Analytical study on stress-induced phase transitions in geometrically graded shape memory alloy layers. Part I: Asymptotic equation and analytical solutions. (September 2017)

• Record Type: Journal Article
• Authors: Liu, Hongwei; Wang, Jiong; Dai, Hui-Hui
• Is Part Of: Mechanics of materials. Volume 112(2017)
• Page Start: 40
• Page End: 55
• Publication Date: 2017-09
• Subjects: Shape memory alloys -- Phase transitions -- Geometrically graded specimen -- WKB Method -- Analytical solutions; Strength of materials -- Periodicals; Mechanics, Applied -- Periodicals; Résistance des matériaux -- Périodiques; Mécanique appliquée -- Périodiques; Mechanics, Applied; Strength of materials; Periodicals; Electronic journals; 620.11
• DOI: 10.1016/j.mechmat.2017.05.013
• Languages: English
• ISSNs: 0167-6636

Abstract

Highlights: An analytical approach is proposed to study phase transitions in geometrically graded SMA layers. The asymptotic equation is derived through the coupled series-asymptotic expansion method. The obtained analytical results can properly predict the stress-strain response of SMA layers. The underlying mechanisms of some key experimental features can be revealed. Graphical abstract: Abstract: In this paper, an analytical approach is proposed to study the stress-induced phase transitions in geometrically graded shape memory alloy (SMA) layers. First, within a two-dimensional setting, the governing PDE system is formulated, which contains the mechanical equilibrium equations and the phase transition criteria. By using the coupled series-asymptotic expansion method, the equilibrium equations can be reduced into one single ODE, which contains the leading-order term of the axial strain and the phase state functions. Besides that, the function representing the varying width of the SMA layer is also involved in this ODE. By further using the phase transition criteria, the phase state functions can be expressed in terms of the axial displacement for the pure loading and pure unloading processes. Then one asymptotic equation with variable coefficients is obtained. For linearly tapered SMA layers, the asymptotic equation is simplified and the WKB method is adopted to solve this equation. The obtained analytical solutions can capture the key features of the mechanical responses of the SMA layers and reveal the underlying mechanisms. The inhomogeneous configurations of the SMA layers during the phase transition process can also be simulated.