Analytical solution for the pseudoelastic response of a shape memory alloy thick-walled cylinder under internal pressure
Analytical solution for the pseudoelastic response of a shape memory alloy thick-walled cylinder under internal pressure
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DOI：
10.1088/0964-1726/22/9/094007
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发表时间：
2012-09
影响因子：
4.1
通讯作者：
Majid Tabesh;Bingfei Liu;J. Boyd;D. Lagoudas
中科院分区：
文献类型：
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作者：
Majid Tabesh;Bingfei Liu;J. Boyd;D. Lagoudas
推导了形状记忆合金（SMA）厚壁圆柱体在内压作用下的等温拟弹性响应的解析解。使用 Tresca 变换准则和线性强化。给出了加载和卸载各个步骤中的径向和周向应力、转变应变和径向位移的方程。为圆柱体提供了结构压力-温度相图，类似于 SMA 材料的应力-温度相图。对最初 100% 奥氏体圆柱体加压会导致马氏体最初在内半径处形成。对于相对薄壁的圆柱体，转变前沿在内半径处完成转变之前到达外半径，而对于厚壁圆柱体，转变在内半径处完成，同时仍然存在100％奥氏体的外环。对于给定的 OD/ID 比率，导出临界温度来规定发生这两种情况中的哪一种。提供了将导致在内半径处完成转变的压力的分析结果。在卸载期间，逆变换可以从圆柱体的内表面或外表面开始，并且可以向外传播，然后反转其方向并传播回内表面。还研究了由于塑性而导致的马氏体转变对结构屈服强度的影响，结果表明，尽管材料的屈服应力与温度无关，但根据温度和所实现的转变状态，开始屈服所需的压力可以显着降低或增加。最后，通过与使用 von Mises 理论的有限元解进行比较，证明了 Tresca 变换准则对于导出该问题的封闭式解的有效性。
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 a relatively thin-walled cylinder the transformation front reaches the outer radius before the transformation has completed at the inner radius, whereas for a thick-walled cylinder the transformation completes at the inner radius while there is still an outer ring of 100% austenite. For a given OD/ID ratio, a critical temperature is derived that stipulates which of these two cases occurs. An analytical result is provided for the pressure that will cause the transformation to complete at the inner radius. During unloading, the reverse transformation can start at either the inner or the outer surface of the cylinder and can propagate outward and then reverse its direction and propagate back to the inner surface. The effect of martensitic transformation on the structural yield strength due to plasticity is also investigated and it is shown that the pressure required to initiate yielding can be substantially decreased or increased depending on the temperature and the state of transformation achieved, even though the yield stress of the material is independent of temperature. Finally, the effectiveness of the Tresca transformation criterion to derive closed-form solutions for this problem is demonstrated by comparing with finite element solutions using the von Mises theory.