Acta Metallurgica Sinica (English Letters) ›› 2020, Vol. 33 ›› Issue (1): 75-87.DOI: 10.1007/s40195-019-00945-9
• Original Paper • Previous Articles Next Articles
Zhao Zhang1(), Zhi-Jun Tan1, Jian-Yu Li1, Yu-Fei Zu2, Jian-Jun Sha2
Received:
2019-03-22
Revised:
2019-05-17
Online:
2020-01-10
Published:
2020-02-20
Contact:
Zhang Zhao
Zhao Zhang, Zhi-Jun Tan, Jian-Yu Li, Yu-Fei Zu, Jian-Jun Sha. Integrated Modeling of Process-Microstructure-Property Relations in Friction Stir Additive Manufacturing[J]. Acta Metallurgica Sinica (English Letters), 2020, 33(1): 75-87.
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Physical property and value | |
---|---|
j | Nucleation rate (#/m3) |
j0 | Material coefficient (3.07?×?1036) |
A0 | Energy barrier for nucleation (18,000 J/mol) |
R | Universal gas constant (8.314 J K-1 mol-1) |
T | Temperature (K) |
$\overline{C}$ | Mean concentration of Mg in matrix (wt%) |
Ce | Equilibrium solute concentration of Mg at the precipitate/matrix interface (wt%) |
Qd | Activation energy for diffusion (J/mol) |
Cs | Pre-exponential term to Ce (290 wt%) |
Qs | Activation energy for solvus boundary (41,000 J/mol) |
Ci | Solute concentration at the particle/matrix interface (wt%) |
Cp | Concentration of element inside the particle (wt%) |
r | Particle radius (m) |
γ | Particle/matrix interfacial energy (0.26 J/m2) |
Vm | Molar volume of precipitation (7.62?×?10-5 m3/mol) |
rc | Critical radius (m) |
f | Volume fraction |
Ni | Number of particles per unit volume within the size class ri (/m3) |
σs | Yield strength (MPa) |
σ0 | Intrinsic yield strength of pure aluminum (10 MPa) |
σss | Contribution from alloying elements in solid solution to the overall macroscopic yield strength (MPa) |
σp | Contribution from hardening precipitates to the overall macroscopic yield strength (MPa) |
kMg | Scaling factor of Mg (66.3 MPa/wt%2/3) |
kSi | Scaling factor of Si (29 MPa/wt%2/3) |
kCu | Scaling factor of Cu (46.4 MPa/wt%2/3) |
M | Taylor factor (3.1) |
b | Magnitude of the Burgers vector (2.84?×?10-10) |
$\overline{r}$ | Mean particle radius (nm) |
β | Constant in expression for the dislocation line tension (0.36) |
G | Shear modulus (2.7?×?1010 N/m3) |
Fi | Interaction force between dislocations and particles within the size class ri (N) |
m | Total number of sites near one lattice point (8) |
N0 | Constant (1024/s/m3) |
J | Lattice energy density |
$\delta_{{q_{i} q_{j} }}$ | Kronecker delta function |
re | Effective radius of SZ (0.007 m) |
Le | Effective depth of SZ (0.008 m) |
A | Accommodation probability (1) |
Z | Average number per unit area (4.31?×?1020 atoms/m2) |
hP | Planck’s constant (6.624?×?10-34 J s) |
Vm | Atom molar volume (1.0?×?10-5 m3/mol) |
$\Delta S_{\text{f}}$ | Fusion entropy (11.5 J/mol/K) |
Na | Avogadro’s number (6.02?×?1023/mol) |
γ | Boundary energy (0.5 J/m2) |
Q | Activation enthalpy (140,000 J/mol) |
α | Ratio constant (1.0) |
n | Ratio constant (0.1) |
Table 1 Material parameters and constants
Physical property and value | |
---|---|
j | Nucleation rate (#/m3) |
j0 | Material coefficient (3.07?×?1036) |
A0 | Energy barrier for nucleation (18,000 J/mol) |
R | Universal gas constant (8.314 J K-1 mol-1) |
T | Temperature (K) |
$\overline{C}$ | Mean concentration of Mg in matrix (wt%) |
Ce | Equilibrium solute concentration of Mg at the precipitate/matrix interface (wt%) |
Qd | Activation energy for diffusion (J/mol) |
Cs | Pre-exponential term to Ce (290 wt%) |
Qs | Activation energy for solvus boundary (41,000 J/mol) |
Ci | Solute concentration at the particle/matrix interface (wt%) |
Cp | Concentration of element inside the particle (wt%) |
r | Particle radius (m) |
γ | Particle/matrix interfacial energy (0.26 J/m2) |
Vm | Molar volume of precipitation (7.62?×?10-5 m3/mol) |
rc | Critical radius (m) |
f | Volume fraction |
Ni | Number of particles per unit volume within the size class ri (/m3) |
σs | Yield strength (MPa) |
σ0 | Intrinsic yield strength of pure aluminum (10 MPa) |
σss | Contribution from alloying elements in solid solution to the overall macroscopic yield strength (MPa) |
σp | Contribution from hardening precipitates to the overall macroscopic yield strength (MPa) |
kMg | Scaling factor of Mg (66.3 MPa/wt%2/3) |
kSi | Scaling factor of Si (29 MPa/wt%2/3) |
kCu | Scaling factor of Cu (46.4 MPa/wt%2/3) |
M | Taylor factor (3.1) |
b | Magnitude of the Burgers vector (2.84?×?10-10) |
$\overline{r}$ | Mean particle radius (nm) |
β | Constant in expression for the dislocation line tension (0.36) |
G | Shear modulus (2.7?×?1010 N/m3) |
Fi | Interaction force between dislocations and particles within the size class ri (N) |
m | Total number of sites near one lattice point (8) |
N0 | Constant (1024/s/m3) |
J | Lattice energy density |
$\delta_{{q_{i} q_{j} }}$ | Kronecker delta function |
re | Effective radius of SZ (0.007 m) |
Le | Effective depth of SZ (0.008 m) |
A | Accommodation probability (1) |
Z | Average number per unit area (4.31?×?1020 atoms/m2) |
hP | Planck’s constant (6.624?×?10-34 J s) |
Vm | Atom molar volume (1.0?×?10-5 m3/mol) |
$\Delta S_{\text{f}}$ | Fusion entropy (11.5 J/mol/K) |
Na | Avogadro’s number (6.02?×?1023/mol) |
γ | Boundary energy (0.5 J/m2) |
Q | Activation enthalpy (140,000 J/mol) |
α | Ratio constant (1.0) |
n | Ratio constant (0.1) |
Fig. 4 Temperature comparison between experiment and numerical model: a temperature in the 1st layer from IRT system, b comparison of temperature in the 1st layer
The 1st layer welded | The 2nd layer welded | The 3rd layer welded | The 4th layer welded | The 5th layer welded | |
---|---|---|---|---|---|
1st layer | 413.772 | 311.842 | 184.893 | 157.761 | 137.457 |
2nd layer | - | 373.093 | 301.951 | 266.616 | 229.218 |
3rd layer | - | - | 362.107 | 304.659 | 262.476 |
4th layer | - | - | - | 358.635 | 299.035 |
5th layer | - | - | - | - | 350.793 |
Table 2 Peak temperature of built layers in case 1 (°C)
The 1st layer welded | The 2nd layer welded | The 3rd layer welded | The 4th layer welded | The 5th layer welded | |
---|---|---|---|---|---|
1st layer | 413.772 | 311.842 | 184.893 | 157.761 | 137.457 |
2nd layer | - | 373.093 | 301.951 | 266.616 | 229.218 |
3rd layer | - | - | 362.107 | 304.659 | 262.476 |
4th layer | - | - | - | 358.635 | 299.035 |
5th layer | - | - | - | - | 350.793 |
The 1st layer welded | The 2nd layer welded | The 3rd layer welded | The 4th layer welded | The 5th layer welded | |
---|---|---|---|---|---|
1st layer | 380.945 | 243.617 | 146.36 | 114.658 | 93.407 |
2nd layer | - | 345.433 | 246.809 | 187.875 | 149.408 |
3rd layer | - | - | 336.052 | 241.118 | 185.395 |
4th layer | - | - | - | 315.929 | 225.253 |
5th layer | - | - | - | - | 310.524 |
Table 3 Peak temperature of built layers in case 2 (°C)
The 1st layer welded | The 2nd layer welded | The 3rd layer welded | The 4th layer welded | The 5th layer welded | |
---|---|---|---|---|---|
1st layer | 380.945 | 243.617 | 146.36 | 114.658 | 93.407 |
2nd layer | - | 345.433 | 246.809 | 187.875 | 149.408 |
3rd layer | - | - | 336.052 | 241.118 | 185.395 |
4th layer | - | - | - | 315.929 | 225.253 |
5th layer | - | - | - | - | 310.524 |
The 1st layer welded | The 2nd layer welded | The 3rd layer welded | The 4th layer welded | The 5th layer welded | |
---|---|---|---|---|---|
1st layer | 363.945 | 210.844 | 115.749 | 86.5807 | 69.6053 |
2nd layer | - | 335.823 | 212.026 | 149.686 | 115.205 |
3rd layer | - | - | 321.065 | 209.375 | 149.501 |
4th layer | - | - | - | 311.498 | 204.751 |
5th layer | - | - | - | 300.105 |
Table 4 Peak temperature of built layers in case 3 (°C)
The 1st layer welded | The 2nd layer welded | The 3rd layer welded | The 4th layer welded | The 5th layer welded | |
---|---|---|---|---|---|
1st layer | 363.945 | 210.844 | 115.749 | 86.5807 | 69.6053 |
2nd layer | - | 335.823 | 212.026 | 149.686 | 115.205 |
3rd layer | - | - | 321.065 | 209.375 | 149.501 |
4th layer | - | - | - | 311.498 | 204.751 |
5th layer | - | - | - | 300.105 |
Fig. 10 Comparison of grains between experimental and numerical model: a first layer for 2-layers specimen, b first layer for 2-layers specimen, c second layer for 2-layers specimen, d second layer for 2-layers specimen
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