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Rene88DT graded material
Materials Science and Engineering A 391 (2005) 325–336
Laser rapid forming of SS316L/Rene88DT graded material X. Lina , T.M. Yuea,∗ , H.O. Yangb , W.D. Huangb a
b
The Advanced Manufacturing Technology Research Centre, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, PR China Received 27 May 2004; received in revised form 30 August 2004; accepted 30 August 2004
Abstract The stainless steel-SS316L/superalloy-Rene88DT graded material was successfully fabricated using laser rapid forming. A linear compositional gradient, from 100% SS316L stainless steel to 100% Rene88DT superalloy, was achieved within a thickness of 40 mm of laser multilayer deposition. The solidification behavior and the morphological evolution along the compositional gradient were investigated. It was found that, in the gradient zone, within the processing parameters of this study, there was continued epitaxial growth of the ␥ phase of the columnar dendrites, starting with 100% SS316L stainless steel to 100% Rene88DT superalloy, with the 1 0 0 crystallographic orientation parallel to the gradient direction. Clad layer bandings were found in the samples; however, the continuity of the growth of the columnar dendrites was not upset. The results are explained by the columnar to equiaxed transition theory and the criteria for planar interface instability and dendritic growth. © 2004 Elsevier B.V. All rights reserved. Keywords: Laser rapid forming; Functionally graded material; Solidification; Stainless steel; Nickel alloy
1. Introduction In recent years, with the rapid development of rapid prototyping (RP) technologies, a new laser solid freeform fabrication technology, namely laser rapid forming (LRF) has been developed to directly fabricate bulk near-net-shape metallic components. LRF works on the principle that after the CAD model of the component is constructed and sliced electronically into a sequence of layers that define the regions that compose the component, a metal component is then fabricated directly by laser multilayer cladding. Since this technique has many outstanding advantages, e.g. a metal component can be fabricated rapidly without using a mold; many methods using a similar principle in the process of fabrication have been developed. These methods are referred to using various terms, such as laser engineered net shaping TM (LENS ) [1,2], direct light fabrication (DLF) [3], epitaxial laser metal forming (E-LMF) [4], laser direct forming (LDF) ∗
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[5], direct metal deposition (DMD) [6], and so forth. It should be noted that most of the present research on LRF has concentrated on homogeneous materials [1–6]. In fact, the forming characteristics of LRF show that if the information on local elemental constituents is coupled with the geometry of the layers, which drives the laser forming path, then fully dense, metallurgically bonded freeform functionally graded materials (FGMs) can be produced. The freedom of selectively cladding different elemental powders or premixed blends at discrete locations and the employment of multiple powder feeder systems make the fabrication of functionally graded materials possible. In 1993, Jasim et al. [7] first showed that a functionally gradient region, with the fraction of SiC reinforcement progressively increasing in steps from 10 to 50 vol.%, can be built by laser cladding with a powder-feeding technique that makes use of premixed aluminum and SiC powders. Their work revealed the possibility of the laser deposition of thick, multiple layers with an essentially discrete composition, rather than depositions with a gradual change in composition. Later, by using the same technique, Abboud et al. [8,9] realized the
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preparation of Ti–Al and Ti–Al/TiB2 functionally gradient coatings. In 1995, by employing two powder feeders, Abboud et al. [10] produced functionally graded nickel–aluminide and iron–aluminide clad layers of a total thickness of about 4 mm on nickel-based and iron-based substrates. The composition of each clad layer was tailor made. This was made possible by changing the flow rate of one powder (aluminum), while keeping the other (nickel or iron) constant. By using a similar two powder-feeding laser cladding process, Seefeld et al. [11] produced NiBSi/Cr3 C2 and NiCrBSi/Cr3 C2 graded composite coatings and components by depositing NiBSi and NiCrBSi alloy powders that were blended in situ with Cr3 C2 powders. The investigation mainly focused on the correlation between the process parameters and the resulting property of the graded composites. Kahlen et al. [12] employed laser deposition of metal layers to create graded materials by varying the composition of the parts from 100% SS304 stainless steel to 100% nickel-based superalloy. They briefly studied the effects of rates of solidification on the mechanical properties of the graded materials. As for process development, Griffith et al. [13,14] and Lewis and Schlienger [15] developed preTM cise multiple powder-feeding capabilities for the LENS and DLF processes, respectively. These processes have been used to fabricate graded or layered material parts, and have realized the preparation of SS316/In690, SS316/MM10, Ti/Ti20Nb, and Ti6Al4V/In690 graded materials. They also performed chemical and microstructural analyses of the FGMs that were produced by LRF. Recently, Collins et al. [16] and Banerjee et al. [17] studied the deposition of graded binary Ti/V and TM Ti/Mo alloys by the LENS process, starting from a powder feedstock consisting of a blend of elemental Ti and V (or Mo) powders. They investigated the influence of compositional changes on phase transformations and concurrent mi-
crostructural evolution in these alloys. Turning to non-ferrous materials, Pei and de Hosson [18] reported that AlSi40 functionally graded material can be produced by a one-step laser cladding process on cast Al-alloy substrates. Although number of studies have been carried out on the laser rapid forming of functionally graded materials, our understanding of the solidification behavior of FGMs is still far from complete. Before the process can be fully appreciated, more detailed studies on the fundamentals of the process of solidification are necessary. In this paper, we focus on the SS316/Rene88DT functionally graded material, which have shown the potential to be applied in aero engines; the solidification behavior and the morphological evolution of SS316L/Rene88DT functionally graded material formed by a laser rapid forming process are discussed.
2. Experimental procedures The compositional graded material was fabricated by using a laser rapid forming system that consists of 5 kW continuous wave CO2 laser (RS850), a four-axis numerical control working table, and a powder feeder with a lateral nozzle. The experiment was conducted inside a glove box, whose atmosphere was controlled. A schematic diagram of the system is given in Fig. 1. The laser was mounted on an overhead carriage and the beam was directed into the glove box through a window on top of the chamber. The controlledatmosphere glove box was filled with argon gas, and argon gas was also used to deliver the metal powders to prevent the melt pool from oxidizing and from oxide contamination occurring during processing. The laser beam was directed onto the substrate to create a molten pool into which the premixed
Fig. 1. A schematic diagram showing the laser freeform fabrication system: (a) glove box; (b) laser window; (c) laser beam; (d) powder feeder; (e) working table; (f) substrate; (g) molten pool; (h) clad layers.
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Phase identification was performed using the Philips Xpert X-ray Diffractometer (XRD) System. The hardness of the graded alloy across the composition gradient was measured by a Shimadzu NT-M001 microhardness tester. 3. Experimental results 3.1. Composition and microhardness
Fig. 2. The solid form of the LRF SS316/Rene88DT functionally graded material. Table 1 The chemical composition of the powders (wt%) Cr
Co
W Ti
Al Nb Mo Si
Mn Fe Ni
C
316L 16.8 2.2 0.75 0.3 bal 13.8 0.03 Rene88DT 16.7 13.1 3.5 3.4 1.6 1.0 3.7 bal 0.04
A series of indentations made by microhardness testing were produced along the compositional gradient, at intervals of 2 mm, to mark the locations for the EDS analysis. Fig. 3 shows the results of the EDS analysis along the vertical direction of the graded deposit. The main elements of the SS316L and Rene88DT alloys, i.e. Fe, Ni, Cr, and Co, exhibited a good linear gradient along the deposition direction in the graded zone. The other elements, such as Mo, Ti, Al, W, and Nb, also showed a reasonably good linear relationship. Based on the measured composition, the equilibrium liquidus temperature, the solidus temperature, and the ␥ phase solvus temperature along the compositional gradient were calculated by using the Thermo–Calc software with the aim of a superalloy database [19]. The results (Fig. 4) show that at a distance of about 35 mm from the substrate, where the composition of
powders were injected through the powder feed nozzle. The metal powders were melted and subsequently resolidified to form the clad layer. A solid structure with a rectangular profile (Fig. 2) was fabricated, with its first 25 layers (∼10 mm) composed of 100% 316L stainless steel. The composition of the deposition was then changed linearly from 0 to 100% Rene88DT over the next 100 layers (∼40 mm). Finally, an additional 10 layers (∼4 mm) of 100% Rene88DT superalloy was deposited. The variation in composition along the height of the solid structure was achieved by the in situ adjustment of the ratio of the volume of 316L stainless steel to the Rene88DT superalloy of the premixed powder according to the predetermined graded structure. The nominal compositions of SS316L stainless steel and Rene88DT superalloy powders are listed in Table 1. The processing parameters are presented in Table 2. The substrate material used for the experiment was cold rolled 316L stainless steel sheet. The surface of the substrate was cleaned by sandblasting prior to laser cladding. In order to eliminate any water that was trapped in the powders, the powders were dried in a vacuum oven for 24 h. The composition and the microstructure along the gradient direction were characterized using the Leica Stereoscan 440 scanning electron microscope (SEM) equipped with the facility of energy disperse X-ray analysis (EDS). Table 2 The laser processing parameters Laser power (kW) Scanning velocity (mm/s) Spot diameter (mm) Powder feed rate (g/min) Shielding gas flow rate (l/min)
2.0–3.3 5–10 4 8–12 4–8
Fig. 3. The compositional gradient of the LRF SS316/Rene88DT functionally graded material.
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Fig. 4. The calculated equilibrium liquidus, solidus, and ␥ phase solvus temperatures.
the alloy was 40% SS316L + 60% Rene88DT, the equilibrium freezing range (T0 ) of the alloy reached a maximum value of 103 K. In addition, the liquidus temperature of the alloy decreased as the amount of Rene88DT increased, while the solvus temperature of the ␥ phase increased as the amount of Rene88DT increased. The increase in the solvus temperature of the ␥ phase means that the serviceability temperature and the high-temperature properties of the alloy could be improved. Fig. 5 shows the calculated fraction of the equilibrium ␥ phase present in the direction of the compositional gradient at 600 ◦ C. The amount of the ␥ phase increased as the amount of Rene88DT increased. The changes in hardness as a measure of the distance from the substrate are shown in Fig. 6. Unlike the variation in composition, which follows a predominantly linear function, the hardness of the alloy showed little changes in the first 15 mm of the build-up of the deposit; thereafter, the hardness value increased gradually until pure Rene88DT was obtained. However, as the pure Rene88DT zone grew thicker, the hardness value decreased. For the first 15 mm build-up, the hardness was hardly changed; this indicates that the initial
Fig. 5. The calculated volume fraction of the equilibrium ␥ phase at a temperature of 600 ◦ C along the compositional gradient.
Fig. 6. Measurements of the hardness of the LRF SS316/Rene88DT functionally graded material.
effect of solid solution on hardening may be small when there are relatively small amounts of solute atoms of Ni and Co. However, as the amount of Rene88 was increased, more Ni and Co would be present, and in addition, the precipitation of the hardening ␥ phase would occur along the compositional gradient (Fig. 7). As a result, the hardness was gradu-
Fig. 7. Showing the ␥ phase distribution of the (a) 55% SS316L + 45% Rene88DT; (b) 20% SS316L + 80% Rene88DT.
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ally increased. The drop in hardness in the Rene88DT zone that was formed towards the end of the deposit may be attributed to a diminished post-deposition heating effect. Since the rapid cooling during LRF prevent the precipitation of an equilibrium volume fraction of ␥ , also the lack of re-heating of the already deposited layer by subsequent laser passes could bring an end to the precipitation of the ␥ strengthening phase.
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3.2. Microstructure Fig. 8 shows the microstructures and the XRD patterns at various locations along the compositional gradient, the microstructures were taken in a section parallel to the gradient direction and XRD patterns are taken in the section perpendicular to the gradient direction. These photos show that the epitaxial growth of the ␥ phase in the form of colum-
Fig. 8. The microstructure and the XRD pattern of the graded material with different compositions: (a) SS316L; (b) 80% SS316L + 20% Rene88DT; (c) 60% SS316L + 40% Rene88DT; (d) 40% SS316L + 60% Rene88DT; (e) 20% SS316L + 80% Rene88DT; (f) Rene88DT.
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Fig. 8. (Continued ).
nar dendrites was obtained in the entire gradient zone, with strong directional growth in the 1 0 0 crystallographic direction. Bandings of clad layers were observed in the deposit. It should be noted that columnar dendritic growth had dominated in the entire graded sample, except at the top of the pure Rene88DT zone, where a columnar to equiaxed dendritic growth transition was observed. The XRD results show that precipitates of phase (Ni3 Ti) were present in the 40–70% Rene88DT alloy, presumably formed in interdendritic regions. According to Fig. 4, this range of composition is where the largest freezing range lies.
Fig. 9 shows the variation in spacing of the average primary dendrite arm along the composition gradient. No apparent relationship was observed, except towards the end of the deposit, where an increase in spacing in the pure Rene88DT zone was observed. The increase in primary arm spacing is considered to be due to a decrease in temperature gradient as a result of the accumulation of heat as the deposit grew thicker. The relationship between primary arm spacing and thermal gradient can be described by the following equation [19]: λ¯ 1 = AG−a V −b
(1)
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and with the LKT model [23] for undercooling melt growth, which takes into consideration high-velocity non-equilibrium effects. Although G¨aumann’s model is primarily for binary alloy systems, it can be used to predict the critical CET condition for the solidification of multi-component alloys after some modification. Based on the marginal stability criterion, the dendrite tip radius R can be obtained by the following equation for a given growth velocity: n−1
mvi GCi ξC (Pei ) − GT =
i=1
Fig. 9. The average primary dendrite arm spacing as a function of the distance from the substrate.
where λ¯ 1 is the average primary dendrite arm spacing, G the temperature gradient, and V the solidification velocity. In the bulk of the graded zone, λ¯ 1 did not appear to change, despite the fact that G was decreasing. This suggests that the enrichment of Rene88DT alloy in the deposit may have had the effect of diminishing the primary arm spacing.
4. Discussion In the fabrication of the SS316L/Rene88DT graded material, it is very important to preserve the continuity of the grain morphology because the material is targeted for application in aero engines where high service temperatures are encountered. Therefore, the epitaxial growth of columnar dendrites should be maintained throughout the entire laser deposited material. In other words, the transition from columnar to equiaxed grain growth should be avoided. Moreover, the so-called white planar layer that is normally formed at the re-melted boundary of the substrate material should also be eliminated from the bulk of the graded material as far as possible. 4.1. Columnar to equiaxed transition (CET) During directional solidification, solute will pile up ahead of the solidification interface, when the distribution coefficient is less than unity. Under such a condition, constitutional undercooling will occur, which may lead to the nucleation of equiaxed crystals. Generally, CET will happen when the amount of the equiaxed crystals reaches a certain fraction and blocks the growth of columnar dendrites. Hunt [20] first developed an analytical model to describe the conditions for steady-state columnar and equiaxed growth. The model qualitatively reveals the effects of alloy composition, nucleation density, and cooling rate on CET. Recently, based on Hunt’s model, G¨aumann et al. [21] developed a modified model by combining the KGT model [22] for directional solidification
Γ
(2)
σ ∗ R2
where Γ is the Gibbs–Thomson coefficient and GT the effective temperature gradient. For columnar dendrite growth, GT = GL ; whereas for equiaxed dendrite growth, GT = GL /2, GL the temperature gradient in the liquid, GCi the concentration gradient of component i in the liquid at the dendrite tip, mvi the velocity dependent liquidus slope of component i, ξ C the stability parameter, and Pei the solute Peclet number for component i. These parameters have the following relationship: (1 − kvi )VCi∗ Di ki − kvi [1 − ln(kvi /ki )] mvi = mi 1 + 1 − ki
GCi = −
ξC (Pei ) = 1 − Pei =
2kvi 1/2 ∗ [1 + (1/σ Pe2 )]
VR 2Di
− 1 + 2kvi
(3) (4) (5)
(6)
where Di is the diffusion coefficient of solute in the liquid of component i, kvi the velocity dependent partition coefficient of component i, ki and mi the equilibrium partition coefficient and the liquidus slope of component i, respectively; andCi∗ the composition of the liquid at the dendrite tip. kvi =
ki + a0 V/Di 1 + a0 V/Di
(7)
Ci∗ =
C0i 1 − (1 − kvi )Iv(Pei )
(8)
where a0 is the characteristic length, C0i the nominal concentration of component i, Iv the Ivantsov function, Iv(Pei ) = Pei exp(Pei )E1 (Pei ), and E1 the exponential integral function. According to the Gibbs–Thomson temperature equation, the dendrite tip temperature Ti is given by: Ti = Tm +
n−1 i=1
mvi Ci∗ −
V 2Γ − R µk
(9)
where Tm is the melting point of the pure component and µk the linear kinetic coefficient. The tip undercooling, T can
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be expressed as: T = TC + Tr + Tk
(10)
where TC , Tr , and Tk are the chemical undercooling, curvature undercooling, and attachment kinetic undercooling, respectively. TC =
m−1
mi
i=1
mvi ∗ C0i − C mi i
(11)
2Γ R
(12)
V Tk = µk
(13)
Tr =
V0 0 1 = Vb
For the growth of free equiaxed crystals, latent heat is dissipated through the liquid, which leads to a thermal undercooling Tt ahead of the solidification interface. However, the magnitude of Tt is relatively small when compared with the total amount of undercooling; therefore, the effect of thermal undercooling can be neglected. Thus, based on Eqs. (2, 9 and 10), and the Ivantsov solution, the amount of constitutional undercooling ahead of the solidification interface and the growth velocity of equiaxed crystals can be determined. The maximum radius, re , of the equiaxed crystal can be obtained by the following function: zn Ve [z] re = dz (14) V 0 where Ve is the equiaxed crystal growth velocity, zn the distance from the solid/liquid interface in the liquid, where the undercooling is equal to the nucleation undercooling Tn . Since the nucleation sites occur randomly, the actual volume fraction of equiaxed crystals is obtained by applying the Avarami equation [24], φ = 1 − exp[−φe ]
(15)
where φ is the actual volume fraction and φe the extended volume fraction. Assuming that the equiaxed crystal growth is of a spherical mode, and because the total number of nucleation sites will rapidly reach the number required for heterogeneous nucleation, the extended volume fraction can be written as: φe =
4πre3 N0 3
Apparently, the temperature gradient G and the solidification velocity V are the two important parameters that govern CET. Thus, it will be desirable to estimate the values of these two for LRF. The thermal gradient can be calculated by solving the heat diffusion equation with a modified Rosenthal approach [25–27], while the solidification velocity can be related to the beam scanning velocity Vb and the melt poolshape, which is dictated by the liquid isotherm. In the calculation, the orientation of the dendritic growth is assumed to be along the 0 0 1 direction. As such, the dendrite tip velocity V0 0 1 is given by the following relationship [28]: cosθ cosψ
(17)
where θ is the angle between the solidification front and the normal of the beam scanning direction, Ψ the angle between the normal to the solidification front and the dendrite trunk axis defined by [0 0 1]. In the present study, the alloy 40% SS316L + 60% Rene88DT, which has the largest freezing range (T0 = 103 K), is considered to be most vulnerable to the occurrence of CET. Using Hunt’s criterion, the conditions under which CET will occur for alloys SS316L, 40% SS316L + 60% Rene88DT, and Rene88DT were obtained and are presented in Fig. 10. It is apparent that the 40% SS316L + 60% Rene88DT alloy is most susceptible to the occurrence of CET. The shaded rectangle in Fig. 10 represents the range of solidification conditions existing in laser multilayer rapid forming, and the arrow path in the figure shows the progress of the solidification condition of the melt pool under the laser processing parameters of this study. During solidification, the crystal growth velocity increases rapidly from zero at the bottom of the melt pool to a value close to the laser scanning velocity at the surface of the melt pool. Also, the temperature gradient is highest when solidification is first initiated, then decreases as solidification approaches the surface of the melt pool. It is evident from the figure that under the present conditions, columnar crystal growth will dominate the initial process in the solidification
(16)
where N0 is the total number of heterogeneous nucleation sites per unit volume. Based on the volume fraction of the equiaxed crystals that are formed ahead of the growth front of the columnar crystals for different growth conditions, the critical temperature gradient and the solidification velocity required for CET can be obtained. This is achieved by using the criterion of Hunt’s model: a columnar crystal growth is maintained when the volume fraction (φ) of the equiaxed crystals is below 0.66%.
Fig. 10. The CET curve showing the regions of columnar dendrites and equiaxed dendrites as a function of solidification parameters G and V (N0 = 2 × 1015 m−3 , Tn = 2.5 ◦ C).
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of each clad layer; the CET condition is reached at the end of solidification. That is to say, according to theoretical predictions (Fig. 10), it is highly possible for CET to occur towards the surface of each clad layer. In fact, there was evidence that this had happened. Fig. 8(f) shows the microstructure of the top clad layer where no further remelting occurred. Apparently, near the surface of the top clad layer, equiaxed crystals had formed. In the bulk of the graded material, no equiaxed zone was found. This is believed to be due to the remelting effect of the successive laser passes, by which the equiaxed crystal zone is re-melted. Upon subsequent cooling, epitaxial columnar crystal growth is initiated from the existing columnar crystals, provided that favorable conditions are obtained. As a result, columnar dendritic growth had become dominant in the entire graded sample, except at the very top of the final clad layer. The conditions for continuous epitaxial columnar growth are discussed in the next section. 4.2. Continuous epitaxial columnar growth During directional solidification, the interface morphology will normally change from planar → cell → dendrite → cell → planar with increasing solidification velocity. This also explains why, in laser melting and cladding, a narrow planar growth white layer is often formed at the re-melted boundary of the substrate material. This is where the solidification velocity has the lowest value. In the present study, the continuous planar growth layer was not observed in the bulk of the graded material. At the re-melt interface of each clad layer (Fig. 11(a–c)), it appears that continuous epitaxial columnar crystal growth rather than planar front growth was obtained. As a result, only a demarcation line shows at the interface, and this occurred for the bulk of the deposit. Fig. 11(a–c) also shows that the microstructures on two sides of the interface are similar: the dendrite size and spacing are of the same order; and the orientation of dendrite growth is mainly in the 1 0 0 crystallographic direction. However, if the texture of the substrate is largely different from the growth direction of the columnar dendrite of the clad layer, a planar growth white layer would be obtained (Fig. 12). Thus, the continuous epitaxial columnar growth obtained in the bulk material is thought to be because the condition where the primary dendrite arm spacing is similar to the perturbation wavelength of instability of the planar growth has been reached and because the growth orientation of the crystals in the melt pool is close to that of the underlying crystals. Recently, Hunziker [29] presented an analytical model for predicting the stability of the planar interface, which is governed by the sign of the following equation: n n Aij δ˙ Vω(KS + KL ) mi −V = + Eij δ KS G S − K L G L Bj i=1
− Γω2 −
j=1
K S GS + K L GL KS + K L
(18)
Fig. 11. The re-melt boundary of the clad layer of compositions: (a) SS316L; (b) 40% SS316L + 60% Rene88DT; (c) 10% SS316L + 90% Rene88DT.
where δ˙ is the time derivative of the perturbation amplitude δ, ω = 2π/λ the wavenumber, λ the perturbation wavelength, KS and KL the thermal conductivity in the solid and the liquid respectively, GS the temperature gradient in the solid. The coefficients Bj are the n eigenvalues of the diffusion matrix, Aij the ith component of the eigenvector Aj corresponding to the eigenvalue Bj , and Eij the components of the eigenvectors Ej of the diffusion matrix. As the first term on the righthand side of Eq. (18) is always positive, the critical stability
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[30], the primary dendrite arm spacing can be expressed as a function of the dendrite tip radius: λ1 =
Fig. 12. Planar growth layer is obtained when the difference of the microstructural scale between the clad layer and the substrate are dissimilar.
condition can be presented as: n n Aij mi −V + Eij Bj i=1
j=1
− Γω2 −
K S GS + K L GL =0 KS + K L
(19)
3T R GT
where T is the non-equilibrium solidification range, i.e. the difference between the tip temperature and the nonequilibrium solidus temperature. Fig. 13 shows the predicted critical perturbation wavelength (λC ), the fastest growth perturbation wavelength (λF ), and the primary dendritic spacing (λ1 ) as a function of the solidification velocity for SS316L, 40% SS316L + 60% Rene88DT, and Rene88DT alloys under the thermal gradient G = 106 K/m. The shaded zone shows the measured primary dendrite arm spacing for this study. First of all, the measured primary arm spacing fall within the predicted values, and their dimensions are similar to the initial fastest growth perturbation wavelengths. It is well known [31–36] that a wide range of primary dendritic spacing for a given growth condition exists, and that the selection of the most favorable primary dendritic spacing depends not only on the current solidification parameters, but also on the sequence of events by which the process of solidification was generated. In fact, the theoretical model of dendritic growth employed in this study mainly concerns with the condition of a constant growth velocity and thermal gradient, therefore the predicted value for primary arm spacing essentially accounts for the lower
However, solute diffusion in liquid metals is very difficult to measure, and very little data has therefore been published. Therefore, diffusional interaction is ignored. We obtain:
p p n−1 2 − ((K G + K G )/(K + K )) m G ξ − Γω Vω ˙δ i S S L L S L i=1 Ci Ci = ∗ δ ((KS GS − KL GL )/(KS + KL )) + n−1 i=1 (mi GCi ω/(ωi − (V/Di )(1 − ki ))) and the critical stability condition can be expressed as: n i=1
K S G S + K L GL p p mi GCi ξCi − Γω2 − =0 KS + K L
(21)
p
where GCi is the solute concentration gradient of component i in the liquid at the unperturbed interface, GCi = − p
(1 − ki )VC0i Di
ξCi = 1 −
(22) 2ki 1/2
[1 + (2ωDi /V )2 ] − 1 + 2ki 1/2 V V 2 ∗ 2 + +ω ωi = 2Di 2Di
(23)
(24)
Thus, the critical perturbation wavelength for the instability of a planar interface can be obtained by solving Eq. (21). From Eq. (2), the dendrite tip radius R can be obtained for a given growth velocity, and according to Kurz’s analysis
(25)
(20)
limit of the selection range [37]. The similarity in dimension between the primary arm spacing and the perturbation wavelength obtained in this study means that columnar crystals at the re-melt boundary are favorable sites for developing perturbations. On the other hand, the solute atoms that are rejected to the perturbation front will suppress the development of a continuous planar layer. As a result, the perturbation will grow with a similar morphology as the underlying columnar crystals. If such a condition persists in each laser clad layer during solidification, then a continued columnar crystal growth will maintain in the entire laser deposit. The only distinct feature that can be seen between clad layers will be the line demarcating the re-melt boundary. However, it should be pointed out that, if the difference in composition of the adjacent clad layers is too large, then the condition in which the primary dendrite arm spacing matches the perturbation wavelength could be destroyed. In the present study, the condition is satisfied because the difference in composition between the adjacent layers was only 1%; moreover, dilution of the composition will occur during remelting.
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length of about 40 mm. The solidification behavior and morphological evolution along the composition gradient were investigated, with special attention given to the phenomena of columnar-to-equiaxed transition and continuous epitaxial columnar growth. The results show that, within the processing parameters of the study, a continued epitaxial growth of the ␥ fcc phase of the columnar dendrites from 100% SS316L stainless steel to 100% Rene88DT superalloy can be achieved in the bulk of the deposit. The growth of the columnar dendrites is primarily in the 1 0 0 crystallographic orientation, which is parallel to the compositional gradient. The evolution of the microstructure can be explained by the columnar-to-equiaxed transition theory and the criteria for planar interface instability and dendritic growth. The results of this study show that in order to ensure continued epitaxial columnar growth, the equiaxed zone at the top of each clad layer must be re-melted, and the columnar dendrite arm spacing of the substrate clay layer and the perturbation wavelength should be similar.
Acknowledgements The work described in this paper was funded by The Hong Kong Polytechnic University under the Postdoctoral Fellowships Scheme (Project no. G-YX10). The work was also supported by the National High Technology Research and Development Program of China.
References
Fig. 13. The predicted critical perturbation wavelength (λC ), the perturbation wavelength (λF ) with a maximum amplification rate, and the predicted primary dendrite arm spacing (λ1 ) under the condition of a solidification velocity (G) of 106 K/m. The shaded zone shows the range of the measured primary dendrite arm spacing: (a) SS316L; (b) 40% SS316L + 60% Rene88DT; and (c) Rene88DT.
5. Conclusions The graded material of SS316L-stainless steel/Rene88DTsuperalloy was fabricated by using laser rapid forming. A linear compositional gradient, from 100% SS316L stainless steel to 100% Rene88DT superalloy, was achieved within a
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Laser rapid forming of SS316L/Rene88DT graded material X. Lina , T.M. Yuea,∗ , H.O. Yangb , W.D. Huangb a
b
The Advanced Manufacturing Technology Research Centre, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, PR China Received 27 May 2004; received in revised form 30 August 2004; accepted 30 August 2004
Abstract The stainless steel-SS316L/superalloy-Rene88DT graded material was successfully fabricated using laser rapid forming. A linear compositional gradient, from 100% SS316L stainless steel to 100% Rene88DT superalloy, was achieved within a thickness of 40 mm of laser multilayer deposition. The solidification behavior and the morphological evolution along the compositional gradient were investigated. It was found that, in the gradient zone, within the processing parameters of this study, there was continued epitaxial growth of the ␥ phase of the columnar dendrites, starting with 100% SS316L stainless steel to 100% Rene88DT superalloy, with the 1 0 0 crystallographic orientation parallel to the gradient direction. Clad layer bandings were found in the samples; however, the continuity of the growth of the columnar dendrites was not upset. The results are explained by the columnar to equiaxed transition theory and the criteria for planar interface instability and dendritic growth. © 2004 Elsevier B.V. All rights reserved. Keywords: Laser rapid forming; Functionally graded material; Solidification; Stainless steel; Nickel alloy
1. Introduction In recent years, with the rapid development of rapid prototyping (RP) technologies, a new laser solid freeform fabrication technology, namely laser rapid forming (LRF) has been developed to directly fabricate bulk near-net-shape metallic components. LRF works on the principle that after the CAD model of the component is constructed and sliced electronically into a sequence of layers that define the regions that compose the component, a metal component is then fabricated directly by laser multilayer cladding. Since this technique has many outstanding advantages, e.g. a metal component can be fabricated rapidly without using a mold; many methods using a similar principle in the process of fabrication have been developed. These methods are referred to using various terms, such as laser engineered net shaping TM (LENS ) [1,2], direct light fabrication (DLF) [3], epitaxial laser metal forming (E-LMF) [4], laser direct forming (LDF) ∗
Corresponding author. Tel.: +852 27666601; fax: +852 23625267. E-mail address: [email protected] (T.M. Yue).
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.08.072
[5], direct metal deposition (DMD) [6], and so forth. It should be noted that most of the present research on LRF has concentrated on homogeneous materials [1–6]. In fact, the forming characteristics of LRF show that if the information on local elemental constituents is coupled with the geometry of the layers, which drives the laser forming path, then fully dense, metallurgically bonded freeform functionally graded materials (FGMs) can be produced. The freedom of selectively cladding different elemental powders or premixed blends at discrete locations and the employment of multiple powder feeder systems make the fabrication of functionally graded materials possible. In 1993, Jasim et al. [7] first showed that a functionally gradient region, with the fraction of SiC reinforcement progressively increasing in steps from 10 to 50 vol.%, can be built by laser cladding with a powder-feeding technique that makes use of premixed aluminum and SiC powders. Their work revealed the possibility of the laser deposition of thick, multiple layers with an essentially discrete composition, rather than depositions with a gradual change in composition. Later, by using the same technique, Abboud et al. [8,9] realized the
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preparation of Ti–Al and Ti–Al/TiB2 functionally gradient coatings. In 1995, by employing two powder feeders, Abboud et al. [10] produced functionally graded nickel–aluminide and iron–aluminide clad layers of a total thickness of about 4 mm on nickel-based and iron-based substrates. The composition of each clad layer was tailor made. This was made possible by changing the flow rate of one powder (aluminum), while keeping the other (nickel or iron) constant. By using a similar two powder-feeding laser cladding process, Seefeld et al. [11] produced NiBSi/Cr3 C2 and NiCrBSi/Cr3 C2 graded composite coatings and components by depositing NiBSi and NiCrBSi alloy powders that were blended in situ with Cr3 C2 powders. The investigation mainly focused on the correlation between the process parameters and the resulting property of the graded composites. Kahlen et al. [12] employed laser deposition of metal layers to create graded materials by varying the composition of the parts from 100% SS304 stainless steel to 100% nickel-based superalloy. They briefly studied the effects of rates of solidification on the mechanical properties of the graded materials. As for process development, Griffith et al. [13,14] and Lewis and Schlienger [15] developed preTM cise multiple powder-feeding capabilities for the LENS and DLF processes, respectively. These processes have been used to fabricate graded or layered material parts, and have realized the preparation of SS316/In690, SS316/MM10, Ti/Ti20Nb, and Ti6Al4V/In690 graded materials. They also performed chemical and microstructural analyses of the FGMs that were produced by LRF. Recently, Collins et al. [16] and Banerjee et al. [17] studied the deposition of graded binary Ti/V and TM Ti/Mo alloys by the LENS process, starting from a powder feedstock consisting of a blend of elemental Ti and V (or Mo) powders. They investigated the influence of compositional changes on phase transformations and concurrent mi-
crostructural evolution in these alloys. Turning to non-ferrous materials, Pei and de Hosson [18] reported that AlSi40 functionally graded material can be produced by a one-step laser cladding process on cast Al-alloy substrates. Although number of studies have been carried out on the laser rapid forming of functionally graded materials, our understanding of the solidification behavior of FGMs is still far from complete. Before the process can be fully appreciated, more detailed studies on the fundamentals of the process of solidification are necessary. In this paper, we focus on the SS316/Rene88DT functionally graded material, which have shown the potential to be applied in aero engines; the solidification behavior and the morphological evolution of SS316L/Rene88DT functionally graded material formed by a laser rapid forming process are discussed.
2. Experimental procedures The compositional graded material was fabricated by using a laser rapid forming system that consists of 5 kW continuous wave CO2 laser (RS850), a four-axis numerical control working table, and a powder feeder with a lateral nozzle. The experiment was conducted inside a glove box, whose atmosphere was controlled. A schematic diagram of the system is given in Fig. 1. The laser was mounted on an overhead carriage and the beam was directed into the glove box through a window on top of the chamber. The controlledatmosphere glove box was filled with argon gas, and argon gas was also used to deliver the metal powders to prevent the melt pool from oxidizing and from oxide contamination occurring during processing. The laser beam was directed onto the substrate to create a molten pool into which the premixed
Fig. 1. A schematic diagram showing the laser freeform fabrication system: (a) glove box; (b) laser window; (c) laser beam; (d) powder feeder; (e) working table; (f) substrate; (g) molten pool; (h) clad layers.
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Phase identification was performed using the Philips Xpert X-ray Diffractometer (XRD) System. The hardness of the graded alloy across the composition gradient was measured by a Shimadzu NT-M001 microhardness tester. 3. Experimental results 3.1. Composition and microhardness
Fig. 2. The solid form of the LRF SS316/Rene88DT functionally graded material. Table 1 The chemical composition of the powders (wt%) Cr
Co
W Ti
Al Nb Mo Si
Mn Fe Ni
C
316L 16.8 2.2 0.75 0.3 bal 13.8 0.03 Rene88DT 16.7 13.1 3.5 3.4 1.6 1.0 3.7 bal 0.04
A series of indentations made by microhardness testing were produced along the compositional gradient, at intervals of 2 mm, to mark the locations for the EDS analysis. Fig. 3 shows the results of the EDS analysis along the vertical direction of the graded deposit. The main elements of the SS316L and Rene88DT alloys, i.e. Fe, Ni, Cr, and Co, exhibited a good linear gradient along the deposition direction in the graded zone. The other elements, such as Mo, Ti, Al, W, and Nb, also showed a reasonably good linear relationship. Based on the measured composition, the equilibrium liquidus temperature, the solidus temperature, and the ␥ phase solvus temperature along the compositional gradient were calculated by using the Thermo–Calc software with the aim of a superalloy database [19]. The results (Fig. 4) show that at a distance of about 35 mm from the substrate, where the composition of
powders were injected through the powder feed nozzle. The metal powders were melted and subsequently resolidified to form the clad layer. A solid structure with a rectangular profile (Fig. 2) was fabricated, with its first 25 layers (∼10 mm) composed of 100% 316L stainless steel. The composition of the deposition was then changed linearly from 0 to 100% Rene88DT over the next 100 layers (∼40 mm). Finally, an additional 10 layers (∼4 mm) of 100% Rene88DT superalloy was deposited. The variation in composition along the height of the solid structure was achieved by the in situ adjustment of the ratio of the volume of 316L stainless steel to the Rene88DT superalloy of the premixed powder according to the predetermined graded structure. The nominal compositions of SS316L stainless steel and Rene88DT superalloy powders are listed in Table 1. The processing parameters are presented in Table 2. The substrate material used for the experiment was cold rolled 316L stainless steel sheet. The surface of the substrate was cleaned by sandblasting prior to laser cladding. In order to eliminate any water that was trapped in the powders, the powders were dried in a vacuum oven for 24 h. The composition and the microstructure along the gradient direction were characterized using the Leica Stereoscan 440 scanning electron microscope (SEM) equipped with the facility of energy disperse X-ray analysis (EDS). Table 2 The laser processing parameters Laser power (kW) Scanning velocity (mm/s) Spot diameter (mm) Powder feed rate (g/min) Shielding gas flow rate (l/min)
2.0–3.3 5–10 4 8–12 4–8
Fig. 3. The compositional gradient of the LRF SS316/Rene88DT functionally graded material.
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Fig. 4. The calculated equilibrium liquidus, solidus, and ␥ phase solvus temperatures.
the alloy was 40% SS316L + 60% Rene88DT, the equilibrium freezing range (T0 ) of the alloy reached a maximum value of 103 K. In addition, the liquidus temperature of the alloy decreased as the amount of Rene88DT increased, while the solvus temperature of the ␥ phase increased as the amount of Rene88DT increased. The increase in the solvus temperature of the ␥ phase means that the serviceability temperature and the high-temperature properties of the alloy could be improved. Fig. 5 shows the calculated fraction of the equilibrium ␥ phase present in the direction of the compositional gradient at 600 ◦ C. The amount of the ␥ phase increased as the amount of Rene88DT increased. The changes in hardness as a measure of the distance from the substrate are shown in Fig. 6. Unlike the variation in composition, which follows a predominantly linear function, the hardness of the alloy showed little changes in the first 15 mm of the build-up of the deposit; thereafter, the hardness value increased gradually until pure Rene88DT was obtained. However, as the pure Rene88DT zone grew thicker, the hardness value decreased. For the first 15 mm build-up, the hardness was hardly changed; this indicates that the initial
Fig. 5. The calculated volume fraction of the equilibrium ␥ phase at a temperature of 600 ◦ C along the compositional gradient.
Fig. 6. Measurements of the hardness of the LRF SS316/Rene88DT functionally graded material.
effect of solid solution on hardening may be small when there are relatively small amounts of solute atoms of Ni and Co. However, as the amount of Rene88 was increased, more Ni and Co would be present, and in addition, the precipitation of the hardening ␥ phase would occur along the compositional gradient (Fig. 7). As a result, the hardness was gradu-
Fig. 7. Showing the ␥ phase distribution of the (a) 55% SS316L + 45% Rene88DT; (b) 20% SS316L + 80% Rene88DT.
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ally increased. The drop in hardness in the Rene88DT zone that was formed towards the end of the deposit may be attributed to a diminished post-deposition heating effect. Since the rapid cooling during LRF prevent the precipitation of an equilibrium volume fraction of ␥ , also the lack of re-heating of the already deposited layer by subsequent laser passes could bring an end to the precipitation of the ␥ strengthening phase.
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3.2. Microstructure Fig. 8 shows the microstructures and the XRD patterns at various locations along the compositional gradient, the microstructures were taken in a section parallel to the gradient direction and XRD patterns are taken in the section perpendicular to the gradient direction. These photos show that the epitaxial growth of the ␥ phase in the form of colum-
Fig. 8. The microstructure and the XRD pattern of the graded material with different compositions: (a) SS316L; (b) 80% SS316L + 20% Rene88DT; (c) 60% SS316L + 40% Rene88DT; (d) 40% SS316L + 60% Rene88DT; (e) 20% SS316L + 80% Rene88DT; (f) Rene88DT.
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Fig. 8. (Continued ).
nar dendrites was obtained in the entire gradient zone, with strong directional growth in the 1 0 0 crystallographic direction. Bandings of clad layers were observed in the deposit. It should be noted that columnar dendritic growth had dominated in the entire graded sample, except at the top of the pure Rene88DT zone, where a columnar to equiaxed dendritic growth transition was observed. The XRD results show that precipitates of phase (Ni3 Ti) were present in the 40–70% Rene88DT alloy, presumably formed in interdendritic regions. According to Fig. 4, this range of composition is where the largest freezing range lies.
Fig. 9 shows the variation in spacing of the average primary dendrite arm along the composition gradient. No apparent relationship was observed, except towards the end of the deposit, where an increase in spacing in the pure Rene88DT zone was observed. The increase in primary arm spacing is considered to be due to a decrease in temperature gradient as a result of the accumulation of heat as the deposit grew thicker. The relationship between primary arm spacing and thermal gradient can be described by the following equation [19]: λ¯ 1 = AG−a V −b
(1)
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and with the LKT model [23] for undercooling melt growth, which takes into consideration high-velocity non-equilibrium effects. Although G¨aumann’s model is primarily for binary alloy systems, it can be used to predict the critical CET condition for the solidification of multi-component alloys after some modification. Based on the marginal stability criterion, the dendrite tip radius R can be obtained by the following equation for a given growth velocity: n−1
mvi GCi ξC (Pei ) − GT =
i=1
Fig. 9. The average primary dendrite arm spacing as a function of the distance from the substrate.
where λ¯ 1 is the average primary dendrite arm spacing, G the temperature gradient, and V the solidification velocity. In the bulk of the graded zone, λ¯ 1 did not appear to change, despite the fact that G was decreasing. This suggests that the enrichment of Rene88DT alloy in the deposit may have had the effect of diminishing the primary arm spacing.
4. Discussion In the fabrication of the SS316L/Rene88DT graded material, it is very important to preserve the continuity of the grain morphology because the material is targeted for application in aero engines where high service temperatures are encountered. Therefore, the epitaxial growth of columnar dendrites should be maintained throughout the entire laser deposited material. In other words, the transition from columnar to equiaxed grain growth should be avoided. Moreover, the so-called white planar layer that is normally formed at the re-melted boundary of the substrate material should also be eliminated from the bulk of the graded material as far as possible. 4.1. Columnar to equiaxed transition (CET) During directional solidification, solute will pile up ahead of the solidification interface, when the distribution coefficient is less than unity. Under such a condition, constitutional undercooling will occur, which may lead to the nucleation of equiaxed crystals. Generally, CET will happen when the amount of the equiaxed crystals reaches a certain fraction and blocks the growth of columnar dendrites. Hunt [20] first developed an analytical model to describe the conditions for steady-state columnar and equiaxed growth. The model qualitatively reveals the effects of alloy composition, nucleation density, and cooling rate on CET. Recently, based on Hunt’s model, G¨aumann et al. [21] developed a modified model by combining the KGT model [22] for directional solidification
Γ
(2)
σ ∗ R2
where Γ is the Gibbs–Thomson coefficient and GT the effective temperature gradient. For columnar dendrite growth, GT = GL ; whereas for equiaxed dendrite growth, GT = GL /2, GL the temperature gradient in the liquid, GCi the concentration gradient of component i in the liquid at the dendrite tip, mvi the velocity dependent liquidus slope of component i, ξ C the stability parameter, and Pei the solute Peclet number for component i. These parameters have the following relationship: (1 − kvi )VCi∗ Di ki − kvi [1 − ln(kvi /ki )] mvi = mi 1 + 1 − ki
GCi = −
ξC (Pei ) = 1 − Pei =
2kvi 1/2 ∗ [1 + (1/σ Pe2 )]
VR 2Di
− 1 + 2kvi
(3) (4) (5)
(6)
where Di is the diffusion coefficient of solute in the liquid of component i, kvi the velocity dependent partition coefficient of component i, ki and mi the equilibrium partition coefficient and the liquidus slope of component i, respectively; andCi∗ the composition of the liquid at the dendrite tip. kvi =
ki + a0 V/Di 1 + a0 V/Di
(7)
Ci∗ =
C0i 1 − (1 − kvi )Iv(Pei )
(8)
where a0 is the characteristic length, C0i the nominal concentration of component i, Iv the Ivantsov function, Iv(Pei ) = Pei exp(Pei )E1 (Pei ), and E1 the exponential integral function. According to the Gibbs–Thomson temperature equation, the dendrite tip temperature Ti is given by: Ti = Tm +
n−1 i=1
mvi Ci∗ −
V 2Γ − R µk
(9)
where Tm is the melting point of the pure component and µk the linear kinetic coefficient. The tip undercooling, T can
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be expressed as: T = TC + Tr + Tk
(10)
where TC , Tr , and Tk are the chemical undercooling, curvature undercooling, and attachment kinetic undercooling, respectively. TC =
m−1
mi
i=1
mvi ∗ C0i − C mi i
(11)
2Γ R
(12)
V Tk = µk
(13)
Tr =
V0 0 1 = Vb
For the growth of free equiaxed crystals, latent heat is dissipated through the liquid, which leads to a thermal undercooling Tt ahead of the solidification interface. However, the magnitude of Tt is relatively small when compared with the total amount of undercooling; therefore, the effect of thermal undercooling can be neglected. Thus, based on Eqs. (2, 9 and 10), and the Ivantsov solution, the amount of constitutional undercooling ahead of the solidification interface and the growth velocity of equiaxed crystals can be determined. The maximum radius, re , of the equiaxed crystal can be obtained by the following function: zn Ve [z] re = dz (14) V 0 where Ve is the equiaxed crystal growth velocity, zn the distance from the solid/liquid interface in the liquid, where the undercooling is equal to the nucleation undercooling Tn . Since the nucleation sites occur randomly, the actual volume fraction of equiaxed crystals is obtained by applying the Avarami equation [24], φ = 1 − exp[−φe ]
(15)
where φ is the actual volume fraction and φe the extended volume fraction. Assuming that the equiaxed crystal growth is of a spherical mode, and because the total number of nucleation sites will rapidly reach the number required for heterogeneous nucleation, the extended volume fraction can be written as: φe =
4πre3 N0 3
Apparently, the temperature gradient G and the solidification velocity V are the two important parameters that govern CET. Thus, it will be desirable to estimate the values of these two for LRF. The thermal gradient can be calculated by solving the heat diffusion equation with a modified Rosenthal approach [25–27], while the solidification velocity can be related to the beam scanning velocity Vb and the melt poolshape, which is dictated by the liquid isotherm. In the calculation, the orientation of the dendritic growth is assumed to be along the 0 0 1 direction. As such, the dendrite tip velocity V0 0 1 is given by the following relationship [28]: cosθ cosψ
(17)
where θ is the angle between the solidification front and the normal of the beam scanning direction, Ψ the angle between the normal to the solidification front and the dendrite trunk axis defined by [0 0 1]. In the present study, the alloy 40% SS316L + 60% Rene88DT, which has the largest freezing range (T0 = 103 K), is considered to be most vulnerable to the occurrence of CET. Using Hunt’s criterion, the conditions under which CET will occur for alloys SS316L, 40% SS316L + 60% Rene88DT, and Rene88DT were obtained and are presented in Fig. 10. It is apparent that the 40% SS316L + 60% Rene88DT alloy is most susceptible to the occurrence of CET. The shaded rectangle in Fig. 10 represents the range of solidification conditions existing in laser multilayer rapid forming, and the arrow path in the figure shows the progress of the solidification condition of the melt pool under the laser processing parameters of this study. During solidification, the crystal growth velocity increases rapidly from zero at the bottom of the melt pool to a value close to the laser scanning velocity at the surface of the melt pool. Also, the temperature gradient is highest when solidification is first initiated, then decreases as solidification approaches the surface of the melt pool. It is evident from the figure that under the present conditions, columnar crystal growth will dominate the initial process in the solidification
(16)
where N0 is the total number of heterogeneous nucleation sites per unit volume. Based on the volume fraction of the equiaxed crystals that are formed ahead of the growth front of the columnar crystals for different growth conditions, the critical temperature gradient and the solidification velocity required for CET can be obtained. This is achieved by using the criterion of Hunt’s model: a columnar crystal growth is maintained when the volume fraction (φ) of the equiaxed crystals is below 0.66%.
Fig. 10. The CET curve showing the regions of columnar dendrites and equiaxed dendrites as a function of solidification parameters G and V (N0 = 2 × 1015 m−3 , Tn = 2.5 ◦ C).
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of each clad layer; the CET condition is reached at the end of solidification. That is to say, according to theoretical predictions (Fig. 10), it is highly possible for CET to occur towards the surface of each clad layer. In fact, there was evidence that this had happened. Fig. 8(f) shows the microstructure of the top clad layer where no further remelting occurred. Apparently, near the surface of the top clad layer, equiaxed crystals had formed. In the bulk of the graded material, no equiaxed zone was found. This is believed to be due to the remelting effect of the successive laser passes, by which the equiaxed crystal zone is re-melted. Upon subsequent cooling, epitaxial columnar crystal growth is initiated from the existing columnar crystals, provided that favorable conditions are obtained. As a result, columnar dendritic growth had become dominant in the entire graded sample, except at the very top of the final clad layer. The conditions for continuous epitaxial columnar growth are discussed in the next section. 4.2. Continuous epitaxial columnar growth During directional solidification, the interface morphology will normally change from planar → cell → dendrite → cell → planar with increasing solidification velocity. This also explains why, in laser melting and cladding, a narrow planar growth white layer is often formed at the re-melted boundary of the substrate material. This is where the solidification velocity has the lowest value. In the present study, the continuous planar growth layer was not observed in the bulk of the graded material. At the re-melt interface of each clad layer (Fig. 11(a–c)), it appears that continuous epitaxial columnar crystal growth rather than planar front growth was obtained. As a result, only a demarcation line shows at the interface, and this occurred for the bulk of the deposit. Fig. 11(a–c) also shows that the microstructures on two sides of the interface are similar: the dendrite size and spacing are of the same order; and the orientation of dendrite growth is mainly in the 1 0 0 crystallographic direction. However, if the texture of the substrate is largely different from the growth direction of the columnar dendrite of the clad layer, a planar growth white layer would be obtained (Fig. 12). Thus, the continuous epitaxial columnar growth obtained in the bulk material is thought to be because the condition where the primary dendrite arm spacing is similar to the perturbation wavelength of instability of the planar growth has been reached and because the growth orientation of the crystals in the melt pool is close to that of the underlying crystals. Recently, Hunziker [29] presented an analytical model for predicting the stability of the planar interface, which is governed by the sign of the following equation: n n Aij δ˙ Vω(KS + KL ) mi −V = + Eij δ KS G S − K L G L Bj i=1
− Γω2 −
j=1
K S GS + K L GL KS + K L
(18)
Fig. 11. The re-melt boundary of the clad layer of compositions: (a) SS316L; (b) 40% SS316L + 60% Rene88DT; (c) 10% SS316L + 90% Rene88DT.
where δ˙ is the time derivative of the perturbation amplitude δ, ω = 2π/λ the wavenumber, λ the perturbation wavelength, KS and KL the thermal conductivity in the solid and the liquid respectively, GS the temperature gradient in the solid. The coefficients Bj are the n eigenvalues of the diffusion matrix, Aij the ith component of the eigenvector Aj corresponding to the eigenvalue Bj , and Eij the components of the eigenvectors Ej of the diffusion matrix. As the first term on the righthand side of Eq. (18) is always positive, the critical stability
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[30], the primary dendrite arm spacing can be expressed as a function of the dendrite tip radius: λ1 =
Fig. 12. Planar growth layer is obtained when the difference of the microstructural scale between the clad layer and the substrate are dissimilar.
condition can be presented as: n n Aij mi −V + Eij Bj i=1
j=1
− Γω2 −
K S GS + K L GL =0 KS + K L
(19)
3T R GT
where T is the non-equilibrium solidification range, i.e. the difference between the tip temperature and the nonequilibrium solidus temperature. Fig. 13 shows the predicted critical perturbation wavelength (λC ), the fastest growth perturbation wavelength (λF ), and the primary dendritic spacing (λ1 ) as a function of the solidification velocity for SS316L, 40% SS316L + 60% Rene88DT, and Rene88DT alloys under the thermal gradient G = 106 K/m. The shaded zone shows the measured primary dendrite arm spacing for this study. First of all, the measured primary arm spacing fall within the predicted values, and their dimensions are similar to the initial fastest growth perturbation wavelengths. It is well known [31–36] that a wide range of primary dendritic spacing for a given growth condition exists, and that the selection of the most favorable primary dendritic spacing depends not only on the current solidification parameters, but also on the sequence of events by which the process of solidification was generated. In fact, the theoretical model of dendritic growth employed in this study mainly concerns with the condition of a constant growth velocity and thermal gradient, therefore the predicted value for primary arm spacing essentially accounts for the lower
However, solute diffusion in liquid metals is very difficult to measure, and very little data has therefore been published. Therefore, diffusional interaction is ignored. We obtain:
p p n−1 2 − ((K G + K G )/(K + K )) m G ξ − Γω Vω ˙δ i S S L L S L i=1 Ci Ci = ∗ δ ((KS GS − KL GL )/(KS + KL )) + n−1 i=1 (mi GCi ω/(ωi − (V/Di )(1 − ki ))) and the critical stability condition can be expressed as: n i=1
K S G S + K L GL p p mi GCi ξCi − Γω2 − =0 KS + K L
(21)
p
where GCi is the solute concentration gradient of component i in the liquid at the unperturbed interface, GCi = − p
(1 − ki )VC0i Di
ξCi = 1 −
(22) 2ki 1/2
[1 + (2ωDi /V )2 ] − 1 + 2ki 1/2 V V 2 ∗ 2 + +ω ωi = 2Di 2Di
(23)
(24)
Thus, the critical perturbation wavelength for the instability of a planar interface can be obtained by solving Eq. (21). From Eq. (2), the dendrite tip radius R can be obtained for a given growth velocity, and according to Kurz’s analysis
(25)
(20)
limit of the selection range [37]. The similarity in dimension between the primary arm spacing and the perturbation wavelength obtained in this study means that columnar crystals at the re-melt boundary are favorable sites for developing perturbations. On the other hand, the solute atoms that are rejected to the perturbation front will suppress the development of a continuous planar layer. As a result, the perturbation will grow with a similar morphology as the underlying columnar crystals. If such a condition persists in each laser clad layer during solidification, then a continued columnar crystal growth will maintain in the entire laser deposit. The only distinct feature that can be seen between clad layers will be the line demarcating the re-melt boundary. However, it should be pointed out that, if the difference in composition of the adjacent clad layers is too large, then the condition in which the primary dendrite arm spacing matches the perturbation wavelength could be destroyed. In the present study, the condition is satisfied because the difference in composition between the adjacent layers was only 1%; moreover, dilution of the composition will occur during remelting.
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length of about 40 mm. The solidification behavior and morphological evolution along the composition gradient were investigated, with special attention given to the phenomena of columnar-to-equiaxed transition and continuous epitaxial columnar growth. The results show that, within the processing parameters of the study, a continued epitaxial growth of the ␥ fcc phase of the columnar dendrites from 100% SS316L stainless steel to 100% Rene88DT superalloy can be achieved in the bulk of the deposit. The growth of the columnar dendrites is primarily in the 1 0 0 crystallographic orientation, which is parallel to the compositional gradient. The evolution of the microstructure can be explained by the columnar-to-equiaxed transition theory and the criteria for planar interface instability and dendritic growth. The results of this study show that in order to ensure continued epitaxial columnar growth, the equiaxed zone at the top of each clad layer must be re-melted, and the columnar dendrite arm spacing of the substrate clay layer and the perturbation wavelength should be similar.
Acknowledgements The work described in this paper was funded by The Hong Kong Polytechnic University under the Postdoctoral Fellowships Scheme (Project no. G-YX10). The work was also supported by the National High Technology Research and Development Program of China.
References
Fig. 13. The predicted critical perturbation wavelength (λC ), the perturbation wavelength (λF ) with a maximum amplification rate, and the predicted primary dendrite arm spacing (λ1 ) under the condition of a solidification velocity (G) of 106 K/m. The shaded zone shows the range of the measured primary dendrite arm spacing: (a) SS316L; (b) 40% SS316L + 60% Rene88DT; and (c) Rene88DT.
5. Conclusions The graded material of SS316L-stainless steel/Rene88DTsuperalloy was fabricated by using laser rapid forming. A linear compositional gradient, from 100% SS316L stainless steel to 100% Rene88DT superalloy, was achieved within a
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