Stress-Strain Diagram
Consider the member shown subjected to an axial load:
If the test sample is subjected to several loads, P, and delta
measurements are taken, a sigma versus epsilon 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 ---
- 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 :
- 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 ---
- 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 to shear
strain( analogous to Hooke's law)
- 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.
- Slip is a time independent plastic deformation
- 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 - L_0 ) / (L_0) * 100.0
- Percent (%) reduction in area at the location of fracture
% Area = ( A_0 - A_f ) / ( A_0 ) * 100.0
- Percent (%) ultimate elongation of the member
- Ultimate Strength ---
- It is the maximum stress developed in a material before rupture.
- Poisson's Ratio ---
- The ratio of the lateral strain to longitudinal strain when the
material is uniaxially loaded.
- Endurance limit ---
- 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
- It is the maximum stress permitted under design load.
Factor of Safety
-
F.S. = Actual Strength / Required Strength = Failure Load / Service Load
- Modulus of resilience
- The value of the strain-energy density obtained by setting the stress
equal to the yield stress and calculating the area under the stress-strain
curve.
- Modulus of Toughness
- The strain-energy density obtained by integrating the area under the
total stress-strain diagram.
