Micromechanical Modeling of the Elasto-Viscoplastic Behavior and Incompatibility Stresses of β-Ti Alloys
Abstract
:1. Introduction
2. Micromechanical Model
2.1. Fields Equations
2.2. Single Crystal’s Constitutive Behavior
2.3. Self-Consistent Approximation Based on Affine Translated Field Method
3. Results and Discussions
3.1. Model Parameters
3.2. Macroscopic Stress–Strain Responses and Strain-Hardening Behavior
3.3. Local Mechanical Fields Analysis
3.4. Effect of Anisotropic Elasticity on Relative Slip Activities in 100% β-Ti
4. Conclusions
- At the macroscopic scale, the two sets of β-phase SEC well predict the tensile elasto-viscoplastic behavior of a randomly oriented and equiaxed β Ti-17 at two strain rates by the EVPSC model. This shows the relevancy of the model for the prediction of the material’s hardening and strain rate sensitivity;
- In contrast, at the grain scale, the two sets of SEC lead to the scattered incompatibility of stresses and strains. These incompatibilities increase in magnitude with the Zener factor A and depend on the grain orientation. The grains oriented with their <100> direction parallel to the tensile axis are more sensitive to the anisotropy factor A (Figure 5). The local mechanical fields analysis demonstrates that considering only the macroscopic behavior is not sufficient to evaluate the effect of the elastic anisotropy of the β-phase;
- Lastly, it is shown that the elastic anisotropy of the β-phase can affect the slip activities of a fully β-phase microstructure. Contrary to the isotropic elastic case, {112} <111> slip systems are clearly predominant at the onset of plasticity in the simulations with A = 2.4 and 3 (Figure 6).
Author Contributions
Funding
Conflicts of Interest
References
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Ti-Based Alloy | SEC (GPa) | A | EYM (GPa) of 100% β (Calculated) | ||
---|---|---|---|---|---|
C11 | C12 | C44 | |||
Ti-17 [4] | 100 | 70 | 36 | 2.4 | 69.4 |
Pure [6] | 134 | 110 | 36 | 3 | 66.6 |
Slip Family | n | K(MPa·s1/n) | r0(MPa) | c(MPa) |
---|---|---|---|---|
{110} <111> 12 slip systems | 20 | 300 | 113 | 200 |
{112} <111> 12 slip systems | 20 | 300 | 113 | 200 |
{123} <111> 24 slip systems | 20 | 300 | 123 | 400 |
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Lhadi, S.; Chini, M.-R.; Richeton, T.; Gey, N.; Germain, L.; Berbenni, S. Micromechanical Modeling of the Elasto-Viscoplastic Behavior and Incompatibility Stresses of β-Ti Alloys. Materials 2018, 11, 1227. https://doi.org/10.3390/ma11071227
Lhadi S, Chini M-R, Richeton T, Gey N, Germain L, Berbenni S. Micromechanical Modeling of the Elasto-Viscoplastic Behavior and Incompatibility Stresses of β-Ti Alloys. Materials. 2018; 11(7):1227. https://doi.org/10.3390/ma11071227
Chicago/Turabian StyleLhadi, Safaa, Maria-Rita Chini, Thiebaud Richeton, Nathalie Gey, Lionel Germain, and Stéphane Berbenni. 2018. "Micromechanical Modeling of the Elasto-Viscoplastic Behavior and Incompatibility Stresses of β-Ti Alloys" Materials 11, no. 7: 1227. https://doi.org/10.3390/ma11071227
APA StyleLhadi, S., Chini, M.-R., Richeton, T., Gey, N., Germain, L., & Berbenni, S. (2018). Micromechanical Modeling of the Elasto-Viscoplastic Behavior and Incompatibility Stresses of β-Ti Alloys. Materials, 11(7), 1227. https://doi.org/10.3390/ma11071227