Coating internal stress measurement through the curvature method: A geometry-based criterion delimiting the relevance of Stoneyʹs formula

The measurement of internal stresses in coatings through the curvature (or bending) method involves a theoretical formula which connects the internal stress with the experimentally measured sample curvature. The linear Stoneyʹs formulae, which are the most commonly used, may be inadequate owing to nonlinear effects resulting from large displacements. In this paper, considering the case of a rectangular plate, the role of the different parameters controlling the geometrical nonlinear effects is first examined, and then the one-to-one mapping that exists between the degree of nonlinearity and the parameter b2/hR (b, h and R are the sample width, thickness and curvature, respectively) is established. Hence, it is shown that the geometrical criterion b2/hR < α ensures an arbitrarily low influence of geometrical nonlinear effects, thereby allowing correct use of Stoneyʹs formulae.