Today we will be covering:
 Stress
 Strain
 Young Modulus
 Graphs of Deformation (StressStrain)
 Elastic & Plastic Deformation
Let’s go!
Objects under deformation (whether it is tensile or compressive) experience STRESS & STRAIN.
These depend on the force, crosssectional area, initial length, extension, & rigidity of the material.
What is Stress?
Force acting per unit perpendicular crosssectional area.
It is denoted by the symbol σ (sigma).
σ = F/A
In units, N m^{2} or Pa (Pascals, like pressure).
If the object’s crosssectional area remains constant, stress is proportional to load.
What is Strain?
Change in length (extension, e) per unit original length.
It is denoted by the symbol ε (epsilon).
ε = e/l_{o}
It has NO UNITS: it is only a ratio of two lengths.
Strain can presented as an ABSOLUTE VALUE:
a/b = 0.01/1.00 = 0.01
OR as a PERCENTAGE:
a/b x 100 = 0.01/1.00 x 100 = 1%
What is the Young Modulus?
Stress experienced per unit strain of a body when it is subjected to a constant force.
It is denoted by the letter E.
The Young Modulus represents the RIGIDITY of the material used to make the body.
Different materials have different Young Moduli, & 2 objects made of the same material both have the SAME Young Modulus (rigidity).
Young Modulus = stress/strain
E = σ/ε
In units, N m^{2} or Pa (Pascals).
Determining E
You can carry out a tensile test & plot a StressStrain graph (see below) to find the Young Modulus of an object:
E = σ/ε
σ = Eε
With stress as the yaxis, strain as the xaxis, the gradient is the Young Modulus.
You can also use the Spring Constant of an object to find the Young Modulus of its material (if you also know the initial dimensions of the object):
E = σ/ε
E = F/A x l_{o}/e
E = Fl_{o}/Ae
Since F/e = k,
E = k(l_{o}/A)
What is Elastic & Plastic Deformation?
Elastic Deformation  Plastic Deformation 
Deformation wherein an object can return to its original size after the applied load is removed.
The object tends to extend proportionally to the force applied. 
Deformation wherein an object cannot return to its original size after the applied load is removed.
The object extends more per unit increase in load than elastic deformation. 
StressStrain Graph
What’s happening here?
 OA: Initially, the object extends according to Hooke’s Law.
The stress (force per unit area) is proportional to the strain (ratio of extension).  A: It reaches the proportionality limit, & no longer obeys Hooke’s Law above that.
 L: It reaches the elastic limit, & the object can no longer return to its original size after load is removed
 B: It reaches the yield point, & the object begins to behave plastically.
 C: It reaches the maximum stress.
 D: It reaches the ultimate tensile stress. The object breaks.
Proportionality Limit  Maximum point of extension where a body obeys Hooke’s Law 
Elastic Limit  Maximum point of extension where a body can still behave elastically (return to its original size after an applied load is removed) 
Yield Point  Point at which a material begins to behave plastically (extends more per unit increase in load than before) 
Maximum Stress  Maximum stress which the object experiences 
Breaking Stress / Ultimate Tensile Stress 
Maximum stress which can be applied to a material before it breaks 
Graphs of Ductile, Brittle & Polymeric Materials
Material  Behaviour  Graph 
Ductile 


Brittle 


Polymeric 

⇐ Previous in Physics: Deformation & Springs
⇒ Next in Physics: Strain Energy