A semi-analytic analysis of shape memory alloy thick-walled cylinders under internal pressure

Abstract

In this paper, a new method for analysis of the pseudoelastic response of shape memory alloy thickwalled cylinders subjected to internal pressure is proposed. Two cases of short and long cylinders are considered by assuming the plane stress and plane strain conditions. In each case, a three-dimensional phenomenological SMA constitutive model is simplified to obtain the corresponding two-dimensional constitutive relations. The cylinder is partitioned into a finite number of narrow annular regions, and appropriate assumptions are made in order to find a closed-form solution for the equilibrium equations in each annular region. The global solution is obtained by enforcing the stress continuity condition at the interface of the annular regions and imposing the boundary conditions. Several numerical examples are presented to demonstrate the efficiency of the proposed method, and the results are compared with three-dimensional finite element simulations.

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

“…It can be observed that both the tangential stress and the effective Tresca stress increase considerably within the fully martensitic region M * , so that the yield condition of the SMA could be reached quickly. A similar trend was observed by Mirzaeifar et al (2012) in their semi-analytical investigations and it must be carefully considered in the design of SMA thick-walled pipe joints. Therefore, in order to avoid severe plastic deformations, the loading process should be interrupted soon after the complete martensitic transformation is achieved at r i , namely when the internal pressure p attains the threshold value σ f .…”

“…14 a,b,c concern three cases with r i < r 4 where the corner region takes place. These results provide a correction to the predictions obtained by Mirzaeifar et al (2012) and Tabesh et al (2013) by neglecting the formation of the secondary Martensite variant. If the wall thickness is very large, e. g. for r i = 0.25 r o < r 1 , Fig.…”

“…The coupling pressure predicted by FEA was in excellent agreement with the measured contact pressure. Mirzaeifar et al (2012) performed a semianalytic study of the pseudoelastic response of a thick-walled SMA cylinder subject to internal pressure, under plane stress or plane strain conditions. These authors partitioned the cylinder into a finite number of annular regions and provided closed-form solutions for the equilibrium equations in each annulus.…”

Thermomechanical Boundary Problems for a Cylinder and Sphere Made of Shape Memory Alloy

“…Задачи о прямом и обратном фазовом превращении в трубе из СПФ, находящейся под действием внешней нагрузки в рамках термомеханической модели поведения СПФ [21], численно решены в [22][23][24]. Численно-аналитическое решение задачи о нагружении толстостенного цилин-дра из СПФ внутренним давлением в режиме сверхупругости получено в [25]. Геометри-чески нелинейные осесимметричные задачи для термоупругих мартенситных фазовых переходов в круглых пластинках и оболочках вращения из СПФ решены в [26][27][28].…”

Nonlinear Free Vibration of Hybrid Composite Moving Beams Embedded with Shape Memory Alloy Fibers

“…The e®ect of SMAs on the free vibration of buckled cross-ply and angle-ply laminates by varying the SMA¯ber spacing was investigated by Shiau et al 28 based on the¯nite element method and approximate data from the curves of SMA. Mirzaeifar et al 29 presented a semi analytical analysis of shape memory alloy thick-walled cylinders under internal pressure. Cho and Rhee 30 presented the nonlinear¯nite element analysis of SMA wire reinforced hybrid composite shells based on the Brinson model.…”