Multimodal Microstructure of Mg-Gd-Y Alloy Through an Integrated Simulation of “Process-Structure-Property”
LI Shaojie1, JIN Jianfeng1,2(), SONG Yuhao1, WANG Mingtao1, TANG Shuai2, ZONG Yaping1, QIN Gaowu1()
1. School of Materials Science and Engineering, Northeastern University, Shenyang 110819, China 2. State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, China
Cite this article:
LI Shaojie, JIN Jianfeng, SONG Yuhao, WANG Mingtao, TANG Shuai, ZONG Yaping, QIN Gaowu. Multimodal Microstructure of Mg-Gd-Y Alloy Through an Integrated Simulation of “Process-Structure-Property”. Acta Metall Sin, 2022, 58(1): 114-128.
Rare earth Mg alloys containing Gd elements can be used in aerospace, automotive, and other industrial fields owing to their high strength and creep resistance at room and high temperatures. However, the poor ductility of Mg alloys limits their application. Recently, it was discovered that the ductility of Mg alloy can be improved without compromising on its strength if sufficient amount of coarse grains is distributed in fine grains. In this study, taking the Mg-8Gd-3Y-0.5Zr (GW83K) alloy as an example, an approach for optimizing multimodal microstructures was investigated, which aimed to improve the mechanical properties of alloys. An alloy with a multimodal grain structure can be used as a particulate compound model, in which the grain boundary is considered the matrix, and different-sized grains are treated as different-types of particles embedded into the grain boundary matrix. A 2D finite element micromechanics model combined with Taylor-based nonlocal plasticity theory, which considers the size effect of the particles, was established to simulate the mechanical response of the multimodal structure Mg alloy in a tensile test. The model was verified through the experimental data of the stress-strain curve. Moreover, the effects of process parameters on the mechanical properties of the GW83K alloy were further evaluated by combining the grain structure under different annealing processes, simulated from a real space-time phase-field model as the geometric input of the finite element model. Finally, the relationships between the annealing parameters, multimodal structure, and mechanical properties of the GW83K alloy were described. The results show that the yield and tensile strengthes of the multimodal GW83K alloy presented a Hall-Petch relationship with the average grain size. The content and distribution of coarse grains greatly affected the plasticity of the GW83K alloy. By annealing the GW83K alloy at 623 K for 90 min, better plasticity could be achieved without sacrificing strength, which is helpful in promoting multimodal microstructural design.
Fund: National Key Research and Development Program of China(2016YFB0701204);Project of Introducing Talents of Discipline to Universities(B20029);Fundamental Research Funds for the Central Universities(N2007011)
About author: QIN Gaowu, professor, Tel: (024)83691565, E-mail: qingw@smm.neu.edu.cn JIN Jianfeng, associate professor, Tel: 13194248493, E-mail: jinjf@atm.neu.edu.cn
Fig.1 Free energy-component data of GW83K Mg alloy at 623, 673, and 723 K, and their fitting curves (cGd—concentration of Gd)
T
A
A1
A2
B1
B2
c1
ϕ2nd
f2nd
d2nd
K
kJ·mol-1
kJ·mol-1
kJ·mol-1
kJ·mol-1
kJ·mol-1
mol·s-1·J-1
%
μm
623
-49.2
297.3
-775.2
371
51.2
0.45
0.46
Lath
0.67
1-2
673
-52.6
308
-869.6
365.7
51.2
1.22
0.46
Lath
1.35
1-2
723
-55.9
322.4
-901.1
373.7
51.2
2.72
0.46
Sphere
1.35
1-2
Table 1 Parameters in the phase-field model for grain growth
Fig.2 Averaged grain sizes obtained by phase field simulation and experiment[67] under different annealing processes
Fig.3 Schematics of the finite element (FE) model for GW83K Mg alloy with multimodal grain size distribution
Fig.4 Experimental tensile stress-strain (σ-ε) curves and constitutive input curves for monolithic grain GW83K Mg alloy with different grain sizes (a) experimental data[13,74] (—average grain size from experiment, -—grain size ranges of the grain-interior phases 1-6) (b) constitutive inputs of grain-interior phases 1-6 (-) for finite element model
Fig.5 Predicted results from the finite element model for GW83K Mg alloy during tensile loading (a) comparison of the predicted σ-ε curves with the experimental data[13] (b) von Mises equivalent (EQV.) stress contours under the applied strain of 11% (c) EQV. strain contours under the applied strain of 11% (GB—grain boundary-matrix phase)
Model
Annealing temperature
Annealing time
No.
K
min
1
623
60
2
623
75
3
623
90
4
673
60
5
673
75
6
673
90
7
723
60
8
723
75
9
723
90
Table 2 The values of annealing temperature and time in phase field models for GW83K Mg alloy
Fig.6 Microstructures and grain size distributions of GW83K Mg alloy under different annealing processes (a, b) microstructures from phase field models with and without the 2nd phase particles after annealing at 723 K for 90 min, respectively (c) grain size distributions for Figs.6a and b (d) from the phase field model with and without the 2nd phase particles under different annealing processes
Fig.7 Microstructures (a) and geometric models (b) of GW83K Mg alloy without the 2nd phase particle from phase-field simulation at different annealing temperatures and time (marked with model Nos.1-9, grain-interior phases 1-6 marked by different colors and grain boundaries marked by black)
Fig.8 Microstructure characteristics in finite element model of GW83K Mg alloy (a) volume fraction of grain boundary (fGB) and of model Nos.1-9 (b-d) grain size distributions under 623 K, 673 K, and 723 K for different annealing time, respectively
Fig.9 Simulation results of finite element model of GW83K Mg alloys under different annealing processes (a) σ-ε curves (b) relationship among average grain size and yield strength (σy), tensile strength (σs), and total elongation (εs) (c) EQV. strain contours of model Nos.1-9, distinguished by the critical strain (εCR) (d) relationship among the and proportion of slip band (γsand volume fraction of coarse grains (fCG)
Fig.10 Mechanical responses from finite element model for GW83K Mg alloy with and without the 2nd phase particles from model A, B, and C after annealing at 723 K for 90 min (a) and EQV. strain contours of models A and C under fractured strain (b) (Model A is the FE simulation from microstructure with the 2nd phase particles after annealing, model B is from microstructure without the 2nd phase particles after annealing, and model C is from Fig.10a without the 2nd phase particles)
1
Shibata T , Kawanishi M , Nagahora J , et al . High specific strength of extruded Mg-Al-Ge alloys produced by rapid solidification processing [J]. Mater. Sci. Eng., 1994, A179-180: 632
2
Decker R F . The renaissance in magnesium [J]. Adv. Mater. Process., 1998, 154: 31
3
Mukai T , Mohri T , Mabuchi M , et al . Experimental study of a structural magnesium alloy with high absorption energy under dynamic loading [J]. Scr. Mater., 1998, 39: 1249
4
Li S B , Yang X Y , Hou J T , et al . A review on thermal conductivity of magnesium and its alloys [J]. J. Magnes. Alloy., 2020, 8: 78
5
Han G M , Han Z Q , Luo A A , et al . Microstructure characteristics and effect of aging process on the mechanical properties of squeeze-cast AZ91 alloy [J]. J. Alloys Compd., 2015, 641: 56
6
Tang W R , Liu Z , Liu S M , et al . Deformation mechanism of fine grained Mg-7Gd-5Y-1.2Nd-0.5Zr alloy under high temperature and high strain rates [J]. J. Magnes. Alloys, 2020, 8: 1144
7
Liu X B , Chen R S , Han E H . High temperature deformations of Mg-Y-Nd alloys fabricated by different routes [J]. Mater. Sci. Eng., 2008, A497: 326
8
Zhang P , Ding W J , Lindemann J , et al . Mechanical properties of the hot-rolled Mg-12Gd-3Y magnesium alloy [J]. Mater. Chem. Phys., 2009, 118: 453
9
Liu H H , Ning Z L , Yi J Y , et al . Effect of Dy addition on microstructure and mechanical properties of Mg-4Y-3Nd-0.4Zr alloy [J]. Trans. Nonferrous Met. Soc. China, 2017, 27: 797
10
Liu X F , Chen X H , Li J B , et al . Effect of micro-alloying Ca on microstructure, texture and mechanical properties of Mg-Zn-Y-Ce alloys [J]. Prog. Nat. Sci. Mater., 2020, 30: 213
11
Zhang T X , Zhao X T , Liu J H , et al . The microstructure, fracture mechanism and their correlation with the mechanical properties of as-cast Mg-Nd-Zn-Zr alloy under the effect of cooling rate [J]. Mater. Sci. Eng., 2021, A801: 140382
12
Kou H N , Lu J , Li Y . High-strength and high-ductility nanostructured and amorphous metallic materials [J]. Adv. Mater., 2014, 26: 5518
13
He J H , Jin L , Wang F H , et al . Mechanical properties of Mg-8Gd-3Y-0.5Zr alloy with bimodal grain size distributions [J]. J. Magnes. Alloys, 2017, 5: 423
14
Xu C , Fan G H , Nakata T , et al . Deformation behavior of ultra-strong and ductile Mg-Gd-Y-Zn-Zr alloy with bimodal microstructure [J]. Metall. Mater. Trans., 2018, 49A: 1931
15
Zhang H , Wang H Y , Wang J G , et al . The synergy effect of fine and coarse grains on enhanced ductility of bimodal-structured Mg alloys [J]. J. Alloys Compd., 2019, 780: 312
16
Jin Z Z , Zha M , Yu Z Y , et al . Exploring the Hall-Petch relation and strengthening mechanism of bimodal-grained Mg-Al-Zn alloys [J]. J. Alloys Compd., 2020, 833: 155004
17
Wei X X , Jin L , Wang F H , et al . High strength and ductility Mg-8Gd-3Y-0.5Zr alloy with bimodal structure and nano-precipitates [J]. J. Mater. Sci. Technol., 2020, 44: 19
18
Liu S S , Zhang J L , Chen X , et al . Improving mechanical properties of heterogeneous Mg-Gd alloy laminate via accumulated extrusion bonding [J]. Mater. Sci. Eng., 2020, A785: 139324
19
Xu C , Zheng M Y , Xu S W , et al . Ultra high-strength Mg-Gd-Y-Zn-Zr alloy sheets processed by large-strain hot rolling and ageing [J]. Mater. Sci. Eng., 2012, A547: 93
20
Peng P , Tang A T , She J , et al . Significant improvement in yield stress of Mg-Gd-Mn alloy by forming bimodal grain structure [J]. Mater. Sci. Eng., 2021, A803: 140569
21
Dobkowska A , Adamczyk-Cieślak B , Kubásek J , et al . Microstructure and corrosion resistance of a duplex structured Mg-7.5Li-3Al-1Zn [J]. J. Magnes. Alloys, 2021, 9: 467
22
Li Y K , Zha M , Jia H L , et al . Tailoring bimodal grain structure of Mg-9Al-1Zn alloy for strength-ductility synergy: Co-regulating effect from coarse Al2Y and submicron Mg17Al12 particles [J]. J. Magnes. Alloys, 2021,9: 1556
23
Wang H Y , Yu Z P , Zhang L , et al . Achieving high strength and high ductility in magnesium alloy using hard-plate rolling (HPR) process [J]. Sci. Rep., 2015, 5: 17100
24
Gao M , Yang K , Tan L L , et al . Role of bimodal-grained structure with random texture on mechanical and corrosion properties of a Mg-Zn-Nd alloy [J]. J. Magnes. Alloys, 2021, doi: 10.1016/j.jma.2021.03.024
25
Cubides Y , Karayan A I , Vaughan M W , et al . Enhanced mechanical properties and corrosion resistance of a fine-grained Mg-9Al-1Zn alloy: The role of bimodal grain structure and β-Mg17Al12 precipitates [J]. Materialia, 2020, 13: 100840
26
Asqardoust S , Hanzaki A Z , Abedi H R , et al . Enhancing the strength and ductility in accumulative back extruded WE43 magnesium alloy through achieving bimodal grain size distribution and texture weakening [J]. Mater. Sci. Eng., 2017, A698: 218
27
Lu K . Making strong nanomaterials ductile with gradients [J]. Science, 2014, 345: 1455
28
Wu X L , Yang M X , Yuan F P , et al . Heterogeneous lamella structure unites ultrafine-grain strength with coarse-grain ductility [J]. Proc. Natl. Acad. Sci. USA, 2015, 112: 14501
29
Zhu Y T , Wu X L . Perspective on hetero-deformation induced (HDI) hardening and back stress [J]. Mater. Res. Lett., 2019, 7: 393
30
Wu J L , Jin L , Dong J , et al . The texture and its optimization in magnesium alloy [J]. J. Mater. Sci. Technol., 2020, 42: 175
31
Zheng R X , Du J P , Gao S , et al . Transition of dominant deformation mode in bulk polycrystalline pure Mg by ultra-grain refinement down to sub-micrometer [J]. Acta Mater., 2020, 198: 35
32
Li X X , Xu D S , Yang R . Crystal plasticity finite element method investigation of the high temperature deformation consistency in dual-phase titanium alloy [J]. Acta Metall. Sin., 2019, 55: 928
Zhang Y , Chen H , Jia Y F , et al . A modified kinematic hardening model considering hetero-deformation induced hardening for bimodal structure based on crystal plasticity [J]. Int. J. Mech. Sci., 2021, 191: 106068
34
Joshi S P , Ramesh K T , Han B Q , et al . Modeling the constitutive response of bimodal metals [J]. Metall. Mater. Trans., 2006, 37A: 2397
35
Yadollahpour M , Hosseini-Toudeshky H . Material properties and failure prediction of ultrafine grained materials with bimodal grain size distribution [J]. Eng. Comput., 2017, 33: 125
36
Guo X , Dai X Y , Zhu L L , et al . Numerical investigation of fracture behavior of nanostructured Cu with bimodal grain size distribution [J]. Acta. Mech., 2014, 225: 1093
37
Dai L H , Ling Z , Bai Y L . Size-dependent inelastic behavior of particle-reinforced metal-matrix composites [J]. Compos. Sci. Technol., 2001, 61: 1057
38
Gao H J , Huang Y G . Taylor-based nonlocal theory of plasticity [J]. Int. J. Solids Struct., 2001, 38: 2615
39
Gao H J , Huang Y , Nix W D , et al . Mechanism-based strain gradient plasticity—I. Theory [J]. J. Mech. Phys. Solids, 1999, 47: 1239
40
Huang Y , Qu S , Hwang K C , et al . A conventional theory of mechanism-based strain gradient plasticity [J]. Int. J. Plast., 2004, 20: 753
41
Shao J C , Xiao B L , Wang Q Z , et al . An enhanced FEM model for particle size dependent flow strengthening and interface damage in particle reinforced metal matrix composites [J]. Compos. Sci. Technol., 2011, 71: 39
42
Cao J Y , Jin J F , Wang L , et al . Finite-element modeling of particle size effect on mechanical properties of SiCp/Fe composites [J]. IOP Conf. Ser. Mater. Sci. Eng., 2018, 422: 012001
43
Zhang J F , Zhang X X , Wang Q Z , et al . Simulation of anisotropic load transfer and stress distribution in SiCp/Al composites subjected to tensile loading [J]. Mech. Mater., 2018, 122: 96
44
Gao X , Zhang X X , Geng L . Strengthening and fracture behaviors in SiCp/Al composites with network particle distribution architecture [J]. Mater. Sci. Eng., 2019, A740-741: 353
45
Schwaiger R , Moser B , Dao M , et al . Some critical experiments on the strain-rate sensitivity of nanocrystalline nickel [J]. Acta Mater., 2003, 51: 5159
46
Wang M T , Zong B Y , Wang G . A phase-field model to simulate recrystallization in an AZ31 Mg alloy in comparison of experimental data [J]. J. Mater. Sci. Technol., 2008, 24: 829
47
Taylor G I . Plastic strain in metals [J]. J. Inst. Met., 1938, 62: 307
48
Mecking H , Kocks U F . Kinetics of flow and strain-hardening [J]. Acta Metall., 1981, 29: 1865
49
Nix W D , Gao H J . Indentation size effects in crystalline materials: A law for strain gradient plasticity [J]. J. Mech. Phys. Solids, 1998, 46: 411
50
Chawla N , Ganesh V V , Wunsch B . Three-dimensional (3D) microstructure visualization and finite element modeling of the mechanical behavior of SiC particle reinforced aluminum composites [J]. Scr. Mater., 2004, 51: 161
51
Chawla N , Chawla K K . Microstructure-based modeling of the deformation behavior of particle reinforced metal matrix composites [J]. J. Mater. Sci., 2006, 41: 913
52
Uthaisangsuk V , Prahl U , Bleck W . Micromechanical modelling of damage behaviour of multiphase steels [J]. Comput. Mater. Sci., 2008, 43: 27
53
Choi K S , Liu W N , Sun X , et al . Microstructure-based constitutive modeling of TRIP steel: Prediction of ductility and failure modes under different loading conditions [J]. Acta Mater., 2009, 57: 2592
54
Uthaisangsuk V , Prahl U , Bleck W . Modelling of damage and failure in multiphase high strength DP and TRIP steels [J]. Eng. Fract. Mech., 2011, 78: 469
55
Ayari F , Ayari F , Bayraktar E , et al . Image processing and finite element modelling for analysis of a metal matrix composite [J]. Int. J. Comput. Sci. Iss., 2012, 9: 448
56
Ramazani A , Mukherjee K , Quade H , et al . Correlation between 2D and 3D flow curve modelling of DP steels using a microstructure-based RVE approach [J]. Mater. Sci. Eng., 2013, A560: 129
57
Qayyum F , Umar M , Guk S , et al . Effect of the 3rd dimension within the representative volume element (RVE) on damage initiation and propagation during full-phase numerical simulations of single and multi-phase steels [J]. Materials, 2021, 14: 42
58
Cao J , Zhuang W , Wang S , et al . An integrated crystal plasticity FE system for microforming simulation [J]. J. Multiscale Model., 2009, 1: 107
59
Zhang P , Karimpour M , Balint D , et al . A controlled poisson voronoi tessellation for grain and cohesive boundary generation applied to crystal plasticity analysis [J]. Comput. Mater. Sci., 2012, 64: 84
60
Song Y H , Wang M T , Zong Y P , et al . Grain refinement by second phase particles under applied stress in ZK60 Mg alloy with Y through phase field simulation [J]. Materials, 2018, 11: 1903
61
He R , Wang M T , Zhang X G , et al . Influence of second-phase particles on grain growth in AZ31 magnesium alloy during equal channel angular pressing by phase field simulation [J]. Modell. Simul. Mater. Sci. Eng., 2016, 24: 055017
62
Han G M , Han Z Q , Luo A A , et al . A phase field model for simulating the precipitation of multi-variant β-Mg17Al12 in Mg-Al-based alloys [J]. Scr. Mater., 2013, 68: 691
63
Shang S , Guo Z P , Han Z Q . On the kinetics of dendritic sidebranching: A three dimensional phase field study [J]. J. Appl. Phys., 2016, 119: 164305
64
Cahn J W . On spinodal decomposition [J]. Acta Metall., 1961, 9: 795
65
Allen S M , Cahn J W . A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening [J]. Acta Metall., 1979, 27: 1085
66
Fan D , Chen L Q . Computer simulation of grain growth using a continuum field model [J]. Acta Mater., 1997, 45: 611
67
Li L , Jie W , Wu Y Z , et al . Effect of static annealing on microstructure and texture in extruded Mg-Gd-Y-Zr Alloy [J]. Rare Met. Mater. Eng., 2016, 45: 2263
68
Verdier M , Groma I , Flandin L , et al . Dislocation densities and stored energy after cold rolling of Al-Mg alloys: Investigations by resistivity and differential scanning calorimetry [J]. Scr. Mater., 1997, 37: 449
69
Andersson J O , Helander T , Höglund L , et al . Thermo-Calc & DICTRA, computational tools for materials science [J]. Calphad, 2002, 26: 273
70
Ganeshan S , Shang S L , Wang Y , et al . Effect of alloying elements on the elastic properties of Mg from first-principles calculations [J]. Acta Mater., 2009, 57: 3876
71
Polk D E , Giessen B C , Gardner F S . State-of-the-art and prospects for magnetic, electronic and mechanical applications of amorphous metals A synopsis of the ONR materials workshop at Northeastern University, Boston, Mass., November 20-21, 1975 [J]. Mater. Sci. Eng., 1976, 23: 309
72
Kim H S , Estrin Y , Bush M B . Plastic deformation behaviour of fine-grained materials [J]. Acta Mater., 2000, 48: 493
73
Fu H H , Benson D J , Meyers M A . Analytical and computational description of effect of grain size on yield stress of metals [J]. Acta Mater., 2001, 49: 2567
74
Li J , Zhao M J , Jin L , et al . Simultaneously improving strength and ductility through laminate structure design in Mg-8.0Gd- 3.0Y-0.5Zr alloys [J]. J. Mater. Sci. Technol., 2021, 71: 195
75
Warlimont H , Martienssen W . Springer Handbook of Materials Data [M]. 2nd Ed., Switzerland: Springer, 2018: 65
76
Shang X Q , Zhang H M , Wang L Y , et al . The effect of stress state and strain partition mode on the damage behavior of a Mg-Ca alloy [J]. Int. J. Plast., 2021, 144: 103040
77
Gao L , Zhou J , Sun Z M , et al . First-principles calculations of the β′-Mg7Gd precipitate in Mg-Gd binary alloys [J]. Chin. Sci. Bull., 2011, 56: 1142
