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

ENERGY APPROACH Center crack through thickness in plate

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.

Strain Energy Release Rate  

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

Energy Equations

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

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:

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 :

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

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

Energy Equations

Energy Equations