The KGD model was developed by Kessler, Gao, and Dieter (KGD) and is the most commonly used crack growth model today. The KGD model is a non-linear differential equation model that characterizes the growth of an existing crack in a material. It is described by the following equation:
This strategy is very common in crack growth studies, and is the approach used by crack growth models, such as the KGD's. In essence, this strategy is to plug cracks with sub-critical material. The material is kept well below the critical shear strength, and the cracks are allowed to grow until they become too large for the material to bear. Once the crack becomes too large for the material to bear, the crack is stopped and the simulation is stopped. The penetration of the crack is measured and the spread factor is calculated.
F is the stress intensity factor
iis a crack number between 1 and N, with N being the number of cracks
A_iis the crack cross sectional area
u_iis the length of the crack tip
E_iis the modulus of elasticity
γ_iis the surface energy
N_iis the concentration of mode I defects
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