形状记忆合金椭圆孔口问题的有限单元法

基于Lagoudas形状记忆合金(SMA)三维本构模型,假设材料为各向同性,推导了SMA平面应力状态的增量型本构方程,继而编写了ABAQUS用户自定义材料(UMAT)子程序,研究了在双向拉伸情况下,外载荷、温度、椭圆孔口长短轴之比对超弹性SMA椭圆孔口板中应力诱发马氏体相变区的影响。数值结果表明:应力诱发马氏体相变首先发生在椭圆孔口长轴端点部位,在外加载荷作用下逐渐扩展到板内,并由内向外形成马氏体相区、相变混合区和奥氏体相区;SMA板内应力诱发马氏体完全相变区面积与施加外载荷成正相关,与温度成负相关;随着椭圆孔口长短轴之比增大,SMA板内应力诱发马氏体完全相变区面积呈现出先减小后增大的趋势;拉应力差值相同时,相较于拉应力沿椭圆孔口长轴方向较大的情况,当拉应力沿椭圆孔口短轴方向较大时,SMA板内完全相变区面积较大,椭圆孔口周边应力集中现象更明显。

Finite element method for elliptical hole problem of shape memory alloy

The incremental constitutive equation of Shape Memory Alloy(SMA)in the plane stress state is derived and then employed in the ABAQUS user material subroutine(UMAT)procedure based on Lagoudas three-dimensional constitutive model for SMA and the assumption of isotropy.The effects of the external load,temperature and the ratio between the major and minor axes of the elliptical hole on the distribution of the martensitic phase transformation region in pseudo-elastic SMA elliptical hole plate under biaxial tension are studied.The numerical results show that the martensite transformation initially forms at the end of the major axis of the elliptical hole and gradually extends into the inner part of plate under the external loads.In general case,there are three phase regions formed in the plate from the inside out:pure martensite phase region,austenite and martensite co-existence phase region and pure austenite phase region.The area of the pure martensite phase region in the plate positively correlates with the external load and negatively correlates with temperature.With the increase of the ratio between the major and minor axes of the elliptical hole,the area of the pure martensite phase region in the plate shows a tendency of decreasing first and then increasing,and when the difference of biaxial tensile stresses is the same,the area of the pure martensite phase region in the plate is larger and the stress concentration around the elliptical hole is more obvious when the tensile stress is larger along the minor axis of the elliptical hole.