Griffith proposed that brittle materials contain small cracks and flaws that concentrate stress enough to reach the theoretical strength at nominal stresses below theoretical values. For a crack to propagate, the decrease in elastic strain energy from crack growth must be equal to or greater than the increase in surface energy. Griffith established a criterion where the stress required for crack propagation is inversely proportional to the square root of the crack length. This theory provides an equation to calculate the maximum crack length possible without fracture given a material's surface energy, modulus of elasticity, and applied stress.

1. Griffith Theory of Brittle Fracture

2. 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.

3. • 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.

4. 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

5. • 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 to
Where 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

6. 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

7. 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.