Comments on “Yield strength of metals as a function of grain size”

LETTERS

TO THE EDITOR

Comments on “Yield strength of metals as a

D-Ii2 definiteIy possible, and D-1/3 a borderline

case.

function of grain size”*

It may be surprising that n for the borderline

case,

which depends not only on a, and b; but also on the range of grain sizes yet investigated, should be 3 for

W. M. Baldwin Jr.(l) points out the interesting and quite significant fact that most data on the dependence of yield

stress

on grain

size can

be equally

all materials.

well

represented as straight lines in plots of a, vs. D-l, D-1/2, or also P1/3 (D = grain diameter). The fact that apparently

law.

zero, which is apparently substantial in about 40 per cent of the cases (e.g. Ti and MO), and

It

both positive and negatkve.t Admittedly the spread could be interpreted as experimental error if there were any other reason to suspect an inverse cube root

should be noted, however, that if gV is represented by an equation

of the form: o;l = aD-lin

with varying values

of

Supposing

n,

n,

+ b

law.

(1)

b m 0 is to be expected for some mere mathematical reasoning. (2)

to Baldwin’s

figure 1) and plotting

seem large

enough

not

to

of the kind drawn by Baldwin and suggests n = 2 as

is the correct law (where a2 and b, are chosen roughIy to correspond

it does

b = 0. The fact, however, that an inverse cube root law would give negative yield stresses at finite grain sizes for many materials precludes general conclusions

that + b2

However

“suggest” any physical law, if indeed a law of the form (1) is found to be less natural than one with

by

c Cd= a,D-li2

that,

around

many materials go through zero is taken by Baldwin and to suggest a physical

out however

the best fitting straight lines would show some spread

on a plot of uV vs. D-1/3 the lines for

to be significant

It must be pointed

although the experimental data can be represented by Baldwin’s lines which go exact,ly through zero,

the highest possible

this

value for all materials

over the

total range of grain diameters. U. F. KOCES Goram McKay Laboratory Harvard University References 1. W. M. BALDWIN, JR., A&

Met. 6, 139 (1958).

* Received March 24, 1958.

t The case of the steels at 78”K, which Baldwin exempts from generalitv bv the incorrect argument that the Cottrell effect -would ge cmportant at that” temperature but not at mm temperature, must be counted as an instance from those materials for which the best fitted straight lines in a plot of o, vs. D-‘13 give an intercept b, # 0.

FIa. 1

in coordinates

An effect of thermal neutrons on Cu,Au$

camvs. D-1/3 (see figure) we see that, in

the range measured,

this curve can well be mistaken

for

a straight line. This line, however, would necessarily cut the ordinate at a value b, lower than b,, and on each plot of d vs. D-l/” for increasing a, this intercept would be lower. For one value of n it will be at about b w 0, and for each higher n value

it will then give negative yield stresses for finite grain diameters, if the law were to hold for all grain sizes. So from the data as represented by Baldwin, a dependence on O-‘/4 would be physically impossible, ACTA METALLURGICA,

VOL. 7, FEBRUARY

1959

Several

investigators

have

reported

that

slow

neutrons seem capable of changing some macroscopic properties of metallic solids.(1*2s3) Cook and Gushing(l) ascribed

the differences

in ordering

of copper-gold

samples when reactor irradiated in and out of cadmium shields to the effect of the 19sHg impurity which results from the radioactive gold.

decay

of

slow

neutron

induced

Blewitt and Coltman(4) rejected this hypothesis both on the grounds that only minute amounts of mercury were formed and that eIectron irradiation, 131

which

is

essentially

unable

to

form