(1. 福建农林大学 机电工程学院， 福州 350002;
2. 北京理工大学 应用力学系， 北京 100081)
摘 要: 将近片层γ-TiAl基合金视为由等轴γ颗粒和多孪晶PST(polysynthetically twinned crystal)单晶颗粒组成的两相复合材料。 基于非均质微极介质塑性理论，构建γ-TiAl基合金整体有效微极柔度张量， 将传统塑性割线模量法推广到微极材料， 建立分析和预测γ-TiAl基合金的塑性行为尺度效应的细观力学模型。 结果表明： γ-TiAl基合金的微结构尺度对其宏观塑性硬化行为存在显著的影响；近片层组织γ-TiAl基合金中PST晶体颗粒的尺寸越小，合金中硬相夹杂PST颗粒的体积分数越大， 合金材料相应的塑性硬化越明显； 微极基体的塑性特征尺度与等轴γ晶粒的平均尺寸大小在同一数量级。
关键字: γ-TiAl基合金； 塑性； 微极理论； 尺度效应； 细观力学
（1. College of Mechanics-Electrics Engineering,
Fujian Agriculture and Forestry University, Fuzhou 350002, China;
2. Department of Applied Mechanics,
Beijing Institute of Technology, Beijing 100081, China）
Abstract: An analytical micromechanical model in a framework of a micropolar continuum was proposed to investigate the size effect of macroscopic plastic behavior for a nearly lamellar γ-TiAl based alloy, which consisted of PST(polysynthetically twinned crystal) grains with random orientation. The γ-TiAl based alloy was considered as a two-phase composite composed of micropolar matrix and PST particles. The Mori-Tanaka's method was advanced to evaluate the effective elastic moduli, and a new secant moduli method based on the second moment of strain and torsion of the matrix was extended to analyze the nonlinear behaviour of the γ-TiAl based alloy. The modeling results show that the size dependence is more pronounced when the PST particle's size approaches to the matrix characteristic length. The plastic stress of a nearly lamellar γ-TiAl based alloy increases with the decrease of PST grain size or with the increasing volume fraction of the PST grains. The characteristic length of plasticity of the micropolar matrix is approximately as the same order of magnitude as the average diameter of the matrix particles.
Key words: γ-TiAl-based alloys； plasticity； micropolar theory； size effect； micromechanics
