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Griffith’s Theory
Analytical Solution – Inglis (1913)
At A,
For a Circular hole:
For an Elliptical hole with a>>b:
Very large!
For a sharp crack:
Even a crack of small length – will instantaneously grow and break the component Contradiction!!!
Ref: 1
Griffith’s TheorySurface Energy
Interior atoms – attraction or repulsion – more or less uniform in all directions
Energy is required to form new surface – Surface Energy
Atom on free surface – no neighboring atoms on one side
– results in different equilibrium
Griffith’s TheoryEnergy Release
Energy release – parts adjacent to the cracked surfaces
Assumption – energy release from the triangular area
Energy released:
Ref: 1
Griffith’s TheorySurface Energy Required
= Surface energy / unit area / unit surface
Energy required:
AtFor an increase in crack length,
For a crack to become critical,
Ref: 1
Griffith’s TheoryCritical crack length
Substituting for ER and ES, in
Critical crack length
Stress required to advance a crack
Material Surface Energy (J/sq.m)
Copper 0.98
Mild Steel 1.20
Aluminum 0.60
1J energy will raise the temperature of one teaspoon of water by 0.05 degree Celcius only
Irwin and Orowan
Energy Release Rate, G : Energy release per unit increase in area during crack growth
Crack Resistance, R : Energy required for a crack to grow per unit area
Crack growth takes place only when,
Energy Release Rate
Conservation of energy
Energy available for crack growth
Work done by the external forces
Increase in strain energy within the body
Energy Release Rate
Work is done on the system
Flexure of cantilever absorbs part of the work done
Potential energy
Constant load case
Ref: 1
Energy Release Rate
No Work is done as the crack advances
Release of strain energy as the crack advance
Potential energy
Fixed Grip case
Ref: 1
Energy Release Rate
HW:Determine the energy release rate of DCB specimen loaded in a tensile testing machine.