摘要
材料发生相变的过程中会出现失稳、滞后回线及多界面的微结构等复杂现象,而稳定性的丧失使其动力学方程的求解十分困难。对于形状记忆合金中的马氏体相变,相变过程中材料的等效杨氏模量变为负值,使得传统的动力学方程成为病态的,无法直接求解,必须要进行正则化。而相变的滞后回线与微结构的出现也说明经典的弹性理论不再适用,必须要引入新的能量项以能刻画这些现象。本文在非线性弹性理论的框架下,引入应变梯度界面能和位移非均匀能,利用变分原理建立了材料相变的一维动力学模型。高阶项的引入极大地改善了方程的性质,使数值求解成为可能。计算结果表明,该模型确能较有效地描述相变时的失稳与微结构。
Nonlinear phenomena such as instability, hysteresis and complicated microstructures are often observed during solid-solid phase transitions. Due to the lack of stability, the solution of the dynamical equations become to be very difficult. Take the martensitic transformation in shape memory alloys as an example, the Young＇s modulus becomes negative during the phase transition process. This makes the classical dynamical equation ill-posed and can not be solved directly. Certain kind of regularization is required. The observation of hysteresis and microsturctures implies also that the classical elastic theory cannot apply any more. New energy terms have to be added to characterize these new phenomena. Within the frame of nonlinear elasticity, the strain gradient dependent interfacial energy and displacement dependent inhomogeneity energy were considered. One dimensional dynamical model was then obtained by means of the variational principle. The additional higher order term improves very strongly the mathematical properties of the equation. Its numerical simulation becomes possible. Our numerical results indicate that both the lack of stability and the microstructures of phase transitions can be simulated quite well by the present model.
出处
《力学季刊》
CSCD
北大核心
2005年第3期377-380,共4页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(10372023)
上海市基础研究重点项目(04JC14034)
关键词
马氏体相变
动力学模拟
多界面微结构
phase transition
dynamic simulation
multi-interface microstructures
