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. 2018 Jul 17;11(7):1227.
doi: 10.3390/ma11071227.

Micromechanical Modeling of the Elasto-Viscoplastic Behavior and Incompatibility Stresses of β-Ti Alloys

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Free PMC article

Micromechanical Modeling of the Elasto-Viscoplastic Behavior and Incompatibility Stresses of β-Ti Alloys

Safaa Lhadi et al. Materials (Basel). .
Free PMC article

Abstract

Near β titanium alloys can now compete with quasi-α or α/β titanium alloys for airframe forging applications. The body-centered cubic β-phase can represent up to 40% of the volume. However, the way that its elastic anisotropy impacts the mechanical behavior remains an open question. In the present work, an advanced elasto-viscoplastic self-consistent model is used to investigate the tensile behavior at different applied strain rates of a fully β-phase Ti alloy taken as a model material. The model considers crystalline anisotropic elasticity and plasticity. It is first shown that two sets of elastic constants taken from the literature can be used to well reproduce the experimental elasto-viscoplastic transition, but lead to scattered mechanical behaviors at the grain scale. Incompatibility stresses and strains are found to increase in magnitude with the elastic anisotropy factor. The highest local stresses are obtained toward the end of the elastic regime for grains oriented with their <111> direction parallel to the tensile axis. Finally, as a major result, it is shown that the elastic anisotropy of the β-phase can affect the distribution of slip activities. In contrast with the isotropic elastic case, it is predicted that {112} <111> slip systems become predominant at the onset of plastic deformation when elastic anisotropy is considered in the micromechanical model.

Keywords: elastic anisotropy; elastic/plastic incompatibilities; elasto-viscoplastic self-consistent scheme (EVPSC); polycrystalline β-Ti; slip activity.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
(a) Inverse pole figure representing the 2016 grains with random texture decomposed into 28 fiber components with respect to the tensile axis; (b) Directional Young’s moduli of single crystals with orientations 1 to 28 parallel to the tensile axis obtained from both considered β-phase single-crystal elastic constants (SEC) (A = 2.4 (triangles) and A = 3 (circles)).
Figure 2
Figure 2
Tensile macroscopic stress (Σ33) vs. macroscopic strain (E33) estimated by the Affine elasto-viscoplastic self-consistent model (EVPSC) model at two strain rates: 2×104 s1 (a) and 2×103 s1 (b) using three anisotropy factors (A). The numerical results are compared to the experimental data provided in [4,21] (red circles). For the calculations, an equiaxed β microstructure with random texture is considered.
Figure 3
Figure 3
Comparison of overall strain-hardening rate evolutions as a function of macroscopic strain for different anisotropy factors (A = 1, 2.4 and 3) and at two tensile applied strain rates (2×104 s1 (a) and 2×103 s1(b)).
Figure 4
Figure 4
Local stress component (σ33) as a function of local strain component (ε33) at 1%, 4%, and 10% of macroscopic strain for three anisotropy factors (A = 1, 2.4 and 3) (cloud of dots) at two strain rates 2×104 s1(a) and 2×103 s1 (b). The macroscopic stress–strain responses (Σ33 vs. E33) are plotted as references (solid lines).
Figure 5
Figure 5
Incompatibility stresses (a,b) and incompatibility strains (c,d) (dimensionless) for grain orientations 1 to 28 at 1% and 10% macroscopic strains. The applied strain rate is ε˙=2×103 s1. Inverse pole figure associated with the tensile axis, which defines the studied 28 grain orientations, were reported in Figure 1a.
Figure 5
Figure 5
Incompatibility stresses (a,b) and incompatibility strains (c,d) (dimensionless) for grain orientations 1 to 28 at 1% and 10% macroscopic strains. The applied strain rate is ε˙=2×103 s1. Inverse pole figure associated with the tensile axis, which defines the studied 28 grain orientations, were reported in Figure 1a.
Figure 6
Figure 6
Relative slip plane family activities (dimensionless) as a function of the macroscopic strain predicted by the EVPSC model for A = 2.4 (a), 3 (b), and 1 (c). The applied tensile strain rate in the X3-direction is ε˙=2×104 s1.
Figure 7
Figure 7
Cumulative distributions F(XX0) of maximum Schmid factors in grains distributed with an isotropic texture. The representation of the distributions is chosen in such a way that the ordinate of a point X0 gives the fraction of grains with the Schmid factor X0 or higher.

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