Plastic deformation behavior of a nickel-based superalloy on the mesoscopic scale

doi:10.1016/j.jmst.2019.09.020

Abstract

Abstract:

Nickel-based superalloys have become the key materials of micro-parts depending on excellent mechanical properties at high temperatures. The plastic deformation behavior is difficult to predict due to the occurrence of size effect on the mesoscopic scale. In this paper, the effect of specimen diameter to grain size ratio (D/d) on the flow stress and inhomogeneous plastic deformation behavior in compression of nickel-based superalloy cylindrical specimens was investigated on the mesoscopic scale. The results showed that when D/d is less than 9.7, the flow stress increases with the grain size. Aiming at this phenomenon, a flow stress size effect model considering compressive strain partitioning was established. The calculated flow stress values agree well with the experimental values, thus revealing the effect of D/d on the flow stress in compression of nickel-base superalloy on the mesoscopic scale. The inhomogeneous plastic deformation during compression deformation increases with the grain size. The end surface profiles evolve from a regular circular shape to an irregular shape with the grain size. The surface folding phenomenon occurs only in partially compressed specimen with a few grains across the diameter. Crystal plasticity finite-element (CPFE) simulation of compression deformation on the mesoscopic scale real-time displayed the evolution of microstructure. The study of this paper has important guiding significance for understanding the influence of D/d on the compression deformation behavior of nickel-based superalloy on the mesoscopic scale.

Key words: Nickel-based superalloy, Size effect, Compression deformation, Surface morphology, Crystal plasticity, Mesoscopic scale

Qiang Zhu, Chuanjie Wang, Kai Yang, Gang Chen, Heyong Qin, Peng Zhang. Plastic deformation behavior of a nickel-based superalloy on the mesoscopic scale[J]. J. Mater. Sci. Technol., 2020, 40: 146-157.

Figures/Tables 22

Fig. 1. Microstructures of specimens under various annealing parameters. (a) 1323 K, 1 h; (b) 1373 K, 1 h; (c) 1423 K, 1 h; (d) 1473 K, 1 h; (e) 1523 K, 1 h; (f) 1523 K, 2 h; (g) 1523 K, 4 h.

Fig. 2. Grain size distribution histograms of specimens under various annealing parameters. (a) 1323 K, 1 h; (b) 1373 K, 1 h; (c) 1423 K, 1 h; (d) 1473 K, 1 h; (e) 1523 K, 1 h; (f) 1523 K, 2 h; (g) 1523 K, 4 h.

Table 1 Statistical results of grain size and specimen diameter to grain size ratio.

Solution temperature (K)	Solution time (h)	Average grain size, d (μm)	Standard deviation (μm)	Specimen diameter, D (mm)	D/d
1323	1	55.8	15.6	1.56	27.9
1373	1	76.2	13.8		20.5
1423	1	98.7	25.6		15.8
1473	1	143.3	37.0		10.9
1523	1	161.4	44.8		9.7
1523	2	181.5	52.2		8.6
1523	4	208.4	56.8		7.4

Fig. 3. Pole figures for specimens under various annealing parameters. (a) 1323 K, 1 h; (b) 1373 K, 1 h; (c) 1423 K, 1 h; (d) 1473 K, 1 h; (e) 1523 K, 1 h; (f) 1523 K, 2 h; (g) 1523 K, 4 h.

Fig. 4. Schematic diagram of uniaxial compression tests on the mesoscopic scale.

Fig. 5. (a) True stress-true strain curves of specimens with various grain sizes; (b) partial enlarged view of the frame selection in Fig. (a).

Fig. 6. Schematic diagram of strain partitioning after compression deformation.

Fig. 7. Relationship of flow stress with the reciprocal of the square root of the grain size under various true strains.

Fig. 8. Strain hardening curve of specimens with various D/d values during compression.

Fig. 9. Schematic diagram of the compression deformation partitioning.

Fig. 10. Variation of the regional ratio of each compression deformation zone.

Fig. 11. Variations of grain boundary size factors with average grain size and specimen diameter.

Fig. 12. Values of critical shear stress τc (ε) and Khp (ε) versus true strain.

Table 2 Effects of parameters on plastic deformation.

Parameter	Effect on plastic deformation
σ₀(ε)	Lattice frictional resistance generated when moving a single dislocation
K_hp(ε)	Propagating general yield across the polycrystal boundaries
d	Grain boundary strengthening
M	Average effect of grain orientation
M₁	Average effect of grain orientation for the grains in Zone I
M₂	Average effect of grain orientation for the grains in Zone II
M₃	Average effect of grain orientation for the grains in Zone III
τ_c(ε)	Ability to resist plastic deformation
θ	Effect of grain boundary density on the overall mechanical property
θ₁	Effect of grain boundary density in Zone I on the mechanical property
θ₂	Effect of grain boundary density in Zone II on the mechanical property
θ₃	Effect of grain boundary density in Zone III on the mechanical property
η₁	Effect of radial change rate of grain boundary on grain boundary factor
η₂	Effect of axial change rate of grain boundary on grain boundary factor

Fig. 13. Comparison between the calculated values and the experimental values of the flow stress for the specimens with various grain sizes.

Fig. 14. End surface topographies of specimens with various grain sizes after uniaxial compression. (a) d = 55.87 μm; (b) d = 76.2 μm; (c) d = 98.78 μm; (d) d = 143.38 μm; (e) d = 161.44 μm; (f) d = 181.51 μm; (g) d = 208.4 μm.

Fig. 15. Side surface topographies of specimens with various grain sizes after uniaxial compression. (a) d = 55.87 μm; (b) d = 76.2 μm; (c) d = 98.78 μm; (d) d = 143.38 μm; (e) d = 161.44 μm; (f) d = 181.51 μm; (g) d = 208.4 μm.

Fig. 16. Folding phenomenon of the specimen with the grain size of 161.44 μm after compression deformation.

Fig. 17. Model of surface folding in uniaxial compression on the mesoscopic scale.

Fig. 18. Compression finite element model of specimens with various grain sizes. (a) d = 55.8 μm; (b) d = 208.4 μm.

Fig. 19. Finite element model of specimens with various grain sizes after assigning attributes. (a) d = 55.8 μm; (b) d = 208.4 μm.

Fig. 20. Longitudinal section microstructure of specimens with various grain sizes based on crystal plasticity.

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