Modification Of The Griffith Theory

It was that Griffith theory of crack instability was introduced and Eq. (15) was mentioned as fracture criterion for a brittle material. Griffith has demonstrated on glass specimens etched with HF acid to make in the centre of glass plate, that this prediction of fracture stress of Eq. (15) was correct. Orowan found that Griffith theory in its original form could not be applied to brittle fracture of metals which have inherent capability to deform plastically. For the purpose of applying the theory to metals Orowan introduced a plastic work term "p" which represented the amount of work required to extend crack in the plastic zone. Therefore, the fracture stress for causing the crack to become unstable in metals could be expressed as

                                          s_f= (2E(g+p)/Pa) ^1/2

 Here g is the surface energy which is much less than plastic work p and hence can be neglected, so that

                                          s_f= (2Ep/Pa)^1/2

The ratio  p / g has been found to vary between 100 to 500. Some experiments have been shown that p decreases with decreasing temperature. Irwin replaced 2p by yet another term G_c which is called crack extension force or strain energy release rate (measured in J/mm² or J/m²). Thus

                                          s_f= (EG c/Pa)^1/2

Gc appears to be a fundamental material property which governs crack extension in metals. Remembering that

in case of centrally cracked plate,

Here G_c has been replaced by G_IC (read as G - one - C) to properly refer to Mode I. GIC and KIC are both experimentally determined. Other terms used to express G_c are toughness or resistance force.

A comparison between original Griffith theory which is similar to Irwin's criterion and modified form of Griffith theory is imperative. The Griffith theory can be applied to continuous elastic fracture. Such a fracture is possible when

1.      material is inherently brittle, i.e. the yield strength is higher than E/10  which is cohesive strength or stress required to break atomic bonds,

2.      temperature is low, and

3.      crack velocity is high.

You may like to compare these statements with before one and also under the heading of Impact Test. The conditions described above permit the stress s_yy to build up to value equal to E /10  and thus initiate the process of breaking the atomic bonds. This type of fracture due to breaking of atomic bonds is also known as cleavage fracture.

On the other hand, when the stress s_yy at crack tip will not increase toE/10

1.     material is inherently tougher,

2.     temperature is high, and

3.     crack is stopped.

Thus the atomic bonds will not break and cleavage fracture does not take place. Instead plastic deformation will occur in the region of crack tip would not extend elastically. In other words, Griffith criterion of fracture stress will not be applicable. Under this condition Orawan's modified criterion will be applicable.