Definitions

Stress-Strain Diagram

Consider the member shown subjected to an axial load:

If the test sample is subjected to several loads, P, and d measurements are taken, a s versus e curve can be generated. A typical curve for mild steels is:

Definitions

Young's Modulus or Modulus of Elasticity --- ( E )

The value is the slope of a stress-strain diagram up to the proportional limit.

Proportional limit ( s_pl ) ---

The proportional limit is the maximum value of the stress from the stress-strain diagram, where the stress and strain are proportional.

Hooke's Law

The stress is proportional to strain. The constant of proportionality is E so that :

s = E e

Elastic Limit ---

Elastic limit is the maximum stress for a material to behave elastically, - the specimen will return to its original undeformed shape if the load is removed so long as the stress is below the elastic limit.

Yield Point ---

This defined as the maximum stress on stress-strain curve, where there is an appreciable increase in strain with no increase in stress. It is generally easier to determine than the proportional limit or elastic limit and is peculiar to certain types of steel.

Some materials do not exhibit a distinct yield point.

Yield Strength ( s_y )---

It is the stress which induces a specified permanent set. This is useful for materials which have no well defined yield point. The offset method is generally used to determine yield stress .

Modulus of Rigidity --- ( G )

It is constant of proportionality relating shear stress ( t ) to shear strain (g ) ( analogous to Hooke's law)

t = G g

Strain Hardening

It is an increase in stress levels in the stress-strain curve at large deformations before ultimate strength is reached.

Plastic Deformation (Permanent Set)

It is the deformation that remains after the load is removed.

1. Slip is a time independent plastic deformation
2. Creep is plastic deformation which continues to increase under a constant stress and usually occurs at high temperatures in most metals.

Creep limit

It is the maximum stress for which plastic strain will not exceed a specified amount in a specified amount of time at a specified temperature

Ductility

It is the ability of a material to deform plastically two measurements of ductility:

• Percent (%) ultimate elongation of the member
  
  % elongation = ( L_f - L₀ ) / (L₀) * 100.0
  
  
• Percent (%) reduction in area at the location of fracture
  
  % Area = ( A₀ - A_f ) / ( A₀ ) * 100.0
  
  

Ultimate Strength ( s_u ) ---

It is the maximum stress developed in a material before rupture.

Poisson's Ratio ( n ) ---

The ratio of the lateral strain to longitudinal strain when the material is uniaxially loaded.

n = - e_lat / e_long

Endurance limit ( s_e ) ---

It is the maximum completely reversed stress to which a material can be subjected to millions of cycles without failure.

Failure ---

It is a state or condition in which a member or structural component no longer functions as originally intended usually results in failure of the total structure. Types of failure are:

• Elastic (excessive elastic deformation)
• Slip (excessive plastic deformation) ---
• Creep {excessive plastic deformation} --- Creep limit
• Fracture (complete separation of material) ---
• Fatigue (excessive stress reversal) ---

Working Stress ( s_allowable )

It is the maximum stress permitted under design load.

Factor of Safety

F.S. = s_failure / s_allowable = P_failure / P_service

Modulus of resilience ( u_r )

The value of the strain-energy density obtained by setting the stress equal to the yield stress ( s_y ) and calculating the area under the stress-strain curve.

u _t = ( ¹ / ₂ ) E e ² = ( ¹ / ₂ ) s ² / E

Modulus of Toughness ( u_t )

The strain-energy density obtained by integrating the area under the total stress-strain diagram.