Method of optimizing heat treatment of alloys by predicting thermal growth
View Patent ↗The present invention discloses a method for optimizing heat treatment of precipitation-hardened alloys having at least one precipitate phase by decreasing aging time and/or aging temperature using thermal growth predictions based on a quantitative model. The method includes predicting three values: a volume change in the precipitation-hardened alloy due to transformations in at least one precipitation phase, an equilibrium phase fraction of at least one precipitation phase, and a kinetic growth coefficient of at least one precipitation phase. Based on these three values and a thermal growth model, the method predicts thermal growth in a precipitation-hardened alloy. The thermal growth model is particularly suitable for Al—Si—Cu alloys used in aluminum alloy components. The present invention also discloses a method to predict heat treatment aging time and temperature necessary for dimensional stability without the need for inexact and costly trial and error measurements.
1. A method for optimizing alloy heat treatment by quantitatively predicting thermal growth during alloy heat treatment, the method comprising the steps of:
(a) predicting a volume change due to transformations in an each precipitate phase;
(b) predicting an equilibrium phase fraction of the each precitate phase;
(c) predicting a kinetic growth coefficient of the each precipitate phase;
(d) predicting thermal growth in a precipitation-hardened Al —Si—Cu alloy according to a thermal growth model using the volume change due to transformations in the each precipitate phase; the equilibrium phase fraction of the each precipitate phase; and the kinetic growth coefficient of the each precipitate phase, wherein the thermal growth model may be expressed mathematically as:
g
(
t
,
T
)
=
(
1
-
γ
)
∑
i
=
1
n
δ
V
i
3
V
i
f
i
(
t
,
T
)
where
δ
V
i
3
V
i
is volume change due to transformations in precipitate phase i,
ƒ i (t,T) is fraction of solute in precipitate phase i as a function of time and temperature,
T is temperature,
t is time, and
γ is fraction of solute lost to eutectic phases; and
(e) aging the precipitation-hardened Al—Si—Cu alloy for an aging time (t) and an aging temperature (T) according to the thermal growth model to produce a dimensionally stable precipitation-hardened Al—Si—Cu alloy.
2. The method of claim 1 , wherein the volume change due to transformations in precipitate phase i may be expressed mathematically as:
Δ
V
i
=
1
x
i
{
V
i
-
[
(
1
-
x
i
)
V
A
l
+
x
V
C
u
]
}
where V 1 is volume per atom in precipitation phase i,
x 1 is atomic fraction of Cu in precipitation phase i,
V Al is volume per atom Al, and
V Cu is volume per atom Cu.
3. The method of claim 2 , wherein the fraction of Cu in precipitate phase θ as a function of time and temperature may be expressed mathematically as:
ƒ 0 ( t,T )= f θ eq ( T )(1−exp[− k θ ( T )( t +Δ θ ) n θ ])
where ƒ θ eq (T) is equilibrium phase fraction of precipitate phase θ,
k θ (T) is kinetic growth coefficient of precipitate phase θ,
Δ θ is time shift applied to guarantee phase fraction continuity for precipitation phase θ, and
n θ is determined by at least precipitate morphology and nucleation rate for precipitation phase θ.
4. The method of claim 3 , wherein the time shift applied to guarantee phase fraction continuity for precipitation phase θ may be expressed mathematically as:
Δ
θ
=
-
1
k
θ
(
T
s
)
ln
[
1
-
f
θ
(
t
a
,
T
a
)
f
θ
eq
(
T
s
)
]
-
t
a
for
t
≥
t
a
Δ θ =0 for t<t a
where T t is in-service temperature,
T a is aging temperature, and
t a is time at which temperature changes from T n to T s .
5. The method of claim 3 , wherein the kinetic growth coefficient of precipitate phase θ may be expressed mathematically as:
k
θ
(
T
)
=
0.43
exp
[
161
473
-
T
-
3.33
3
]
where T is temperature in degrees Kelvin, and
k θ (T) is the kinetic growth coefficient of precipitate phase θ in units of inverse hours.
6. The method of claim 3 , wherein the equilibrium phase fraction of precipitate phase θ may be expressed mathematically as:
f
θ
eq
(
T
)
=
0.01417
-
exp
[
-
11.6045
*
370.9
-
0.097
T
T
]
where T is temperature in degrees Kelvin.
7. The method of claim 1 , wherein the precipitation phases include at least the precipitate phase θ and the precipitate phase θ′.
8. The method of claim 7 , wherein the fraction of Cu in precipitate phase θ′ as a function of time and temperature may be expressed mathematically as:
ƒ θ′ ( t,T )=ƒ θ′ eq ( T )(1−exp[− k θ′ ( T )( t +Δ θ′ ) n θ′ ])−ƒ θ ( t,T )
where ƒ θ′ eq (T) is equilibrium phase fraction of precipitate phase θ′,
k θ′ (T) is kinetic growth coefficient of precipitate phase θ′,
Δ θ′ is time shift applied to guarantee phase fraction continuity for precipitation phase θ′, and
n θ′ is determined by at least precipitate morphology and nucleation rate for precipitation phase θ′, and
ƒ θ′ (t,T) is fraction of Cu in precipitate phase θ′ as a function of time and temperature; wherein
ƒ θ′ (t,T) is greater than or equal to zero.
9. The method of claim 8 , wherein the time shift applied to guarantee phase fraction continuity for precipitation phase θ′ may be expressed mathematically as:
Δ
θ
′
=
-
1
k
θ
′
(
T
s
)
ln
[
1
-
f
θ
′
(
t
a
,
T
a
)
f
θ
′
eq
(
T
s
)
]
-
t
a
Δ θ′ =0 for t<t a
where T s is in-service temperature,
T n is aging temperature, and
t n is time at which temperature changes from T n to T s .
10. The method of claim 8 , wherein the kinetic growth coefficient of precipitate phase θ′ may be expressed mathematically as:
k
θ
′
(
T
)
=
0.43
exp
[
-
11800
T
+
24.34
]
where T is temperature in degrees Kelvin, and
k θ′ (T) is the kinetic growth coefficient of precipitate phase θ′ in units of inverse hours.
11. The method of claim 8 , wherein the equilibrium phase fraction of precipitate phase θ′ may be expressed mathematically as:
f
θ
′
eq
(
T
)
=
0.01420
-
exp
[
-
11.6045
*
396.2
-
0.165
T
T
]
where T is temperature in degrees Kelvin.
12. The method of claim 1 , wherein the predicting steps (a), (b), and (c) use a combination of first-principles calculations, computational thermodynamics, and electron microscopy and diffraction techniques.
13. A method for optimizing alloy heal treatment, the method comprising the steps of:
defining a thermal growth for dimensional stability;
predicting a combination of an aging time and an aging temperature which yields the thermal growth for dimensional stability; and
aging a precipitation-hardened Al—Si—Cu alloy for about the predicted aging time and about the predicted aging temperature, wherein the predicting step uses a function of form:
g
(
t
,
T
)
=
(
1
-
γ
)
∑
i
=
1
n
δ
V
i
3
V
i
f
i
(
t
,
T
)
wherein the function is inverted to solve for the predicted aging time and the predicted aging temperature based on a thermal growth of stability, and wherein aging for a combination of about the predicted aging time and about the predicted aging temperature produces a dimensionally stable precipitation-hardened Al—Si—Cu alloy.