Crack-like grain-boundary sliding wedges in nano-films. Issue 6 (19th March 2019)

• Record Type: Journal Article
• Authors: Wang, Cuiying; Wang, Xu
• Is Part Of: Mechanics of advanced materials and structures. Volume 26:Issue 6(2019)
• Page Start: 480
• Page End: 492
• Publication Date: 2019-03-19
• Subjects: Rate-dependent grain-boundary sliding -- surface elasticity -- Cauchy singular integro-differential equation -- state-space equations -- eigenmode; Composite materials -- Mechanical properties -- Periodicals; Composite construction -- Periodicals; 620.118
• DOI: 10.1080/15376494.2017.1400620
• Languages: English
• ISSNs: 1537-6494

Abstract

ABSTRACT: Time-dependent grain-boundary (GB) sliding in a nano-film on a substrate is studied. The Gurtin–Murdoch surface elasticity is incorporated onto the GB by ignoring the residual surface tension, and the GB is allowed to slide by the diffusion-controlled mechanism. The sliding viscosity can be homogeneous or heterogeneous along the GB. By using the Green's function method, the original boundary value problem is reduced to a Cauchy singular integro-differential equation of the first order which can be further changed into state-space equations by means of an adapted collocation method. The state-space equations can be solved through a rigorous eigenmode analysis. We demonstrate that such a sliding process leads to the formation of a crack-like GB wedge which causes the shear stress along the GB to decay exponentially with time. Furthermore, the stress field exhibits the weak logarithmic singularity at the tip of the sliding wedge due to the incorporation of surface elasticity. Detailed numerical results are obtained for eigenvalues, eigenfunctions, the transient shear stress along the GB, the opening displacement of the wedge and the strength of the logarithmic singularity at the wedge tip.