A numerical investigation of interfacial and channelling crack growth rates under low-cycle fatigue in bi-layer materials relevant to cultural heritage

Abstract

In traditional and modern paintings on canvas or wood, two crack types have been identified, these are: (i) delamination between two of the many layers and (ii) channelling through the paint layer, terminating at the paint-substrate interface. One cause of this damage can be attributed to environment-induced low-cycle fatigue, specifically through relative humidity and temperature fluctuations. We present novel 2D as well as 3D finite element models that, for the first time, identify the time for each type of crack to initiate under a variety of realistic relative humidity (RH) cycles, as well as the corresponding crack growth rates. The focus is on modern paintings that have some layers executed in alkyd paint, found to be a vulnerable layer in a relatively short period of time. The paintings are idealised as a two-layer construction with a visco-hyperelastic alkyd paint layer on a linear elastic (acrylic) primed canvas substrate. Cracks, both interfacial and channelling, are represented using cohesive elements. To simulate the damage caused by a relative humidity cycle, a fatigue damage parameter was incorporated in the traction-separation law using a user-defined field. It was found that channelling cracks initiate slightly earlier than interfacial cracks for all the environmental conditions studied. Specifically, for an RH cycle of 35%–90%, channelling cracks initiate at 2.2 years and grow at an accelerating rate, while the interfacial crack initiates at 2.6 years and grows at a stable rate of approximately 0.1 mm/year. Narrower RH cycles lead to longer crack initiation times, e.g. the channelling crack initiates at 13.9 years under 40%–65% RH, and when the RH cycle was further narrowed to 45%–55%, the initiation time increased to 86 years. Our models are applicable to other painted or coated cultural heritage objects and can be used to inform preservation and environmental control strategies.