9.5 FeAl 365
above which the contribution is small. k is again Boltzmann’s constant, ˙γ the
(shear) strain rate and ˙γ
0
the pre-exponential factor in the Arrhenius equation
of the strain rate (4.8). With a characteristic value of ln( ˙γ
0
/ ˙γ) ≈ 25, T
0
becomes about 200
◦
C. Consequently, vacancies of the estimated concentration
at the flow stress peak may contribute to the flow stress at low temperatures,
e.g., quenched-in vacancies at room temperature, but they should not cause
the flow stress anomaly at much higher temperatures. The fact that such small
and relatively weak obstacles as individual vacancies are easily surmounted
at high temperatures by the aid of thermal activation is generally neglected
in the literature of the vacancy hardening model of the flow stress anomaly
in FeAl. Vacancy agglomerates, which may act also at higher temperatures,
usually occur at much lower concentrations than the individual vacancies do.
Several experimental results can well be interpreted by dynamic strain age-
ing. Effects of strain ageing were observed in FeAl in several experiments (e.g.,
[606–608]), but not in all. In the experimental material above, this concerns, in
particular, the occurrence of the flow stress anomaly itself, the inverse behavior
of the strain rate sensitivity (Fig. 9.35), and the appearance of serrated yield-
ing (Fig. 9.33) connected with slip localization. According to [608], serrated
yielding depends on the orientation of the loading axis. The present orienta-
tion is in the range of unstable slip. Serrated yielding is certainly favored in
single crystals in single slip orientation where slip localization is promoted.
It is also supported in a stiff testing machine used here, where sudden strain
increments cause large stress drops. As described in Sect. 5.3, the so-called
strain rate softening instabilities do not require a negative strain rate sensi-
tivity. It is sufficient if the strain rate sensitivity is small, which is fulfilled in
the present experiments.
It was discussed in Sect. 4.11 that diffusion processes in the dislocation
cores like the Cottrell effect may cause a flow stress anomaly. This idea was
applied in Sect. 9.3.4 to the anomaly in γ TiAl. The respective formulae are
(4.100) for the maximum contribution of this effect to the flow stress, and
(4.99) for the relation between the critical strain rate and the diffusion coef-
ficient and the temperature. It may be assumed that the diffusing defects are
the Fe vacancies. The interaction strength β is given by (3.32) for solutes
with a hydrostatic stress field. By comparing this formula with (14–42) in
[12] it may be concluded that for vacancies ΔΩ is given by the relaxation
volume of the vacancy. Since it is not known, it is assumed that it amounts
to 30% of the atomic volume, i.e., ΔΩ =0.3a
3
/2. Using again K
e
for the
shear modulus, the maximum flow stress contribution is only σ
max
=8.6MPa.
With a characteristic dislocation density of
m
=2× 10
13
m
−2
, the diffusion
coefficient D necessary to obtain the flow stress maximum at the specific
temperature T
max
= 550
◦
C and strain rate ˙ε
max
=10
−5
s
−1
turns out to be
D =10
−19
m
2
s
−1
. This is exactly the diffusion coefficient of Fe at 550
◦
C
[609]. Thus, the Cottrell effect model of dynamic strain ageing can qualita-
tively interpret the dynamic deformation properties. It is consistent with the