Lecture 14 Failure of Engineering
Materials
Jayant Jain Assistant Professor,
Department of Applied Mechanics, IIT Delhi, Hauz Khas, 110016
Recap
Condition for fast fracture: energy criteria
cEGa
Understood the toughness, fracture toughness, stress intensity factor
Understood the variation of observed values of these quantities
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
The local stress local is proportional to the number
of lines of force which rises
steeply as the crack tip is
approached
c crack length r distance from crack tip remote stress Y geometric constant
Remote stress applied to a cracked material
* valid when r
Imagine you have a pre-existing crack in ductile material How your material should respond to an external stress?? Examination of fracture surface will reveal extremely rough surface Roughness over surface reveal great amount of plastic work has been done prior to failure
Process Zone
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
A plastic zone forms at the
crack tip where the stress
would otherwise exceed
the yield strength
Size of process zone:
2
Note the variation of plastic zone size with yield strength of material
Ductile Fracture of Cracked Sample
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
If a material is ductile, a plastic zone forms at the crack tip Within the plastic zone, voids nucleate, join, and link to cause fracture The plasticity blunts the crack tip, reducing the severity of the stress concentration
Mechanism of ductile tearing
Imagine you have a pre-existing crack in brittle material How your material should respond to an external stress?? Examination of fracture surface will reveal extremely flat surface
Brittle Cleavage Fracture
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
Characteristic of ceramics and glasses: high yield strength very small plastic zone Local stress rises as 1/r toward the crack tip if it exceeds that required to break inter-atomic bonds they separate, giving a cleavage fracture Little or no crack blunting
Ductile-to-Brittle Transition
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
At low temperatures some metals and all polymers become brittle As temperatures decrease, yield strengths of most materials increase leading to a reduction in the plastic zone size Only metals with an FCC structure remain ductile at the lowest temperatures Steel structures are more likely to fail in winter than in summer
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
Stress required for
fracture for a given
crack length
Crack length necessary
for fracture at a materials
yield strength
A material transitions
from yield to fracture
at a critical crack length
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
Tough metals are able to contain
large cracks but still yield in a
predictable, ductile, manner
Critical crack lengths are a measure of the
damage tolerance of a material
Toughening by Fibers Polymers in general behave more or less like bcc/hcp metals:
rubber band in liquid nitrogen
However, polymer based composites behave differently:
When a crack grows in a matrix, the fibers remain intact
and bridge the crack: fibers as crack stoppers
Embrittlement from Chemical Segregation
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon
Impurities in an alloy are normally found in
grain boundaries this leads to a network of low-toughness paths
that can lead to brittle fracture
Raising the yield strength of material reduces the plastic zone size, hence makes the material less tough Presence of compounds or particles reduces the toughness dramatically Presence of segregation at boundaries forms low toughness paths
Summary of key points
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