Numerical modelling for predicting degradation of historical oil paintings

What is metal soap formation?

Metal soap formation is mainly a problem in paintings that contain lead- or zinc-based pigment particles. Unfortunately, most oil paintings from the 15^th century until the present day contain one or more of these pigments. Therefore, metal soap formation threatens a large portion of our cultural heritage.

Metal soaps develop from a series of complex chemical reactions between the metal-based pigment particles and the oil binder. They may develop as crystalline aggregates and, over a time span of decades to centuries, may reach sizes up to several hundreds of micrometres. Accordingly, these crystals cause significant deformation of paint layers, and can protrude through the outer surface, leading to damage to the paintings.

Volume change

To understand the mechanical response of oil paintings due to the formation of metal soap crystals, Gijs Eumelen developed a numerical model that simulates their formation and growth.

The formation of metal soaps is accompanied by a change in volume, which is accounted for in the model through a chemical growth strain. This provides a coupling between the chemical processes and the mechanical response. Crystal growth leads to the formation of cracks in the painting, which in turn affect the chemical processes. The predicted mechanical response of the system, in the form of the surface deformations, cracking and delamination patterns, appears to be in good agreement with observations from cross-sectional photographs of real paintings.

Non-invasive testing

Another issue in understanding the mechanical behaviour of oil paintings is related to the uncertainty on the actual mechanical properties of the paint. These are affected by the age of the paint and the constituents used to create the paint in the first place.

In general, the mechanical properties of paint materials can be assessed by performing tests on the actual paintings. However, this is not possible as such tests would most likely damage valuable, historical paintings. With this in mind, the mechanical properties of the paint can be obtained through non-invasive nanoindentation tests on very small samples from a painting.

Non-invasive tests are relatively easy to perform, but difficult to interpret, also because the small paint sample during testing is embedded in a relatively stiff, supporting resin. To accurately account for the influence of the supporting resin on the indentation response of a paint sample, Eumelen derived an analytical indentation model that describes the elastic and plastic indentation behaviour of embedded material samples. The practical applicability of the indentation model has been demonstrated by deducing the elastic properties of a paint sample as reported in the literature.

Understanding the mechanical behaviour of these paintings due to metal soap formation might ultimately be of assistance when formulating conservational treatments. The model developed by Eumelen during his PhD can contribute to this, but it’s just a first step. It will take several years before the model is at a level that it can be used for this purpose.

Title of PhD thesis: Numerical modelling of metal soap formation in historical oil paintings. Supervisors: Akke Suiker and Emanuela Bosco.