ch2位错-2.4位错与晶体缺陷作用

1、1Ch2 Ch2 位错位错2.1 2.1 位错理论的产生位错理论的产生2.2 2.2 位错的几何性质位错的几何性质2.3 2.3 位错的弹性性质位错的弹性性质2.4 2.4 位错与晶体缺陷的位错与晶体缺陷的相互作用相互作用2.5 2.5 位错的动力学性质位错的动力学性质2.6 2.6 实际晶体中的位错实际晶体中的位错22.1 2.1 位错理论的产生位错理论的产生一、晶体的塑性变形方式一、晶体的塑性变形方式二、单晶体的塑性变形二、单晶体的塑性变形三、多晶体的塑性变形三、多晶体的塑性变形四、晶体的理论切变强度四、晶体的理论切变强度五、位错理论的产生五、位错理论的产生六、位错的基本知识六、位错的基本

2、知识32.2 2.2 位错的几何性质位错的几何性质一、位错的几何模型一、位错的几何模型二、柏格斯矢量二、柏格斯矢量三、位错的运动三、位错的运动四、位错环及其运动四、位错环及其运动五、位错与晶体的塑性变形五、位错与晶体的塑性变形六、割阶六、割阶42.3 2.3 位错的弹性性质位错的弹性性质一、弹性连续介质、应力和应变一、弹性连续介质、应力和应变二、刃型位错的应力场二、刃型位错的应力场三、螺型位错的应力场三、螺型位错的应力场四、位错的应变能四、位错的应变能五、位错的受力五、位错的受力六、向错六、向错七、位错的半点阵模型七、位错的半点阵模型52.4 2.4 位错与晶体缺陷的相互作用位错与晶体缺陷的相

3、互作用一、位错间的相互作用力一、位错间的相互作用力二、位错与界面的交互作用二、位错与界面的交互作用三、位错与点缺陷的交互作用三、位错与点缺陷的交互作用6Interactions Between DislocationsWe will first investigate the interaction between two straight and parallel dislocations of the same kind.q If we start with screw dislocations, we have to distinguish the following cases: 7

4、In analogy, we next must consider the interaction of edge dislocations, of edge and screw dislocations and finally of mixed dislocations. q 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 addin

5、g the results. With the formulas for the stress and strain fields of edge and screw dislocations one can 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 tha

6、t. We can classify some basic cases without calculating anything by just examining one obvious rule: q If 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 comb

7、ined strain field is lower than that of the single dislocation, they will attract each other.8This leads to some simple cases: 1. Arbitrarily curved dislocations with identical b on the same glide plane will always repel each other. 92. Arbitrary dislocations with opposite b vectors on the same glid

8、e plane will attract and annihilate each other Edge dislocations with identical or opposite Burgers vector 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.10The ge

9、neral formula for the forces between edge dislocations in the geometry shown above isFx = Gb2 / 2p p(1 n n) x (x2 y2) /(x2 + y2)2 Fy = Gb2 / 2p p(1 n n) y (3x2 + y2) /(x2 + y2)2 q 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 b

10、etween the dislocations.qFor y 0 we find zones of repulsion and attraction. At some specific positions the force is zero - this would be the equilibrium configurations; it is shown below. q The formula for Fy is just given for the sake of completeness. Since the dislocations can not move in y-direct

11、ion, it is of little relevance so far.11The illustration in the link gives a quantitative picture of the forces acting on one dislocation on its glide plane as a function of the distance to another dislocation.12一、位错间的相互作用力一、位错间的相互作用力1314（一）相互平行的两个螺位错间的作用力（一）相互平行的两个螺位错间的作用力（二）相互平行的两个刃位错间的作用力（二）相互平行的

12、两个刃位错间的作用力（三）其它情况的位错之间的作用力（三）其它情况的位错之间的作用力（四）位错运动的晶格阻力（四）位错运动的晶格阻力P-NP-N力力15（一）相互平行的两个螺位错间的作用力（一）相互平行的两个螺位错间的作用力16上式说明，两平行螺位错之间只有径向交互作用径向交互作用，因而交互作用力是一中心力。（即F=Fz=0,Fr0）17（二）相互平行的两个刃位错间的作用力（二）相互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18根据根据F=bF=b有：有：F Fyx= =yxbb，F Fxx= =xxbb1920212223Forces

13、between Edge Dislocations Shown is the force between edge dislocations of identical and opposite Burgers vectors as a function of their normalized distance.q The distance x between the dislocations is expressed in units of y, the distance of the glide planes.24qThe force changes from repulsive to at

14、tractive or vice verse for a distance x = y; i.e. if the dislocations are at an angle of 45o relative to the glide plane.q The 45o position is a stable equilibrium position for opposite Burgers vectors, because at this position F = 0, and dF/dx 基体原子基体原子R 柯垂耳柯垂耳(Cottrell)处理处理: 假设假设(1)晶体为连续弹性介质晶体为连续弹性

15、介质;(2)溶质原子为刚球溶质原子为刚球;(3)溶质溶质原子引起的点阵畸变是球形对称畸变原子引起的点阵畸变是球形对称畸变.则溶质原子溶入则溶质原子溶入,相当于在相当于在(r,)处挖一个处挖一个R的球形洞的球形洞,再挤入再挤入一个一个R的刚球的刚球. 交互作用能交互作用能=刚球挤入过程中反抗位错应力场做的功刚球挤入过程中反抗位错应力场做的功=位位错应力场做的负功错应力场做的负功由4041溶质原子R基体原子R,即4243（二）螺位错与点缺陷的交互作用（二）螺位错与点缺陷的交互作用因为螺位错是纯切应力场，所以当点缺陷引起因为螺位错是纯切应力场，所以当点缺陷引起球球形对称畸变时，两者无交互作用；形对称

16、畸变时，两者无交互作用；若点缺陷引起的是若点缺陷引起的是非球形对称畸变非球形对称畸变时，则溶质原时，则溶质原子与位错仍发生交互作用，结果使溶质原子向位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；错偏聚，形成溶质原子气团；例如，钢中的例如，钢中的C、N溶入溶入bcc铁的八面体间隙时，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，能与位错发生交互场既有正应力，又有切应力，能与位错发生交互作用；作用；螺型位错的纯切应力场可以等效一个正应力场，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

17、优分布，形成使溶质原子择优分布，形成史诺克（史诺克（Snock）气团气团，对位错有强烈的钉扎作用。对位错有强烈的钉扎作用。4445（三）关于空位与位错的作用（三）关于空位与位错的作用46The fundamental interactions between The fundamental interactions between dislocations and elastic obstaclesdislocations and elastic obstacles The goal of the work is to understand the fundamental interactio

18、ns between dislocations and elastic obstacles. The primary tool that will be used is the in-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 magni

19、tude of the pinning strength, the bypass mechanism, and the process by which dislocation loops are destroyed can be ascertained. Copper was selected simply for ease of comparison with computer simulation studies. In-situ TEM straining specimens of 99.999% pure polycrystalline Cu were cut from 250 mm thick cold rolled strip into 11mm by 2.7 mm pieces. Holes for the straining pins in the stage were drilled in the ends of the tensile bars followed by polishing the surfaces to a 600-grit finish. Samples were then annealed at 750 C in a vacuum furnace for 2 hours and allowed to