SOLUTION HOMEWORK #5

EXERCISE 5.1

Copper is FCC with r =0.157nm. We can calculated a_o and \

q = 0.5^o = 0.0087 rad

dislocation spacing in the symmetrical tilt boundary, is D = b/q

EXERCISE 5.9

We have e=ln(1+e), e=ln (l_e/l_o) and

Since

, We can write or

Substituting this value of in the Hall-Petch relation

We have

or

EXERCISE 5.11

0.1mm =100mm and the thickness of the specimen is 0.1mm.The grain size is the same dimension as the thickness. So, the 100mm would be not considered truly polycrystalline material because only a few grain boundaries could be find in the section of the specimen. For the Dum’s foils, the “truly polycrystalline” increase as grain size decrease.

EXERCISE 5.12

(a) The best linearity

(b) You can determine the correct exponent by plotting the equation

, this equation is a lineal equation:

The slope of the plot of ln s_y vs. ln D would yield the value of n, which would be the exponent for D, n=-0.45.

EXERCISE 5.18

We have n=2

(a)The grain size should be

and

(b) The grain diameter is

EXERCISE 5.21

(a) The magnification of the picture in the textbook is

, Using the lineal intercept method, we draw two test lines, each 70mm. The number of intercepts on the test line is 32. The mean lineal intercept is

and

(b) Using the ASTM method, the number of the grains in 1 in² at 115X is 27. Then the number of the grains in 1in² at 100x is:

and