ch2位错24位错与晶体缺陷作用详解

1、ch2位错24位错与晶体缺陷作用详解2.1 位错理论的产生一、晶体的塑性变形方式二、单晶体的塑性变形三、多晶体的塑性变形四、晶体的理论切变强度五、位错理论的产生六、位错的根本知识22.2 位错的几何性质一、位错的几何模型二、柏格斯矢量三、位错的运动四、位错环及其运动五、位错与晶体的塑性变形六、割阶32.3 位错的弹性性质一、弹性连续介质、应力和应变二、刃型位错的应力场三、螺型位错的应力场四、位错的应变能五、位错的受力六、向错七、位错的半点阵模型42.4 位错与晶体缺陷的互相作用一、位错间的互相作用力二、位错与界面的交互作用三、位错与点缺陷的交互作用5Interactions Between D

2、islocationsWe will first investigate the interaction between two straight and parallel dislocations of the same kind. If we start with screw dislocations, we have to distinguish the following cases: 6In analogy, we next must consider the interaction of edge dislocations, of edge and screw dislocatio

3、ns and finally of mixed dislocations. The case of mixed dislocations - the general case - will again be obtained by considering the interaction of the screw- and edge parts separately and then adding the results. With the formulas for the stress and strain fields of edge and screw dislocations one c

4、an calculate the resolved shear stress caused by one dislocation on the glide plane of the other one and get everything from there. But for just obtaining some basic rules, we can do better than that. We can classify some basic cases without calculating anything by just examining one obvious rule: I

5、f the superposition of the strain fields of dislocations add up to values of the compressive or tensile strain larger than those of a single dislocations, they will repulse each other. If the combined strain field is lower than that of the single dislocation, they will attract each other.7This leads

6、 to some simple cases: 1. Arbitrarily curved dislocations with identical b on the same glide plane will always repel each other. 82. Arbitrary dislocations with opposite b vectors on the same glide plane will attract and annihilate each other Edge dislocations with identical or opposite Burgers vect

7、or b on neighboring glide planes may attract or repulse each other, depending on the precise geometry. The blue double arrows in the picture below thus may signify repulsion or attraction.9The general formula for the forces between edge dislocations in the geometry shown above isFx =Gb2 / 2p(1 n)x (

8、x2 y2) /(x2 + y2)2 Fy =Gb2 / 2p(1 n)y (3x2 + y2) /(x2 + y2)2 For y = 0, i.e. the same glide plane, we have a 1/x or, more generally a 1/r dependence of the force on the distance r between the dislocations.For y 0 we find zones of repulsion and attraction. At some specific positions the force is zero

9、 - this would be the equilibrium configurations; it is shown below. The formula for Fy is just given for the sake of completeness. Since the dislocations can not move in y-direction, it is of little relevance so far.10The illustration in the link gives a quantitative picture of the forces acting on

10、one dislocation on its glide plane as a function of the distance to another dislocation.11一、位错间的互相作用力1213一互相平行的两个螺位错间的作用力二互相平行的两个刃位错间的作用力三其它情况的位错之间的作用力四位错运动的晶格阻力P-N力14一互相平行的两个螺位错间的作用力15上式说明，两平行螺位错之间只有径向交互作用，因此交互作用力是一中心力。即F=Fz=0,Fr016二互相平行的两个刃位错间的作用力yy 与zz 不考虑，它们对位错运动无影响xx 使b2攀移yx使b2滑移17根据F=b有：Fyx=yx

11、b，Fxx=xxb1819202122Forces between Edge Dislocations Shown is the force between edge dislocations of identical and opposite Burgers vectors as a function of their normalized distance. The distance x between the dislocations is expressed in units of y, the distance of the glide planes.23The force chan

12、ges from repulsive to attractive or vice verse for a distance x = y; i.e. if the dislocations are at an angle of 45o relative to the glide plane. The 45o position is a stable equilibrium position for opposite Burgers vectors, because at this position F = 0, and dF/dx 基体原子R柯垂耳(Cottrell)处理: 假设(1)晶体为连续

13、弹性介质;(2)溶质原子为刚球;(3)溶质原子引起的点阵畸变是球形对称畸变.那么溶质原子溶入,相当于在(r,)处挖一个R的球形洞,再挤入一个R的刚球.交互作用能=刚球挤入过程中对抗位错应力场做的功=位错应力场做的负功由3940溶质原子R基体原子R,即4142二螺位错与点缺陷的交互作用因为螺位错是纯切应力场，所以当点缺陷引起球形对称畸变时，两者无交互作用；假设点缺陷引起的是非球形对称畸变时，那么溶质原子与位错仍发生交互作用，结果使溶质原子向位错偏聚，形成溶质原子气团；例如，钢中的C、N溶入bcc铁的八面体间隙时，引起非球形对称畸变称为四方畸变，其应力场既有正应力，又有切应力，能与位错发生交互作用

14、；螺型位错的纯切应力场可以等效一个正应力场，使溶质原子择优分布，形成史诺克Snock气团，对位错有强烈的钉扎作用。4344三关于空位与位错的作用45The fundamental interactions between dislocations and elastic obstaclesThe goal of the work is to understand the fundamental interactions between dislocations and elastic obstacles. The primary tool that will be used is the in

15、-situ TEM deformation technique. With this technique it is possible to directly observe the interaction between dislocations and elastic obstacles at high spatial resolution. From these observations, the magnitude of the pinning strength, the bypass mechanism, and the process by which dislocation lo

16、ops are destroyed can be ascertained. Copper was selected simply for ease of comparison with computer simulation studies. In-situ2.46Figure 1. The captured video frame contains a pinned dislocation at the instant before breaking free (Left). The distance between obstacles, l, is measured. In an image editing computer application, circles are d