reaction equal to that after the reaction, so this dislocation reaction is both vectorially proper and energetically favorable.
作业6：原版教材第181页第18题
18. Suppose a metal single crystal is loaded (stressed) in the [101] direction.
a. If the critical resolved shear stress for this material is 0.34MPa, what magnitude of
10] slip system? applied stress is necessary for dislocations to begin to move in the (111) [1 b. If the slip system listed in part a is valid, does this metal have the FCC HCP, or BCC
crystal structure? Solution:
a. we know that：?k?0.34MPa loaded in the direction：[101] slip system：[111][110] ???k cos?cos?[101]?[111]12?02?12?1?12?122cos???1?12? 2?36?1?0?01? 22?2cos???101???110?12?02?12?1?12?02???0.34?0.34?6??0.833MPa 21?62So the magnitude of applied stress is 0.833MPa
b. If the slip system listed in part a is valid, then this metal has the FCC crystal structure.
作业7：原版教材第181页第19题
19. Suppose you have an FCC metal single crystal which is known to have a critical resolved shear stress of 55.2MPa.Find the largest normal stress that could be applied to a bar of this material in the [112] direction before dislocations begin to move in the 101 direction on the (111) plane. Solution:
??
We know that ?k?55.2MPa loaded in the direction：[112] slip system：(111) 101 ?????k
co?s?cos?then cos???112???111?12?12?22?12?12?12?1?1?24?
6?332 cos???112???101?12?12?22?12?02?12?1?21 ??6?223 ?max?55.255.2?36 ??202.8MPa42?1?32???????23?So the largest normal stress is 202.8MPa.
作业8：原版教材第181页第22题
22. The critical resolved shear stress of a BCC metal is 7 MPa. A single crystal of this alloy is stressed along the [001] direction. a. What slip systems will be activated? b. What normal stress will cause plastic deformation? Solution:
slip systems in BCC: {110}<111> {112}<111> {123}<111> 10) (101) (011) {110}： (110) (101) (011) (1s 若点乘[001]， 只有第三个位置不为0的cos?值不为0 co? cos??11??0.707
2?12{112}：(112) (112) (112) (112)
(121) (121) (121) (121)
1) (211) (211) (211) (21 点剩[001] 最大为第三位为2的
cos??2?0.816
6?1
{123}：(123) (132) (213) (231) (312) (321) (123) (132) (213) (231) (312) (321)
(123) (132) (213) (231) (312) (321)
(123) (132) (213) (231) (312) (321) 点剩[001]，最大为第三位为3的：
cos??33??0.8017
1?4?9?11411??0.577 3?13所有的λ相同：cos??故被首先激活的将为：红色所示，所需的??
作业9：原版教材第182页第24题 ?cos??cos??7?14.867
0.816?0.57724. Calculate the magnitude of the applied stress in the [123] direction necessary to promote slip in the [111] direction on the (110) plane in a BCC crystal with ?CR?5.5MPa. [It may or may not help you to know that a certain FCC single crystal with ?CR?0.55MPa slips in the [110] direction on the (111) plane under an applied stress of 9.63?10MPa applied in the [123] direction. ] Solution:
Loaded in the direction: [123] slip system: [111], 110,
?2???CR?5.5MPa
cos???123???110?12?22?32?12?12?02?1?21 ??13?226 cos???123???111??13?36 39
???CR?5.5?13?3?13?25.5?13?6 ???cos??cos?6?16
作业10：
分析下列位错反应能否进行： 几何条件：?b前??b后
22能量条件：?前??后
解答：
a???a???a???（1）?101???121???111?
2??6??3??a???a???a???a???a???a???几何：?101???121???303???121???222???111? 满足几何条件
2??6??6??6??6??3??a2a???22能量：b1??101?， 其长度=1?0???1?22??a2a???22 b2??121?， 其长度=1?2?166????12?2a 2??12?6a 63a 3a222a??? b3??111? ， 其长度=1?1?133????12?2b12?b2?22628222a?a?a?a 43612331b32?a2?a2
9322??b前??b后 故可以进行
aa???（2）a?100???101???101?
22??aa???a ?101???101???200??a?100?
22??2满足几何条件：b1?a
a22 b2?1?0?12??12?2a 2
b3?2a 223a2a2b?a b?b???a2
2221222能量相等
aaa???（3） ?112???111???111?
326??aaaa??? b1?b2??224???333???557???111? 故不能反应
6666??aa????（4）a?100???111???111?
22?? b1 b2 b3 b2?b3?212a?200??a?100? 满足几何条件 2223a2322 b?a b? b3?a 44 b2?b3?22622a?b1 不能反应 4
作业11：
在一个简单立方二维晶体中，画出一个正刃型位错和一个负刃型位错，并
（1） 用柏氏回路求出正刃型位错的柏氏矢量:
（2）若将正、负刃型位错反向时，其b是否也反向？ 是
（3）具体写出该柏氏矢量的大小和方向
正刃 b??a?100? ?100?