J. Mater. Sci. Technol. ›› 2020, Vol. 59: 138-148.DOI: 10.1016/j.jmst.2020.03.079
• Research Article • Previous Articles Next Articles
Yu Zhoua,b, Qunbo Fana,b,c,*(), Xin Liua,b, Duoduo Wanga,b,c, Xinjie Zhua,b,c, Kai Chena,b,c
Received:
2020-02-09
Revised:
2020-03-24
Accepted:
2020-03-26
Published:
2020-12-15
Online:
2020-12-18
Contact:
Qunbo Fan
Yu Zhou, Qunbo Fan, Xin Liu, Duoduo Wang, Xinjie Zhu, Kai Chen. Multi-scale crystal plasticity finite element simulations of the microstructural evolution and formation mechanism of adiabatic shear bands in dual-phase Ti20C alloy under complex dynamic loading[J]. J. Mater. Sci. Technol., 2020, 59: 138-148.
Mo | Al | Zr | Sn | Cr | Fe | Zn | Ti |
---|---|---|---|---|---|---|---|
4.5 | 5 | 2 | 1 | 2.5 | 0.5 | 3 | Bal. |
Table 1 Chemical composition (wt.%) of Ti20C.
Mo | Al | Zr | Sn | Cr | Fe | Zn | Ti |
---|---|---|---|---|---|---|---|
4.5 | 5 | 2 | 1 | 2.5 | 0.5 | 3 | Bal. |
E (GPa) | v | A (MPa) | B (MPa) | C | n | m |
---|---|---|---|---|---|---|
113.74 | 0.323 | 1175 | 251 | 0.016 | 0.229 | 0.422 |
P (kg/m3) | ε0 (s-1) | D1 | D2 | D3 | D4 | D5 |
4.67 | 103 | 0 | 0.33 | 0.48 | 0.004 | 3.9 |
Table 2 Constitutive model parameters of Ti20C.
E (GPa) | v | A (MPa) | B (MPa) | C | n | m |
---|---|---|---|---|---|---|
113.74 | 0.323 | 1175 | 251 | 0.016 | 0.229 | 0.422 |
P (kg/m3) | ε0 (s-1) | D1 | D2 | D3 | D4 | D5 |
4.67 | 103 | 0 | 0.33 | 0.48 | 0.004 | 3.9 |
Fig. 4. (a) Process of extracting load information from the macro to the micro model and (b) phase distribution and grain orientation distribution based on the grain microstructure.
Density (g/cm3) | Poisson’s ratio | C11 (GPa) | C12 (GPa) | C13 (GPa) | C33 (GPa) | C44 (GPa) |
---|---|---|---|---|---|---|
4.4 | 0.3 | 160 | 86 | 55 | 183 | 54 |
Slip system | CRSS (GPa) | τ1 (GPa) | θ0 (GPa) | θ1 (GPa) | ||
<110> {0001} | 0.36 | 0.13 | 0.115 | 0.0021 | ||
<110> {100} | 0.38 | |||||
<110> {101} | 0.5 | |||||
<113> {101} | 0.52 |
Table 3 Crystal plastic constitutive parameters of the Ti20C α phase.
Density (g/cm3) | Poisson’s ratio | C11 (GPa) | C12 (GPa) | C13 (GPa) | C33 (GPa) | C44 (GPa) |
---|---|---|---|---|---|---|
4.4 | 0.3 | 160 | 86 | 55 | 183 | 54 |
Slip system | CRSS (GPa) | τ1 (GPa) | θ0 (GPa) | θ1 (GPa) | ||
<110> {0001} | 0.36 | 0.13 | 0.115 | 0.0021 | ||
<110> {100} | 0.38 | |||||
<110> {101} | 0.5 | |||||
<113> {101} | 0.52 |
Density (g/cm3) | Poisson’s ratio | C11 (GPa) | C12 (GPa) | C13 (GPa) | C33 (GPa) | C44 (GPa) |
---|---|---|---|---|---|---|
4.8 | 0.3 | 130.2 | 70.6 | 70.6 | 130.2 | 45.8 |
Slip system | CRSS (GPa) | τ1 (GPa) | θ0 (GPa) | θ1 (GPa) | ||
<111> {110} | 0.45 | 0.13 | 0.105 | 0.0016 | ||
<111> {112} | 0.46 | |||||
<111> {123} | 0.47 |
Table 4 Crystal plastic constitutive parameters of the Ti20C β phase.
Density (g/cm3) | Poisson’s ratio | C11 (GPa) | C12 (GPa) | C13 (GPa) | C33 (GPa) | C44 (GPa) |
---|---|---|---|---|---|---|
4.8 | 0.3 | 130.2 | 70.6 | 70.6 | 130.2 | 45.8 |
Slip system | CRSS (GPa) | τ1 (GPa) | θ0 (GPa) | θ1 (GPa) | ||
<111> {110} | 0.45 | 0.13 | 0.105 | 0.0016 | ||
<111> {112} | 0.46 | |||||
<111> {123} | 0.47 |
Fig. 6. Effective plastic strain and effective stress contour maps of the dual-phase multiple grains: (a, c, e, g) effective plastic strain and (b, d, f, h) effective stress at εT = 0.02, 0.025, 0.04, and 0.10, respectively.
Fig. 8. Simulation results of the micro model: (a) schematic showing the positions of grains Gα1, Gα2, Gβ1, and the centroid elements Eα1, Eα2, Eβ1; (b) effective stress history of the centroid elements.
Fig. 10. Orientation evolution of the three grains during the late stages of deformation: orientation distribution (a, c, e, g, i) and rotation angle distribution (b, d, f, h, j) at εT = 0.15, 0.21, 0.214, 0.218, and 0.222, respectively.
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