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

Abstract 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.