(1. 福建農(nóng)林大學(xué) 機(jī)電工程學(xué)院， 福州 350002;
2. 北京理工大學(xué) 應(yīng)用力學(xué)系， 北京 100081)
摘 要: 將近片層γ-TiAl基合金視為由等軸γ顆粒和多孿晶PST(polysynthetically twinned crystal)單晶顆粒組成的兩相復(fù)合材料。 基于非均質(zhì)微極介質(zhì)塑性理論，構(gòu)建γ-TiAl基合金整體有效微極柔度張量， 將傳統(tǒng)塑性割線模量法推廣到微極材料， 建立分析和預(yù)測(cè)γ-TiAl基合金的塑性行為尺度效應(yīng)的細(xì)觀力學(xué)模型。 結(jié)果表明： γ-TiAl基合金的微結(jié)構(gòu)尺度對(duì)其宏觀塑性硬化行為存在顯著的影響；近片層組織γ-TiAl基合金中PST晶體顆粒的尺寸越小，合金中硬相夾雜PST顆粒的體積分?jǐn)?shù)越大， 合金材料相應(yīng)的塑性硬化越明顯； 微極基體的塑性特征尺度與等軸γ晶粒的平均尺寸大小在同一數(shù)量級(jí)。
關(guān)鍵字: γ-TiAl基合金； 塑性； 微極理論； 尺度效應(yīng)； 細(xì)觀力學(xué)
（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
