This paper gives a critical review of theories used for the design of thick-walled cylindrical pressure vessels. An evaluation of experimental studies on such vessels shows that much of the data is incomplete and cannot be used to determine the accuracy of some of the theories proposed. In some cases, the comparison of the remaining test data with the available theories shows poor agreement between theoretical and actual values. In other cases, the theories arc unsatisfactory because they are either empirical in nature, they have an unsound theoretical basis or the assumptions upon which they are based are incorrect. For these reasons, a new theory was developed. This theory is one which considers the plastic range of the material. It determines the maximum or instability internal pressure that can be applied to a thick-walled cylindrical vessel closed at the ends. Based upon this pressure, a design relation is obtained for the determination of the wall thickness.
The theory proposed differs from most other plasticity theories, since it is based upon the true stress-strain tension relation of the material. It differs from all the other theories in considering that finite or large strains are produced and in not assuming that only small strains are produced. Furthermore, the new theory assumes an analytical relation between the tension stress and strain, thereby eliminating the time consuming procedure of numerical or graphical integration required by some of the plasticity theories. A comparison of the maximum pressure, as defined by the proposed theory, with test results shows that it is in approximate agreement with the test data. It can also be noted that the proposed theory is in as good agreement with test data as any of the other theories. Furthermore, it has the merit that it is based upon sounder assumptions than a.re used in other theories.
In order to provide a theory which can be easily applied by the designer, an approximate formula is developed in this paper based upon the proposed theory.
In this study, consideration was also given to types of failure other than instability. The possibilities of failure by shear fracture and cleavage are considered.
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| Number of Pages : | 24 |
| Published : | 1958 |
