Determination of Elastic Parameters of Thin Layers Used in Paintings by Air-Coupled Ultrasound Transmission Measurements under Varying Incidence

Paintings are intricate structures made up of multiple layers of materials that possess different properties and thicknesses. Due to their fragility, they can be damaged by exposure to various environmental factors such very large amplitude vibrations, as well as temperature and humidity variations. Restorers use various techniques such as raking light, x-rays, infrared, and UV to gather information about the condition of the artwork. Unlike these methods, ultrasonic techniques use elastic waves and can thus provide information about the mechanical properties of the materials and their interfaces. The goal of this work is twofold. First, it consists in numerically analyzing the sensitivity of elastic parameters of painting layers through their influence on the acoustic transmission coefficient and dispersion curves. Then, an experimental device is set up to confirm some of these results by the determination of the values of the elastic parameters of the constituent layers of paintings. To this aim, we have developed an original association of numerical and experimental methods for characterization and determination of the layer elastic parameters of some materials used in paintings. A matrix stiffness model associated to a genetic algorithm are used for the numerical study and optimization process between the theoretical transmission coefficient and the experimental one. Then, focused Air-Coupled Transducers (ACTs) in conjunction with a rotary motor are used to perform measurements of transmitted signal amplitude on several components used in paintings under various angles of incidence. Our results concerning the determination of elastic parameters values on various materials including plexiglass (PMMA), acrylic paint, varnish, gesso and wood, taken as single plates, and bi-layered structures, are strongly supported by theoretical results obtained using the matrix stiffness model.