Griffith Theory of Brittle Fracture

Griffith Theory of brittle fracture

Introduction:

Griffith proposed that a brittle material contains a

population of fine small cracks and flaws that have a

variety of sizes , geometries and orientation which

produces a stress concentration of sufficient magnitude

so that the theoretical cohesive strength is reached in

localized regions at a nominal stress which is well

below the theoretical value.

• When one of the cracks spreads, it produces an increase in the surface area of the side of the crack.

• This requires energy to overcome the cohesive force of the atom

• Or express in another way• It requires an increase in surface

energy.• The source of increased in surface

energy is the elastic strain energy which is released as the crack spreads.

Griffith Criteria: Griffith established the following criterion

for the propagation of a crack.“A crack will propagate when the decrease in elastic strain energy is at least equal to create the new Crack.” Or, the decrease in strain energy results from the formation of a crack. Consider the crack model as shown in

figure. The thickness of the plate is negligible so

the problem can be treated as one in plane stress.

The cracks are assumed to have an elliptical shape.

Crack length = interior = 2c = edge = c

The effect of both types of cracks on the fracture behavior

is the same

• According to Griffith’s criterion, the crack will propagate under a constant applied stress σ if an incremental increase in crack length produces no change in the total energy of the system; i.e. the increased surface energy is compensated by a decrease in elastic strain energy.

• ΔU = total change in potential energy resulting from the creation of the crack which is equal to

Us = the surface energy due to presence of the crack is

UE = the elastic strain energy per unit of the plate thickness is equal toWhere σ is the tensile stress acting normal to the crack of the length and a negative sign is used because growth of the crack releases elastic strain energy

The above equation gives the stress required to propagate a crack in a brittle material as a function of the size of the micro-crack.

Note that this equation indicates that the fracture stress is inversely proportional to the square root of the crack length

Problem No: 01

A relatively large plate of a glass is subjected

to a tensile stress of 40 MPa.

If the specific surface energy and modulus of

elasticity for this glass are 0.3 J/m2 and 69

GPa, respectively.

Determine the maximum length of a surface

flaw that is possible without fracture.