Analysis of a “barb test” for measuring the mixed-mode delamination toughness of coatings

The durability of thermal barrier coatings (TBCs) employed in most turbine engines is limited by delamination, both within the coating and at the coating–substrate interface. A test used for evaluating the mixed-mode toughness pertinent to such delaminations has been fully-analyzed by determining the steady-state energy release rate, the mode mixity and the critical length for buckling. An analytic solution based on beam theory establishes basic estimates and scaling relationships. Selected finite-element calculations have been used to affirm the fidelity of the results. The energy release rate attains steady-state, but the phase angle changes throughout because of a small (but significant) bending moment induced at the supports. The coating buckles at a critical delamination length, whereupon the energy release rate increases rapidly and violates steady state. The solutions are used to re-interpret measurements reported in the literature for an electron beam physically deposited TBC.