Biaxial Constrained Recovery in Shape Memory Alloy Rings

Abstract

In this article biaxial constrained recovery in a thick-walled shape memory alloy (SMA) ring with a rectangular cross-section is modeled using the theory of generalized plasticity, which is developed by Jacob Lubliner and Ferdinando Auricchio. As a mechanical obstacle that delays free recovery in a SMA ring, a steel ring is used. The result of constrained recovery is the generation of high stresses in both the rings. All equations are written in a closed form in terms of infinite series. Theoretical results are compared with experimental findings and good agreement is found when SMA rings are in the domain of recoverable strains.

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

“…In particular, the forward martensitic transformation occurring under proportional axisymmetric loading and plane stress conditions is investigated systematically. The phenomenological SMA constitutive model adopted here assumes that the Martensite fractions evolve as linear functions of the Tresca effective stress, in agreement with the constitutive models proposed by Kasper (1997, 1999 ), Arghavani et al (2010), Marfia and Rizzoni (2013) for multi-variants Martensite and by Videnic et al (2008) and Luig and Bruhns (2008) for single variant Martensite. These models are derived from the theory of generalized plasticity developed by Lubliner and Auricchio (1996) and Auricchio and Lubliner (1997) .…”

“…Wang et al (2005) investigated experimentally the effects of the wall thickness and temperature range on the reverse transformation behavior of SMA pipe joints. Videnic et al (2008) presented a mathematical model of biaxial constrained recovery in a SMA ring. These authors adopted a generalized effective stress of Tresca type, which allows to consider unequal response in tension and compression.…”

“…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.…”

A finite element–based numerical tool for Ni47Ti44Nb9 SMA structures design: Application to tightening rings

“…Tightening devices have also been used. Videnic et al (2007) have studied the constrained recovery in a thick-walled SMA ring. Peultier et al (2008) have developed a device which consists of the tightening of a shape memory ring on an elastic one.…”

Mechanics of Shape Memory Alloy Materials – Constitutive Modeling and Numerical Implications

“…The basic objective of this section is the introduction of a material model that will help make the application of the generalized plasticity concept in modeling phase transformations clearer. The model is based on a geometrically linear model proposed earlier within a stress space formulation by Panoskaltsis and co-workers (Panoskaltsis et al, 2004, Ramanathan et al, 2002 and which has been extensively used in several applications of engineering interesting (e.g., see Videnic et al, 2008;Freed and Banks -Sills, 2007). …”