Question

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

          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

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 g 28538

Added by Barbara Y.

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