Computational modelling of metal soap formation in historical oil paintings: the influence of fatty acid concentration and nucleus geometry on the induced chemo-mechanical damage.

Metal soap formation is one of the most wide-spread degradation mechanisms observed in historical oil paintings, affecting works of art from museum collections worldwide. Metal soaps develop from a chemical reaction between metal ions present in the pigments and saturated fatty acids, which are released by the oil binder. The presence of large metal soap crystals inside paint layers or at the paint surface can be detrimental for the visual appearance of artworks. Moreover, metal soaps can possibly trigger mechanical damage, ultimately resulting in flaking of the paint. This paper departs from a recently proposed computational model to predict chemo-mechanical degradation in historical oil paintings, as presented in Eumelen et al. (J Mech Phys Solids 132:103683, 2019). The model describes metal soap formation and growth, which are phenomena that are driven by the diffusion of saturated fatty acids and proceed by a nucleation process from a crystalline nucleus of small size. This results into a chemically-induced strain in the paint, which may promote crack nucleation and propagation. The proposed model is here used to investigate the effects of saturated fatty acid concentration and initial nucleus geometry on the amount of chemo-mechanical damage generated. Numerical simulations show that both factors have a marginal influence on the growth rate of the metal soap crystal, but play a significant role on the extent of fracture induced in the paint.

金属皂（metal soap）生成是历史油画中最为普遍的劣化机制之一，影响着全球范围内博物馆馆藏的艺术作品。金属皂由颜料中含有的金属离子与油黏合剂（oil binder）释放的饱和脂肪酸发生化学反应生成。颜料层内部或颜料表面出现的大型金属皂晶体，会对艺术作品的视觉外观造成不利影响。此外，金属皂还可能引发机械损伤，最终导致颜料层剥落。本文采用Eumelen等人于2019年发表于《固体力学与物理学杂志》（J Mech Phys Solids 132:103683, 2019）中提出的计算模型，开展历史油画化学-机械（chemo-mechanical）劣化的预测研究。该模型刻画了金属皂的生成与生长过程：该过程由饱和脂肪酸的扩散驱动，并通过微小晶核的成核过程逐步进行。这会在颜料中产生化学诱导应变，进而促进裂纹的成核与扩展。本文利用所提出的模型，探究了饱和脂肪酸浓度与初始晶核几何形态对所产生的化学-机械损伤程度的影响。数值模拟结果表明，上述两个因素对金属皂晶体的生长速率影响微弱，但对颜料层中诱发的断裂程度具有显著作用。