COURSE WORK

Course Work



Course Work

Introduction

Elastic modulus is sometimes called Young's modulus after Thomas Young who published the concept back in 1807.  An elastic modulus (E) can be determined for any solid material and represents a constant ratio of stress and strain (stiffness):

Discussion Analysis

A material is elastic if it is able to return to its original shape or size immediately after being stretched or squeezed.  Almost all materials are elastic to some degree as long as the applied load does not cause it to deform permanently.  Thus, the "flexibility" of any object or structure depends on its elastic modulus and geometric shape (Pennington & Nash, 1997:391). 

The modulus of elasticity for a material is basically the slope of its stress-strain plot within the elastic range (as shown in Figure 1).  Figure 2 shows a stress versus strain curve for steel.  The initial straight-line portion of the curve is the elastic range for the steel.  If the material is loaded to any value of stress in this part of the curve, it will return to its original shape.  Thus, the modulus of elasticity is the slope of this part of the curve and is equal to about 207,000 MPa (30,000,000 psi) for steel.  It is important to remember that a measure of a material's modulus of elasticity is not a measure of strength.  Strength is the stress needed to break or rupture a material (as illustrated in Figure 1), whereas elasticity is a measure of how well a material returns to its original shape and size (Lings & Pennington, 2000: 109).

Figure 1: Stress-Strain Plot Showing the Elastic Range

Figure 2: Example Stress-Strain Plot for Steel

Tensile Properties

Tensile properties indicate how the material will react to forces being applied in tension. A tensile test is a fundamental mechanical test where a carefully prepared specimen is loaded in a very controlled manner while measuring the applied load and the elongation of the specimen over some distance (Kuwano & Jardine, 2002: 727). Tensile tests are used to determine the modulus of elasticity, elastic limit, elongation, proportional limit, and reduction in area, tensile strength, yield point, yield strength and other tensile properties.

The main product of a tensile test is a load versus elongation curve which is then converted into a stress versus strain curve. Since both the engineering stress and the engineering strain are obtained by dividing the load and elongation by constant values (specimen geometry information), the load-elongation curve will have the same shape as the engineering stress-strain curve. The stress-strain curve relates the applied stress to the resulting strain and each material has its own unique stress-strain curve. A typical engineering stress-strain curve is shown below. If the true stress, based on the actual cross-sectional area of the specimen, is used, it is found that the stress-strain curve increases continuously up to fracture.

Linear-Elastic Region and Elastic Constants

As can be seen in the figure, the stress and strain initially increase with a linear relationship. This is the linear-elastic portion of the curve and it indicates that no plastic deformation ...