[Type text][Type text][Type text]CASING MECHANICAL PROPERTIES

FAILURE THEORY OF MATERIALSAs per definition in literature term failure is defined as a change in normal constitutive behavior of the material, usually in response to excessive loads or deformations that cause irreparable changes to the microstructure[Solid Mechanics Part I, Kelly]. Multiple material failure theories are used in solid mechanics to estimate change in constitutive behavior of materials under influence of external loading. Commonly used theories are mentioned below; MAXIMUM PRINCIPAL STRESS THEORYThis theory assumes when maximum principle stress at any point in the material reaches to appropriate failure stress f of the material, it will fail.

This theory holds good for brittle materials such as ceramic or glass.

Graphical representation of theory:All the failure theories can be represented in a single stress-plot. For a representation purpose assume 3 = 0. Analysis: Plot 1 & 2 along the X-axis and Y-axis respectively. When point (1, 2) lies inside the closed curve called as failure locus then material remains elastic. When point (1, 2) lies outside of the failure locus, then failure criteria is satisfied and material is said to be fail.

Figure 1 Maximum Principle stress diagram MAXIMUM SHEAR STRESS THEORYThis theory assumes material failure occurs when the shear stress acting on plane of failure are large enough to shear material along these planes. This plane of failure roughly appears at an angle of 450 to the direction of loading. This theory works best for ductile material. Yield in ductile material usually caused by slippage of crystal planes along the shear stress surface.

Graphical representation of theory:All the failure theories can be represented in a single stress-plot. For a representation purpose assume 3 = 0. Analysis: Plot 1 & 2 along the X-axis and Y-axis respectively. When point (1, 2) lies inside the closed curve called as failure locus then material remains elastic. When point (1, 2) lies outside of the failure locus, then failure criteria is satisfied and material is said to be fail.

Figure 2 Maximum shear stress diagram

THE VON-MISSES THEORYThis theory takes 3-D stresses into account. These stresses namely include radial stress, tangential stress and axial stress acting on body. Three stresses together converted to uniaxial stress called Von-Misses stress in order to compare it with yield stress of the material.

This is most suitable for ductile material. Design of casing string specially uses this theory.Graphical representation of failure theories:All the failure theories can be represented in a single stress-plot. For a representation purpose assume 3 = 0. Analysis: Plot 1 & 2 along the X-axis and Y-axis respectively. When point (1, 2) lies inside the closed curve called as failure locus then material remains elastic. When point (1, 2) lies outside of the failure locus, then failure criteria is satisfied and material is said to be fail.

Figure 3 the Von-Misses Stress diagram