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Acta Materialia 56 (2008) 4858–4868 www.elsevier.com/locate/actamat
General aspects of interface bonding in kinetic sprayed coatings Gyuyeol Bae, Yuming Xiong, S. Kumar, Kicheol Kang, Changhee Lee * Kinetic Spray Coating Lab (NRL), Division of Materials Science and Engineering, Hanyang University, 17 Haengdang-Dong, Seongdong-Gu, Seoul 133-791, Republic of Korea Received 26 March 2008; received in revised form 29 May 2008; accepted 1 June 2008 Available online 27 June 2008
Abstract In this study, different engineering materials are classified into four impact cases according to their physical and mechanical properties, i.e., soft/soft, hard/hard, soft/hard, and hard/soft (particle/substrate). Based on finite-element modeling, impact behaviors of the four cases were numerically analyzed. For soft/soft and hard/hard cases, the size variation of the thermal boost-up zone (TBZ), accompanied with the different aspects of adiabatic shear instability, was numerically estimated and is theoretically discussed. Meanwhile, for soft/hard and hard/soft cases, the specific aspect of shear instability, which has a very high heat-up rate, is always observed on the relatively soft impact counterpart where a thin molten layer is expected as well. Based on these phenomenological characteristics, bonding aspects are characterized, and a database for numerically estimated critical velocities of different particle/substrate combinations was developed for kinetic spraying process. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Kinetic spraying; Finite-element modeling (FEM); Impact behaviour; Coating; Bonding
1. Introduction In this decade, kinetic spraying, or cold gas dynamic spraying, has been developed as a novel coating technology to obtain dense and high-quality coatings, which have low oxygen content and high bond strength. These properties can be achieved because the technique is a low-temperature and high-pressure coating process and is therefore unique when compared to conventional thermal spraying processes. Besides the many metallic coatings used, bulk metallic glass coatings [1], various composites coatings [2–4], and unique coatings for restoration of worn metals [5] have shown potential for various industrial applications. In kinetic spraying, adiabatic shear instability (hereafter referred to as ASI) has been understood as one of the dominant mechanisms for successful bonding between micronsized particles and the substrate (or previously deposited layer). This phenomenological characteristic is directly related to the abnormal temperature/strain rise and stress *
Corresponding author. Tel.: +82 2 2220 0388; fax: +82 2 2299 0389. E-mail address:
[email protected] (Changhee Lee).
collapse, which is attributed to severe and localized plastic deformation at the impacting interface [6,7]. Based on this theoretical concept, some investigators have numerically examined deformation behaviors and have also estimated critical velocities for different impact cases using computational simulations [6–9]. Copper has often been employed as standard material to describe high-strain-rate deformation behaviors, such as the ASI, because it is feasible to simulate its behavior, and highly reliable high-strain-rate material data are available [6]. However, these highstrain-rate thermomechanical behaviors, especially the ASI characteristic of copper, cannot be applied for all other cases, because the onset of material instability depends upon the thermal-softening and strain-rate hardening characteristics of a material. Thus, it is important to consider how mechanisms operating within the materials may affect the initiation of shear instability upon a highstrain-rate impact. Furthermore, ASI behaviors need to be characterized as fundamental aspects. Additionally, it is quite challenging to numerically estimate the critical velocities for pure metals, let alone various engineering metallic alloys that are candidates for kinetic spraying.
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.06.003
G. Bae et al. / Acta Materialia 56 (2008) 4858–4868
Previous research has focused mainly on examining the cohesive bonding (between the similar metals) through numerical modeling. However, the impact behaviors and mechanisms of adhesive bonding (between the dissimilar metals) have not been sufficiently investigated due to the one-time process characteristic of first layer coating. As regards both cohesion and adhesion, one should also consider the physical phenomenon that can affect adhesive bonding using available sophisticated numerical modeling techniques. In this study, 22 kinds of engineering materials were classified into four impact cases (soft/soft, hard/hard, soft/hard, and hard/soft), according to their physical and mechanical properties. The impact behaviors of each case were numerically analyzed through finely tuned finite-element dynamic thermomechanical modeling. As a result, ASI aspects different from the conventional copper case were revealed. In accordance with the findings, the existence of a thermal boost-up zone (TBZ) is theoretically proposed. In view of ASI, general bonding features of the four cases were also characterized with respect to recoverable strain energy, plastic dissipation energy, contact area and contact time (which were evaluated based upon the energy balance concept). Furthermore, critical velocities for different particle/substrate combinations were numerically estimated. 2. Numerical modeling 2.1. Finite-element methodology Non-linear transient finite-element (FE) modeling of the high-velocity micron-sized particle impacting process was performed using a commercial finite-element package, ABAQUS 6.7-2. In order to conduct the non-linear transient dynamic analysis of the particle bonding process, which has relatively short dynamic response times and large deformations, the explicit time integration algorithm [10] was chosen. An axisymmetric model was used to reduce computational costs, and fully coupled thermal-stress analysis was performed to obtain the thermomechanical responses of the particle impacting process. Fig. 1 shows the FE model constructed for the present work. Four-node bilinear axisymmetric quadrilateral mesh elements with reduced integration and hourglass control (CAX4R) from the ABAQUS element library were used, and a surface-to-surface penalty contact algorithm with balanced contact pair formulation [10] was applied between particle and substrate. Refinement of mesh at the impacting interfaces was subsequently performed for more accurate computations. Arbitrary Lagrangian Eulerian (ALE) adaptive remeshing [10] was also performed to avoid mathematical truncation errors due to severely distorted elements. 2.2. Numerical model The Johnson–Cook plasticity model, which includes strain hardening, strain-rate hardening, and thermal-soft-
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Fig. 1. Finite-element model for particle/substrate impact simulation.
ening effects, was employed to describe the rate and temperature dependence of material behavior during plastic deformation. The model can be written as follows [11]: e_ p m n r ¼ ½A þ Bep 1 þ C ln ð1Þ ½1 ðT Þ e_ 0 where r is the equivalent flow stress, ep and e_ p are the equivalent plastic strain and strain rate, respectively, and e_ 0 is the normalizing reference strain rate. Parameters A, B, C, n, and m are material specific parameters; A is the yield stress in a quasi-static simple tension or compression test, B is the strain-hardening parameter, whereas C is the dimensionless strain-rate hardening coefficient. Parameters n and m are power exponents of the strain hardening and thermal-softening terms. T* is the normalized temperature defined as follows: 8 T < T trans > < 0; T ¼ ðT T trans Þ=ðT melt T trans Þ; T trans 6 T 6 T melt > : 1; T melt < T ð2Þ where Tmelt is the melting temperature above which the material is fluid and the hardening effect should totally vanish. Ttrans is a reference transition temperature at or below which there is no temperature dependence of the response [10]. In the modeling, the particle/substrate interaction is assumed to be an adiabatic process. Theoretical calculations [6,8] and numerical experiments [12] have shown that heat conduction is negligible during the high-strain-rate deformation process due to its relatively short thermal diffusivity distance as compared to the characteristic system dimension. The balance of internal energy with heat conduction neglected can be written as follows: qct dT ¼ b r dep
ð3Þ
where q is the mass density, ct is the specific heat, and bð 0:9Þ is the Taylor–Quinney constant that equals the fraction of the viscoplastic work converted into heat.
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2.3. Computational simulations In all, 22 different engineering materials were chosen for high-velocity individual particle impact simulations including some pure metals, such as copper, aluminum, nickel, and titanium. All these materials were combined and classified into four different cases; soft/soft, hard/hard (similar cases), soft/hard, and hard/soft (dissimilar cases) according to their relative stiffness, hardness, and yield strength, as shown in Tables 1 and 2. For the simulations, the impact velocity of the particle was increased from 200 m s1 to 1000 m s1 at a rate of 5 m s1, while the particle size remained fixed at 25 lm. It was also assumed that the initial temperature of both particle and substrate was 25 °C. Also, the impact of a 35 lm nickel particle on three kinds of substrates (copper, 6061-T6 aluminum alloy and SKH 51 steel) was modeled under the same impact conditions to confirm the reliability of our modeling with experimental results. Generally, the five model parameters (A, B, C, m, and n) can be obtained by compression quasi-static and dynamic
Table 1 Particle/substrate combinations for soft/soft (A–J) and hard/hard (K–T) cases I.D.
Particle material
Substrate material
ID
Particle material
Substrate material
A B C D
Al 1100-H12 Copper Cartridge brass Al 2024-T351
Al 1100-H12 Copper Cartridge brass Al 2024-T351
K L M N
E F G H I J
Al 6061-T6 Al 7039 Armco Iron Tantalum Nickel Magnesium alloy (AM50A)
Al 6061-T6 Al 7039 Armco Iron Tantalum Nickel Magnesium alloy (AM50A)
O P Q R S T
Titanium Ti6Al4V Inconel 718 Tungsten heavy alloy Du-0.75 Ti AISI H13 AISI 1018 AISI 4340 STS 316L Mild steel
Titanium Ti6Al4V Inconel 718 Tungsten heavy alloy Du-0.75 Ti AISI H13 AISI 1018 AISI 4340 STS 316L Mild steel
Hopkinson bar experiments with varying temperature and strain rates. All the material properties and parameters used in the FE model were taken from material databases and the literature [11,13–20]. Although high-strain-rate data for most materials pose some uncertainty, reasonable descriptions of high-strain-rate deformation can be supplied through approximated numerical simulations [7]. General properties and JC-parameters of some materials are given in Table 3. 3. Experimental To confirm the reliability of modeling, individual particle impact experiments were carried out by a commercially available CGT kinetic spraying system (Kinetic3000, Germany). A de-Laval type converging–diverging MOC nozzle with a round exit was used, and the diameter of the nozzle exit and the diameter ratio of exit to throat were 6.34 mm and 2.34, respectively. Nitrogen and helium gases were used as carrier and process gases. The temperature and pressure of the process gas were fixed at 300 °C and 25 bar, respectively. The carrier gas was set to be 7% of the flow rate of the process gas, and a low powder feed rate (6 g min1) with high nozzle traveling speed (600 mm s1) was employed. A commercially available pure nickel powder (Sulzer Metco), which has a mean size of 35 lm and a nearly spherical morphology, was chosen as feedstock. Hardness and elastic modulus of the particle, 542 HV and 209 GPa, were measured using a nanoindentation technique (Nanoindenter XP, MTS) with a diamond Berkovich (three-sided pyramid) indenter mounted in a nanoindenter at a constant strain rate (0.05 s1). In order to examine the bonding between dissimilar metals, polished copper, 6061-T6 aluminum alloy and SKH 51 steel (Ra < 1.5) were used as substrates, which were fixed at 30 mm in front of the nozzle exit. The Vickers hardness of the substrates (90, 110, and 777 HV, respectively) was measured using a microhardness tester (HMV-2, Shimadzu) under a load of 1.961 N. The mean hardness value over ten readings was obtained for each sample.
Table 2 Particle/substrate combinations for soft/hard (A–J) and hard/soft (K–T) cases I.D.
Particle material
Substrate material
ID
Particle material
Substrate material
Table 3 Material properties used in FE models
A B C D
Al 1100-H12 Copper Al 6061-T6 Al 5083-H116
Mild steel AISI H13 Mild steel STS 316L
K L M N
Titanium Ti6Al4V Tantalum Titanium
Parameter/material
E
Al 2024-T351
AISI 1018
O
Nickel
F G H
Al 1100-H12 Cartridge brass Magnesium alloy (AM50A) Al 7075-T6 Al 6061-T6
AISI H13 AISI 4340 Tungsten heavy alloy Tantalum STS 316L
P Q R
AISI H13 AISI 1018 AISI 4340
Al 1100-H12 Al 6061-T6 Al 7075-T6 Magnesium alloy (AM50A) Magnesium alloy (AM50A) Al 1100-H12 Al 2024-T351 Al 7039
S T
STS 316L Nickel
Al 5083-H116 Al 6061-T6
I J
3
Density (kg m ) Young’s modulus (GPa) Poison’s ratio Heat capacity (J kg1 K1) Melting temperature (K) A (MPa) B (MPa) n C m Reference temperature (K) Reference strain rate (s1)
Cu
Al
Ni
Ti
Mild steel
8960 124 0.34 383 1356 90.0 292.0 0.310 0.025 1.09 298 1
2710 68.9 0.33 904 916 148.4 345.5 0.183 0.001 0.895 293 1
8890 207 0.31 456 1726 163.0 648.0 0.330 0.006 1.44 298 1
4510 116.0 0.34 528 1923 806.57 481.61 0.319 0.0194 0.655 298 1
7870 200.1 0.30 481 1793 532.0 229.0 0.3024 0.0274 1.0 283 1
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After the individual particle impact test, the surface and cross-sectional micrographs of the craters and deposits were characterized by SEM (JSM 5600, JEOL). The bond ratio, defined as the fraction of bonded particles (deposits) to the total incident particles (craters plus deposits), was calculated by an image analysis method. A mean value from 10 images was taken in each case. 4. Results and discussion 4.1. Particle impact behavior In order to account for different particle impact behavior in the four classified cases, four representative particle/substrate combinations, which are Al/Al (soft/soft), Ti/Ti (hard/hard), Al/mild steel (soft/hard), and Ti/Al (hard/soft), were selected and analyzed. Deformation aspects of all four cases after impact at each critical velocity, which was determined by the conventional concept [6], are shown in Fig. 2. This concept will be further discussed in the following section. In the case of Al/Al (Fig. 2a), relatively large deformation is observed as compared to the Ti/Ti case (Fig. 2b) due to the relatively low material strength of Al. Critical velocities for Al/Al and Ti/Ti cases are estimated as 775 m s1 and 865 m s1, respectively. These values are relatively high compared to that (550 m s1) of Cu/Cu. This can be attributed mainly to the relatively low density and high heat capacity of aluminum and titanium. Fig. 3 shows deformation and temperature distribution on the side of the particle and substrate after the impact of Al/Al (Fig. 3a) and Ti/Ti (Fig. 3b). The results show that the outer edge side of particle and substrate interface has a
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higher temperature than that of the center, which is in good agreement with previous work [6]. In both cases, the maximum temperature at the substrate side, which approaches the melting point, is higher than that of the particle side at the critical velocity. Furthermore, the Al/Al case shows a wider high-temperature region in the substrate than that of Ti/Ti owing mainly to its relatively high ductility, high thermal-softening effect, and low strain hardening, as listed in Table 3. The cases of Al/mild steel (Fig. 2c) and Ti/Al (Fig. 2d), which are dissimilar combinations, reveal quite different deformation behavior as compared to the previously mentioned similar cases. The initial kinetic energy of the particle is mostly dissipated into plastic deformation of the relatively soft counterpart. Accordingly, much higher temperature on the soft side is achieved. Impact morphologies and temperature profiles for these cases are shown in Fig. 4. The simulation results demonstrate a flattened particle with a very slightly deformed substrate for the soft/hard case (Fig. 4a) and a deeply penetrated substrate with a less deformed particle for the hard/soft case (Fig. 4b) at the critical velocity. Relatively low estimated critical velocities of 365 m s1 for Al/mild steel and 665 m s1 for Ti/Al are revealed as compared to those of the previous cases (Fig. 3). Taking into account the significantly different physical and mechanical properties between particle and substrate in the dissimilar cases, the results of critical velocities are understandable. By previous experimental work, the critical velocities of Al–12%Si (25 lm)/mild steel [21] and Cu (5 lm)/AISI304 stainless steel [22] were reported to be around 400 and 300 m s1. It should also be noted that the zone with temperatures near the melting temperature spreads over a very
Fig. 2. Classified four cases of particle impact on substrate: (a) soft/soft (Al particle onto Al substrate at 775 m s1), (b) hard/hard (Ti particle onto Ti substrate at 865 m s1), (c) soft/hard (Al particle onto mild steel substrate at 365 m s1), (d) hard/soft (Ti particle onto Al substrate at 655 m s1).
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Fig. 3. Deformation and temperature profiles at the side of particle and substrate after impact: (a) Al particle/Al substrate (at v = 775 m s1, t = 32.5 ns), (b) Ti particle/Ti substrate (at v = 865 m s1, t = 23.3 ns).
Fig. 4. Deformation and temperature profiles at the side of particle and substrate after impact: (a) Al particle/mild steel substrate (at v = 365 m s1, t = 36.5 ns), (b) Ti particle/Al substrate (at v = 655 m s1, t = 49.5 ns).
large area on the soft side in the dissimilar cases, as shown in Fig. 4. A close view of this zone shows that the thicknesses of the ‘thin-molten-layer’ are 11.5 nm (Fig. 5a) and 53.5 nm (Fig. 5b), respectively. Alkhimov et al. numerically suggested that the impact of an aluminum particle on a rigid barrier can cause melting in the contact zone [23]. It has also been argued that the melting at the contact area upon impact of a solid particle may result in reliable metallurgical bonding [24].
4.2. Adiabatic shear instability aspects ASI is a sudden event accompanied by a rapid temperature rise within the near-surface of the material during high-strain-rate viscoplastic deformation [6]. The high temperature (approaching the melting point) causes local thermal softening and leads to instant flow stress breakdown. As previously reported [6–8], the ASI has been explained as only one form of the abnormal ‘thermal run-away’ phenomenon of thermoviscoplastic materials, e.g. standard
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Fig. 5. Thin molten layers at particle side of (a) Al/mild steel, and at substrate side of (b) Ti/Al.
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‘thermal boost-up height’ and the normalized ‘thermal boost-up width’, respectively. Thermomechanical analyses for the four cases are provided in Fig. 8. Each set of temperature and equivalent (Von Mises) flow stress integrated from the selected element at the impacting interfaces shows distinguishable aspects compared with that previously presented [6,8]. As shown in Fig. 7, it is clearly seen that the Cu/Cu case has a conventional ASI aspect, which has a large TBZ at the critical velocity. Cases Al/Al (Fig. 8a) and Ti/Ti (Fig. 8b) both have smaller ‘thermal boost-up width (Wtb)’ than Cu/Cu (Fig. 7) (estimated Wtb for Al, Ti and Cu is 1.9 101, 1.3 101, and 3.5 101, respectively). In the same way, both cases also have smaller ‘thermal boost-up height (Htb)’ than Cu/Cu (estimated Htb is 19.4 102, 11.5 102, and 32.3 102). Consequently, it is clear that the TBZ of Al/Al, which is wider than that of Ti/Ti, is narrower than that of Cu/Cu (estimated Ztb is approximately 3.7 102, 1.5 102, and 11.3 102). As described in Eq. (3), temperature evolution of the material during high-strain-rate deformation is dependent on not only deformability, but also mass density and specific heat. The delay in the onset of material instability depends upon the thermal-softening and strain- and
material copper. Normally, there is an obvious transition point prior to the onset of ASI. After some incubation time, a ‘thermal boost-up zone’ can be formed as shown in Fig. 6. In other words, this zone is a result of unstable plastic deformation when the rate of thermal softening exceeds the rate of work hardening, which includes not only strain hardening but also its strain-rate sensitivity effect described by Eq. (1). The thermal boost-up zone (hereafter referred to as TBZ) is theoretically defined as follows: TBZðZ tb Þ ¼ H tb W tb ¼ ½ðT max –T r Þ=T m ½ðtc –ti Þ=tc where Tmax is the maximum temperature, Tr the temperature of transition point, Tm the melting temperature, ti the incubation time, and tc the total contact time as illustrated in Fig. 6. Htb and Wtb are defined as the normalized
Fig. 6. Schematic of thermal boost-up zone (TBZ), termed Ztb. Marked box indicates TBZ.
Fig. 7. Thermomechanical analysis of 25 lm sized copper particle impact onto copper substrate: (a) impact morphology and temperature distribution at critical velocity of 550 m s1, after 62.7 ns, (b) temporal evolutions of temperature and flow stress at the interfacial jet of crater.
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strain-rate-hardening characteristics of the material. Therefore, ASI initiation resistance is dependent on these material properties, and they affect the final size of TBZ. Interestingly, in the Al/mild steel (Fig. 8c) and Ti/Al (Fig. 8d) cases, a specific form of ASI exhibiting an extremely high heat-up rate is observed. It is also noted that there is no ‘transition point’ prior to the onset of ASI due to the very fast temperature rise to the melting point in these cases. Similar to the temperature evolution, flow stress also very sharply collapsed to near zero, in contrast to the occurrence of flow stress fluctuations by the competition between thermal-softening and strain-hardening as shown in Fig. 7b and Fig. 8a. The reason for this is the rapid and severe deformation of the relatively soft counterpart. Moreover, highly saturated temperature and extremely low equivalent flow stress result in high ‘adhesion’ and low ‘rebound energy’, which are beneficial for successful bonding [21]. 4.3. Energy balance and recoverable strain energy During the kinetic spraying process, the initial kinetic energy of the in-flight particle is mainly dissipated into plastic deformation and viscous effects/frictional work of the impacting particle and substrate. Moreover, some of the initial kinetic energy is stored as ‘recoverable strain energy’ (elastic strain energy) in the contacting bodies.
Since only a few percent of initial kinetic energy is normally dissipated as elastic wave propagations [25], it is neglected in this study. The conversion of energy during impact can be simply described by following macroscopic Eqs. (4)– (6) based on the conservation of energy implied by the first law of thermodynamics [10]: Z Z 1 qt t dV ¼ qU dV þ EF ð4Þ V 2 V where q is the mass density, t the velocity, V the unit volume, and U is the internal energy per unit mass. EF is defined as energy dissipated by frictional work between the contact surfaces. In Eq. (4), work done to the body by external forces was not considered. Consequently, the initial kinetic energy is equal to the sum of the internal energy (EU) and the frictional dissipation energy (EF). FE simulation results show that the fraction of the frictional dissipation energy is relatively small compared with the energy converted into internal energy. The internal energy can be written as follows: EU ¼ EI þ E V
ð5Þ
where EI is the remaining energy, which we continue to call the ‘internal energy,’ and EV the energy dissipated by viscous effects. (EV is also relative very small compared to EI.) The internal energy, EI, can be expressed as follows:
Fig. 8. Temporal developments of interface temperature and flow stress of: (a) Al particle onto Al substrate, (b) Ti particle onto Ti substrate, (c) Al particle onto mild steel substrate and (d) Ti particle onto Al substrate at critical velocities of 775 m s1, 865 m s1, 365 m s1 and 655 m s1, respectively.
G. Bae et al. / Acta Materialia 56 (2008) 4858–4868
EI ¼ E R þ EP ¼
Z t Z 0
V
rc : e_ el dV
ds þ
Z t Z 0
rc : e_ pl dV
ds
V
ð6Þ
where ER is the recoverable strain energy, EP is the energy dissipated into plastic deformation, rc is the stress derived from the constitutive equation (the Johnson–Cook model), e_ el is the elastic strain rate, and e_ pl is the plastic strain rate. According to the energy balance concept, adiabatic local heating at the interface induced by the plastic dissipation energy and the viscous/frictional dissipation energy contributes to ‘adhesion energy’, and only the stored elastic strain energy can be recovered as ‘rebound energy’. In the model suggested by Wu [21], the rebound energy (ER) is associated with the elastic modulus of the particle and substrate. In addition, ER will normally increase with particle velocity. In contrast, for the all cases, it is revealed that the ratio between recoverable strain energy (ER) and plastic dissipation energy (EP) decreased with particle velocity, as shown in Fig. 9. This results from the flow stress which decreases at the impacting interfaces due to the adiabatic heating and resultant thermal softening with increasing particle velocity. In the similar cases, the ratio (ER/EP) for Al/Al (Fig. 9a), which is lower than that of Ti/Ti (Fig. 9b) is relatively higher than that of Cu/Cu at the critical velocity (estimated
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values are 50.7 103, 90.1 103, and 24.2 103, respectively). In the case of Al/Al, it is apparent that the ratio decreases steeply just below the critical velocity. These results are closely correlated with the thermomechanical behavior of each case, and all are inversely proportional to the results of TBZ previously estimated. For the dissimilar cases, at the critical velocity, the ratio (ER/EP) for Al/mild steel (Fig. 9c) and Ti/Al (Fig. 9d) are evaluated as 17.8 103 and 54.6 103, respectively. Al/ mild steel has the lowest ratio among the four cases at relatively low velocity (365 m s1), but it is seen that the rate of recoverable strain energy drastically increases above the critical velocity; accordingly, the ratio (ER/EP) also increases slightly. These results are consistent with the rebound phenomenon of the soft/hard case [21]. Meanwhile, Ti/Al (hard/soft) has a relatively high ratio (ER/ EP) at critical velocity as compared to other cases except the Ti/Ti case. This is because of the much lower deformation of the particle than that of the substrate, such that a relatively high amount of elastic strain energy affects the bonding. 4.4. Reliability of modeling by experimental results As shown in Fig. 10, scanning electron micrograph analysis shows significantly different bonding features of nickel
Fig. 9. Plots of ratio between recoverable strain energy and plastic dissipation energy: (a) Al particle onto Al substrate (Vp = 300–775 m s1), (b) Ti particle onto Ti substrate (Vp = 300–865 m s1), (c) Al particle onto mild steel substrate (Vp = 100–450 m s1), and (d) Ti particle onto Al substrate (Vp = 300–655 m s1).
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Fig. 10. Surface morphologies (a–c) and cross-section images (d–f) of individual nickel particle depositions (using 300 °C/25 bar helium as process gas) onto different substrates: copper (a and d), Al 6061-T6 (b and e), and SKH 51 steel (c and f).
particles onto copper, Al 6061-T6, and SKH 51 steel substrates. With respect to the relative deformability, the impact behavior of nickel particles on the substrates can be considered as soft/soft, hard/soft, and soft/hard cases. The velocity of a 35 lm sized nickel particle accelerated by 300 °C/25 bar helium gas is estimated to be 760 m s1 by the empirical equation [26]. Under this condition, FE modeling results show different deformation behaviors for the three cases (similar to the deformation features as described in Section 4.1): comparable deformation of the particle and substrate in the Ni/Cu case, severe plastic deformation of substrate and slight deformation of the particle in the Ni/Al 6061-T6 case, and severe plastic deformation of the particle without deformation of the substrate in the Ni/SKH 51 steel case. These results are in good agreement with the experimental observations shown in Fig. 10d–f. The measured bond ratios for these three impact cases are 63%, 33%, and 52%, respectively. It is seen that the highest bond ratio is obtained in the Ni/Cu case, where the particle and substrate are comparably deformed (Fig. 10d). The lowest ratio is seen in Ni/Al 6061-T6, where the particle is barely deformed (Fig. 10e). Apparently, the deformation of the particle may be a prerequisite for successful bonding. These different bonding processes in the three impact cases can be explained in comparison with the modeling results. From FE modeling, it is seen that the maximum interfacial temperature reaches the melting point of the substrate side in the Ni/Cu and Ni/Al 6061-T6 cases and of the particle side in the Ni/SKH 51 steel case. In terms of the opinion provided in Ref. [21], adhesion energy can be affected by not only contact temperature, but also by the contact area and contact time. As shown in Fig. 11, the bond ratios for these three cases are associated with the contact areas (Fig. 11b), but inversely proportional to the recoverable strain energies (Fig. 11a). Fig. 11c shows that the contact time in all the cases is similar. Based upon a comparison between numerical and experimental results,
it can be concluded that the successful bonding between dissimilar metals depends not only on the degree of deformation of the impacting counterparts, but also the resultant interfacial temperature, contact area, contact time, and recoverable strain energy. Thus, the modeling results are reliable to explain the experimental phenomena of the impact cases presented in this study. 4.5. Critical velocities for various metal combinations Based on the concept of ASI in Section 4.2, the critical velocities for 40 combinations of engineering materials were numerically estimated. The velocity at the ASI, with the occurrence of ‘saturation limit’ of interface temperature, can be defined as the theoretical ‘critical velocity’ to confirm the firmly bonded state. The estimated critical velocity (775 m s1) for the Al/Al case is slightly higher than the experimentally determined value (721 m s1) of aluminum (99.0% purity, 0.001 wt.% oxygen content, 45– 90 lm) [27]. This difference in critical velocity between numerical and experimental can be attributed to the particle size effect [7]. Critical velocities and interface temperatures estimated by FE modeling for the similar cases (soft/soft and hard/ hard) and dissimilar cases (soft/hard and hard/soft) are shown in Figs. 12 and 13. Compared with the critical velocity (550 m s1) of copper, relatively high critical velocities of titanium, aluminum, and steel alloys are seen. The data also reveal that tungsten heavy alloy and Du-0.75 Ti (depleted uranium) have noticeably low critical velocities due to their relatively high mass density and lower specific heat than other materials. Tantalum shows a critical velocity similar to copper, even though it has a very high melting temperature (3269 K) and refractory crystal structure (body centered cubic); this characteristic is due to its very high density and low heat capacity. For some impact cases at critical velocities, the temperature reaches 100% of the melting point, such as Inconel 718, Al 2024-T351, and
G. Bae et al. / Acta Materialia 56 (2008) 4858–4868
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Fig. 13. Critical velocities and maximum temperature (which refers to the softer materials) at interface for soft/hard and hard/soft (particle/ substrate) combinations (columns indicate critical velocities).
magnesium alloy (AM50 A), among others. It is also worth noting that the softer materials (regardless of particle and substrate) are melted at the interface in all dissimilar cases (Fig. 13). In short, it is clear that the critical velocities in the similar cases are higher than those of the dissimilar cases, and within the dissimilar cases, soft/hard cases have lower critical velocities than hard/soft cases. Contact area and contact time were also evaluated at the critical velocity for the similar and dissimilar cases. In the similar cases (Fig. 14), the copper case has a relatively large contact area and long contact time compared with other cases. On the other hand, relatively small contact area and short contact time are seen in aluminum and titanium cases, while steel alloy cases show relatively large contact areas and short contact times. In the dissimilar cases (Fig. 15), it is revealed that hard/soft cases have longer contact time than soft/hard cases. Fig. 11. Recoverable strain energy (a), contact area (b) versus bond ratio plots and contact time (c) plots of individual nickel particle impact onto copper, Al 6061-T6, and SKH 51 steel substrates.
5. Summary and conclusions In the present investigation, individual particle (25 lm) impact behaviors of four cases were numerically analyzed
Fig. 12. Critical velocities and maximum temperature at interface for soft/ soft and hard/hard (particle/substrate) combinations (columns indicate critical velocities).
Fig. 14. Contact area and contact time for soft/soft and hard/hard (particle/substrate) combinations at critical velocity (dark gray columns indicate contact area).
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energy, accompanied with the different aspects of ASI. Finally, these factors significantly affect the bonding features and properties of kinetic sprayed coatings. Acknowledgements This work was supported by a Korean Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MOST) (No. 2006-02289). References
Fig. 15. Contact area and contact time for soft/hard and hard/soft (particle/substrate) combinations at critical velocity (dark gray columns indicate contact area).
[1] [2] [3] [4] [5]
and characterized through finely designed micro thermomechanical modeling using finite-element code (ABAQUS/Explicit 6.7-2). With respect to the bonding aspects, the results show distinguishable ASI aspects compared with the conventional copper case. Based on that analysis, a thermal boost-up zone (TBZ) is theoretically defined and numerically proposed. The TBZ was then quantitatively estimated for different metallic materials. In the similar cases (soft/soft and hard/hard cases), it is clearly seen that the ratio between recoverable strain energy and plastic dissipation energy is inversely proportional to the evaluated TBZ at critical velocities. Meanwhile, in the dissimilar cases (soft/hard and hard/soft cases), ASI, which has extremely high heat-up rate and no transition point, is always observed at the soft impact counterpart. Accordingly, the numerically predicted thin molten layer of the soft counterpart contributes to the low critical velocities. Overall, these critical velocities are relatively lower than those of the similar cases. Moreover, it is obvious that experimentally measured bond ratios for dissimilar cases are in good correspondence with the modeling results, including not only interface temperature, but also contact area, contact time, and recoverable strain energy. Based on the reliability of the modeling, a database for numerically estimated critical velocities (with interface temperature, contact area, and contact time) was developed and is quite useful to predict successful bonding and the bonding state of various engineering materials. In conclusion, general aspects of the interface bonding of metallic materials can be explained and characterized by the interface temperature evolution (related to the size of TBZ), contact area, contact time, and recoverable strain
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