high-pressure field are constantly increasing, demanding high-pressure vessels that call for the utmost skill and caution in their design. Unfortunately, knowledge of theories of failure of materials is in such an elementary state that the design of very high-pressure vessels becomes almost more of an art than a science. Nevertheless, there have been established some more or less well founded principles which assist in their design ( 2 ) .
Design limitations Failure is assumed to occur either by plastic flow or fracture, or possibly a combination of both. For obvious reasons, tests involving only simple stresses or a combination of simple stresses are carried out to determine when failure takes place; on the basis of these tests, criteria of failure are established. Actually what is determined is either yielding on a macroscopic scale or the initiation of macrocracks. In order to use these criteria which are usually in the form of limitations on stress or on some combination of stresses, it is necessary to know the state of stress in the complex system under examination-namely, the pressure vessel. This, however, can be found only approximately. For example, in the case of thick cylinders, the Lam6 formulas which are used may give accurate results in the central portion away from the ends of the vessel, for the stresses due to the internal pressure, but near the ends of the cylinder, the stress system is quite complicated. Various approximations have been used to get more accurate results. Also, in the neighborhood of cut-outs, holes, slots, and threads, the stress distribution cannot be determined accurately, nor can stress calculations be other than nominal for stresses in the longitudinal direction. To further complicate the situation, the criteria for failure depend on many other factors such as temperature, rate of loading, prior strain, atmosphere, cycling, and time. The last two are
generally referred to as fatigue and creep, respectively (7). Thus, the stress calculations are really nominal and as they are macroscopic constitute only average values. Plastic flow and fracture originate locally and are dependent upon conditions at some very highly localized region which may be critical. I n fact, two separate criteria are of the utmost importance-one is the criterion for the initiation of either plastic flow or fracture and the other is that for the continuance of the plastic flow or the propagation of the crack after its initiation. This leads us to a study of microscopic conditions and brings such factors as metallurgical structure and heat treatment into the picture. Theories of Macroscopic Fracture The basis of macroscopic theories of fracture at the present time is generally the theory of Griffith. There is some controversy in this matter. Although nobody claims that the Griffith theory is the final answer, or even claims that there will be any final answer, this concept is still the simplest and best approach for a macroscopic quantitative treatment. This theory assumes that cracks or
microcracks already exist in the body. O n the basis of an energy criterion, the tensile stress T necessary to propagate the crack is given by
T
=
(4)112. E is
the modulus of elasticity of the material, y is the surface energy, and G is the crack length. This, however, leads to strength values several orders of magnitude higher than those found in practice. Without the concept of the preexisting crack, it is difficult to understand the discrepancy between theoretical and actual values of strength. This difference ranges from one to several orders of magnitude. In the Griffith formula given above, if for c one substitutes the atomic spacing, the ideal strength of the material is about E/lO. This can almost be attained in the caee of glass fibers where freshly drawn fibers in a vacuum have attained strengths of about 106 p.s.i. The Griffith criterion is based on purely elastic behavior. In the case of metals and, in particular, polycrystalline materials, fracture is accompanied by plastic flow, even in what is termed brittle fractures. Brittle fracture is characterized by a flat break caused by normal stresses and results in a break of granular appearance. A relatively small amount of
Recommendations on Testing Materials for a Pressure Vessel Naturally, one wishes to get adequate information with a minimum of testing. What constitutes adequate information depends upon safety as well as the economics of the situation. I n general, it is very difficult, if not impossible, to duplicate by means of simple tests the exact conditions to which the pressure vessel will be subjected, and it will be necessary to draw conclusions from insufficient information. No hard and fast rules can be laid down to cover all cases, but it should be obvious that the closer one can come to actual conditions in the test, the more information he will have and the better the chances of success in his design. ~
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Table I.
Longitudinal Tests Room Temp. 750' F. Initial material Annealed Initial material Annealed 144,000 136,500 165,000 174,000 123,000 110,000 135,000 154,000 15.0 16 16 13.5 59.6 57.3 43.7 43.2
Tensile strength, p.s.i. Yield strength, p.s.i. Elongation, yo Reduction in area, %
Table II.
Results of Testing on Failed Autoclave Body
All tests located as close as possible to bore.
All notches on impacts toward the I.D.
Longitudinal Tests Tensile 72' F. Ultimate, p s i . Yield (0.2y0),p.s.i. Elongation, r0 Reduction of area, % Impact, 72 72 212 212 300 325 330 400 750 750
O F .
Tangential Tests 159,750 129,000 5.5 11.9
162,000 131,000 15.5 38.2
Ft. Lb. 3.0 1.5 15.0 14.0 24.0 26.0 27.0 41 .O 43.0 45.0
Fiber, % 0 0 0 0
Ft.Lb.
Fiber, yo
3.0
0
... ... ... ... ...
35 45 50 95 100 100
17.0 31.0 27.5 31.0
... ... ... ...
energy is absorbed from the system, over-all ductility is low, but on the surface of the crack, large plastic flow which is highly localized may be seen. Of particular concern are the conditions under which the transition from ductile to brittle behavior occur since brittle behavior is catastrophic in nature. Materials cannot be classified per se as either brittle or ductile but exhibit brittle or ductile behavior depending on the conditions under which they are used. Thus they should be tested under conditions as close to actual service as is possible. Orawan (3) has modified the original Griffith concept to take this plastic deformation into account, suggesting that the formula be modified to T =
[""
Yp)]li2
strain energy. Furthermore, since y p >> y, the surface energy may be neg-
Figure 1.
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Details o f the pressure vessel which failed
r$]'".
..*
lected
50 100 100 100
Since it has not been found possible to predict the volume affected by plastic flow, y p serves as an experimental factor with which to modify the Griffith formula. The term yp is temperature dependent and is large above the transition temperature so that to make a crack grow 7 must be large in this region. Below the transition temperature, y p is small and the stress necessary to cause a crack to progress is small. The transition temperature is usually found from notched impact tests in which the energy absorbed during fracture is measured as a function of temperature. Considerable scatter is found in such tests, and usually the drop in energy absorbed with decrease of temperature occurs over a range and,does not take place at a sharply defined temperature ( 4 ) .
resulting
Mechanism
B-l/2" DIA.
where y p is the plastic
in
T
=
of Crack Propagation
I t is useful to separate the problem into two parts-the conditions under which a crack forms and the conditions under which the crack propagates. It is reasonable to suppose, as Griffith did, that cracks exist in the body in one form or another. The main concern here is with the conditions for the propagation of these cracks. I n the model of Griffith, the body was considered elastic, containing potential energy in the forms of strain energy. The strain energy is stored in the body by virtue of the work done by the externally impressed forces. Some strain energy may exist as residual stresses due to conditions existing before the body was loaded. If the body were purely elastic, strain energy would be available for the creation of fresh surface, that is for the propagation of the crack and the kinetic
INDUSTRIAL AND ENGINEERING CHEMISTRY .
H I G H - P R E S S U R E VESSELS energy associated with the dynamics of the propagation. If, however, plastic deformation occurs, the role played by surface energy beA possible comes relatively minor. mechanism for the propagation of the crack fallows. At the root of the crack, the stresses become very large, and a zone of plastic deformation forms at the root. As the crack propagates, this region unloads, but some permanent deformation is left. Another region of plastic deformation forms and is partially relieved, and so the process continues. If the plastic layer is considered to be of uniform thickness, the energy dissipated can be calculated and the same sort of energy balance set up as was done in the Griffith theory-the only difference being in the use of the magnitude of the dissipated energy instead of the energy of formation of new surface. In this manner, such questions as critical crack length, minimum rates at which energy must be fed to enable cracks to propagate, and minimum elastic stress levels for crack propagation may be calculated.
The strain energy, including that which has been stored from residual stress systems, is also available to assist in chemical reactions which may take place and which may affect fracture propagation. One such fracture ( 5 ) appears to have arisen from this source.
A Particular Case of Fracture
Figure 2. The fractured vessel. Note the brittle nature of the fracture. Also note that the fracture occurred in a region where the nominal (average) longitudinal stress in the cylinder was least
Properties of Initial Autoclave. The first example of a failure is the vessel shown in Figure 1. This was made from a 4140 Steel having the following composition: C, 0.44; Mn, 0.92; P, 0.011; S, 0.011; Si, 0.27; Ni, 0.16; Cr, 1.00; and Mo, 0.55. Ultrasonic tests indicated no discernible flaws. The mechanical properties before testing are given in Table I. I n this condition the cylinder was subjected to a hydrostatic test a t ambient temperature (about 70' F.). Water, with a small percentage of emulsifying oil, was used to develop the pressure. When the hydrostatic pressure reached p = 38,500 p.s i., the cylinder failed with disastrous results, Figure 2. At this internal pressure, the usual calculations showed the maximum wall stress to be 56,000 p s i . , less than half the yield stress and presumably safe. The fracture appeared to have originated at the base of the first thread where stress calculations were purely nominal because of notch conditions. Details of the fracture are shown in Figure 3. The failed body was then subjected to a series of tests the results of which are shown in Table 11. These tests were made of specimens located as close as possible to the bore. O n the impact tests, all notches were toward the inside diameter, Figure 4. I t is not quite clear what the transition temperature is, but a 50% fibrous fracture is not reached until the temperature is 330' F.
Figure 3. Close-up of the fracture. seen at the right
The probable origin of the fracture may b e
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used in the autoclave. Actual service conditions are much less severe in that the full load is not applied until the vessel has reached about 500’ F.
7.
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90 ..
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2
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literature Cited
35
(1) Cottrell, A. H., in “Theoretical Aspects of Fracture,” Felbeck Averbach and Thomas Hahn, eds., pp. 20-53, Technology, Cambridge, Mass., and Wiley, New York, 1957. (2) Mott, N. F., in “Theories of Fracture in Metals,” R. Grammel, ed., pp. 53-9, Springer, Berlin, 1956. (3) Parker, E. R., “Brittle Behavior of Engineering Structure,” p. 64, Wiley, New York, 1957. 16 id.,p. 108. 5) Saibel, Edward, IND.ENG. CHEM.53, No. 7, 56A (1961).
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RECEIVED for review April 24, 1961 ACCEPTEDSeptember 19, 1961
72O
150. ZOOo
3000
I t does seem probable, however, that a combination of unfavorable circumstances had occurred: the presence of a notch and a temperature below the notch transition. Redesigned Vessel. T h e properties of the steel were then changed by the appropriate heat treatment to bring about a more ductile behavior. These properties are given in Table I. The design was also modified by the removal of the shoulder. The removal of the shoulder may have helped increase ductility, so unfortunately there is not a clear cut answer to what factor or factors improved the design. Ordinarily, it would be thought that this would have a weakening effect, as the removal would raise the nominal (average)
978
500°
4000
600°
700°
800.
stress. However, this may not be the case at all, again emphasizing the importance of local rather than average conditions in the consideration of fracture. The test was carried out again at room temperature, and the pressure was raised to 45,000 p s i . This produced a tangential stress in the wall of about 67,200 p s i . , by LamC’s formula. The test was successful. The increased ductility enabling a relief of stress through plastic flow undoubtedly brought about the improvement. Although increased ductility could have been obtained also by increasing the percentage of nickel, it could not be done in this manner in this particular instance because the nickel reacted with the product to be
INDUSTRIAL AND ENGINEERING CHEMISTRY
Division of Industrial and Engineering Chemistry, 139th Meeting, ACS, St. Louis, Mo., March 1961.
Correction
A Rapid Method for Obtaining Vapor-Liquid Equilibrium Data -Theoretical Aspects In the blurb of this article by R. S. Ramalho, F. M. Tiller, W. J. James, and D. W. Bunch [IND.ENG.CHEM.53, 895 (1961)], the first checked statement, “The experimenter can obtain three points per hour,” is incorrect. I t should read “The entire vapor liquid curve may be obtained in a single experiment lasting 2 or 3 hours.’’ In some cases, more than 50 points were obtained in this period of time.
