R&DE (Engineers), DRDO
Theories of Failure
rd_mech@yahoo.co.in
Ramadas Chennamsetti
Summary
R&DE (Engineers), DRDO
Maximum principal stress theory Maximum principal strain theory Maximum strain energy theory Distortion energy theory Maximum shear stress theory Octahedral stress theory
rd_mech@yahoo.co.in
Ramadas Chennamsetti
2
Introduction
R&DE (Engineers), DRDO
Ramadas Chennamsetti
3
rd_mech@yahoo.co.in
Failure occurs when material starts exhibiting inelastic behavior Brittle and ductile materials – different modes of failures – mode of failure – depends on loading Ductile materials – exhibit yielding – plastic deformation before failure Yield stress – material property Brittle materials – no yielding – sudden failure Factor of safety (FS)
Introduction
R&DE (Engineers), DRDO
Ductile and brittle materials
σ σY
σF
σY
σ
σF
εe
εp
Ductile material
ε
0.2% ε Brittle material
ε
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Well – defined yield point in ductile materials – FS on yielding No yield point in brittle materials sudden failure – FS on failure load 4
Ramadas Chennamsetti
Introduction
R&DE (Engineers), DRDO
Stress developed in the material < yield stress Simple axial load
σx σx
If σx = σY => yielding starts – failure Yielding is governed by single stress component, σx Similarly in pure shear – only shear stress. If τmax = τY => Yielding in shear Multi-axial stress state ??
5
σx
σx
rd_mech@yahoo.co.in
Ramadas Chennamsetti
Introduction
R&DE (Engineers), DRDO
Various types of loads acting at the same time
T N Axial, moment and torque M
Internal pressure and external UDL
Ramadas Chennamsetti
6
rd_mech@yahoo.co.in
p
Introduction
R&DE (Engineers), DRDO
Ramadas Chennamsetti
7
rd_mech@yahoo.co.in
Multiaxial stress state – six stress components – one representative value Define effective / equivalent stress – combination of components of multiaxial stress...