1. The energy-balance approach
When A.A. Griffith (1893–1963) began his pioneering studies of fracture in glass in the years just prior to 1920, he was aware of Inglis’ work in calculating the stress concentrations around elliptical holes, and naturally considered how it might be used in developing a fundamental approach to predicting fracture strengths. However, the Inglis solution poses a mathematical difficulty: in the limit of a perfectly sharp crack, the stresses approach infinity at the crack tip. Rather than focusing on the crack-tip stresses directly, Griffith employed an energy-balance approach that has become one of the most famous developments in materials science

2. ENERGY APPROACH
Center crack through thickness in plate

3. Griffith’s Energy Balance Approach
A.A Griffith laid the foundations of modern farcture mechanics by designing a criterian for fast fracture.
He assumed:
Pre-existing cracks propagate under the influence of an applied stress if the total energy of the system is reduced.

4. Strain Energy Release Rate

5. Crack propagation occurs when
is the material toughness and the resistance of a material to the fracture
strain energy release rate (crack driving force)

6. Energy Equations

7. BRITTLE FRACTURE THEORY OF GRIFFITH
If elastic energy near the crack tip = surface energy of new crack , therefore, crack propagates
Note: Degreasing the potential energy in the brittle plate due to the axiall loading is balanced with increasing the surface energy
DEÜ, Makina MÜhendisliği Bölümü

8. GRIFFTH THEORY Potential Energy depends on elastic strain energy and
work done by the external forces
As the crack propagates, the potential energy degreases due to strain energy release rate.
Potential energy in cracked plate:

9. GRIFFTH THEORY
Surface Energy: If the surface energy increases then the rate of the crack growth increases.
The surface energy according to Griffith is:
energy / unit area
Total surface area of the crack :
Specific Surface Enegy :

10. GRIFFTH THEORY Change of potential energy due to crack initiation:
U0 : potential energy of plate without crack

11. GRIFFTH THEORY
For the crack propagation
Griffith equation can be obtained as:
Second derivative sign gives the idea about crack stability and negative sign defines the instability and crack continued propagation.
DEÜ, Makina MÜhendisliği Bölümü

12. Energy Equations

13. Energy Equations