COD – CRACK OPENING DISPLACEMENT

(Note:Students are reminded to be clear about the difference between crack length, (2a) and displacement, u. There is one more, term radius of (curvature) of the notch, ρ)

Conditions surrounding the initiation and progression of crack depend upon bluntness (or sharpness) of the crack tip (notch). In practice it is found that blunt cracks (with higher radius,) require greater fracture loads (So) than sharp cracks. Since the stress intensity factor, K increases with loading, as seen in (15),

K = Soa (15)

K also therefore is higher with higher (higher bluntness). Further it is found that there is a critical value of Kc and a corresponding critical value of c. Below this c, the value of Kc is approximately constant. This suggests that cracks have a “natural radius c” at which they initiate and propagate. The value of this c depends upon the material. Even the so-called sharp cracks are not sharp in practice; but are quite blunt only, since c is in the order of the inter-atomic spacing. Once initiated, a crack tends to propagate with its own “natural bluntness”, when sharp crack resulting from blunter notches have attained radius c. This leads to the concept of a critical displacement called crack tip opening displacement (CTOD) at the crack tip and another, a crack opening displacement (COD), δc determined outside of the crack tip.

The COD is given by

δc = Kc2 /E SY (A)

It may be noted also that δc is in the same order of c and δc ≈ 2c (B)

E =Modulus of elasticity and SY = Yield strength/stress. Since

K2 = GE

δc = G/ SY (C)G = δc SY (C1)

Since in most cases G, the strain energy release rate of linear elastic fracture = J, the integral of strain energy release rate for more general cases, including non-linear elastic and dissipative cases

J = G = δc SY (D)