图  1  孪晶晶粒数与孪晶Schmid因子的关系^[8]

Figure  1.  Relationship between twin grain number and twin Schmid factor^[8]

图  2  (a)应变为0.08时AM30样品2个压缩孪晶的EBSD图（黑色圆圈表示应变兼容）；(b)临近轧制方向取向的晶粒内形成的{$10\overline {1}1$}压缩孪晶（红色）的EBSD图；(c) 2(b)图中基体的(0002)极图（黑色六边形）、6个孪晶取向（黑色正方形）和选择的临近晶粒孪晶取向（黑色圈内）以及它们的Schmid因子^[9]

Figure  2.  (a) EBSD map of AM30 sample pulled to 0.08 strain showing two contraction twins (The black circles indicate strain compatibility.); (b) EBSD map of a {$10\overline {1}1$} contraction twin (in red) formed within a near rolling direction orientation; (c) (0002) pole figure for the Fig.2 (b) matrix (black hexagon), the six twin variants (black squares), the selected variant (circled in black), and their respective Schmid factors^[9]

图  3  晶粒内孪晶数量和厚度随晶粒面积的变化^[27]

Figure  3.  Evolution of the number and thickness of twins with grain area^[27]

图  4  双峰晶粒AZ91合金的晶粒尺寸分布(a)和应力-应变曲线(b)^[38]

Figure  4.  Grain size distribution (a) and stress-strain curves of bimodal-grained AZ91 sample (b)^[38]

图  5  (a)基于传统孪晶理论的孪晶相互作用（由于孪晶位错不能穿透孪晶界，当两者相互靠近时将阻碍孪晶的增长）；(b)非位错形式的孪晶增长（T₁）（孪晶能够通过改变孪晶面产生分支而包围另一个孪晶）；(c) 非位错形式的孪晶增长（T₂）（孪晶通过侧向成长而绕过另一个孪晶）^[45]

Figure  5.  (a) Twin-twin interaction based on classical twinning theory (The growth of the twin variants will be impeded as the variants approach close to each other because the twinning dislocations are unable to penetrate the twin boundaries.); (b) non-dislocation mediated twin growth (T₁) (A twin variant can branch out by changing the habit plane and surround the other variant.); (c) non-dislocation mediated twin growth (T₂) (A twin variant can spread laterally and grow around the other variant.)^[45]

图  6  冲击波传播和材料微结构：(a)冲击示意图和3个观测点；(b)冲击波传播的时间-位置图和3个观测点在不同时刻（t）的微结构^[1]

Figure  6.  The propagation of shock wave and the microstructure of material: (a) The schematic diagram of shock and three observation point; (b) the time-distance diagram of the shock experiment and corresponding schematic diagrams of the microstructure at 3 location at different times (t)^[1]

图  7  包含孪晶的变形梯度F分解示意图^[60]

Figure  7.  Extension of the multiplicative decomposition of the deformation gradient F to include deformation twinning^[60]

图  8  单晶镁平面应变压缩模拟（实线）和实验（A～G）的应力-应变曲线比较^[80]

Figure  8.  Comparison of stress–strain responses from single crystal Mg plane-strain compression simulations (solid lines) with experiments (A–G)^[80]

图  9  晶粒内的孪晶和退孪晶过程示意图（绿色实线为孪晶界，蓝色和红色点线代表晶格取向；${s}^{\alpha {\mathrm{M}}}$和${n}^{\alpha {\mathrm{M}}}$分别表示基体中孪晶面和法线，${s}^{\alpha {\mathrm{T}}}$和${n}^{\alpha {\mathrm{T}}}$表示孪晶区域中孪晶面和法线方向）^[91]

Figure  9.  Schematic representation of twinning and de-twinning in a grain (Solid green lines represent twinning boundaries; Lattices orientations are represented by dotted blue lines and dotted red lines; ${{{s}}}^{\alpha {\mathrm{M}}}$ and ${{{n}}}^{\alpha {\mathrm{M}}}$ are the twinning plane and normal direction in matrix; ${{{s}}}^{\alpha {\mathrm{T}}}$ and ${{{n}}}^{\alpha {\mathrm{T}}}$ are the twinning plane and normal direction in twin domain.)^[91]

图  10  (a)孪晶不全位错通过孪晶面滑动和垂直于孪晶面增长到临近点X的传播示意图（$ {l}_{\mathrm{g}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{e}} $和$ {l}_{\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{w}\mathrm{t}\mathrm{h}} $为孪晶成核点到增长点X的水平和垂直距离，$ {v}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}} $和$ {v}_{\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{w}\mathrm{t}\mathrm{h}} $为孪晶沿孪晶面和孪晶面法线的增长速度）；(b)包含孪晶的多晶微结构（晶粒内不同颜色代表不同取向）^[95]

Figure  10.  (a) Sketch map of a twin partial dislocation propagation to a neighboring point X by respectively gliding on the twin plane and growing normal to it ($ {l}_{\mathrm{g}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{e}} $ and $ {l}_{\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{w}\mathrm{t}\mathrm{h}} $ are the horizontal and vertical distances from twin nucleation point to growth point X. $ {v}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}} $ and $ {v}_{\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{w}\mathrm{t}\mathrm{h}} $ are the growth velocity of twins along the twin plane and its normal.); (b) polycrystalline microstructure with twins (Different colors in grains represent different orientations.)^[95]