Stress – Strain Curve
Contents
• Basics (Stress and Strain, Hooke’s Law and Young’s Modulus)
• Stress – Strain Curve
• Curves for Different type of material
• Toughness and Modulus of Resilience
What is Stress?
• Stress is restoring or deforming force per unit
area.
• It generally expresses the ‘internal forces.’
• Stress is the effect of strain.
• It is represented by ‘σ’.
• Mathematically,
σ = Force(F)/Area(A)
Its unit is kg.m−1s−2 or Pascal.
What is Strain?
• Strain is the ratio of change in dimensions of body by
its initial dimensions.
• It is the measure of deformation in body after forces
are applied.
• For a rod of initial length ‘L’ and final length ‘l’ , strain
Hooke’s Law And Young Modulus
• Hooke’s law states that the elongation in objects length is directly
proportional to the force applied.
For springs, Fs = kx where, k = spring constant.
• Young’s modulus (E) is the ratio of tensile stress and axial strain of the
body.
It is also known as modulus of elasticity.
Young’s modulus is considered as specific form of Hooke’s law.
Stress Strain Curve
• Stress-Strain Curve is the locus of points that are
plotted for different stresses against the strain for a
given material.
• These curves are extremely important graphical
measure of a material’s mechanical properties.
• These curves are unique for each and every
material.
• These curves are computer generated and are made
using Universal Testing Machine (UTM) or Universal
tester or Tensometer.
• Elastic region – Region where if stress is released from the material, it
will return to its original state.
• Plastic region – Region where if stress is released from the material it
will retain permanent deformation and strain hardening.
• Proportionality limit – The point till Hooke’s law is followed.
• Elastic limit – The point at which additional stress causes permanent
deformation.
• Yield strength – Max Stress that can be developed without causing
plastic deformation. (approx. at 0.2% strain)
• Ultimate strength/stress – The maximum stress that a material can
withstand.
• Fracture limit/point – The point at which a material will fail
catastrophically through fracturing
• Strain Hardening – When a metal is strained beyond the yield point.
An increasing stress is required to produce additional plastic
deformation and the metal apparently becomes stronger and more
difficult to deform.
• Necking – It occurs after a material hits it’s ultimate strength or
stress. At this point the cross sectional area starts shrinking within the
necking region. While the stress in this region is technically still
increasing since the cross sectional area is shrinking,
Necking
Fracture
Stress Strain Curve for Different materials
1.Ductile Materials
These are the materials which have a large
plastic region beyond the elastic limit i.e.,
the breaking point is far away from the
elastic limit.
Iron, copper silver, aluminum, etc. fall
under the category of ductile materials.
Rods of these materials can be drawn into
wires.
Generally shows cup-cone fracture.
2. Brittle Materials
These materials have a very small plastic region so
that their breaking point lie close to the elastic
limit.
Glass, dry clay balls, etc. fall under the category of
brittle materials.
These materials break into pieces on being
beaten.
Generally shows flat fracture.
3. Elastomers
These are the materials for which stress-strain
graph is not a straight line even within the
elastic limit, and the strain produced is in
much larger proportion than the stress.
Such materials have one plastic region, the
breaking point lies just close to the elastic
limit.
Substances like rubber, tissue of aorta etc.
which can be stretched to cause large strains
are called elastomers.
(Fig. from NCERT)
Toughness of Material
The area under the stress-strain curve is
called toughness.
Mathematically,
Modulus of Resilience
• The modulus of resilience is the amount of strain
energy per unit volume (i.e. strain energy density)
that a material can absorb without permanent
deformation resulting.
• The modulus of resilience is calculated as the
area under the stress-strain curve up to the
elastic limit.
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