a) identifying elastic limit, proportional limit, yield strength, and modulus of elasticity and

b) defining Hooke’s law and applying it to that portion of the curve where it is valid.

 

 

Elastic limit is the limit along the stress-strain curve when the tested sample starts deforming permannnently.

Proportional limit is the point along the stress-strain curve when the curve starts deviating from the straight line part. It means that Hooke's law is valid up to the proportional limit. Even though the proportional limit has been exceeded, the material may still recover completely when the load is removed as long as the elastic limit has not been exceeded. In other words, the elastic limit is generally higher than the proportional limit.

The elastic limit, or the true yield strength, is difficult to determine experimentally. Because of these difficulties, the yield strength is often determined by use of a certain set-off strain value. For example, one can set of 0.5% along the strain axis and draw a line parallel to the straight-line part of the stress-strain curve. The point where the drawn line intercepts the stress-strain curve is called the 0.005 off-set yield strength.

Modulus of elasticity is a measure of the interatomic bond strength. High bond strength means high modulus, and high modulus suggests that the material has a high melting point and a low thermal expansion.

Hooke's law says that stress is proportional to strain. The proportionality constant is called the modulus of elasticity. This relationship is written as:

Stress = Modulus of Elassticity * strain