Thick-walled Cylinder Theory Research Articles

Larch and white birch growth stresses’ experimental investigation and analysis

In this paper, the equations of tree growth stresses are given by using thick-walled cylinder theory under the assumption that tree trunk is considered as a homogeneous orthogonal anisotropic cylinder. Through a lot of calculation of the experimental data, some figs of growth stresses’ distributions are given, and growth stresses distributions are analyzed.

Formula omitted] Determination—a non-standard approach

The ballizing process of forcing a 19.06 mm diameter tungsten carbide ball through a slightly undersize 18.70 mm diameter bore has been used in the present investigation to determine the fracture toughness of polymethyl methacrylate. The specimen consisted of a 10.65 mm wall thickness thick-walled cylinder. A notch of constant depth was machined on the outer surface in the direction of the axis of the cylinder. The depth of the notch was increased such that when the specimen was ballized, a crack was generated from the notch. The critical crack depth was found to be 2.0 mm. With this depth, fracture toughness of the material was determined using thick-walled cylinder theory together with the appropriate stress intensity factor. Fracture toughness of the material was also determined using standard 3-point bend specimens according to ASTM E399-81 standard procedures. It was found that the result from the ballizing process closely estimated that from the standard test.

External Pressure Loading of Spiral Paper Tubes: Theory and Experiment

A closed-form elasticity solution is developed to predict stresses and strains in spiral paper tubes loaded axisymmetrically. No assumptions are made on stress distributions through the tube wall. Thus, the solution is valid for thick-walled tubes. The validity of this solution is established by comparison with experimental results. Measured strains in tubes subjected to external pressure showed remarkable agreement with the elasticity solution. After experimental verification, the elasticity solution is used to examine stress distributions in paper tubes loaded in external pressure. In both paper and isotropic tubes, the hoop stress dominates the other three stresses. However, the hoop stress distribution in paper tubes was radically different from the isotropic case. In paper tubes: (1) hoop stress was concentrated at the outer wall, especially for thicker tubes and (2) maximum hoop stress remained constant as tube thickness was increased. These differences can be attributed to the extremely small modulus in the radial direction of a paper tube. The hoop stress distributions indicate that isotropic, thick-walled cylinder theory is inapplicable for modeling paper tubes.

Application of finite element methods to the design of prestressed tooling

The finite element method (FEM) was used to calculate stresses and deformations in metalworking tooling. This procedure provides a tool designer with an accurate method to specify the shape of tooling for a net shape forming operation. This method includes effects that the classical design procedure, based on thick wall cylinder theory, does not include.

Stress analysis of dies having multiple shrink rings

The finite element method was used to calculate stresses and deformations in metalworking tooling that utilizes shrink rings. This procedure provides a tool designer with an accurate method to compute the stresses in the tooling and to specify the shape of tooling for a net shape forming operation. This method includes effects that are not included in the classical design procedure, which is based on thick wall cylinder theory. The analysis presented here is applicable for one or multiple shrink rings.

A 100 MHz NMR probe head for hydrostatic pressures up to 200 MPa

The techniques used to record NMR spectra under high pressures fall into two groups: (1) The sample is placed in a glass or quartz capillary which is then pressurized (Z-3); (2) the sample and rf coil are enclosed in an overall metal cylinder (4-7). In the first case the main advantage is that standard NMR equipment can be used: the capillary is simply lowered into the commercial NMR probe head. However, this is counterbalanced by poor filling factors and the fact that capillaries often break at low pressures. For the second case, the much better mechanical properties of some nonmagnetic metals or alloys allow safe handling at higher pressures, at the cost, however, of some electronic changes in the spectrometer system. The device we describe below belongs to the second type. It is a single-coil high-pressure probe head adapted to a spectrometer system which was originally double coil (Varian XL-loo). Designs recently published (4-7) are for single-coil spectrometers. A sketch of the high-pressure cell is shown in Fig. 1. The cell made of Berylco 25 consists of a thick-walled cylinder (A) (i.d. = 8 mm, o.d. = 18 mm, 1 = 70 mm) closed with two plugs (B, C). Dimensions were calculated from tenacity data using the shape-energy hypothesis and the theory of thick-walled cylinders (8, 9). The inner volume of the cell is divided into two concentric chambers which can be filled separately from the outside. The inner chamber (probe volume) consists of a deformable separator (D) made of Vespel. The outer chamber is filled with a noninterfering liquid (e.g., CCL,) to pressurize the probe by deforming the separator which is kept in place by a perforated case (H) made of Berylco. Each plug has a center hole leading to the probe and an excentric bore leading to the pressure transducing chamber. The rf coil body with the separator mounted upon it is firmly attached to the upper plug (B). A cone at the lower plug (C) fastens and seals the probe arrangement. Plug (B) contains the rf feed-through which is sealed by a PA6 cone (G). The general layout of the whole probe is shown in Fig. 2. Commercial nonmagnetic high-pressure tubing (1 mm and l/8 in. o-d.) and valves fastened outside the magnetic field complete the setup. Pressure is applied with a screw press (pressure transducing circuit (I)). If corrosive samples are studied, the sample loop (K) should

Burst Resistance of Pipe Cemented Into the Earth

Abstract A mathematical study has been made of the amount of support a cement sheath could provide to casing cemented into the earth. Several assumptions were required to make the analysis, but only two of them are limiting:the pipe must be completely surrounded with cement, andany mud filter cake between the cement and formation has the same physical properties as either the cement or formation. The calculations showed that little support would be provided to the pipe before an unsupported cement sheath failed in tension; however, when the cement is confined between the pipe and wellbore and is loaded in compression, the pipe could receive a considerable amount of support. In fact, the theoretical results indicate the lower grades and larger sizes of pipe could have their working pressures doubled when reasonable compressive loads were applied to a surrounding cement sheath. These data are shown in six charts. Other down-hole conditions such as setting the cement under pressure, increased temperature and cement confinement all tend to increase the potential usefulness of the sheath. Because of size limitations, a laboratory program to verify the most important results of this mathematical study would be very difficult. However, small-scale field tests would be practicable. This paper shows that, if a solid cement sheath can be obtained in the field by either primary cementing or by repair after detection of flaws by surveys such as the new cement-bond logs, the use of this approach to reducing pipe costs merits further consideration. Introduction A modification in casing design practices is proposed which may either reduce the amount and grade of steel required to contain a specified internal pressure or permit the working pressure to be increased for a specified weight and grade of pipe. One of the more important considerations in casing design is its resistance to collapse; however, Bowers' and, more recently, O'Brien and Goins have shown many casing programs are unnecessarily conservative in this respect, and they have indicated how savings can be made by designing for more realistic down-hole conditions. Earlier, Saye and Richardson showed that pipe costs could be reduced by considering the cement sheath as a part of the casing string when collapse resistance was being calculated. More recently, Rogers has raised the question as to whether a cement sheath might be considered in the design for burst resistance of the cemented casing. Calculations have been made for the increased burst resistance a cement sheath would provide for casing in a wellbore, and the results show that a sizable amount of support could be obtained in some instances. These data are presented in addition to a discussion of several other factors that are considered to affect the burst strength of pipe supported by cement. Two types of support are treated: Case I for tensile loading of the unconfined cement sheath, and Case II for compressive loading of the confined cement sheath. ANALYTICAL TREATMENT AND RESULTS CASE I-TENSILE STRESSES IN AN UNCONFINED CEMENT SHEATH Conditions like this would most likely occur in a greatly enlarged portion of the hole where the cement was not in immediate contact with either the formation or a thin and hard mud cake. The mathematical analysis for this condition, as shown in the Appendix, rests on the following concepts. Pressure inside a unit length of pipe causes:a tensile or tangential stress to be exerted over the longitudinal cross-sectional areas of the pipe and cement; andan equal amount of strain in both the pipe and cement that is uniformly distributed over the wall thickness of each. This analysis was then used to make several calculations for a cement sheath around 5 1/2-in. OD pipe. The results are illustrated in Fig. 1, which shows that a tensile stress of 500 psi is imposed on a 5-in. thick sheath when the casing contains a pressure of only 1,450 psi. It also shows that a 10-in. thick sheath would be stressed to 500 psi in tension when the pipe contained a pressure of only 2,350 psi. Alternatively, if the stress analysis is made by means of the Lame thick-wall cylinder theory, the inner fibers of the 10-in. thick sheath will be stressed to 500 psi in tension when the pressure in the pipe is only 990 psi. This, of course, reveals that an unconfined sheath is of little support to the pipe in burst; however, an entirely different result is obtained when the cement is confined between the pipe and formation. JPT P. 1033^

Closure to “Discussion of ‘Partially Plastic Thick-Walled Cylinder Theory’” (1952, ASME J. Appl. Mech., 19, p. 569)

Closure to “Discussion of ‘Partially Plastic Thick-Walled Cylinder Theory’” (1952, ASME J. Appl. Mech., 19, p. 569)