Crack channelling is predicted in a brittle coating-substrate system that is subjected to a moisture or temperature gradient in the thickness direction. Competing failure scenarios are identified, and are distinguished by the degree to which the coating-substrate interface delaminates, and whether this delamination is finite or unlimited in nature. Failure mechanism maps are constructed, and illustrate the sensitivity of the active crack channelling mechanism and associated channelling stress to the ratio of coating toughness to interfacial toughness, to the mismatch in elastic modulus and to the mismatch in coefficient of hygral or thermal expansion. The effect of the ratio of coating to substrate thickness upon the failure mechanism and channelling stress is also explored. Closed-form expressions for the steady-state delamination stress are derived, and are used to determine the transition value of moisture state that leads to unlimited delamination. Although the results are applicable to coating-substrate systems in a wide range of applications, the study focusses on the prediction of cracking in historical paintings due to indoor climate fluctuations, with the objective of helping museums developing strategies for the preservation of art objects. For this specific application, crack channelling with delamination needs to be avoided under all circumstances, as it may induce flaking of paint material. In historical paintings, the substrate thickness is typically more than ten times larger than the thickness of the paint layer; for such a system, the failure maps constructed from the numerical simulations indicate that paint delamination is absent if the delamination toughness is larger than approximately half of the mode I toughness of the paint layer. Further, the transition between crack channelling with and without delamination appears to be relatively insensitive to the mismatch in the elastic modulus of the substrate and paint layer. The failure maps developed in this work may provide a useful tool for museum conservators to identify the allowable indoor humidity and temperature fluctuations for which crack channelling with delamination is prevented in historical paintings.

中文翻译：

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在湿度或温度梯度下脆性涂层系统中的裂纹通道机制

在易碎的涂层 - 基材系统中预测裂纹通道，该系统在厚度方向上受到水分或温度梯度。确定竞争性故障情况，并通过涂层-基材界面分层的程度以及这种分层本质上是有限的还是无限的来区分。构建失效机制图，并说明活性裂纹沟道机制和相关沟道应力对涂层韧性与界面韧性之比、弹性模量失配以及湿膨胀系数或热膨胀系数失配的敏感性。还探讨了涂层与基材厚度的比率对失效机制和沟道应力的影响。导出稳态分层应力的闭式表达式，并用于确定导致无限分层的水分状态的过渡值。尽管结果适用于广泛应用的涂层-基材系统，但该研究侧重于预测历史绘画因室内气候波动而开裂，目的是帮助博物馆制定保护艺术品的策略。对于这种特定应用，在任何情况下都需要避免分层裂纹通道，因为它可能会导致油漆材料剥落。在历史绘画中，基材厚度通常比漆层厚度大十倍以上；对于这样的系统，根据数值模拟构建的失效图表明，如果分层韧性大于涂料层 I 型韧性的大约一半，则不存在涂料分层。此外，有分层和无分层的裂纹沟道之间的过渡似乎对基材和涂料层的弹性模量的失配相对不敏感。在这项工作中开发的故障图可以为博物馆保护人员提供一个有用的工具，以识别允许的室内湿度和温度波动，从而防止历史绘画中出现分层裂缝。有分层和无分层的裂纹沟道之间的过渡似乎对基材和涂料层的弹性模量的不匹配相对不敏感。在这项工作中开发的故障图可以为博物馆保护人员提供一个有用的工具，以识别允许的室内湿度和温度波动，从而防止历史绘画中出现分层裂缝。有分层和无分层的裂纹沟道之间的过渡似乎对基材和涂料层的弹性模量的不匹配相对不敏感。在这项工作中开发的故障图可以为博物馆保护人员提供一个有用的工具，以识别允许的室内湿度和温度波动，从而防止历史绘画中出现分层裂缝。