Generalized Irwin plastic zone correction of a sub-interface Zener–Stroh crack in a coating-substrate system

• We model a sub-interface Zener–Stroh crack in a bi-material system.
• The generalized Irwin model is proposed to estimate crack tip plastic zones.
• Plastic zone size differs among two tips due to mixed mode load.
• CTOD is evaluated by changing crack depth and material mismatch.
• Effective stress intensity factors could better represent stress state at tips.

Elastic–plastic stress analysis of a Zener–Stroh crack paralleling to the interface of a coating-substrate system has been carried out in this work. The sum of the Burgers vectors of the climb and the glide dislocations along the crack line accounts for the stress field around its blunt tip where dislocation enters, and the sharp tip where crack propagates. Firstly, Gauss–Chebyshev quadrature technique is applied to solve the governing equation of dislocation density functions constrained by load-free crack faces. When taking plasticity into account at both crack tips where stresses are high, the generalized Irwin plastic zone correction is recommended. Plastic zone size (PZS) for both tips, crack tip opening displacement (CTOD) and effective stress intensity factors for the sharp tip are then obtained. The effects of coating thickness, crack depth, material mismatch and displacement loads ratio onto PZSs and CTOD have been analyzed in detail.