Yang Fuqian, Zhao Ya-Pu
Materials Program, Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY 40506, USA.
Soft Matter. 2016 Feb 7;12(5):1586-92. doi: 10.1039/c5sm02643a. Epub 2015 Dec 14.
Young's relation is based on the equilibrium of horizontal components of surface tensions for a liquid droplet on a "rigid" substrate without addressing the substrate deformation induced by the net vertical component of surface tensions. Upon realizing the importance of wetting in controlling the integrity of flexible structures and electronics, the effect of a capillary bridge or a liquid droplet on the crack opening of a penny crack under the action of a far-field tensile stress is analyzed. Closed-form solutions are derived for both the crack opening and the stress intensity factor, which are functions of the size of the capillary bridge or the droplet, surface tension, and the contact angle. Both the capillary bridge and the droplet can introduce the crack closure. The minimum far-field tensile stresses needed for complete crack opening, i.e. no crack closure, are obtained analytically. The net vertical component of the surface tensions introduces the formation of a surface ridge on the crack face at the edge of the droplet for an open crack. The amplitude of the surface ridge increases with the increase of the net vertical component of the surface tensions and the decrease of the breadth width.
杨氏关系基于“刚性”基底上液滴表面张力水平分量的平衡，而未考虑由表面张力净垂直分量引起的基底变形。在认识到润湿性对控制柔性结构和电子产品完整性的重要性后，分析了毛细桥或液滴在远场拉伸应力作用下对硬币形裂纹开口的影响。推导了裂纹开口和应力强度因子的封闭形式解，它们是毛细桥或液滴尺寸、表面张力和接触角的函数。毛细桥和液滴都会导致裂纹闭合。通过解析得到了完全打开裂纹（即无裂纹闭合）所需的最小远场拉伸应力。对于开口裂纹，表面张力的净垂直分量会在液滴边缘的裂纹面上形成表面脊。表面脊的幅度随着表面张力净垂直分量的增加和宽度的减小而增大。
