- Email: [email protected]
Effect of stacking fault energy on densification behavior of metal powder during hot isostatic pressing
Effect of stacking fault energy on densification behavior of metal powder during hot isostatic pressing Hosam ElRakayby, KiTae Kim PII: DOI: Reference:
S0264-1275(16)30332-X doi: 10.1016/j.matdes.2016.03.057 JMADE 1535
To appear in: Received date: Revised date: Accepted date:
5 January 2016 11 March 2016 13 March 2016
Please cite this article as: Hosam ElRakayby, KiTae Kim, Effect of stacking fault energy on densification behavior of metal powder during hot isostatic pressing, (2016), doi: 10.1016/j.matdes.2016.03.057
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Effect of stacking fault energy on densification behavior of metal powder during hot isostatic pressing Hosam ElRakayby and KiTae Kim* Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang
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(37673), Republic of Korea
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*Corresponding author: KiTae Kim
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Email: [email protected]
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Postal address: Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH) 77 Cheongam-Ro, Nam-Gu, Pohang, Gyeongbuk, Republic of Korea (37673).
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Phone number: +82-54-279-2838
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ACCEPTED MANUSCRIPT Abstract This paper reports the effect of the stacking fault energy on densification behavior and deformation of 316L stainless steel powder during hot isostatic pressing. Abouaf’s creep densification model was modified by
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considering the stacking fault energy as a material parameter. The new model was implemented into Abaqus -
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FEA, and finite element calculations were compared with various experimental data such as densification
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behavior, relative density distribution of powder compacts, and final deformed shape of powder compacts of 316L stainless steel under hot isostatic pressing. The new model was also examined to predict densification
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behavior of 316L stainless steel powders in the literature.
Keywords:
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Densification; Stainless steel; Hot isostatic pressing; Constitutive equations; Stacking fault energy.
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ACCEPTED MANUSCRIPT 1. Introduction Near net shape manufacturing technology has been widely used to fabricate metal parts of complex shapes by powder metallurgy processes to save costs and time. Hot isostatic pressing process (hipping) is a
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powder metallurgy process for consolidation of metal powders to fully density, and near net shape parts by
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applying hydrostatic pressure at high temperature [1–3]. In the hipping process, metal powders are densified
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dominantly by power-law creep deformation [4]. Various researchers [4–6] proposed creep densification models to predict densification behavior of metal powders at high temperatures.
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There are a number of studies for densification models to investigate the effect of various physical parameters on the creep densification behavior of metal powder. Yang and Kim [7] included the grain size as a
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parameter in Abouaf’s [5] model. Gillia et al. [8] modified Abouaf’s [5] model by including strain hardening of the powder material. Wolff et al. [9] extended the validity of various micromechanical models to the range
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of 50% porosity. Aryanpour et al. [10] proposed a densification model of metal powder that considers the
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deformation resulting from viscoplastic, and plastic deformation mechanisms during loading. They employed
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the constitutive equations of Abouaf [5] for the viscoplastic part in their model. Creep response is a complicated process that is controlled by various physical parameters. The stacking
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fault energy (SFE) is a parameter to determine the creep strength for various types of metal alloys [11]. McLean [12] showed that the SFE affects the deformation behavior of metal alloys and thus the creep, and the primary creep value can be a function of the SFE. Various researchers [12–15] studied the relationship between steady-state creep rate and the SFE for various alloys. They reported that the steady-state creep rate is proportional to the SFE powered to various values. All proposed power values for the SFE are within the range 1.2-4.2 that is reported by Mohamed and Langdon [14]. The present paper investigates the SFE effect on creep densification behavior and deformation of 316L stainless steel powder during hot isostatic pressing. The SFE was introduced to the model of Abouaf et al. [5] as a new material parameter, and the model’s rheological relative density functions were developed, as well, to consider the SFE effect. The new model was implemented into Abaqus - FEA. Finite element calculations 3
ACCEPTED MANUSCRIPT from the new model were compared with experimental data for densification behavior, relative density distribution, and shape distortion. Finally, experimental data from Kim and Jeon [16], and Yang and Kim [7] were also compared with finite element calculations from the new model to predict densification behavior and
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deformation of 316L stainless steel with various particle sizes.
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2. Experiment
316L stainless steel powder with an average particle size of 8 µm (Epson Atmix Corporation, Japan) was
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used in the present work, the powder has irregular shapes and a theoretical density of 7.95 g/cm3. The chemical composition of 316L stainless steel powder is shown in Table 1. Fig. 1 shows a scanning electron
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micrograph of 316L stainless steel powder.
Ni
Mo
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Cr 15.7
11.3
2.07
Si
Mn
Cu
0.86
0.09
0.03
P
S
C
0.028 0.002 0.019
O2
Fe
0.35
Balance
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Chemical Composition (Wt. %)
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Table 1 Chemical composition of 316L stainless steel powder
Fig. 1 Scanning electron micrograph of 316L stainless steel powder
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ACCEPTED MANUSCRIPT For encapsulation, 316L stainless steel powder was used to fill a 304 stainless steel container with 0.6 mm in thickness, 60 mm in height, and 22.9 mm in inner diameter. The container was vibrated to attain the initial relative density of 0.45. Subsequently, the container was sealed with a 304 stainless steel plug by welding and
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degassed through the ventilation tube on the plug for 5 hours at 250 oC. After that, the ventilation tube was
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sealed by air-tight clamping and welding.
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The sample was placed in a hot isostatic press (AIP10-30H, AIP, USA) and heated to 925 oC at a heating rate of 10 oC/min. A maximum hydrostatic pressure of 30 MPa was applied on the sample with a pressurizing
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rate of 0.33 MPa/min. The maximum holding time was 4 hours. Fig. 2 shows the applied temperature and
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pressure change with the variation of time during hipping.
Fig. 2 HIP schedule
After hipping, the container was removed by machining, and relative density was measured by Archimedes’ principle according to (ASTM-B962). Hardness of the 316L stainless steel compacts was measured by using a micro-Vickers hardness tester (FM-700, Future-Tech Corp., Japan) with 2,000 gmf load and 15 seconds holding time to obtain a relationship between relative density and hardness values of the powder compacts. Experimental data from Kim and Jeon [16], and Yang and Kim [7] were also used to compare with the new model calculations for densification of 316L stainless steel powder with the average particle sizes of 110
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ACCEPTED MANUSCRIPT µm and 175 µm, respectively. Kim and Jeon [16] applied hydrostatic pressure of 50 MPa at 1125 oC for 4 h,
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whereas Yang and Kim [7] applied hydrostatic pressure of 30 MPa at 850 oC for 4 h.
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3. Development of the creep-densification model 3.1. Densification equations for porous metals
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In metal alloys, the relationship between the steady-state strain rate s and stress in the power-law
n
(1)
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Qc n s 0 A(T ) n A0 exp . R T 0
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creep can be written as [7]
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Here, 0 , 0 , n, A, A0 , Qc , and R, are reference strain rate, reference stress, stress sensitivity index, a
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temperature-dependent constant, reference constant, creep activation energy, and the gas constant, respectively. As mentioned in the introduction, previous works [12–15] have related the steady-state creep strain rate to the SFE powered to various values in a range of 1.2-4.2. Thus, in terms of the creep potential, the general form
3 2
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of creep strain rate ij can be written as
ij A m eq n1 cS ij 3 f m ij ,
(2)
where , S ij , m , and ij are the stacking fault energy, deviatoric components of stress state, hydrostatic components of stress state, and Kronecker’s delta, respectively. Creep strain rate ij can also be written as [6]
ij
eq , eq ij
(3)
where the creep potential is 6
ACCEPTED MANUSCRIPT eq n 1 0
0 0
n 1
m
A m n1 . eq n 1
(4)
eq 2 3cJ 2 fI 12 ,
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(5)
1 S ij S ij and I 1 kk . 2
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where J 2
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The equivalent stress of a porous metal eq can be written as [17]
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Here, the functions f and c are relative density-dependent functions that represent the contribution of the hydrostatic part and the deviatoric part of the stress state, respectively, during densification. Thus,
c s 2n /( n1) f ,
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(6)
(7)
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2 /( n 1) 1 D / D f m n , 9 A P
where s is a relative density-dependent function that represents the flow stress ratio of porous powder
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compacts to fully dense ones. D is the densification rate of the powder compact and can be written as [2] (8)
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D Dkk . 3.2. Finite element model
Finite element calculations of the hipping process for 316L stainless steel powder were achieved by implementing the constitutive equations from the new model into the user-defined subroutine creep of Abaqus - FEA. Fig. 3 shows the finite element mesh used for the hipping of 316L stainless steel powder. Because of the axial symmetry in the y-axis and the symmetry in the x-axis, a quarter model for a powder compact was used. A total of 586 four-node axisymmetric thermally coupled quadrilateral, bilinear, and temperature (CAX4T) elements, and 3 three-node thermally coupled axisymmetric triangle, linear displacement, and temperature (CAX3T) elements were used.
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Fig.3 Finite element meshes for 316L stainless steel powder during hot isostatic pressing
4. Results and discussion
4.1. Stacking fault energy The SFE is usually hard to measure experimentally [18]. The value of the SFE for 316L stainless steel can also be obtained using JMatPro 8.0 software. This software is capable of calculating mechanical, thermophysical, and physical properties of various alloys [19]. Saunders et al. [19] examined the accuracy of JMatPro calculations for these properties. Fig. 4 shows the SFE of 316L stainless steel at various temperatures calculated by using JMatPro 8.0 software.
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4.2. Relative density-dependent functions f and c
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Fig. 4 Stacking fault energy of 316L stainless steel obtained by using JMatPro 8.0 software
4.2.1. Function f
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Fig. 5 shows the variations of function f with relative density. The empirical form of these functions can
1 D f 11 D 0.45
,
1 D f 1.3 D 0.69
,
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be written
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1.06
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1.2
1 D f 2.9 , D 0.69
(9)
(10)
1.6
(11)
for the present work, Kim and Jeon [16], and Yang and Kim [7], respectively. These functions were calculated by using Eq. 7. The densification rate D in Eq. 7 was obtained from the slope of the continuous densification curve of 316L stainless steel powder. Creep constants (A,n) in Eq. 7 for 316L stainless steel were used from Yang and Kim [7].
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Fig. 5 Variation of functions f with relative density
4.2.2. Function c
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Fig. 6 shows the variations of function c with relative density. The empirical form of these functions can
2.5
0.85
,
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1 D c 1 2.5 D 0.69
,
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1 D c 1 8 D 0.45
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be written
1 D c 1 1.8 , D 0.69
(12)
(13)
1.9
(14)
for the present work, Kim and Jeon [16], and Yang and Kim [7], respectively. These functions were calculated by using Eq. 6. The flow stress ratio (s) in Eq. 6 for 316L stainless steel powder compacts were used from Yang and Kim [7], and Kim and Jeon [16].
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Fig. 6 Variation of functions c with relative density
4.3. Densification behavior of powder compacts
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The constant m = 2 was used in the SFE for 316L stainless steel. This value was chosen by comparisons
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between finite element calculations with various m values in the new model and experimental data of Kim and
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Jeon [16] for 316L stainless steel powder. The m values used in comparison were within the limit suggested by Mohamed and Langdon [14]. Fig. 7 shows the effect of m in the SFE on densification behavior of 316L stainless steel. Fig. 7 also shows finite element calculations from the original model of Abouaf. Finite element
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calculations with m = 2 agreed well with experimental data. Fig. 8 shows the comparison between experimental data and finite element calculations from the new model for the variation of relative density with time. Fig. 8 also shows experimental data of Kim and Jeon [16] and Kim and Yang [7]. The curves are finite element calculations from the new model with m = 2. The particle size affects on the initial relative density of packed powders. The initial relative density is a material parameter in the new model that determines densification behavior of 316L stainless steel powder. Finite element calculations from the new model agreed well with various experimental data. The new model agrees better with experimental data than the original model of Abouaf.
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Fig. 7 Effect of m in the stacking fault energy on densification behavior of 316L stainless steel
Fig. 8 Variations of relative density with time for 316L stainless steel under hipping
The relationship between hardness and relative density can be used to obtain relative density distributions of a powder compact [16]. Fig. 9 shows the variation of Vickers hardness values (HV) of 316L stainless steel powder compacts with relative density. The relationship between hardness and relative density of 316L stainless steel can be written RD 0.995 0.444 exp 0.0005 HV
1.637
(15)
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Fig.9 Variation of Vickers hardness for 316L stainless steel powder compacts with relative density
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Fig. 10 shows (a) finite element calculations from the new model and (b) measured density distribution for 316L stainless steel powder compact after 10 min under 30 MPa at 925 oC. Relative density distribution
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calculated from the new model somewhat overestimated measured data at the corner. However, it predicts well at the center of the compact. Similarly, Fig 11 shows (a) finite element calculations from the new model,
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(b) experimental data and (c) finite element calculations from Kim and Jeon [16] for density distribution for
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316L stainless steel powder compact after 10 min under 50 MPa at 1125 oC. Finite element calculation from
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the new model predicted better than the original model of Abouaf for density distribution in Kim and Jeon’s results [16]. But it somewhat underestimated measured data. This variation of relative density distribution over
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the compact cross section is due to the deviatoric stress state caused by the rigidity of the container wall.
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ACCEPTED MANUSCRIPT Fig. 10 Relative density distribution from (a) finite element calculations from the new model and (b) measured data for 316L
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stainless steel powder compact after 10 min under 30 MPa at 925 oC
Fig. 11 Relative density distribution from (a) finite element calculations from the new model, (b) measured data from Kim and Jeon
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[17] and (c) finite element calculations from Kim and Jeon [17] for 316L stainless steel powder compact after 10 min under 50 MPa at 1125 oC
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Fig. 12 shows a comparison between experimental data and finite element calculations from the new model for shape change of the powder compact after 240 min under 30 MPa at 925 oC. Fig. 13 compares experimental data from Yang and Kim [7] with finite element calculations from the new model for shape
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change of the powder compact after 240 min under 30 MPa at 850 oC. Finite element calculations from the new model agreed well with experimental data for final shape change of the specimen.
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Fig. 12 Comparison between experimental data and finite element calculations from the new model for final deformed shape of
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316L stainless steel powder compact after 240 min under 30 MPa at 925 oC
Fig. 13 Comparison between finite element calculations from the new model and experimental data from Yang and Kim [7] for final deformed shape of 316L stainless steel powder compact after 240 min under 30 MPa at 850 oC
5. Conclusion
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ACCEPTED MANUSCRIPT This paper investigated the effect of stacking fault energy on densification behavior and deformation of 316L stainless steel powder with various particle sizes under hot isostatic pressing process. The stacking fault energy was included in Abouaf’s model as a material parameter, and new relative density-dependent functions
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were obtained. The finite element calculations from the new model accurately predicted various experimental
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data, such as densification behavior, relative density distribution of powder compacts, and final deformed
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shape of powder compacts of 316L stainless steel powders under hot isostatic pressing. Finally, by employing the stacking fault energy in the constitutive equations of metal powders, a better theoretical results were
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obtained compared to the original model.
[3]
[4] [5] [6] [7] [8]
[9]
[10]
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[2]
K. Essa, R. Khan, H. Hassanin, M.M. Attallah, R. Reed, An iterative approach of hot isostatic pressing tooling design for net-shape IN718 superalloy parts, Int. J. Adv. Manuf. Technol. (2015). doi:10.1007/s00170-015-7603-3. H. ElRakayby, H. Kim, S. Hong, K.T. Kim, An investigation of densification behavior of nickel alloy powder during hot isostatic pressing, Adv. Powder Technol. 26 (2015) 1314–1318. doi:10.1016/j.apt.2015.07.005. C. Van Nguyen, A. Bezold, C. Broeckmann, Inclusion of initial powder distribution in FEM modelling of near net shape PM hot isostatic pressed components, Powder Metall. 57 (2014) 295–303. doi:10.1179/1743290114Y.0000000087. L.T. Kuhn, R.M. McMeeking, Power-law creep of powder bonded by isolated contacts, Int. J. Mech. Sci. 34 (1992) 563–573. doi:10.1016/0020-7403(92)90031-B. M. Abouaf, J.L. Chenot, G. Raisson, P. Bauduin, Finite element simulation of hot isostatic pressing of metal powders, Int. J. Numer. Methods Eng. 25 (1988) 191–212. doi:10.1002/nme.1620250116. A.C.F. Cocks, Inelastic deformation of porous materials, J. Mech. Phys. Solids. 37 (1989) 693–715. doi:10.1016/0022-5096(89)90014-8. H.C. Yang, K.T. Kim, Creep densification behavior of micro and nano metal powder: Grain sizedependent model, Acta Mater. 54 (2006) 3779–3790. doi:10.1016/j.actamat.2006.04.009. O. Gillia, B. Boireau, C. Boudot, A. Cottin, P. Bucci, F. Vidotto, et al., Modelling and computer simulation for the manufacture by powder HIPing of blanket shield components for ITER, Fusion Eng. Des. 82 (2007) 2001–2007. doi:10.1016/j.fusengdes.2007.03.037. C. Wolff, S. Mercier, H. Couque, A. Molinari, Modeling of conventional hot compaction and Spark Plasma Sintering based on modified micromechanical models of porous materials, Mech. Mater. 49 (2012) 72–91. doi:10.1016/j.mechmat.2011.12.002. G. Aryanpour, S. Mashl, V. Warke, Elastoplastic–viscoplastic modelling of metal powder compaction: application to hot isostatic pressing, Powder Metall. 56 (2013) 14–23. doi:doi:10.1179/1743290112Y.0000000027.
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References
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ACCEPTED MANUSCRIPT C. Tian, G. Han, C. Cui, X. Sun, Effects of stacking fault energy on the creep behaviors of Ni-base superalloy, Mater. Des. 64 (2014) 316–323. doi:10.1016/j.matdes.2014.08.007. [12] D. McLean, The physics of high temperature creep in metals, Reports Prog. Phys. 29 (1966) 1–33. doi:10.1088/0034-4885/29/1/301. [13] R.M. Bonesteel, O.D. Sherby, Influence of diffusivity, elastic modulus, and stacking fault energy on the high temperature creep behavior of alpha brasses, Acta Metall. 14 (1966) 385–391. doi:10.1016/00016160(66)90096-4. [14] F.A. Mohamed, T.G. Langdon, The transition from dislocation climb to viscous glide in creep of solid solution alloys, Acta Metall. 22 (1974) 779–788. doi:10.1016/0001-6160(74)90088-1. [15] Z. Guo, A.P. Miodownik, N. Saunders, J.-P. Schillé, Influence of stacking-fault energy on high temperature creep of alpha titanium alloys, Scr. Mater. 54 (2006) 2175–2178. doi:10.1016/j.scriptamat.2006.02.036. [16] K.T. Kim, Y.C. Jeon, Densification behavior of 316L stainless steel powder under high temperature, Mater. Sci. Eng. A. 245 (1998) 64–71. doi:10.1016/S0921-5093(97)00696-5. [17] C. Van Nguyen, A. Bezold, C. Broeckmann, Anisotropic shrinkage during hip of encapsulated powder, J. Mater. Process. Technol. 226 (2015) 134–145. doi:10.1016/j.jmatprotec.2015.06.037. [18] L. Vitos, J.-O. Nilsson, B. Johansson, Alloying effects on the stacking fault energy in austenitic stainless steels from first-principles theory, Acta Mater. 54 (2006) 3821–3826. doi:10.1016/j.actamat.2006.04.013. [19] N. Saunders, U.K.Z. Guo, X. Li, A.P. Miodownik, J.-P. Schillé, Using JMatPro to model materials properties and behavior, JOM. 55 (2003) 60–65. doi:10.1007/s11837-003-0013-2.
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[11]
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ACCEPTED MANUSCRIPT
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Graphical abstract
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ACCEPTED MANUSCRIPT Highlights
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New stacking fault energy dependent model with higher predictability for densification behavior of metal powder is proposed. New relative density functions for 316L stainless steel were obtained.
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S0264-1275(16)30332-X doi: 10.1016/j.matdes.2016.03.057 JMADE 1535
To appear in: Received date: Revised date: Accepted date:
5 January 2016 11 March 2016 13 March 2016
Please cite this article as: Hosam ElRakayby, KiTae Kim, Effect of stacking fault energy on densification behavior of metal powder during hot isostatic pressing, (2016), doi: 10.1016/j.matdes.2016.03.057
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Effect of stacking fault energy on densification behavior of metal powder during hot isostatic pressing Hosam ElRakayby and KiTae Kim* Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang
IP
T
(37673), Republic of Korea
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*Corresponding author: KiTae Kim
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Email: [email protected]
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Postal address: Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH) 77 Cheongam-Ro, Nam-Gu, Pohang, Gyeongbuk, Republic of Korea (37673).
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Phone number: +82-54-279-2838
1
ACCEPTED MANUSCRIPT Abstract This paper reports the effect of the stacking fault energy on densification behavior and deformation of 316L stainless steel powder during hot isostatic pressing. Abouaf’s creep densification model was modified by
T
considering the stacking fault energy as a material parameter. The new model was implemented into Abaqus -
IP
FEA, and finite element calculations were compared with various experimental data such as densification
SC R
behavior, relative density distribution of powder compacts, and final deformed shape of powder compacts of 316L stainless steel under hot isostatic pressing. The new model was also examined to predict densification
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behavior of 316L stainless steel powders in the literature.
Keywords:
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Densification; Stainless steel; Hot isostatic pressing; Constitutive equations; Stacking fault energy.
2
ACCEPTED MANUSCRIPT 1. Introduction Near net shape manufacturing technology has been widely used to fabricate metal parts of complex shapes by powder metallurgy processes to save costs and time. Hot isostatic pressing process (hipping) is a
T
powder metallurgy process for consolidation of metal powders to fully density, and near net shape parts by
IP
applying hydrostatic pressure at high temperature [1–3]. In the hipping process, metal powders are densified
SC R
dominantly by power-law creep deformation [4]. Various researchers [4–6] proposed creep densification models to predict densification behavior of metal powders at high temperatures.
NU
There are a number of studies for densification models to investigate the effect of various physical parameters on the creep densification behavior of metal powder. Yang and Kim [7] included the grain size as a
MA
parameter in Abouaf’s [5] model. Gillia et al. [8] modified Abouaf’s [5] model by including strain hardening of the powder material. Wolff et al. [9] extended the validity of various micromechanical models to the range
D
of 50% porosity. Aryanpour et al. [10] proposed a densification model of metal powder that considers the
TE
deformation resulting from viscoplastic, and plastic deformation mechanisms during loading. They employed
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the constitutive equations of Abouaf [5] for the viscoplastic part in their model. Creep response is a complicated process that is controlled by various physical parameters. The stacking
AC
fault energy (SFE) is a parameter to determine the creep strength for various types of metal alloys [11]. McLean [12] showed that the SFE affects the deformation behavior of metal alloys and thus the creep, and the primary creep value can be a function of the SFE. Various researchers [12–15] studied the relationship between steady-state creep rate and the SFE for various alloys. They reported that the steady-state creep rate is proportional to the SFE powered to various values. All proposed power values for the SFE are within the range 1.2-4.2 that is reported by Mohamed and Langdon [14]. The present paper investigates the SFE effect on creep densification behavior and deformation of 316L stainless steel powder during hot isostatic pressing. The SFE was introduced to the model of Abouaf et al. [5] as a new material parameter, and the model’s rheological relative density functions were developed, as well, to consider the SFE effect. The new model was implemented into Abaqus - FEA. Finite element calculations 3
ACCEPTED MANUSCRIPT from the new model were compared with experimental data for densification behavior, relative density distribution, and shape distortion. Finally, experimental data from Kim and Jeon [16], and Yang and Kim [7] were also compared with finite element calculations from the new model to predict densification behavior and
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deformation of 316L stainless steel with various particle sizes.
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2. Experiment
316L stainless steel powder with an average particle size of 8 µm (Epson Atmix Corporation, Japan) was
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used in the present work, the powder has irregular shapes and a theoretical density of 7.95 g/cm3. The chemical composition of 316L stainless steel powder is shown in Table 1. Fig. 1 shows a scanning electron
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micrograph of 316L stainless steel powder.
Ni
Mo
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Cr 15.7
11.3
2.07
Si
Mn
Cu
0.86
0.09
0.03
P
S
C
0.028 0.002 0.019
O2
Fe
0.35
Balance
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Chemical Composition (Wt. %)
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Table 1 Chemical composition of 316L stainless steel powder
Fig. 1 Scanning electron micrograph of 316L stainless steel powder
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ACCEPTED MANUSCRIPT For encapsulation, 316L stainless steel powder was used to fill a 304 stainless steel container with 0.6 mm in thickness, 60 mm in height, and 22.9 mm in inner diameter. The container was vibrated to attain the initial relative density of 0.45. Subsequently, the container was sealed with a 304 stainless steel plug by welding and
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degassed through the ventilation tube on the plug for 5 hours at 250 oC. After that, the ventilation tube was
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sealed by air-tight clamping and welding.
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The sample was placed in a hot isostatic press (AIP10-30H, AIP, USA) and heated to 925 oC at a heating rate of 10 oC/min. A maximum hydrostatic pressure of 30 MPa was applied on the sample with a pressurizing
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rate of 0.33 MPa/min. The maximum holding time was 4 hours. Fig. 2 shows the applied temperature and
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pressure change with the variation of time during hipping.
Fig. 2 HIP schedule
After hipping, the container was removed by machining, and relative density was measured by Archimedes’ principle according to (ASTM-B962). Hardness of the 316L stainless steel compacts was measured by using a micro-Vickers hardness tester (FM-700, Future-Tech Corp., Japan) with 2,000 gmf load and 15 seconds holding time to obtain a relationship between relative density and hardness values of the powder compacts. Experimental data from Kim and Jeon [16], and Yang and Kim [7] were also used to compare with the new model calculations for densification of 316L stainless steel powder with the average particle sizes of 110
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3. Development of the creep-densification model 3.1. Densification equations for porous metals
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In metal alloys, the relationship between the steady-state strain rate s and stress in the power-law
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temperature-dependent constant, reference constant, creep activation energy, and the gas constant, respectively. As mentioned in the introduction, previous works [12–15] have related the steady-state creep strain rate to the SFE powered to various values in a range of 1.2-4.2. Thus, in terms of the creep potential, the general form
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of creep strain rate ij can be written as
ij A m eq n1 cS ij 3 f m ij ,
(2)
where , S ij , m , and ij are the stacking fault energy, deviatoric components of stress state, hydrostatic components of stress state, and Kronecker’s delta, respectively. Creep strain rate ij can also be written as [6]
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eq , eq ij
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where the creep potential is 6
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0 0
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A m n1 . eq n 1
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eq 2 3cJ 2 fI 12 ,
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1 S ij S ij and I 1 kk . 2
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where J 2
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Here, the functions f and c are relative density-dependent functions that represent the contribution of the hydrostatic part and the deviatoric part of the stress state, respectively, during densification. Thus,
c s 2n /( n1) f ,
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where s is a relative density-dependent function that represents the flow stress ratio of porous powder
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compacts to fully dense ones. D is the densification rate of the powder compact and can be written as [2] (8)
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D Dkk . 3.2. Finite element model
Finite element calculations of the hipping process for 316L stainless steel powder were achieved by implementing the constitutive equations from the new model into the user-defined subroutine creep of Abaqus - FEA. Fig. 3 shows the finite element mesh used for the hipping of 316L stainless steel powder. Because of the axial symmetry in the y-axis and the symmetry in the x-axis, a quarter model for a powder compact was used. A total of 586 four-node axisymmetric thermally coupled quadrilateral, bilinear, and temperature (CAX4T) elements, and 3 three-node thermally coupled axisymmetric triangle, linear displacement, and temperature (CAX3T) elements were used.
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Fig.3 Finite element meshes for 316L stainless steel powder during hot isostatic pressing
4. Results and discussion
4.1. Stacking fault energy The SFE is usually hard to measure experimentally [18]. The value of the SFE for 316L stainless steel can also be obtained using JMatPro 8.0 software. This software is capable of calculating mechanical, thermophysical, and physical properties of various alloys [19]. Saunders et al. [19] examined the accuracy of JMatPro calculations for these properties. Fig. 4 shows the SFE of 316L stainless steel at various temperatures calculated by using JMatPro 8.0 software.
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4.2. Relative density-dependent functions f and c
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Fig. 4 Stacking fault energy of 316L stainless steel obtained by using JMatPro 8.0 software
4.2.1. Function f
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Fig. 5 shows the variations of function f with relative density. The empirical form of these functions can
1 D f 11 D 0.45
,
1 D f 1.3 D 0.69
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1 D f 2.9 , D 0.69
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(10)
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for the present work, Kim and Jeon [16], and Yang and Kim [7], respectively. These functions were calculated by using Eq. 7. The densification rate D in Eq. 7 was obtained from the slope of the continuous densification curve of 316L stainless steel powder. Creep constants (A,n) in Eq. 7 for 316L stainless steel were used from Yang and Kim [7].
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Fig. 5 Variation of functions f with relative density
4.2.2. Function c
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Fig. 6 shows the variations of function c with relative density. The empirical form of these functions can
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(12)
(13)
1.9
(14)
for the present work, Kim and Jeon [16], and Yang and Kim [7], respectively. These functions were calculated by using Eq. 6. The flow stress ratio (s) in Eq. 6 for 316L stainless steel powder compacts were used from Yang and Kim [7], and Kim and Jeon [16].
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Fig. 6 Variation of functions c with relative density
4.3. Densification behavior of powder compacts
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The constant m = 2 was used in the SFE for 316L stainless steel. This value was chosen by comparisons
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between finite element calculations with various m values in the new model and experimental data of Kim and
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Jeon [16] for 316L stainless steel powder. The m values used in comparison were within the limit suggested by Mohamed and Langdon [14]. Fig. 7 shows the effect of m in the SFE on densification behavior of 316L stainless steel. Fig. 7 also shows finite element calculations from the original model of Abouaf. Finite element
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calculations with m = 2 agreed well with experimental data. Fig. 8 shows the comparison between experimental data and finite element calculations from the new model for the variation of relative density with time. Fig. 8 also shows experimental data of Kim and Jeon [16] and Kim and Yang [7]. The curves are finite element calculations from the new model with m = 2. The particle size affects on the initial relative density of packed powders. The initial relative density is a material parameter in the new model that determines densification behavior of 316L stainless steel powder. Finite element calculations from the new model agreed well with various experimental data. The new model agrees better with experimental data than the original model of Abouaf.
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Fig. 7 Effect of m in the stacking fault energy on densification behavior of 316L stainless steel
Fig. 8 Variations of relative density with time for 316L stainless steel under hipping
The relationship between hardness and relative density can be used to obtain relative density distributions of a powder compact [16]. Fig. 9 shows the variation of Vickers hardness values (HV) of 316L stainless steel powder compacts with relative density. The relationship between hardness and relative density of 316L stainless steel can be written RD 0.995 0.444 exp 0.0005 HV
1.637
(15)
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Fig.9 Variation of Vickers hardness for 316L stainless steel powder compacts with relative density
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Fig. 10 shows (a) finite element calculations from the new model and (b) measured density distribution for 316L stainless steel powder compact after 10 min under 30 MPa at 925 oC. Relative density distribution
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calculated from the new model somewhat overestimated measured data at the corner. However, it predicts well at the center of the compact. Similarly, Fig 11 shows (a) finite element calculations from the new model,
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(b) experimental data and (c) finite element calculations from Kim and Jeon [16] for density distribution for
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316L stainless steel powder compact after 10 min under 50 MPa at 1125 oC. Finite element calculation from
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the new model predicted better than the original model of Abouaf for density distribution in Kim and Jeon’s results [16]. But it somewhat underestimated measured data. This variation of relative density distribution over
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the compact cross section is due to the deviatoric stress state caused by the rigidity of the container wall.
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stainless steel powder compact after 10 min under 30 MPa at 925 oC
Fig. 11 Relative density distribution from (a) finite element calculations from the new model, (b) measured data from Kim and Jeon
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[17] and (c) finite element calculations from Kim and Jeon [17] for 316L stainless steel powder compact after 10 min under 50 MPa at 1125 oC
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Fig. 12 shows a comparison between experimental data and finite element calculations from the new model for shape change of the powder compact after 240 min under 30 MPa at 925 oC. Fig. 13 compares experimental data from Yang and Kim [7] with finite element calculations from the new model for shape
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change of the powder compact after 240 min under 30 MPa at 850 oC. Finite element calculations from the new model agreed well with experimental data for final shape change of the specimen.
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Fig. 12 Comparison between experimental data and finite element calculations from the new model for final deformed shape of
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316L stainless steel powder compact after 240 min under 30 MPa at 925 oC
Fig. 13 Comparison between finite element calculations from the new model and experimental data from Yang and Kim [7] for final deformed shape of 316L stainless steel powder compact after 240 min under 30 MPa at 850 oC
5. Conclusion
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ACCEPTED MANUSCRIPT This paper investigated the effect of stacking fault energy on densification behavior and deformation of 316L stainless steel powder with various particle sizes under hot isostatic pressing process. The stacking fault energy was included in Abouaf’s model as a material parameter, and new relative density-dependent functions
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were obtained. The finite element calculations from the new model accurately predicted various experimental
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data, such as densification behavior, relative density distribution of powder compacts, and final deformed
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shape of powder compacts of 316L stainless steel powders under hot isostatic pressing. Finally, by employing the stacking fault energy in the constitutive equations of metal powders, a better theoretical results were
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obtained compared to the original model.
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[4] [5] [6] [7] [8]
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K. Essa, R. Khan, H. Hassanin, M.M. Attallah, R. Reed, An iterative approach of hot isostatic pressing tooling design for net-shape IN718 superalloy parts, Int. J. Adv. Manuf. Technol. (2015). doi:10.1007/s00170-015-7603-3. H. ElRakayby, H. Kim, S. Hong, K.T. Kim, An investigation of densification behavior of nickel alloy powder during hot isostatic pressing, Adv. Powder Technol. 26 (2015) 1314–1318. doi:10.1016/j.apt.2015.07.005. C. Van Nguyen, A. Bezold, C. Broeckmann, Inclusion of initial powder distribution in FEM modelling of near net shape PM hot isostatic pressed components, Powder Metall. 57 (2014) 295–303. doi:10.1179/1743290114Y.0000000087. L.T. Kuhn, R.M. McMeeking, Power-law creep of powder bonded by isolated contacts, Int. J. Mech. Sci. 34 (1992) 563–573. doi:10.1016/0020-7403(92)90031-B. M. Abouaf, J.L. Chenot, G. Raisson, P. Bauduin, Finite element simulation of hot isostatic pressing of metal powders, Int. J. Numer. Methods Eng. 25 (1988) 191–212. doi:10.1002/nme.1620250116. A.C.F. Cocks, Inelastic deformation of porous materials, J. Mech. Phys. Solids. 37 (1989) 693–715. doi:10.1016/0022-5096(89)90014-8. H.C. Yang, K.T. Kim, Creep densification behavior of micro and nano metal powder: Grain sizedependent model, Acta Mater. 54 (2006) 3779–3790. doi:10.1016/j.actamat.2006.04.009. O. Gillia, B. Boireau, C. Boudot, A. Cottin, P. Bucci, F. Vidotto, et al., Modelling and computer simulation for the manufacture by powder HIPing of blanket shield components for ITER, Fusion Eng. Des. 82 (2007) 2001–2007. doi:10.1016/j.fusengdes.2007.03.037. C. Wolff, S. Mercier, H. Couque, A. Molinari, Modeling of conventional hot compaction and Spark Plasma Sintering based on modified micromechanical models of porous materials, Mech. Mater. 49 (2012) 72–91. doi:10.1016/j.mechmat.2011.12.002. G. Aryanpour, S. Mashl, V. Warke, Elastoplastic–viscoplastic modelling of metal powder compaction: application to hot isostatic pressing, Powder Metall. 56 (2013) 14–23. doi:doi:10.1179/1743290112Y.0000000027.
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ACCEPTED MANUSCRIPT C. Tian, G. Han, C. Cui, X. Sun, Effects of stacking fault energy on the creep behaviors of Ni-base superalloy, Mater. Des. 64 (2014) 316–323. doi:10.1016/j.matdes.2014.08.007. [12] D. McLean, The physics of high temperature creep in metals, Reports Prog. Phys. 29 (1966) 1–33. doi:10.1088/0034-4885/29/1/301. [13] R.M. Bonesteel, O.D. Sherby, Influence of diffusivity, elastic modulus, and stacking fault energy on the high temperature creep behavior of alpha brasses, Acta Metall. 14 (1966) 385–391. doi:10.1016/00016160(66)90096-4. [14] F.A. Mohamed, T.G. Langdon, The transition from dislocation climb to viscous glide in creep of solid solution alloys, Acta Metall. 22 (1974) 779–788. doi:10.1016/0001-6160(74)90088-1. [15] Z. Guo, A.P. Miodownik, N. Saunders, J.-P. Schillé, Influence of stacking-fault energy on high temperature creep of alpha titanium alloys, Scr. Mater. 54 (2006) 2175–2178. doi:10.1016/j.scriptamat.2006.02.036. [16] K.T. Kim, Y.C. Jeon, Densification behavior of 316L stainless steel powder under high temperature, Mater. Sci. Eng. A. 245 (1998) 64–71. doi:10.1016/S0921-5093(97)00696-5. [17] C. Van Nguyen, A. Bezold, C. Broeckmann, Anisotropic shrinkage during hip of encapsulated powder, J. Mater. Process. Technol. 226 (2015) 134–145. doi:10.1016/j.jmatprotec.2015.06.037. [18] L. Vitos, J.-O. Nilsson, B. Johansson, Alloying effects on the stacking fault energy in austenitic stainless steels from first-principles theory, Acta Mater. 54 (2006) 3821–3826. doi:10.1016/j.actamat.2006.04.013. [19] N. Saunders, U.K.Z. Guo, X. Li, A.P. Miodownik, J.-P. Schillé, Using JMatPro to model materials properties and behavior, JOM. 55 (2003) 60–65. doi:10.1007/s11837-003-0013-2.
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Graphical abstract
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New stacking fault energy dependent model with higher predictability for densification behavior of metal powder is proposed. New relative density functions for 316L stainless steel were obtained.
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