The constitutive relation of an axisymmetric detached coating on a rigid substrate

In this work, the constitutive relation between the external force (P) and central deflection (w0) of the coating in a blister test is studied by elasticity theory. The studied cases are that the coating in the presence of the residual tensile stress is deflected by a concentrated force on the central area of the coating surface. Closed-form solutions for force and deflection are obtained, and used to analyze the feature of the constitutive relations without and with delamination. The results show that the constitutive relation expresses as P∝w0n with n=1-3 for the case without delamination, while it expresses in a non-monotonic fashion for the case with delamination. The details of the constitutive relation are influenced by the radius of detached coating, residual tensile stress and interfacial toughness.