The design of thick walled cylinders for operation at very high

temperatures and pressure is a complex

problem involving various considerations including definition of the operating

and permissible stress levels, criteria of failure, material behavior etc. Generally

problems involving cylinders have been widely used due to their practical

importance. In order to improve the safety and reliability of cylinder under various

thermo-mechanical loads it is really important for engineers to optimize the

design.

Over the last decade, finite element analysis (FEA) stopped being

regarded only as an analyst’s tool and entered the practical world of design

engineering. CAD software now comes with built-in FEA capabilities and design

engineers use FEA as an everyday design tool in support of the product design

process. However, until recently, most FEA applications undertaken by design

engineers were limited to linear analysis. Such linear analysis provides an

acceptable approximation of real-life characteristics for most problems design

engineers encounter. Nevertheless, occasionally more challenging problems

arise, problems that call for a nonlinear approach. Non-linear behavior of solids takes two forms:

material non-linearity and geometric non-linearity. The simplest form of non-linear

material behavior is that of elasticity for which the stress is not linearly proportional

to the strain. More general situations are those in which the loading and unloading

response of the material is different. Typical here is the case of classical

elastic– plastic behavior. The term “stiffness” defies the fundamental

difference between linear and nonlinear analysis. Stiffness is a property of a

part or assembly that characterizes its response to the applied load.

The materials are classified based on the behavior for a particular loading

condition. These are Anisotropic materials, Monoclinic materials, Orthotropic

materials, Transversely isotropic materials and Isotropic materials. Orthotropic

materials are materials whose properties are directionally dependent .Here

Yong’s Modulus change with the direction along the object. There are three

mutually orthogonal planes of material property symmetry in an orthotropic material.

The intersections of these three planes of symmetry are called the principal

material directions. The material behavior is called as especially orthotropic,

when the normal stresses are applied in the principal material directions.

Otherwise, it is called as general orthotropic which behaves almost equivalent

to anisotropic material. Orthotropic materials are a subset of anisotropic

materials, because their properties change when measured from different

directions. Examples of orthotropic materials are wood, many

crystals, and rolled metals. Because of good heat resistance orthotropic bonded

material may work at super high temperatures or under high temperature

difference field. Real materials are not perfectly isotropic. In case of

isotropic material mechanical properties are constant in all direction.

Directionally dependent physical properties of orthotropic bonded materials are

significant due to the affects it has how materials behaves. For example in the

case of fracture mechanics, the way the microstructure of the material oriented

will affect the strength and stiffness of the material in various direction of

crack growth.

Thick walled cylinders are broadly used in chemical, petroleum, military

industries as well as in nuclear power plants .They are usually subjected to

high pressure & temperatures which may be constant or cycling. Industrial

problems often witness ductile fracture of materials due to some discontinuity

in geometry or material characteristics. The conventional elastic analysis of

thick walled cylinders to final radial & hoop stresses is applicable for

the internal pressure up to yield strength of material. General application of

Thick- Walled cylinders include, high pressure reactor vessels used in

metallurgical operations, process plants, air compressor units, pneumatic

reservoirs, hydraulic tanks, storage for gases like butane LPG etc. 1

1.1 Isotropic

Material:

In an isotropic material, properties are the same in all directions

(axial, lateral, and in between). Thus, the material contains an infinite

number of planes of material property symmetry passing through a point. i.e.,

material properties are directionally independent. So, there are two independent

elastic constants. Isotropic materials are those which have the same material properties

in all directions, and normal loads create only normal strains. By comparison, anisotropic

materials have different material properties in all directions at a point in the

body. There are no material planes of symmetry, and normal loads create both

normal strains and shear strains. A material is isotropic if the properties are

independent of direction within the material. For example, consider the element

of a material. If the material is loaded along its 0°, 45°, and 90° directions

and for isotropic material, the modulus of elasticity (E) is the same in

each direction (E0° = E45° = E90°). However, if the

material is anisotropic, it has properties that vary with direction within the

material. In this example, the moduli are different in each direction (E0°

? E45° ? E90°). 2

1.2

Transversely isotropic

Material:

If

a material has axes of symmetry in its longitudinal axis and all directions

perpendicular to its longitudinal axis (i.e., more than three mutually

perpendicular axes of symmetry) then such material is transversely isotropic. (e.g., unidirectional

composites). There are five independent elastic constants for these materials.

1.3

Monoclinic Material:

It

has a single plane of material property symmetry. If xy plane (i.e.; 1-2 plane)

is considered as the plane of material symmetry then, there are 13 independent

elastic constants in the stiffness matrix as given below. As there is a single

plane of material property symmetry, shear stresses from the planes in which

one of the axis is the perpendicular axis of the plane of material symmetry

(i.e.; 2-3 and 3-1 planes) will contribute only to the shear strains in those

planes. And normal stresses will not contribute any shear strains in these planes.

1.4 Orthotropic

Material:

There

are three mutually orthogonal planes of material property symmetry in an

orthotropic material. Fiber-reinforced composites, in general, contain the

three orthogonal planes of material property symmetry and are classified as

orthotropic materials. The intersections of these three planes of symmetry are called

the principal material directions. The material behavior is called as specially orthotropic, when the

normal stresses are applied in the principal material directions. Otherwise, it

is called as general orthotropic which behaves almost equivalent to anisotropic

material. There

are nine independent elastic constants in the stiffness matrix for a specially

orthotropic material. From the stress-strain relationship it is clear that normal

stresses applied in one of the principal material directions on an orthotropic

material cause elongation in the direction of the applied stresses and

contractions in the other two transverse directions. However, normal stresses

applied in any directions other than the principal material directions create

both extensional and shear deformations

In this project the effect of internal

and external pressure and temperature on thick walled cylinder, how radial

stress & hoop Stress will vary with change of radius will be investigated.