THEORIES OF FAILURE /YIELDING
Theories of failure
Ultimate Aim DESIGN
Failure material failure
Uncertainties
Material
Loading ,Geometry
Ignorance
Mathematical limitations etc.
Simplified Criteria
Theories of yielding
Principal stress
Principal strain
are extremum
1. Maximum-Principal Stress Theory
More useful for Brittle material ,is also called Rankine criteria for failure.
2. Maximum-Principal Strain Theory
In case of compressive state of stress
3. Maximum Shear Stress Theory
is called Tresca theory useful for ductile material--- cup and cone in simple tension 45
^{0 Tresca theory fails in hydro static state of stresses }
4. Total strain energy theory --( Beltrami & Haigh)
5. Shear or Distortion Strain Energy Theory