MODELLING INVESTIGATION OF PRECIPITATION KINETICS AND STRENGTHENING FOR NEEDLE/ROD-SHAPED PRECIPITATES INAl-Mg-Si ALLOYS
Rui CHEN,Qingyan XU(),Baicheng LIU
Key Laboratory for Advanced Materials Processing Technology (MOE, School of Materials Science and Engineerin, Tsinghua Universit, Beijing 10008, China
Cite this article:
Rui CHEN,Qingyan XU,Baicheng LIU. MODELLING INVESTIGATION OF PRECIPITATION KINETICS AND STRENGTHENING FOR NEEDLE/ROD-SHAPED PRECIPITATES INAl-Mg-Si ALLOYS. Acta Metall Sin, 2016, 52(8): 987-999.
The aging hardening is the main strengthening mechanism of Al-Mg-Si alloy, and the hardening effect is determined by the microstructural features of precipitates including the morpholog, compositio, volume factio, nucleation density as well as the size distribution. In present wor, an integrated mathematical model coupling with the CALPHAD software is developed to simulate the precipitation kinetics and strengthening effects of needle/rod-shaped precipitates in ternary Al-Mg-Si aluminum alloys. This model takes into account the effects of morphology on the nucleatio, growth and coarsening of precipitates and on the strengthening effects. The yield strength model accounts for the whole precipitate size distributio, shape of precipitates and their specific spatial distribution based on the consideration of the competing shearing and bypassing strengthening mechanisms. Appli cation of the model to various aging treatments of Al-Mg-Si alloys is conducted and the predictions both for microstructural features and yield strength are validated with experimental results and the predictions by LSW model. Using this mode, the effects of aspect rati, interfacial energ, alloy composition and Mg/Si atom ratio in precipitates on precipitation kinetics and yield strength are investigated and analyzed. The results reveal that the different interfacial energy and aspect ratio will affect the predicted density and size of precipitat, and further have an influence on the prediction precision of yield strength. An increase of Mg content in the matrix of Al-Mg-Si alloy will accelerate the precipitation and improve the yield strengt, while increasing the Si content in the matrix will produce little influence on the yield strength.
Fund: Supported by National Basic Research Program of China (No.2011CB706801, National Natural Science Foundation of China (Nos.51374137 and 51171089) and National Science and Technology Major Projects (No.2012ZX04012-011)
Fig.1 Schematic representation of precipitate morphology comprising a cylinder of length lp-2rp and radius rp (lp and rp are the length and radius of precipitates; dz is the length of solute diffusion zone ahead of precipitates)
Fig.2 Schematic representation of the variation of Gibbs free energy with the precipitate radius during nucleation process (?G, ?Gv, ?Ge, ?Gs, ?G*correspond to the total energ, chemical energ, interfacial energ, strain energy and critical nucleation barrie, respectively; T is the temperature; γ is the precipitate/matrix interface energy; ? is the aspect ratio of precipitates; Δgv, Δgs correspond to the chemical free energy and strain energy per unit volum, respectively; Rp* is the critical radius for stable precipitates and rp* is the radius at which stable precipitates nucleate)
Fig.3 Schematic representation of solute distribution ahead of the precipitate with radius rp (xiβ is the mole fraction of atom i in β phase;xi0 is the initial composition of element i in the matrix;xiα∞ is the average concentration of element i in the matrix;xiα(rp)is the equilibrium mole fraction of element i in the matrix at the precipitate/matrix interfac, andxi,eαis the equilibrium solid solubility of element i in α phase; de is the effective diffusion distance; ?xiα(rp) is the concentration gradient of element i at the interface; vm is the growth rate of precipitates)
Fig.4 Schematic representation of balance force between a precipitate and a dislocation (a, and the orientation and disposition of needle/rod shaped precipitates in the slip plane (b) (ψc is the dislocation bending angle; Rc is the radius of curvature of the dislocation at critical breaking stress; θc is the angle through dislocation bending behind two precipitates; θ is the angle between precipitate direction and slip plane normal direction; F is the precipitate resistance force; Γ is the dislocation line tension; L is the distance between two precipitates along dislocation; LF is the average spacing of precipitates on the slip plane)
Parameter
Unit
Value
Aspect ratio ?
-
6[20]
Interface energy γ
Jm-2
0.35[35]
Precipitate mean atomic volume vatβ
m3
1.92×10-29[20]
Precipitate lattice parameter aβ
m
2.86×10-10[20]
Atomic fraction of Mg in precipitate xMgβ
%
66.7
Atomic fraction of Si in precipitate xSiβ
%
33.3
Factor for adjusting the effective diffusion distance ξ
-
1
Ratio of matrix to precipitate molar volumes ε
-
1
Molar volume of precipitate Vm β
m3mol
3.95×10-5[11]
Constant depends on the shape and nature of discolation δ
-
0.5[19]
Interaction coefficient between Al and Mg LAlMg0
Jmol
4945.7-1.381T
Interaction coefficient between Mg and Si LMgSi0
Jmol
-15839-12T
Interaction coefficient between Si and Al LSiAl0
Jmol
-2880.2-0.09T
Shear modulus G
Nm-2
2.7×1010[15]
Magnitude of the burgers vector b
m
2.84×10-10[15]
Taylor factor M
-
3.1[15]
Exponent for superposition law q
-
2[36]
Table 1 Parameters of Al-Mg-Si alloys for precipitation kinetics and yield strength calculation
Fig.5 Comparisons of predicted and experimental results of mean radius (a) and volume fraction (b) of precipitate for Al-1.12%Mg-0.57%Si alloy at ageing temperature of 464 K
Fig.6 Predicted evolutions of the cube of mean radius rm with time (a) and normalized size distribution of precipitates (b) for Al-1.12%Mg-0.57%Si alloy at ageing temperature of 464 K
Fig.7 Comparisons of predicted and experimental results of yield strength of Al-0.79%Mg-0.6%Si alloy at ageing temperatures of 433 K (a, 453 K (b) and 473 K (c)
Fig.8 Evolutions of shear stress for shearing and bypassing precipitates with ageing time at 473 K
Fig.9 Influences of the aspect ratio (?) on density (a, radius (b) and yield strength (c) of precipitate in Al-0.79%Mg-0.6%Si alloy as a function of the ageing time at 433 K
Fig.10 Influences of the interfacial energy (γ) on density (a, radius (b) and yield strength (c) of precipitate in Al-0.79%Mg-0.6%Si alloy as a function of the ageing time at 433 K
Fig.11 Variations of yield strength of Al-x%Mg-0.6%Si alloys with ageing time under different Mg compositions at 473 K
Fig.12 Evolutions of nucleation number density (a) and average radius (b) of precipitates for Al-x%Mg-0.6%Si alloys with aging time under different Mg compositions at 473 K
Fig.13 Variations of yield strength of Al-0.6%Mg-y%Si alloys with ageing time under different Si compositions at 473 K
Fig.14 Comparisons of yield strength of Al-0.6%Mg-1.0%Si alloy with precipitates of Mg2Si and MgSi at 473 K
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