Fracture Mechanics

Ref: Prashant Kumar, “Elements of Fracture Mechanics”, Tata McGraw Hill

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 RateConstant load test

C - Compliance

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 RateFixed Grip case

Energy Release RateGeneral case

Ref: 1

Energy Release Rate

HW:Determine the energy release rate of DCB specimen loaded in a tensile testing machine.

Other approaches

Energy Release Rate, G : Energy based for brittle or less brittle materials

Stress Intensity factor, K : Stress basedfor brittle or less brittle materials

J- Integral, J : for ductile materials

Crack Tip Opening Displacement, CTOD: Displacement based