Analytical solution for the pseudoelastic response of a shape memory alloy thick-walled cylinder under internal pressure

Abstract

Analytical solutions are derived for the isothermal pseudoelastic response of a shape memory alloy (SMA) thick-walled cylinder subjected to internal pressure. The Tresca transformation criterion and linear hardening are used. Equations are given for the radial and circumferential stresses, transformation strains and radial displacement at various steps of loading and unloading. A structural pressure-temperature phase diagram is provided for the cylinder, analogous to the stress-temperature phase diagram of SMA materials. Pressurization of an initially 100% austenitic cylinder causes the martensite to initially form at the inner radius. For

Evolution of multiple Martensite variants in a SMA thick-walled cylinder loaded by internal pressure

“…5 b that the secondary Martensite variant is produced only for very thick-walled cylinders satisfying r i < r a , for q > q c . Therefore, the results provided by Tabesh et al (2013) by neglecting the formation of the secondary Martensite variant are accurate for r i > r a , for the particular TA set considered there.…”

“…In the following, two different sets of constitutive parameters will be considered. They correspond to those adopted by Brinson and Lammering (1993) and Tabesh et al (2013) and are denoted by BL and TA, respectively. In particular, the temperature T 0 , the Young's modulus E and Poisson coefficient ν of both phases (Martensite and Austenite), the threshold stresses σ s and σ f for start and finish martensitic transformations at temperature T 0 , and the maximum residual strain ε L are reported in Table 1 for both sets.…”

“…In order to exploit the full potential of SMA coupling systems, it becomes essential to estimate the stress distribution within these components accurately. Severe stresses may develop during the production stage or the installation of SMA coupling and may cause unexpected mechanical deformation, damage and failure or just loss of efficiency ( Tabesh et al, 2013( Tabesh et al, , 2017. To avoid such technological problems, it becomes necessary to predict the me-E-mail addresses: enrico.radi@unimore.it , eradi@unimore.it chanical stresses originated in SMA connections during each step of their production and installation.…”

“…Then, a numerical solution was found by solving the system of nonlinear algebraic equations obtained by enforcing stress continuity at the interface between annular regions. Tabesh et al (2013) provided a closed form solution for the pseudoelastic response of a SMA thick-walled cylinder subjected to internal pressure under plane stress or plane strain loading conditions, for temperature higher than the finish austenitic transformation A f . They assumed a simplified 2D constitutive model for SMA that incorporates the Tresca transformation criterion with associative flow rule and linear transformation law.…”

“…The model is able to describe several phenomena occurring in the radial expansion of a SMA thick-walled cylinder, such as phase transformations, Martensite reorientation and multiple lattice shearing mechanisms. It keeps the essence of the approach used in Videnic et al (2008) and Tabesh et al (2013) , but extends these studies by considering corner transformation flow rule, thus allowing for the formation of multi-variant Martensite. Moreover, in the present analysis the axial strain may vary within the wall thickness.…”