Computational Micromechanics Modeling of Polycrystalline Superalloys. . .
135
3.2.2 Low Cycle Fatigue Tests
Experimental Procedure
A set of uniaxial strain control LCF tests were carried out for the two microstructures analyzed in this work, ASTM 3 and ASTM 8.5, and a fixed temperature of
400 ◦ C. The tests were performed according to the standard ASTM E606-04 on
a MTS servo hydraulic fatigue load frame with a 100 kN load cell. Cylindrical
smooth specimens with a diameter of 6.35 mm for the ASTM 3 Alloy and a diameter
of 5.08 mm for the ASTM8, with a gauge length of 12.7 mm, were used. The
axial displacement in the central zone of the specimen was measured with a MTS
extensometer directly mounted on the gauge length. The specimens present the same
grain size in the surface and in the interior, and the grain sizes observed in both
longitudinal and transversal directions were also very similar. A trapezoidal wave
form was applied according to 1 s (dwell) – 5 10 −3 s −1 (ramp up) – 1 s (dwell)- 5
10 −3 s −1 (ramp down).
For the ASTM 8.5 Alloy, tests were carried with cyclic strain ranges of
min = 1, 1.5, 2, 2.5, 3, and 3.5 for a strain ratio of R ε = −1 and with cyclic
strain ranges of ε//ε min = 1, 1.25, 1.5, 1.75, 2.25 and 2.75 for a strain ratio of
R ε = 0. The normalizing factor, ε min , is the same value used for the monotonic
behavior (Fig. 5) and corresponds to the smallest cyclic strain range applied in the
experimental tests. For the ASTM 3 alloy, only fully reversed cyclic deformation
tests R ε = −1 under cyclic strain ranges of ε//ε min = 1, 1.5, 2, 2.5, 3 and 3.5 were
performed. The cyclic stress-strain curves derived from these tests are used first to
describe the cyclic behavior of Inconel 718.
Cyclic Behavior
The characteristics of the macroscopic cyclic plastic behavior of Inconel 718 are
obtained from the cyclic stress-strain response obtained at different number of
cycles during a strain-controlled LCF tests. Those characteristics will be described
using the particular case of LCF tests at 400 ◦ C for the ASTM 8.5 microstructure.
The alloy presents a strong Bauschinger effect [11] or strain-hardening asymmetry
(i.e., kinematic hardening). This effect can be observed in Fig. 6a, which shows that
yielding in compression starts well before the applied stress has reached −σ 1 , equal
to the flow stress in the previous tensile deformation up to ε 1 . However, the actual
yield stress in compression of Inconel 718 is smaller (in absolute value) than the
prediction of pure kinematic hardening. This is associated with an initial softening
that suffers the material during the initial unloading [23]. The physical origin of
kinematic hardening can be associated with two mechanisms acting at different
length scales. At the grain level, back stresses on the mobile dislocations are due
to the development of dislocation substructures as a result of the interaction of the
dislocations with the shearable γ and γ precipitates as well as with the grain
boundaries [38, 65]. At the polycrystal level, kinematic hardening is induced by the
135
3.2.2 Low Cycle Fatigue Tests
Experimental Procedure
A set of uniaxial strain control LCF tests were carried out for the two microstructures analyzed in this work, ASTM 3 and ASTM 8.5, and a fixed temperature of
400 ◦ C. The tests were performed according to the standard ASTM E606-04 on
a MTS servo hydraulic fatigue load frame with a 100 kN load cell. Cylindrical
smooth specimens with a diameter of 6.35 mm for the ASTM 3 Alloy and a diameter
of 5.08 mm for the ASTM8, with a gauge length of 12.7 mm, were used. The
axial displacement in the central zone of the specimen was measured with a MTS
extensometer directly mounted on the gauge length. The specimens present the same
grain size in the surface and in the interior, and the grain sizes observed in both
longitudinal and transversal directions were also very similar. A trapezoidal wave
form was applied according to 1 s (dwell) – 5 10 −3 s −1 (ramp up) – 1 s (dwell)- 5
10 −3 s −1 (ramp down).
For the ASTM 8.5 Alloy, tests were carried with cyclic strain ranges of
min = 1, 1.5, 2, 2.5, 3, and 3.5 for a strain ratio of R ε = −1 and with cyclic
strain ranges of ε//ε min = 1, 1.25, 1.5, 1.75, 2.25 and 2.75 for a strain ratio of
R ε = 0. The normalizing factor, ε min , is the same value used for the monotonic
behavior (Fig. 5) and corresponds to the smallest cyclic strain range applied in the
experimental tests. For the ASTM 3 alloy, only fully reversed cyclic deformation
tests R ε = −1 under cyclic strain ranges of ε//ε min = 1, 1.5, 2, 2.5, 3 and 3.5 were
performed. The cyclic stress-strain curves derived from these tests are used first to
describe the cyclic behavior of Inconel 718.
Cyclic Behavior
The characteristics of the macroscopic cyclic plastic behavior of Inconel 718 are
obtained from the cyclic stress-strain response obtained at different number of
cycles during a strain-controlled LCF tests. Those characteristics will be described
using the particular case of LCF tests at 400 ◦ C for the ASTM 8.5 microstructure.
The alloy presents a strong Bauschinger effect [11] or strain-hardening asymmetry
(i.e., kinematic hardening). This effect can be observed in Fig. 6a, which shows that
yielding in compression starts well before the applied stress has reached −σ 1 , equal
to the flow stress in the previous tensile deformation up to ε 1 . However, the actual
yield stress in compression of Inconel 718 is smaller (in absolute value) than the
prediction of pure kinematic hardening. This is associated with an initial softening
that suffers the material during the initial unloading [23]. The physical origin of
kinematic hardening can be associated with two mechanisms acting at different
length scales. At the grain level, back stresses on the mobile dislocations are due
to the development of dislocation substructures as a result of the interaction of the
dislocations with the shearable γ and γ precipitates as well as with the grain
boundaries [38, 65]. At the polycrystal level, kinematic hardening is induced by the