Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-08 GTBL042-Callister-v3 October 4, 2007 11:51

2nd Revised Pages

8.7 Plastic Deformation of Polycrystalline Metals • 253

x

y

z

Slip

direction

[111]

Slip plane

(110)

Direction of

applied stress

[010]

Normal to

slip plane







For the determination of the value of φ, let [u 1 v 1 w 1 ]=[110] and

[u 2 v 2 w 2 ]=[010] such that

φ=cos−^1

⎧

⎪⎨

⎪⎩

(1)(0)+(1)(1)+(0)(0)

√

[(1)^2 +(1)^2 +(0)^2 ][(0)^2 +(1)^2 +(0)^2 ]

⎫

⎪⎬

⎪⎭

=cos−^1

(

1

√

2

)

= 45 ◦

However, forλ, we take [u 1 v 1 w 1 ]=[111] and [u 2 v 2 w 2 ]=[010], and

λ=cos−^1

⎡

⎣√ (−1)(0)+(1)(1)+(1)(0)

[(−1)^2 +(1)^2 +(1)^2 ][(0)^2 +(1)^2 +(0)^2 ]

⎤

⎦

=cos−^1

(

1

√

3

)

= 54. 7 ◦

Thus, according to Equation 8.2,

τR=σcosφcosλ=(52 MPa)(cos 45◦)(cos 54. 7 ◦)

=(52 MPa)

(

1

√

2

)(

1

√

3

)

= 21 .3 MPa (3060 psi)

(b)The yield strengthσymay be computed from Equation 8.4;φandλwill be

the same as for part (a), and

σy=

30 MPa

(cos 45◦)(cos 54. 7 ◦)

= 73 .4 MPa (10,600 psi)

8.7 PLASTIC DEFORMATION OF

POLYCRYSTALLINE METALS

For polycrystalline metals, because of the random crystallographic orientations of

the numerous grains, the direction of slip varies from one grain to another. For

each, dislocation motion occurs along the slip system that has the most favorable