Computational Methods for Debonding in Composites

4 Analytical and Numerical Investigation of the Length of Cohesive Zone 79
τ = τ o
� �n x
(4.2)
lcz
where n is a material parameter.
In the elastic zone, the traction profile follows the expression given by the Linear
Elastic Fracture Mechanics (LEFM) solution:
τ =
KI
� 2π (x − r1)
(4.3)
The size of the inelastic zone, lcz, also called cohesive zone or fracture process
zone, is obtained by assuming that the traction given by Eqs. (4.2) and (4.3) must be
equal at x = lcz, and that the areas A1 and A2 represented in Fig. 4.1 are equal [2].
Assuming that there are no size effects, the crack propagates when the stress intensity
factor KI equals to the critical value KIc. Therefore, the size of the cohesive zone
when the crack is propagating in a self-similar way can be solved using the previous
equations, resulting in:
l ∞ cz =
n + 1
π
K 2 Ic
(τ o ) 2
(4.4)
Cox and Marshall [5] proposed an alternative approach to predict the length of
the cohesive zone. The Cox and Marshall [5] model is based on the concept of a
bridged crack, where the length of the bridging zone is calculated by imposing two
Fig. 4.1 Stress profile ahead of the crack tip