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Acta Metall Sin  2023, Vol. 59 Issue (8): 1042-1050    DOI: 10.11900/0412.1961.2023.00083
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Simulation of Deformation Coordination and Hardening Behavior in Ferrite-Ferrite Grain Boundary
XU Yongsheng, ZHANG Weigang(), XU Lingchao, DAN Wenjiao
School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
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XU Yongsheng, ZHANG Weigang, XU Lingchao, DAN Wenjiao. Simulation of Deformation Coordination and Hardening Behavior in Ferrite-Ferrite Grain Boundary. Acta Metall Sin, 2023, 59(8): 1042-1050.

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Abstract  

The deformation coordination of grain boundaries determines the nucleation and evolution of microvoids and affects the damage and fracture behavior of materials. However, grain boundary deformation is extremely complex and difficult to predict owing to the difference in intergranular orientation and grain stress state. Among them, two important ways of coordinating deformations are the accumulation of dislocations at grain boundaries and intergranular transfer. The geometric relationship of the activated intergranular slip systems determines the difficulty of slip transfer and the uniformity of deformation at grain boundaries. Moreover, owing to the complex grain boundary conditions of polycrystalline materials, it is difficult to accurately measure the actual stress state and deformation of grain boundaries, so there is a substantial discreteness between the experimentally observed slip transfer behavior and theoretical prediction results. Herein, based on the advantages of the crystal plasticity finite element method (CPFEM) in polycrystalline model construction, grain orientation, and mechanical boundary condition setting, the ferrite-ferrite symmetrical tilt and twist bicrystal models under different stress states was used to analyze the impact of stress state and relative grain orientation on grain boundary strain coordination and hardening behavior. The results show that the intergranular slip transfer factor and the resolve shear stress factor determine the strain uniformity at the grain boundary. The deformation uniformity at the grain boundary is positively correlated with the slip transfer factor, which mainly controls the intergranular deformation coordination behavior. However, the deformation at the grain boundaries of soft-oriented grains (determined by stress state and orientation) is uniform, and the slip transfer factor has little effect on strain coordination. When the slip transfer factor and the resolve shear stress factor are very small, strain concentration at the grain boundary easily occurs, making intergranular deformation coordination difficult. Therefore, the prediction results of intergranular deformation coordination combined with the slip transfer factor and resolving the shear stress factor are reasonable. In addition, the flow stress of the bicrystal model is negatively correlated with the slip shear stress factor, and the uneven deformation at the grain boundary easily causes geometrically necessary dislocations to proliferate and promote grain boundary hardening.

Key words:  grain boundary      crystal plasticity      deformation coordination      hardening      bicrystal model     
Received:  02 March 2023     
ZTFLH:  TG142  
Corresponding Authors:  ZHANG Weigang, professor, Tel:13801875720, E-mail: wgzhang@sjtu.edu.cn

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2023.00083     OR     https://www.ams.org.cn/EN/Y2023/V59/I8/1042

Fig.1  Symmetrically tilt bicrystal model (a) and twist bicrystal model (b)
AngleΣEuler angle / (o)
(axis: <100>)Right grainLeft grain
0.001(0 0 0)(0 0 0)
16.2625(180 8.13 180)(0 8.13 0)
22.6213(180 11.31 180)(0 11.31 0)
28.0717(180 14.04 180)(0 14.04 0)
36.875(180 18.44 180)(0 18.44 0)
53.135(180 26.57 180)(0 26.57 0)
61.9317(180 30.97 180)(0 30.97 0)
67.3813(180 33.69 180)(0 33.69 0)
73.7425(180 36.87 180)(0 36.87 0)
90.001(180 45 180)(0 45 0)
Table 1  Grain orientations in <100> axis symmetrically tilt/twist bicrystal models[27]
AngleΣEuler angle / (o)
(axis: <110>)Right grainLeft grain
0.001(0 0 0)(0 0 0)
26.5319(-135 13.26 135)(45 13.26 -45)
31.5927(-135 15.79 135)(45 15.79 -45)
38.949(-135 19.47 135)(45 19.47 -45)
50.4811(-135 25.24 135)(45 25.24 -45)
70.533(-135 35.26 135)(45 35.26 -45)
109.473(-135 54.74 135)(45 54.74 -45)
129.5211(-135 64.76 135)(45 64.76 -45)
141.069(-45 70.53 135)(45 70.53 -45)
148.4127(-135 74.21 135)(45 74.21 -45)
180.001(-135 90 135)(45 90 -45)
Table 2  Grain orientations in <110> axis symmetrically tilt/twist bicrystal models[27]
AngleΣEuler angle / (o)
(axis: <111>)Right grainLeft grain
0.001(0 0 0)(0 0 0)
13.1719(-136.9 5.37 133.1)(46.9 5.37 -43.1)
21.797(-138.1 8.89 131.8)(48.1 8.89 -41.8)
27.8013(-139.0 11.34 131.0)(49.0 11.34 -41.0)
32.2013(-139.7 13.13 130.3)(49.7 13.1 -40.3)
38.217(-140.5 15.6 129.5)(50.5 15.6 -39.5)
46.8219(-141.8 19.1 128.2)(51.8 19.1 -38.2)
60.001(-143.8 24.4 126.2)(53.8 24.4 -36.2)
Table 3  Grain orientations in <111> axis symmetrically tilt/twist bicrystal models[27]
Fig.2  Schematics of bicrystal model loading in various stress states (U marks the displacement loading of the model)
(a) shear condition
(b) uniaxial tension condition
(c) plane strain condition
Fig.3  Grain boundary strain ratios (a1-c1), resolve shear stress factors (a2-c2), and slip transfer factors m (a3-c3) and m* (a4-c4) curves with tilt angle (NO. represents the number of participants in the average after sorting the corresponding parameters from largest to smallest)
(a1-a4) shear condition (b1-b4) uniaxial tension condition (c1-c4) plane strain condition
Fig.4  Strain map of <110> axis symmetric tilt grain boundary with tilt angle is 70.53° (LE indicates logarithmic strain)
Fig.5  Geometrically necessary dislocation (GND) density curves with distance (a1-c1) and tilt angle (a2-c2) at grain boundary (a1, a2) shear condition (b1, b2) uniaxial tension condition (c1, c2) plane strain condition
Fig.6  Scatter maps of strain ratio with m (a1-c1), m* (a2-c2), and resolve shear stress factor (a3-c3)
(a1-a3) shear condition (b1-b3) uniaxial tension condition (c1-c3) plane strain condition
Fig.7  Flow stress vs resolve shear stress factor scatter maps of bicrystal model
(a) shear condition (b) uniaxial tension condition (c) plane strain condition
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