中文摘要：

提出一个利用无限小应变理论（infinitesimal strain theory）计算孪生在宏观试样坐标系下应变张量的模型，该模型利用基体晶粒取向数据和外加载荷方向计算{1122}，{1012}和{1121）3种孪生系统在孪晶坐标系下的应变张量，并将其转换至宏观试样坐标系下．将计算结果和工业纯钛的单轴压缩实验数据对比，得到较好吻合，从而提出并验证了多晶钛的孪生系统选择准则，即特定取向的晶粒中只能激发微观应变张量与宏观变形一致的孪生系统．通过计算，绘制了分别沿TD，RD和ND3个方向的单轴压缩和拉伸两种变形下可激发{1122}，l1012l和{112ll3种孪生系统的晶体取向分布{0002}极图；同时，发现{1122}和{1012）两种孪生系统所引起的差取向和激发所需的晶体取向条件之间相互协调，二者在晶体学取向的角度上可相互以对方为基体反复激发，这是钛及其合金塑性变形的重要机制之一．

英文摘要：

This paper describes a new method for infinitesimal strain theory calculations of twinning strain tensors within the macroscopic sample coordinate frame. In calculating the strain tensors within this frame, the method uses the data from the initial grain orientation and the force direction, and transforms these into the sample coordinate frame. The calculated result was compared to the experimental result for uniaxial compression and yields a very satisfactory agreement. The criterion for the selection of twinning systems can be established is that only the twinning systems for which the strain tensors fit the macro strain can be activated in the specific orientated grains. The paper produced {0002} pole figures indicating the orientation distribution of grains can accommodate the {1122}, {1012}, and {1121} twinning systems along the respective transvers, rolling and normal directions under uniaxial tension and compression. It is also found that the {1122} and {1012} twinning systems can be activated repeatedly taking the other as initial parent crystal, which is an important plastic deformation mechanism in titanium and its alloys.