Transformation thermomechanics in an Fe-based shape momory alloy

引入了一个依赖于热力学广义力和内变量的相变条件来描述马氏体相变的开始和发展。通过求解一个由耗散不等式和变形条件组成的条件极值问题，得到了一组关于内变量的演化方程。合金的热弹性本构关系、速率型本构关系和演化方程控制着合金的行为。介绍的相变条件被证明是冶金中讨论的相变驱动力。从理论上提出了“等向硬化”和“运动硬化”的概念，并通过实验确定了多轴应力状态下的马氏体形变条件和奥氏体形变条件。用椭圆锥表示的马氏体初始面在应力-温度空间是不对称的，从而验证了应力偏移量第三不变量理论。奥氏体形变条件由应力-温度空间中的平面给出。平面的方向取决于加载过程中诱发的马氏体量，而平面的位移量则取决于马氏体量。奥氏体起始面随马氏体量的不同而平移。在加载过程中诱发许多马氏体变种的情况下，奥氏体形变条件用一个多边形锥表示。

A transformation condition, which depends on the thermodynamic generalized forces and the internal variables, was introduced to describe the start and progress of the martensitic transformation. A set of evolution equations for the internal variables were derived by solving a conditional extremum problemcomposed of the dissipation inequality and the tranformation condition. The thermoelastic, rate-type, constitutive relations and the evolution equations govren the behavior of the alloy. The transformation condition introduced was proved to be judt the transformation driving force discussed in metallurgy. The concepts of the "isotropicphardening" and the "kinematical hardening" were developed theoretically.The martensite start condition and the austenite start/finish conditions were determined experimentally under the multiaxial stress state. The martensite start surface, represented by an oval cone, was asymmetric in the stress-temperature space, thus approving the theory with the third invariant of the stress deviator. The austenite start consition was given by a plane in the stress-temperature space. The direction of the plane depends on the martensite variants induced during loading, whereas the posion of the plane the amount ofthe martensite. The austenite start plane translates depending on the amount of martensite. In case many martensite variants are induced during loading, the austenite start condition is represented by a polygonal cone.