146
A. Cruzado et al.
Table 2 Viscoplastic and hardening parameters obtained from pillar compression
τ 0 (Mpa)
τ s (MPa)
h 0 (GPa)
h s (GPa)
q αβ
465.5
598.5
6.0
0.3
1
Fig. 11 Experimental result
and numerical simulation
obtained by computational
homogenization of an RVE of
the true stress-strain curve in
compression of Inconel 718
0
400
800
1200
1600
2000
0
0.04
0.08
0.12
0.16
0.2
Compressive stress (MPa)
Compressive strain
Experiment Simulation
where h 0 is the initial hardening modulus, τ 0 is the initial yield shear stress, τ s is the
saturation yields shear stress, h s is the saturation hardening modulus at large strains,
and stands for the accumulated shear strain in all slip systems, which is given by
=
α
| ˙
γ
α
|dt.
(16)
The strain rate sensitivity found from pillar compression was m = 0.017, and the
Voce hardening parameters obtained also using this technique are given in Table 2.
The crystal plasticity model described was used as constitutive equation in
a Voronoi RVE (Fig. 10a) with 210 grains and around 600 finite elements per
grain. This RVE size was enough to capture macroscopic behavior, based on
volume averaged fields, and only small differences were observed between different
realizations of the same size. In order to account for the scatter obtained using
several RVEs of the same microstructure, the numerical predictions were obtained
using four different realizations of the random grain orientation distribution.
Uniaxial compression was simulated using the framework described, and the
stress-strain curve obtained as the average of the four realizations is represented
in Fig. 11 together with the experimental result of a compression test performed
under the same conditions.
A. Cruzado et al.
Table 2 Viscoplastic and hardening parameters obtained from pillar compression
τ 0 (Mpa)
τ s (MPa)
h 0 (GPa)
h s (GPa)
q αβ
465.5
598.5
6.0
0.3
1
Fig. 11 Experimental result
and numerical simulation
obtained by computational
homogenization of an RVE of
the true stress-strain curve in
compression of Inconel 718
0
400
800
1200
1600
2000
0
0.04
0.08
0.12
0.16
0.2
Compressive stress (MPa)
Compressive strain
Experiment Simulation
where h 0 is the initial hardening modulus, τ 0 is the initial yield shear stress, τ s is the
saturation yields shear stress, h s is the saturation hardening modulus at large strains,
and stands for the accumulated shear strain in all slip systems, which is given by
=
α
| ˙
γ
α
|dt.
(16)
The strain rate sensitivity found from pillar compression was m = 0.017, and the
Voce hardening parameters obtained also using this technique are given in Table 2.
The crystal plasticity model described was used as constitutive equation in
a Voronoi RVE (Fig. 10a) with 210 grains and around 600 finite elements per
grain. This RVE size was enough to capture macroscopic behavior, based on
volume averaged fields, and only small differences were observed between different
realizations of the same size. In order to account for the scatter obtained using
several RVEs of the same microstructure, the numerical predictions were obtained
using four different realizations of the random grain orientation distribution.
Uniaxial compression was simulated using the framework described, and the
stress-strain curve obtained as the average of the four realizations is represented
in Fig. 11 together with the experimental result of a compression test performed
under the same conditions.