STRESSSTRAIN CURVES

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STRESS-STRAIN CURVES
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CONCEPT OF STRESS
CUTCUTCUT ! EQUILIBRIUM EQUILIBRIUM EQUILIB
RIUM !
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CONCEPT OF STRESS
CUTCUTCUT ! EQUILIBRIUM EQUILIBRIUM EQUILIB
RIUM !
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NINE COMPONENTS OF THE STRESS TENSOR
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TRANSFORMATION OF COORDINATES
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TRANSFORMATION OF COORDINATES
Real Plane
tx'y'
Convention for drawing (1) A txy that is
clockwise on a face resides above the s axis a
txy anticlockwise on a face resides below s
axis. (2) An angle q on real plane transfers as
an angle 2q on Mohr's circle plane.
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PRINCIPAL STRESSES COORDINATES
s

• There always exists a co-ordinate system at any
  point of the body, such that the faces of the
  cube only have normal stresses. These stresses
  are called Principal Stresses (s1,s2,s3), and the
  coordinate system is called the principle
  coordinate system at that point.
• Eg. In simple tension, the loading direction and
  any two orthogonal directions constitute a
  principal coordinate system.

• Similarly with Strains

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CONCEPT OF STRAIN
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u
udu
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HOOKE'S LAW IN ELASTICITY
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General Problem
Stresses
Loads
Pi
IF Elastic, Then Use Elastic Stress-Strain
Relations (Hooke's Law)
Strains
d
di
Displacements
Arrows indicate typical mode of problem solving.
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INVARIANTS
Invariants are Scalar Quantities that are
Independent of the Coordinates

• The mean normal stress (sm) or negative
  pressure is 1/3rd. the value of I1 . Here
  s1,s2, and s3 refer to the principal stresses.
• Similarly for strains

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Compression Loading
Forging
Uniaxial Ideal
Multiaxiality Actual
Multiaxiality of Stress
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MULTIAXIAL LOADING DURING PROCESSING