镍基高温合金低能孪晶界密度与热塑性变形参数的响应关系.pdf

Trans. Nonferrous Met. Soc. China 312021 438-455 Correspondence between low-energy twin boundary density and thermal-plastic deation parameters in nickel-based superalloy Guo-zheng QUAN1,2, Yu-qing ZHANG1, Pu ZHANG1, Yao-yao MA1, Wei-yong WANG3 1. College of Materials Science and Engineering, Chongqing University, Chongqing 400044, China; 2. State Key Laboratory of Materials Processing and Die 3. School of Civil Engineering, Chongqing University, Chongqing 400045, China Received 12 March 2020; accepted 25 September 2020 Abstract To deeply understand and even describe the evolutions of the low-energy twin boundary density BLD∑3n in a thermal-plastic deation process, an improved twin density model as a function of average grain size and stored energy is developed. For Nimonic 80A superalloy, the model is solved based on the EBSD statistical results of grain size and BLD∑3n in the specimens compressed at temperatures of 1273-1423 K and strain rates of 0.001-10 s-1. The corresponding relationships of BLD∑3n with stored energy and grain size varying with temperature and strain rate are clarified by the superimposed contour plot maps. It is summarized that BLD∑3n increases with increasing stored energy and decreasing grain size, and higher BLD∑3n with finer grains corresponds with lower temperatures and higher strain rates. Such relationships are described by the improved twin density model, and the prediction tolerance of the solved model is limited in 2.8. Key words Nimonic 80A superalloy; twin boundary; microstructure evolution; dynamic recrystallization; grain size; stored energy 1 Introduction Nimonic 80A, a nickel-based superalloy with low stacking fault energy SFE, has been widely used for aircraft jet engines, gas turbines, marine diesel engines, etc., owing to its excellent combination of properties such as strong corrosion- resistance, high strength and superior creep- resistance [1-3]. A common point of view is that the Nimonic 80A products with salient comprehensive properties usually achieved by thermal-plastic deation, are attributed to the grain refinement induced by dynamic recrystallization DRX to a great extent [3,4]. Generally, DRX grains nearly nucleate at the bulge of original grain boundaries, which profits from sub-grain rotation and annealing twin ation [5]. The annealing twins, separated from parent grains by long straight grain boundaries, can not only increase the amount of grain boundaries in favor of DRX grain nucleation, but also change the orientation and motivate further the slip of crystals [6]. Some ‘special boundaries’, low-energy twin boundaries, Σ3n n1, 2, 3, have relatively coherent interfaces that contain comparatively fewer vacancies and defects. The occurrence of mass transport and diffusion along the coherent interfaces also become sluggish, which can enhance the anti-fatigue and creep-resistance of alloys [7]. Thus, such high proportions of low-energy twin boundaries are desirable for alloys applied in elevated temperature environments. In the thermal- plastic deation process of a Nimonic 80A Corresponding author Guo-zheng QUAN; Tel 86-15922900904; E-mail quangz3000 DOI 10.1016/S1003-63262165508-5 1003-6326/ 2021 The Nonferrous Metals Society of China. Published by Elsevier Ltd D0 is the critical grain size; D is average grain size; γg is grain boundary energy; k is a constant. During grain growth, the driving force for grain boundary migration has decisive effect on the annealing twin ation. In PANDE’s model, the driving force F is strongly determined by grain boundary energy γg and average grain size D g 1 γ Fk D 2 where k1 is a constant. By considering the difference in Gibbs energy ΔG0 between growing and shrinking grains, ΔG04γg/D [12], and substituting this into Eq. 2, the driving force F is derived as Fk2ΔG0 3 where k2 is a constant. Then, the of ΔG0 was modified by LI et al [20] when accounting for the residual strain in a cold deation process 02 4 1 g γ GA S D ∆ 4 where A is a material constant; S is the amount of residual plastic strain. The existing for the difference in Gibbs energy only accounts for the strain resulting from cold deation. However, in a thermal-plastic deation process of alloys, the deation temperature, strain and strain rate have influence on the amount of residual plastic strain. In the work of DETROIS et al [7], the of ΔG0 was further modified by accounting for the stored strain energy in thermal deation 0 3s 4 1 g γ Gk E D  ∆   5 where Es is the stored energy; k3 is a constant. There is a proportional relationship between grain boundary energy γg and twin boundary energy γtb as k4γg/γtb, where k4 is a constant [7,13]. So, the ulation of driving force F can be derived when considering the effect of twin boundary energy 3s 5 1k E Fk D 6 where k5 is a constant. In the classic theory [13], twin content variation per grain ΔN is considered as a function of the variation of grain size ΔD and the driving force F for grain boundary migration ΔN∝FΔD 7 Then, substituting Eq. 6 into Eq. 7 yields Eq. 8 3s 66 5 1k E Nk F D k kD D ∆∆∆ 8 where k6 is a proportional coefficient. Integrating and using the boundary condition N0 as DD0, the content of twin boundary can be derived as 73s 0 1ln D Nkk E D 9 where k7 is a constant. Since NpD, the twin density can be expressed as Eq. 10, a function of stored energy and grain size 3s 7 0 1 ln k ED p k DD 10 During a deation, the stored energy of deed samples can be estimated from dislocation density [21] 21 s ln 4 EGbb K ρ ρ - π 11 where G is the shear modulus, b is the absolute value of the Burger vector, ρ is the dislocation density, K denotes the arithmetic average of 1 and 1-v, with v as the Poisson ratio. 万方数据 Guo-zheng QUAN, et al/Trans. Nonferrous Met. Soc. China 312021 438-455 441 Then, the dislocation density is related to the steady-state flow stress σ [22] 1 c Gbσρ 12 where c1 is a constant. Under a steady-state thermal deation process of alloys, the nucleation rate of DRX grains and average grain size remain constant. The average grain size shows a power-law relationship with the steady-state flow stress [23] 2 n c D G σ - 13 where n is the relevant exponent of grain size, ranging from 0.4 to 0.8; c2 is a constant. Consequently, combining Eq. 11, Eq. 12 with Eq. 13, the ulation of stored energy Es can be expressed as 4 s 2 3 ln n n cD E cD 14 where c3 and c4 are constants. In the present work, the boundary length density BLD that stands for the length of Σ3n twin boundaries per unit area BLD∑3n, μm-1 was used to quantify twin boundary content. Based on the stereology concepts, the density of Σ3n twin boundary BLD∑3n and p are related to each other by a proportionality factor as BLD∑3npπ/2. Therefore, the improved twin density model can be summarized as 3s 7 3 0 4 s 2 3 1 BLDln 2 ln n n n k ED k DD cD E cD ∑ π       15 3 Experimental 3.1 Materials and isothermal compression tests The studied material in this work is an as-forged Nimonic 80A superalloy, whose chemical compositions are presented in Table 1. Twenty-three specimens of 10 mm in diameter and 12 mm in height were machined by wire-electrode cutting from the same as-forged billet, and these specimens were prepared for a series of isothermal compression tests carried out on a Gleeble-3500 thermal mechanical simulator. Twenty of them were conducted at four different temperatures of 1273, 1323, 1373 and 1423 K and five different strain rates of 0.001, 0.01, 0.1, 1 and 10 s-1 to obtain the basic computation data for solving the improved twin density model. The remaining three specimens were prepared for the verification experiments of the improved model at the temperature of 1473 K and the strain rates of 0.001, 0.01 and 0.1 s-1. Before compression, the specimens were heated to a proposed temperature with a heating rate of 5 K/s and held at that temperature for 180 s. Subsequently, the specimens were isothermally compressed to a fixed true strain of 0.916 with a proposed strain rate, followed by water quenching to ambient temperature rapidly to decrease material anisotropy and retain the elevated temperature microstructures. The experimental procedure of isothermal compression tests is schematically illustrated in Fig. 1. Table 1 Chemical compositions of studied Nimonic 80A superalloy wt. Cr Fe Ti MnSi Al C Ni 20.871.262.070.630.55 0.68 0.069Bal. Fig. 1 Experimental procedure of isothermal compression tests 3.2 Microstructure measurement The deed specimens were sectioned into semi-cylinders along their longitudinal axis, and 5 mm 5 mm 3 mm samples were separated from the center of the semi-cylinders for microstructure observation, as shown in Fig. 2. Subsequently, the section surfaces were electro-polished at 20 V for 22 s in an electrolyte consisting of 10 HClO4, 10 CH3COOH and H2O. The microstructures were characterized using an electron backscattered diffraction EBSD detector attached to a JEOL JSM-7800F scanning electron microscope SEM at an accelerating voltage of 20 kV. In order to minimize the errors originated from grain boundary 万方数据 Guo-zheng QUAN, et al/Trans. Nonferrous Met. Soc. China 312021 438-455 442 Fig. 2 Schematic representation of sample location in compressed specimen Arrow shows applied load direction thickness and accounting for the limit resolution of EBSD, the scanning step size was limited in 0.2-2.5 m depending on the grain size. As for microstructural characterization, Channel 5 software was applied to analyzing the collected EBSD data. For Nimonic 80A superalloy, the critical angles judging sub-grain boundary and grain boundary are generally set to be 3 and 15, respectively [24]. The identification of Σ3n twin boundaries is based on the Brandon criterion, and the maximum allowed deviation is 8.7 [25]. The grain is defined as a region being completely bounded by HAGBs, excluding Σ3n twin boundaries. The local intragranular misorientation of microstructures is characterized on the basis of the fifth nearest neighbor with a maximum misorientation angle of 5. In order to quantify the content of Σ3n twin boundaries obtained from EBSD maps, the density of Σ3n twin boundary is calculated using NpΔ/A [26], where Np is the number of map-pixels that compose the Σ3n twin boundaries in the EBSD maps, Δ is the step size in μm, and A is the surface area in μm2. The initial microstructure of specimen is shown in Fig. 3. The microstructure in Fig. 3a is characterized as uni equiaxed grains with an average grain size of 34.8 m. From the Band contrast BC map in Fig. 3b, it is obvious that high angel grain boundaries HAGBs are severely interrupted by Σ3n clusters containing inter- connected Σ3, Σ9 and Σ27 twin boundaries in grains, and the content of Σ3 twin boundaries is the largest. Fig. 3 Initial microstructures of Nimonic 80A super- alloy without deation a Optical microstructure; b Band contrast BC map with Σ3n twin boundaries HAGBs with misorientation angles larger than 15 in black, LAGBs with misorientation angles of 2-15 in gray, Σ3 in red, Σ9 in fuchsia and Σ27 in aqua 4 Characterization of twin density evolution by improved model 4.1 Evolution of grain size and its characterization In the thermo-plastic deation of Nimonic 80A superalloy, occurrence of DRX can result in significant grain refinement. More importantly, the DRX process is usually accompanied by the ation of Σ3n twin boundaries. As thus, the influence of deation parameters on DRX behaviors is analyzed, which significantly assists in understanding the synergistic effects between DRX behaviors and the Σ3n twin boundaries density. Figure 4 shows the EBSD maps with DRX fraction and Σ3n twin boundaries of the specimens deed to a fixed true strain of 0.916 at temperatures of 1273-1423 K and strain rates of 0.001-10 s-1. A common feature of these EBSD maps is that most of them are characterized as homogeneous and almost equiaxed DRX grains, especially at high temperatures. However, in the low temperature 万方数据 Guo-zheng QUAN, et al/Trans. Nonferrous Met. Soc. China 312021 438-455 443 Fig. 4 EBSD maps with DRX fraction and Σ3n twin boundaries of Nimonic 80A superalloy deed at temperatures of 1273-1423 K and strain rates of 0.001-10 s-1 with fixed true strain of 0.916 DRX grains in navy, sub-grains in yellow, deed grains in red, HAGBs in black, and LAGBs in gray range of 1273-1323 K and the intermediate strain rate range of 0.1-1 s-1, it is obvious that many grain boundaries still remain the original morphologies because of the low mobility of grain boundaries at lower temperatures. Meanwhile, the original elongated grains surrounded by fine DRX grains present as the ‘necklace’ microstructures. It is worth noticing that the new DRX grains almost nucleate at grain boundaries firstly, especially at the bulge of original grain boundaries. This is mainly due to the fact that the dislocation slipping and pile-up at grain boundaries would induce orientation evolution, which contributes to the preferential nucleation at these boundaries [6]. In order to further uncover the effects of deation parameters on DRX behaviors, the 万方数据 Guo-zheng QUAN, et al/Trans. Nonferrous Met. Soc. China 312021 438-455 444 volume fraction of DRX grain and average grain size for Nimonic 80A superalloy are collected from the EBSD maps in Fig. 4, and their variations along with temperature and strain rate are exhibited in Fig. 5. As shown in Fig. 5a, a multilayered contour map is constructed to characterize the responses of the volume fraction of DRX grain Layer 1, sub-grain Layer 2 and deed grain Layer 3 to temperature and strain rate. By combining Fig. 5a with Fig. 4, it is apparently found that DRX becomes sluggish in the low temperature range of 1273-1323 K and the intermediate strain rate of 0.1-1 s-1. The micro- structures are mainly composed of deed grains and sub-grains, and the volume fraction of sub-grain is the highest, which indicates an incomplete DRX process. It is noteworthy that the microstructures with more than 65 vol. of DRX can be obtained in all deation conditions except for the regions in low temperatures and mediate strain rates. With increasing temperature, DRX occurs more completely and the DRX grains grow. As well known, the average gr