1. Roth et. al. (1997) modeled solid
solution strengthening in nickel
alloys. They estimated the yield
stress increment in a nickel alloy due
to alloying with different elements
according to the Gypen and
Deruyttere equation:
$$Δσ = (\sum_{i} k_{i}^{1/n} c_{i})^{n}$$
where n can be estimated as 1/2 for the
case of Roth et. al.'s work, c₁ is the
concentration of solute I, and k₁ is the
strengthening constant for solute i.
Knowing that the yield stress of pure
nickel is 59 Mpa, plot the calculated
new yield stress as a function of
concentration for:
a) Zirconium, c₁ = 0 to 15 atomic %
b) Cobalt, c₁ = 0 to 15 atomic %
c) Zr and Co, cco = 0 to 15 atomic %, Czr
= 1 atomic %
Propose an explanation for the trend
you see between a) and b).
Table II. Strengthening Constants for Solution
Strengthening in Nickel
Alloying Element
Strengthening Constant, k,
(MPa At. Fraction 1/2)
Al
225
Si
275
Zn
386
Ga
310
Ge
332
In
985
Sn
1225
Sb
960
Ti
775
V
408
Zr
2359
Hf
1401
Nb
1183
Ta
1191
Cr
337
Mo
1015
W
977
Mn
448
Fe
153
Ru
1068
Co
39.4
Rh
520
Cu
86.7
Cu
1061
Pd
492