Michel Saby

Elisabeth Massoni

Nathalie Bozzolo

A metallurgical approach to individually assess the rheology of alpha and beta phases of Ti-6Al-4V in the two-phase domain

Keywords: titanium alloys, phase transformation, high-temperature deformation, torsion test

An original hot torsion procedure is presented using Ti-6Al-4V in the two-phase domain.

Kinetics

of phase transformation are used to obtain stress-strain curves in off-equilibrium states. The individual influences of phase fraction and of temperature are quantitatively assessed in the two-phase domain. Between the two forging temperatures 1143 K (870 • C) and 1228 K (955 • C), a 95 MPa stress difference is observed. The paper shows that this flow stress drop is mainly due to thermal activation, by 80 MPa, while 15 MPa is due to the change of phase fraction. The stresses in each phase are individually assessed and stress-strain curves for each phase are obtained within the two-phase domain.

Introduction

Due to their considerable resistance to hard solicitations, fatigue, corrosion, and to their low density, titanium alloys today remain major candidates for the production of aeronautic structural parts. Immense effort is devoted to the improvement of the hot forging process of such large-scale parts. Constitutive models, associated with numerical simulation, are powerful tools to optimize forging stages. Empirical and semi-empirical constitutive models, considering thermo-mechanical variables (effective strain ε, strainrate ε, and temperature T ) are widely used [START_REF] Sellars | On the mechanism of hot deformation[END_REF][START_REF] Hensel | Kraft-und arbeitsbedarf bildsamer formgebungsverfahren[END_REF][START_REF] Johnson | A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[END_REF][START_REF] Sung | A plastic constitutive equation incorporating strain, strain-rate, and temperature[END_REF]. Over last decades, physically-based models including internal-state-variables [START_REF] Vo | Flow stress prediction during hot working of near-alpha titanium alloys[END_REF][START_REF] Fan | Internal-state-variable based self-consistent constitutive modeling for hot working of two-phase titanium alloys coupling microstructure evolution[END_REF][START_REF] Luo | Constitutive model for high temperature deformation of titanium alloys using internal state variables[END_REF] and self-consistent models [START_REF] Semiatin | Self-consistent modeling of the flow behavior of wrought alpha/beta titanium alloys under isothermal and nonisothermal hot-working conditions[END_REF][START_REF] Kim | A self-consistent approach for modeling the flow behavior of the alpha and beta phases in Ti-6Al-4V[END_REF] were developed, according to numerous studies regarding deformation mechanisms and metallurgical changes in the material. Among all, phase fraction emerges as a very influent parameter on flow stress, and the alloy's rheological behavior may be expressed using a rule of mixture (rom):

σ(ε, ε, T ) = rom [σ α (ε, ε, T ), σ β (ε, ε, T ), f α (T )] ( 1
)
where σ is the flow stress of the alloy, σ α and σ β the individual flow stresses of each phase, and f α the volume phase fraction of alpha phase. In the two-phase domain, the temperature dependence of σ is therefore driven by two complementary effects: (i) the change of phase fraction f α (T ) according to phase equilibrium thermodynamics, and

(ii) the temperature dependence of σ α (T ) and σ β (T ) due to thermal activation in each phase. This paper presents an experimental procedure to assess those two influences individually.

Experimental setup for in-and off-equilibrium torsion testing

Two-phase α + β titanium alloy Ti-6Al-4V was supplied by TIMET Savoie. Its chemical composition is given in C), and at the strain-rate ε = 0.5/s. These temperatures are in the range of classical forging temperatures, in the two-phase domain. Hot torsion was preferred as it enables large deformation to be reached. This experimental testing is well suited for rheology characterization, as it avoids the presence of friction during testing, unlike compression testing.

The specimens have a cylindrical effective zone (diameter 6mm, length 10mm). In a first series of tests, a classical in-equilibrium procedure was conducted. They were heated up using a lamp furnace and held at the desired temperature before deformation, as presented in Fig. 1(a). Protection against oxidation was provided using argon flow.

Heating rate is 10 K/s and holding time is 10 min. For preliminary verification of the microstructure, one specimen was water-quenched after holding time (dashed line in Fig. 1(a)). Its microstructure is presented in Fig. 2(b). Dark alpha nodules, as well as dark alpha lamellae can be observed in a brighter beta matrix. During quenching, the beta phase has transformed into a lamellar α+β structure, while alpha nodules remained unchanged. The volume fraction of alpha phase before quenching can thus be obtained by measuring the volume fraction of alpha nodules on the quenched specimen at room temperature. The values are presented in Fig. 3 using full dots, as well as theoretical values of phase fraction, given by Eq. ( 2) [START_REF] Castro | Contribution à l'étude métallographique et structurale de l'alliage de titane TA6V[END_REF]. The good agreement obtained between the measured values and the theoretical curve shows that thermodynamic equilibrium was indeed reached at the end of the holding time.

f α (T ) = 0.92 1 -e -0.0085(T β -T ) (2)
In a second series of tests, the so-called off-equilibrium torsion tests, holding time was suppressed, as presented in Fig. 1(b), in order to enable the deformation to start before thermodynamical equilibrium was reached, i.e. when the alloy presents a different phase fraction.

Alpha phase fraction was measured on the quenched specimen (see Fig. 2(c). It shows that the alpha nodules remain equiaxed after deformation (verification of (i) and (iii) conditions) and that phase fraction is unchanged (verification of the (ii) condition).

Analysis of rheological data

Effects of temperature and phase fraction

Stress-strain curves were obtained for the two temperatures 1228 K (955 • C) and 1143 K (870 • C), at equilibrium and off-equilibrium. Each condition was repeated three times to ensure reproducibility of the results. Experimental stress-strain curves for the four tested cases are presented in Fig. 4(a). The values of flow stress obtained at equilibrium (in full dots) at both temperatures are in good agreement with literature [START_REF] Luo | Constitutive model for high temperature deformation of titanium alloys using internal state variables[END_REF][START_REF] Zhong | Modelling the high temperature deformation of Ti-6Al-4V[END_REF].

At the temperature 1228 K (955 • C) the flow stress values obtained in the off-equilibrium state (f α = 0.58) are higher than the values obtained at thermodynamical equilibrium (f α = 0.31). A change of ∆f α = 0.27 in phase fractions involves a relative difference in flow stress by about 20%, which confirms that phase fraction has a significant influence on rheology [START_REF] Kim | A self-consistent approach for modeling the flow behavior of the alpha and beta phases in Ti-6Al-4V[END_REF]. At the temperature 1143 K (870 • C), both values of flow stress are roughly comprised in the same range [160-170] MPa. In this case, the difference of phase fraction obtained using the experimental procedure at this temperature (∆f α = 0.12) was probably not sufficient to involve a significant effect on rheology.

Strain hardening and softening effects are rather moderate at such temperatures and strain rate. However, a slight difference in the strain hardening and softening behaviours can observed at the beginning of the stress-strain curves. It was shown [START_REF] Vo | Flow stress prediction during hot working of near-alpha titanium alloys[END_REF][START_REF] Colin | A physically based flow rule for the simulation of Ti-6Al-4V forging in the α-β range[END_REF] that the presence of a peak in flow stress tends to vanish over transus temperature, i.e. in pure beta phase. In Fig. 4(a), the curves at highest values of f α exhibit a sharper change of slope than the ones at the low f α . This results confirms that, in the two-phase domain, the presence of a peak can also be attributed to the behaviour of the alpha phase. On Fig. 3, let us note that phase fractions measured at 1143 K (870 • C) at equilibrium, and at 1228 K (955 • C) off-equilibrium are very similar, respectively equal to 0.62 and 0.58. By assuming that both phase fractions are equal, it is possible to deduce the T β

Values at equilibrium

Off-equilibrium value Theoretical value from Eq.( 2) To summarize, the total flow stress reduction of 95 MPa due to heating alloy from 1143 K (870 • C) to 1228 K (955 • C) (at thermodynamic equilibrium) is due for 84% to pure thermal activation and for 16% to phase change.

Stress-strain curves in each individual phase

The overall flow stress of two-phase alloys can be expressed, in a first approximation, as a linear combination of individual flow stresses in each phase [START_REF] Luo | Constitutive model for high temperature deformation of titanium alloys using internal state variables[END_REF][START_REF] Zhong | Modelling the high temperature deformation of Ti-6Al-4V[END_REF][START_REF] Colin | A physically based flow rule for the simulation of Ti-6Al-4V forging in the α-β range[END_REF]. At a given temperature, the stress of the alloy in each case (equilibrium or off-equilibrium) is thus expressed as

σ(T ) eq = σ α (T )f eq α +σ β (T ) [1 -f eq α ] σ(T ) off eq = σ α (T )f off eq α +σ β (T ) 1 -f off eq α (3)
with σ α (T ) and σ β (T ) the stress in each phase, respectively. σ(T ) eq and σ(T ) off eq are the flow stress that were measured by torsion testing at equilibrium and off-equlibrium. is additionnally found that the flow stress of pure beta phase has a value by about 60% lower than that of pure alpha phase at the temperature 1228 K (955 • C). An evaluation of individual phase behaviours is also pointed out. It also verifies the presence of a sharp peak for the rheology of alpha phase, and a relatively smooth change of slope in the rheology of beta phase, as shown in [START_REF] Vo | Flow stress prediction during hot working of near-alpha titanium alloys[END_REF][START_REF] Colin | A physically based flow rule for the simulation of Ti-6Al-4V forging in the α-β range[END_REF].

In order to better predict the behaviour of the two-phase material, the linear form used in Eq. ( 3) in a first approximation might obviously be improved. For example, the absence of significant difference between both flow stresses in-and off-equilibrium at the lower temperature 1143 K (870 • C) cannot be predicted using Eq. ( 3). Additionnal rheological data might be obtained using the presented procedure of off-equilibrium torsion testing, at various temperatures, and by varying phase fraction values using different holding times. It is worth noticing that kinetics of phase dissolution are a key parameter to take into account in the experimental procedure. The difference of phase fraction is obtained by a competition between heating rate and α → β phase transformation. A fast heating device is therefore recommended. Let us also note that initial microstructure (equixed or lamellar structure, grain size, etc.) has a non-negligible impact on phase transformation kinetics. A fully-equiaxed initial microstructure shall be prefered rather than a bi-modal or lamellar microstructure. Slower kinetics of phase transformation also help to better satisfy the assumption of constant phase fraction during deformation.

Conclusions

The original experimental procedure consists in performing hot torsion tests in offequilibrium conditions, by dealing with kinetics of phase transformation within the twophase domain of Ti-6Al-4V alloy. It is possible to obtain stress-strain curves for two different phase fractions, at constant temperature. It is also possible to obtain stressstrain curves at two different temperatures, for a constant phase fraction. Using such rheological data, it is therefore possible to individually assess rheological behaviours of each phase. The results for Ti-6Al-4V show that, between the two forging temperatures 1143 K (870 • C) and 1228 K (955 • C), the 95 MPa stress difference that is obtained is mainly due to thermal activation, by 80 MPa, while 15 MPa is due to the change of phase fractions. The obtained stress-strain curves were also used to provide an individual evaluation of both phase rheologies within the two-phase domain. It was shown that, for Ti-6Al-4V at 1228 K (955 • C), the flow stress of beta phase is about 60% lower than that of alpha phase.

This metallurgical approach shows great potential to be adapted for further two-phase alloys.

Acknowledgements

This work was carried out in the frame of a project funded by an industrial consortium involving Airbus, TIMET Savoie, Forges de Bologne (Manoir Aerospace), Aubert & Duval (Eramet), and EADS IW.

  2(a)) in the off-equilibrium condition. The values are plotted with white dots in Fig.3. A difference of about 27% phase fraction was obtained between in-and off-equilibrium cases at the temperature 1228 K (955 • C), and about 12% at the temperature 1143 K (870 • C).The total deformation duration for each torsion test is 1s. Kinetics of phase transformation are neglected on this duration and phase fractions are therefore considered as constant during the whole deformation. Stress-strain curves are obtained using Fields & Backofen's analysis[START_REF] Fields | Determination of strain-hardening characteristics by torsion testing[END_REF], and the three associated assumptions are discussed in the following: (i) The fully-plastic deformation of the specimen was verified by a visual inspection of post-mortem specimens, by the absence of any localization effect. (ii) The temperature was measured by thermocouples and the increase due to self-heating remained lower than 10 K. Isothermal conditions must be considered for Fields & Backofen's analysis. (iii)The material is assumed to be macroscopically homogeneous and isotropic according to 3.98 0.15 0.19 0.015 0.007 remainder

Figure 1 :

 1 Figure 1: Temperature pattern for (a) in-and (b) off-equilibrium torsion test

  (a) Before holding (b) After 10' holding at 1228 K (955 • C) (c) After 10' holding and deformation

Figure 2 :

 2 Figure 2: Microstructure obtained by quenching from the temperature 1228 K (955 • C), at different instants, using back-scattered electron microscopy 6

Figure 3 :

 3 Figure 3: Measured primary alpha phase fractions vs. temperature

Figure 4 :

 4 Figure 4: Stress-strain curves: (a) experimental data at various tested temperatures and phase fractions, and (b) experimental and computed data at 1228 K (955 • C) for pure alpha and beta phases

Table

Table 1 :

 1 Chemical composition of Ti-6Al-4V in weight percent

Email address: michel.saby@mines-paristech.fr, +33493957415 (Michel Saby) Preprint submitted to Elsevier December 2, 2013


Andreea Paunoiu

Jean-Michel Mataigne

Florence Bertrand

David Zapico Álvarez

Jonas Staudte

Marie-Laurence Giorgi

Study of the inhibition layer formed in a ga bath on a trip mn-al steel

Keywords: TRIP Mn-Al, selective oxides, hot-dipping, inhibition layer, GA bath

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Commonly referred to as the inhibition layer, a thin intermetallic layer is formed between the zinc overlay and the steel substrate during hot-dipping in a GA bath (Fe saturated Zn bath with 0.110-0.135 wt.% Al). Many controversial results related to the structure of this layer on IF substrates are proposed in the literature [START_REF] Saito | Formation Behavior of Alloy Layer in Initial Stages of Galvanizing[END_REF][START_REF] Guttmann | Diffusive phase transformations in hot-dip galvanizing[END_REF][START_REF] Chen | Morphology and Kinetics of Interfacial Layer Formation during Continuous Hot-Dip Galvanizing and Galvannealing[END_REF][START_REF] Úřednίček | Mechanism of iron attack inhibition arising from additions of aluminium to liquid Zn(Fe) during galvanizing at 450°C[END_REF][START_REF] Yamaguchi | Reaction Mechanism of the Sheet Galvanizing[END_REF][START_REF] Álvarez | Nature of the inhibition layer in GA baths[END_REF][START_REF] Tang | Determination of liquid-phase boundaries in Zn-Fe-Mx systems[END_REF] . It has been reported that the inhibition layer was either formed as a single phase of metastable Fe2Al5Znx [START_REF] Saito | Formation Behavior of Alloy Layer in Initial Stages of Galvanizing[END_REF][START_REF] Guttmann | Diffusive phase transformations in hot-dip galvanizing[END_REF] or as transient FeAl3 [START_REF] Chen | Morphology and Kinetics of Interfacial Layer Formation during Continuous Hot-Dip Galvanizing and Galvannealing[END_REF][START_REF] Úřednίček | Mechanism of iron attack inhibition arising from additions of aluminium to liquid Zn(Fe) during galvanizing at 450°C[END_REF] and FeAl2 [START_REF] Úřednίček | Mechanism of iron attack inhibition arising from additions of aluminium to liquid Zn(Fe) during galvanizing at 450°C[END_REF] with Fe2Al5Znx. Other studies revealed a biphasic structure comprised of a δ (FeZn7) layer over a metastable Fe2Al5Znx layer [START_REF] Yamaguchi | Reaction Mechanism of the Sheet Galvanizing[END_REF][START_REF] Álvarez | Nature of the inhibition layer in GA baths[END_REF] . Nevertheless, by taking into account the Al-Fe-Zn ternary phase diagram at 460°C [START_REF] Tang | Determination of liquid-phase boundaries in Zn-Fe-Mx systems[END_REF] , the inhibition layer in a GA bath should contain the δ (FeZn7) phase, which is in thermodynamic equilibrium with the liquid phase.

The challenge of producing lighter automotive structures with improved crashworthiness has led to the development of new steel grades such as TRansformation-Induced Plasticity (TRIP) steels containing higher concentrations of alloying elements such as Mn, Si and Al. These elements undergo oxidation during recrystallization annealing, influencing the reactivity between the substrate and the liquid Zn [START_REF] Bellhouse | Selective Oxidation and Reactive Wetting during Galvanizing of a CMnAl TRIP-Assisted Steel[END_REF][START_REF] Wang | Role of Al in Zn bath on the formation of the inhibition layer during hot-dip galvanizing for a 1.2Si-1.5Mn transformation-induced plasticity steel[END_REF][START_REF] Prabhudev | Effect of oxides on the reaction kinetics during hot-dip galvanizing of high strength steels[END_REF] . In-depth characterization of the galvanized interface in presence of selective oxides was performed in the case of GI baths (~ 0.2 wt.% Al) on steel grades such as TRIP Mn-Si [START_REF] Wang | Role of Al in Zn bath on the formation of the inhibition layer during hot-dip galvanizing for a 1.2Si-1.5Mn transformation-induced plasticity steel[END_REF] and Dual-Phase [START_REF] Sagl | The role of surface oxides on annealed high-strength steels in hot-dip galvanizing[END_REF][START_REF] Aslam | Transmission electron microscopy characterization of the interfacial structure of a galvanized dual-phase steel[END_REF] . In these studies the inhibition layer consisted of Fe2Al5Znx as expected for GI baths [START_REF] Tang | Determination of liquid-phase boundaries in Zn-Fe-Mx systems[END_REF] . Moreover, they examined the selective oxidation state after hot-dipping showing that the oxides were incorporated into the inhibition layer. No quantitative data related to the structure of the inhibition layer formed in a GA bath on high alloyed steels is available in the literature. Hence, the main goal of this study is to investigate the nature of the inhibition layer formed in a GA bath in presence of selective oxides on a TRIP Mn-Al steel grade.

EXPERIMENTAL PROCEDURE

The substrate used in the present work was a cold-rolled TRIP 780 MnAl steel. Its chemical composition is shown in Table 1. The analysis was performed by means of Spark-Optical Emission Spectrometry (Spark-OES) in ArcelorMittal laboratories. The steel has been industrially coated in a Fe saturated Zn bath with 0.122 wt. % Al at T = 460°C on a Continuous Galvanizing line (CGL) with the Galvannealing inductor turned off. Prior to hot-dipping, recrystallization annealing was performed at 860°C during 129 s in a N2 + 3 vol.% H2 gas mixture with dew point DP =-40 and -5°C. In parallel, the recrystallization annealing cycle was simulated using an IWATANI Rhesca device in order to evaluate the selective oxidation state of the substrate. The recrystallization annealing trials were performed at laboratory scale, because sampling just after annealing and before hot-dipping was not possible on CGL. The selective oxidation state of annealed samples was characterized by means of Glow-Discharge Optical Emission Spectroscopy (GDOES-Horiba Jobin Yvon GD Profiler 2) and Energy Dispersive X-ray (EDX) in a Scanning Electron Microscope (FEG-SEM, JEOL JSM-7800F). The EDX mapping was performed on cross section specimens prepared through Ar+ ion beam Cross Section Polishing (CSP -JEOL SM-09010) technique. A nickel layer was deposited after annealing treatment for the sake of EDX analysis on cross section samples.

Concerning the galvanized samples, the steel/coating interface was investigated on CSP specimens using SEM and EDX elemental mappings. In addition, Focused Ion Beam (FIB, SII Nanotechnology Inc SMI 3050TB) thin foils were prepared after selective dissolution of the Zn overlay. The FIB thin foils were analyzed by EDX and Electron Diffraction in a Transmission Electron Microscope (TEM, JEOL JEM-2100F) in order to determine the nature of the phases present in the inhibition layer. By increasing the DP of the annealing atmosphere to 0°C, nodular Mn-rich oxides precipitated on the steel surface as illustrated on the EDX mapping of Mn in Figure 2 (b). Moreover, Mn oxidation occurred also within the sub-surface. Both EDX mapping and GDOES spectrum surface (Figure 2 (c andd)) clearly show that Al underwent oxidation essentially within the sub-surface and on a longer depth than Mn. The Mn-rich external oxides have been reported as MnO by Bellhouse et al. [START_REF] Bellhouse | Selective Oxidation and Reactive Wetting during Galvanizing of a CMnAl TRIP-Assisted Steel[END_REF] and Maki et al. [START_REF] Maki | Galvanisability of silicon free CMnAl TRIP steels[END_REF] on steel grades with comparable chemical composition in high DP annealing conditions (DP = 0, +5°C). The general aspect of the inhibition layer on the sample annealed in a gas atmosphere with high DP (Figure 4) is akin to the one described above. The Al-rich layer present at the steel/coating interface in Figure 4 (c) corresponds to Fe-Al intermetallic compound since Al-rich oxides formed only underneath the steel surface in these annealing conditions. The MnO precipitates observed before galvanizing were incorporated to the inhibition layer (Figure 4 (d-e)). which appears discontinuous in some areas.

RESULTS

Selective oxidation

Phases determination

A discontinuous Al-rich layer has been observed on CSP specimens as shown in the previous section. However, EDX signal of Al in SEM could arise from Fe-Al intermetallic compounds, but also from Al external oxides, in particular for the sample annealed in a gas atmosphere with low DP = -40°C. Results from TEM characterization (Figure 5) on thin FIB foils allowed to quantitatively differentiate the Fe-Al intermetallic compound of the inhibition layer from Al oxides and to determine its chemical nature. According to EDX (TEM) quantitative analysis (Table 2), the Fe-Al intermetallic compound has a similar composition to Fe2Al5Znx identified on IF substrates (38.5 wt.% Al, 36.9 wt.% Fe and 24.6 wt. % Zn [START_REF] Álvarez | Nature of the inhibition layer in GA baths[END_REF] ). Its structure is confirmed by the Electron Diffraction pattern shown in Figure 5 (right). JCPDS file #049-1381 (orthorhombic, space group Cmcm, lattice parameters a = 0.7656 nm, b = 0.6404 nm, c = 0.4241 nm) was used for indexing the experimental pattern. Concerning the Zn-rich phase, its chemical composition (Figure 6 (left) and Table 2) fits with the one reported by Chen et al. [START_REF] Chen | Fe-Al-Zn ternary phase diagram at 450°C[END_REF] for δ phase (2.8 wt.% Al, 9.0 wt.% Fe and 88.2 wt.% Zn). The Electron Diffraction pattern taken from this phase (Figure 6 (right)) was indexed as δ phase by using the JCPDS file #45-1186 (hexagonal lattice, space group P, lattice parameters a = b = 1.28 nm, c = 5.76 nm). TEM results related to the galvanized sample after annealing in a gas atmosphere with DP = -5°C are not illustrated here, as they are definitely similar to the ones obtained for DP = -40°C. Finally, TEM analyses revealed that the inhibition layer formed in a Zn bath with 0.122 wt.% Al on TRIP Mn-Al substrate is composed by discontinuous Fe2Al5Znx and δ phase for both investigated recrystallization annealing conditions.

DISCUSSIONS

Despite the selective oxides on steel surface, reactive wetting by liquid Zn occurred and led to the formation of the inhibition layer. The mechanism for the formation of the inhibition layer in a GA bath in presence of external oxides can be summarized as follows: liquid Zn penetration into the porous / discontinuous film oxide (DP = -40°C) or in between nodular oxides (DP = -5°C) in order to reach the steel, Fe dissolution and supersaturation at the steel / liquid Zn interface, nucleation of Fe2Al5Znx and/or δ phases. Subsequently, the inhibition layer incorporates the external oxides during its growth leading to the final structure illustrated in Figure 7. Similar interaction between liquid Zn, external oxides and substrate has been proposed by Sagl et al. 11) in the case of a Dual-Phase substrate galvanized in a GI bath (0.2 wt.% Al). It is worth to note that the inhibition layer in their study is composed essentially by Fe2Al5Znx owing to the higher Al content in the Zn bath. The observed microstructure of the inhibition layer can be explained through the diffusion path approach in the Al-Fe-Zn ternary phase diagram at 460°C [START_REF] Leprêtre | Reactive interdiffusion in the Fe-Al-Zn system: Reaction mechanisms during hot-dip galvanizing[END_REF][START_REF] Mataigne | Key mechanisms in galvanization of steel sheets[END_REF] shown in Figure 8. This microstructure is comparable to one described by Zapico et al. on IF substrates [START_REF] Álvarez | Nature of the inhibition layer in GA baths[END_REF] . Because of the discontinuity of Fe2Al5Znx layer, two local microstructures are distinguished, namely Fe/Fe2Al5Znx/δ/Zn and Fe/δ/Zn. Each sequence of phases can be described by real diffusion paths  and  as depicted in Figure 8. Moreover, the overall microstructure of the inhibition layer can be represented by the virtual diffusion path . Thus, a ternary equilibrium Fe -Fe2Al5Znxδ is established along the steel surface. The formation of δ phase enables all the interfaces to reach thermodynamic equilibrium. It can also be inferred that the selective oxides at the steel surface do not affect the thermodynamic equilibrium.

CONCLUSION

The dew point (DP) of recrystallization annealing atmosphere modifies the morphology, the nature and the location of selective oxides with respect to the steel surface. Annealing in a gas atmosphere with low DP resulted in external Al-Mn-O film oxides, whereas high DP led to external MnO with a nodular shape. The selective oxidation state aforementioned allowed the reacting wetting by liquid Zn during hot-dipping in a typical GA bath. The resulted inhibition layer incorporated the external oxides during its growth.

The present study provides compelling evidence that the inhibition layer formed in a GA bath (0.122 wt.% Al) has a biphasic structure, namely a thick layer of δ upon a thin discontinuous layer of Fe2Al5Znx. We can point out that neither the recrystallization annealing atmosphere (DP) nor the steel substrate (TRIP, IF) affect the biphasic structure of the inhibition layer in the case of GA baths.

Figure 1 (

 1 Figure 1(a) shows a cross-section micrograph of the steel annealed in laboratory in a low DP (-40°C) atmosphere. Al enrichment on the steel surface can be observed on the corresponding elemental mapping (Figure 1(b)). In addition, GDOES spectra (Figure 1 (c)) confirm the external selective oxidation of Al and Mn. Hence, it can be inferred that Al and/or Al-Mn film oxides formed on the steel surface during recrystallization annealing in a low DP. It should be noted that the Al signal appearing underneath the surface does not correspond always to Al-rich oxides. The rod shape of some Al-rich particles seems to correspond to AlN nitrides as analyzed by Li et al. 13).

Figure 1 :

 1 Figure 1: (a) SEM micrograph of the CSP specimen annealed in a gas atmosphere with DP =-40°C, (b) Qualitative elemental mapping of Al (EDX, in red) and (c) GDOES spectra of O, Mn and Al

Figure 2 :

 2 Figure 2: (a) SEM micrograph of the CSP specimen annealed in a gas atmosphere with DP = 0°C, (b) Qualitative elemental mapping of Mn, (c) Qualitative elemental mapping of Al, (d) GDOES spectra of O, Mn and Al 2. Inhibition layer 2.1. General features SEM micrograph and EDX mappings (Figure 3) of the steel/coating interface after annealing in a gas atmosphere with DP = -40°C and galvanizing on CGL indicate that the inhibition layer is composed by a layer of Zn-rich compounds over a thin Al-rich layer. By considering the EDX mappings of Mn and O (Figures(d)and (e)), the external Al-Mn-O film described before (section 1) can be distinguished from the Al-rich phase of the inhibition layer (Figure3(c)). In addition, the latter seems to be discontinuous. It is worth to that the external oxides are embedded in the inhibition layer.

Figure 3 :

 3 Figure 3: (a) SEM micrograph of CSP specimen annealed in a gas atmosphere with DP = -40°C and galvanized in a Zn bath with 0.122 wt.% Al, (b) EDX mapping of Zn-Al-O, (c) Al, (d) Mn and (e) O recorded from the selected area (green rectangle)

Figure 4 :

 4 Figure 4: (a) SEM micrograph of CSP specimen annealed in a gas atmosphere with DP = -5°C and galvanized in a Zn bath with 0.122 wt.% Al, (b) EDX mapping of Zn -Al-O, (c) Al, (d) O and (e) Mn recorded from the selected area (green rectangle)

Figure 5 :

 5 Figure 5: EDX spectrum (left) and Electron diffraction pattern (right) of Fe-Al intermetallic compound (right) of the inhibition layer formed on samples annealed in a gas atmosphere with low DP = -40°C

Figure 6 :

 6 Figure 6: EDX spectrum (left) and Electron diffraction pattern (right) of Zn-rich phase (right) of the inhibition layer formed on sample annealed in a gas atmosphere with low DP = -40°C

Figure 7 :

 7 Figure 7: EDX (TEM) mapping on FIB foil prepared from a sample annealed in a gas atmosphere with DP = -40°C and galvanized in a Zn bath with 0.122 wt.% Al (Zn-blue, Al-red, Mn-yellow, Fegreen)

Figure 8 :

 8 Figure 8: Diffusion paths on Zn-rich corner of Al-Fe-Zn ternary phase diagram at 460°C representing the local and the global microstructure of the inhibition layer investigated (adapted from 6) )

Table 1 :

 1 Chemical composition (wt.%) of TRIP steel investigated

	C	Mn	Al	Si
	0.22	1.65	1.5	0.08

Table 2 :

 2 Chemical composition (wt. %) of intermetallic compounds present in the inhibition layer on the sample annealed in a gas atmosphere with DP = -40°C determined by EDX (TEM)

		Fe2Al5Znx	δ
	Al	38.0 ± 1.4	1.8 ± 0.1
	Fe	44.8 ± 1.3	10.0 ± 0.4
	Zn	17.2 ± 0.6	88.2 ± 2.7

ACKNOWLEDGMENTS

The authors would like to thank Patrick Barges for TEM analysis. The authors also thank Sébastien Crémel for GDOES analysis and Annick Willems for the FIB thin foils preparation.


Marie-Laurence Giorgi

Alexey Koltsov

WETTING ASSESSMENT USING THE DISPENSED DROP METHOD IN THE FIELD OF HOT-DIP GALVANIZING

Keywords: Selective oxidation, heterogeneous wetting, kinetic and surface energies

In hot-dip galvanizing, the steel strip is annealed in an atmosphere of N2 and H2, containing only traces of water. One of the main purposes of this heat treatment is to reduce the iron oxides present at the steel surface, in order to improve the wettability by liquid zinc. At the same time, the less-noble alloying elements (Mn, Si, P, Cr, Al) of the steel segregate to the surface and preferentially oxidize. The steel surface is then composed of metallic iron (wetted by liquid zinc) and oxide particles or films (non-wetted by liquid zinc).

The main features of wetting are first presented (surface energy, triple line, contact angle) together with simple models to estimate the equilibrium contact angle (Young's, Wenzel's and Cassie's models). Two examples of studies performed by means of the dispensed drop technique in the field of hot-dip galvanizing will then be presented: the forced wetting of a partly oxidized steel by liquid Zn -Al and the final contact angle of a liquid Zn -Al droplet on iron / silica heterogeneous surfaces.

INTRODUCTION

Wetting refers to the study of how a liquid deposited on a solid (or liquid) substrate spreads out. To begin with, the main features of wetting will be defined, namely the surface energy, the triple line, the static and dynamic contact angles and the contact angle hysteresis. Then, it will be shown how to predict the equilibrium contact angle in the case of ideal surfaces (Young's equation) and rough or heterogeneous surfaces (Wenzel's and Cassie's equations).

Wetting can be studied at the laboratory scale by means of the dispensed drop technique, in which a liquid droplet is released on a solid sample and its spreading is filmed using a high-speed camera. The parameters characteristic of the wetting can be determined from the images of the film, e.g. the impact velocity of the droplet on the solid substrate, the spreading diameter, the left and right contact angles, the contact angle hysteresis. The dispensed drop technique is particularly well suited to investigate the wettability by liquid metals. This technique will be described in the second part of the paper.

In hot-dip galvanizing, the wetting of the steel substrate by the liquid metal bath is the first critical step. Before immersion in the molten metal bath, the steel strip is annealed at about 800 °C in a mixture of N2 and H2 (5 to 15 vol.%) containing a low water partial pressure (20 to 50 Pa). This annealing allows to recrystallize the structure of the steel after cold rolling and to prevent the iron oxidation of the steel surface. However, the conditions used favour the segregation towards the surface and the oxidation of the strengthening alloying elements in steel (Si, Al and Mn for example). After annealing, the steel surface is then composed of metallic iron (wetted by liquid zinc) and oxide particles or films (nonwetted by liquid zinc). In this context, two examples of studies performed by means of the dispensed drop technique will be presented: 1) the forced wetting of a partly oxidized steel by a liquid Zn -Al droplet as a function of its initial kinetic energy and 2) the final contact angle of a liquid Zn -Al droplet obtained on heterogeneous surfaces composed of silica and iron as a function of the surface area fraction covered by silica. [1][2][3] Wetting refers to the study of how a liquid deposited on a solid (or liquid) substrate spreads out. To begin with, the main features of wetting will be defined, namely the surface energy, the triple line, the static and dynamic contact angles and the contact angle hysteresis. Then, it will be shown how to predict the equilibrium contact angle in the case of ideal surfaces (Young's equation) and rough or heterogeneous surfaces (Wenzel's and Cassie's equations).

SOME FUNDAMENTALS EQUATIONS OF WETTING

Definitions (surface or interfacial tension, triple line, contact angle)

The increase in the surface of a liquid L in contact with a vapour V requires work so that:

= .

(1) The surface (or interfacial) tension of liquid L in contact with vapour V is then defined as the work by surface unit (in mJ.m -2 ) required to increase the area of the liquid. For pure liquid zinc, at a temperature T in the range [420, 600°C] 4) , [mJ m ] = 817 ± 15 -0.23 ± 0.03 . [°C] -420

(2) and, in particular, at 450°C, = 810 ± 16 mJ m . Surface energies for solid / vapour and solid / liquid interfaces, called interfacial tensions and noted ! and ! respectively, are defined in the same way. To our knowledge, the surface energies required in the field of hot-dip galvanizing, namely α-iron in equilibrium with saturated zinc vapour and α-iron in contact with liquid zinc, have not been measured yet.

As a consequence of Eq. ( 1), in order to minimize the system's energy, a droplet placed on a solid takes the shape of a spherical cap if it is small enough in size for gravity to have negligible effect (Figure 1a). The rim of the droplet where the three phases (liquid, solid and vapour) are in contact is called the triple line. The wetting or contact angle θ is defined by the tangent to the droplet and the horizontal substrate. The term of perfect wetting is used if θ = 0°, high partial wetting if θ < 90°, low partial wetting if θ > 90° and no wetting if θ = 180°. When the droplet is spreading on the solid, the contact angle depends on time and is called dynamic contact angle.

Equilibrium, advancing and receding contact angles

The contact angle at equilibrium on an ideal surface (i.e., smooth and homogeneous), " # , is called the Young contact angle. " # is constant at every point of the triple line and is given by Young's equation:

cos " # = ! -! (3)
For non-ideal solids (i.e. rough and / or chemically heterogeneous), the contact angle θ is not unique but lies between a receding contact angle " ) and an advancing contact angle " * . This is called the contact angle hysteresis.

Wenzel's and Cassie's equation

As mentioned earlier, the Young's equation is only valid for a smooth and chemically homogeneous surface. Wenzel 5) and Cassie 6) were among the first ones to be interested in the equilibrium contact angle obtained on rough and heterogeneous surfaces (Figures 1b and1c).

On a randomly rough substrate (Figure 1b), the apparent contact angle at the macroscopic scale " $ is given by Wenzel's law. Let us consider an infinitesimal displacement + of the triple contact line on the homogeneous rough surface. The change in the Helmholtz free energy , $ associated with this infinitesimal displacement per unit length of the triple contact line is given by: , $ = ! -! -$ + + cos " $ + (4) Assuming that the local contact angle corresponds to the Young contact angle (Eq. 3), the macroscopic contact angle " can be given by Wenzel's law at equilibrium ( , $ = 0): /01" $ = -$ × /01" # (5) with -$ the surface roughness, also called Wenzel's roughness, defined by the ratio between the actual surface area and its apparent value obtained by the horizontal plane (-$ ≥ 1).

Let us now consider the case of a smooth and randomly heterogeneous surface (Figure 1c), consisting of two different solids 1 and 2, with Young contact angles " #4 and " # and surface area fractions 5 4 and 5 = 1 -5 4 . An infinitesimal displacement + of the triple contact line on the surface causes a change in the Helmholtz free energy , % per unit length of the triple contact line:

, % = ! 4 -! 4 5 4 + + ! -! 5 + + cos " % + (6) where ! 6 and ! 6 are the surface energies for the solid / liquid and solid / vapour interfaces of solid i (i = 1 or 2). At equilibrium, the apparent contact angle is given by Cassie's law: /01" % = 5 4 /01" #4 + 5 /01" # (7)

METHODS OF MEASURING WETTABILITY PARAMETERS

At high temperature, wetting can be studied by means of the sessile drop method or the wetting balance technique. There are several variants of the sessile drop method: classic technique, in-situ formation of a liquid alloy, dispensed drop, transferred drop, double substrate and tilted plate [START_REF] Eustathopoulos | Wettability at High Temperatures[END_REF] .

The dispensed drop technique is particularly well suited to study the wettability by liquid metals. With this technique, a liquid droplet is released on a solid sample (Figure 2) and its spreading is filmed using a high-speed camera (Figure 3). The parameters characteristic of wetting can be determined from the images of the film. The impact velocity 7 8 of the droplet on the solid substrate is given by:

7 8 = 7 9 + 1 2 : ; <)=> (8)
where 7 9 is the average velocity, i.e. the ratio of the displacement h of the droplet (from the capillary exit to the substrate) to the time ; <)=> it had taken to cover that displacement (Figures 2a and2d) and g is the gravitational acceleration. The initial kinetic energy of the droplet is therefore given by:

? @8 = 1 2 A 7 8 (9)
The spreading diameter and the left and right contact angles can be measured as a function of spreading time as shown in Figure 3 (t = 1000 ms). The contact angle hysteresis can also be determined when the drop advances and reaches a maximal spreading diameter before receding. The spreading rate of the triple line is then zero for a few ms, which makes it possible to measure the advancing and receding contact angles. This is the case when the initial kinetic energy of the drop is high enough. In hot-dip galvanizing, the wetting of the steel substrate by liquid zinc is the necessary condition to ensure the adhesion and homogeneity of zinc coating. As it was already mentioned in the Introduction section, before immersion in the liquid metal bath, steel undergoes an annealing treatment at about 800°C in a reducing atmosphere N2-H2 (5 to 15 vol.%) containing traces of water (about -30°C frost point). During this treatment, the iron oxides are reduced and the less-noble alloying elements of the steel (e.g., Si, Mn, Al) segregate to the steel surface where they form oxide particles or films that are poorly wetted by liquid zinc 8,9) . Several studies have investigated the influence of steel oxidation on wettability by liquid zinc [10][11][12][13][14][15][16][17] . In these experimental studies, the wettability by liquid zinc alloys of heterogeneous surfaces composed of metallic iron and oxides was investigated at approximately 460°C by means of the wetting balance technique 10,11) or the dispensed drop method [12][13][14][15][16][17] . It was shown that wettability is deteriorated (i.e., higher contact angle, slower wetting rate) if the surface area fraction covered by oxides is increased.

a) t = 0 ms b) t = 2 ms c) t = 5 ms d) t = 6 ms = tdrop
Two examples of studies performed by means of the dispensed drop technique in the field of hot-dip galvanizing will be presented below: 1) the forced wetting of a partly oxidized steel by liquid Zn -Al and 2) the influence of the surface area fraction covered by silica (for heterogeneous surfaces composed of silica and iron) on the final contact angle of a liquid Zn -Al droplet at short contact time.

FORCED WETTING OF A PARTLY OXIDIZED STEEL BY LIQUID ZN -AL

The forced wetting of a partly oxidized steel by liquid Zn -Al was investigated by means of the dispensed drop technique. The spreading of the liquid metal droplet as a function of its initial kinetic energy was observed and filmed.

Brief description of the dispensed drop experiments

The experimental system is described in details elsewhere 18) . The solid substrate is first heated to 850 ± 2°C in 1 hour in an atmosphere of N2-5 vol.% H2 with a frost point equal to -45°C. It is then cooled down to 452 ± 4°C and maintained at this temperature. The liquid metal droplet is then released on the solid substrate at the same temperature. For these trials, the impact velocity 7 8 of the droplet on the solid substrate was increased from 0.6 to 1.5 m s -1 . The spreading of the liquid metal droplet on the solid sample is filmed by means of a high-speed camera (pco.1200hs) with a recording speed of 1000 images per second and a 780 × 501 pixel resolution. During the wettability experiments, the frost point in the furnace chamber is equal to -54 ± 3°C (i.e., partial pressure of water of 1.6 -3.5 Pa). This frost point corresponds to a partial pressure of oxygen in the range of 3.10 -32 -7.10 -33 Pa at 450°C (assuming that the thermodynamic equilibrium is reached). An image analysis procedure is performed to obtain the experimental contour of the droplet. Contact angles and spreading diameters are calculated by means of the Drop Snake Approach 19) with ImageJ software [START_REF] Rasband | Image J[END_REF] . The error of the contact angle has been estimated to be less than ± 5°.

Materials

The wettability experiments were performed on a cold-rolled Interstitial Free Titanium (IF Ti) ferritic steel (ArcelorMittal). Its composition is listed in Table 1. Before the experiments, the substrates were polished up to 1 µm. The average surface roughness Ra obtained was less than 2 nm. During the annealing treatment described before, the steel substrate became covered with tiny particles (Figures 4a and4b). Mn, Al, Si and O were detected in these particles by Energy Dispersive Spectroscopy (EDS Princeton Gamma-Tech in a Field Emission Gun Scanning Electron Microscope FEG-SEM LEO 1530). Thermodynamic calculations show that iron oxides are completely reduced under the annealing conditions chosen and Mn, Al and Si are oxidized [START_REF] Huin | [END_REF] . The surface studied will then be metallic iron partly covered with oxide particles.

The steel surface also exhibits a strong faceting, varying from one grain to the other. The average roughness Ra and maximum roughness Rt were measured by Atomic Force Microscopy (AFM Digital Instruments Nanoscope IIIA) or 3D optical surface profiler (ZYGO, NView 6K): Ra = 9 ± 2 nm and Rt ~ 100 nm. In all cases, the samples can be presumed to be smooth for the wettability experiments [START_REF] Eustathopoulos | Wettability at High Temperatures[END_REF] . The liquid metal droplets are produced from shots of zinc containing 0.18 ± 0.05 wt.% Al and 0.010 ± 0.010 wt.% Fe. The analysis was performed by Atomic Absorption Spectroscopy (AAS, SpectrAA, Varian). The liquid metal is saturated in iron (liquid phase in equilibrium with Fe2Al5Znx). The droplet weight m is equal to 80.0 ± 0.2 mg in all experiments. If the liquid metal droplet is supposed to be spherical before spreading, its diameter D0 is given by:

(c) A = E 6 F 8 G H 6I (10)
where H 6I is the liquid metal density supposed to be equal to the liquid zinc density (6525 kg.m -3 at 450°C [START_REF] Lucas | Techniques de l'ingénieur[END_REF] ), the Al and Fe contents being very low.

Dynamic spreading of the liquid zinc droplet

The evolution of both the dimensionless diameter and the contact angle as a function of spreading time and initial kinetic energy of the drop are shown in Figure 5. During the first milliseconds of spreading, the contact angle remains constant at a value of about 120° and the spreading diameter increases. The contact angle then decreases sharply until it reaches its minimum value after 14 ms of spreading. Meanwhile, the spreading diameter continues to increase up to its maximum value Dmax. Finally, after approx. 100 ms of spreading, the contact angle and spreading diameter reach their final value. As a conclusion, the final spreading diameter increases and the final contact angle decreases as the drop's initial kinetic energy increases. The wetting between metallic iron and liquid Zn-Al is reactive with the dissolution of iron and the nucleation and growth of Fe2Al5Znx (0<x<1) 8,9) . The preferential dissolution of the solidified droplet makes it possible to highlight the interface compound formed at the iron / Zn-Al alloy interface (Figure 4c). The surface is covered with small crystals, whose shape is characteristic of Fe2Al5Znx observed on industrial products. An EDS analysis confirms that these small crystals are rich in aluminium. The average surface roughness of this interface alloy Ra is of the order of 180 nm.

During the first stage of spreading, until the drop spreading diameter reaches its maximum value, the wetting of the liquid metal drop is forced by its initial kinetic energy. It can be assumed that the initial contact angle (which is high) corresponds to the contact angle of the liquid metal on the partly oxidized solid metal (Figures 4a and4b) before the formation of the interface alloy. The final contact angle corresponds to the contact angle obtained on Fe2Al5Znx.

The final contact angle is unique and given by the Young contact angle for a smooth and chemically homogeneous surface (Eq. 3). In our case, the final contact angle decreases with the increasing initial kinetic energy of the drop, which means that the liquid zinc drop remains pinned in a metastable position. In fact, the interfacial reaction occurring during drop spreading blocks the receding of the droplet. Consequently, the contact angle hysteresis in this case is induced by the interfacial reactivity.

WETTING OF IRON / SILICA SURFACES BY LIQUID ZN -AL

Wetting experiments were performed by means of the dispensed drop technique. The objective was to study the influence of the surface area fraction covered by silica on the final contact angle of liquid Zn -Al droplets on iron / silica heterogeneous surfaces at short contact time. The final contact angles obtained were compared to Cassie's law (Eq. 7). The experimental setup was described before.

Materials

The wettability experiments were performed on iron -silicon substrates (Goodfellow), with a Si content in the range [0.032, 0.485] wt.% (Table 2). The principal impurities are C (< 0.0015 wt.%), Mn (< 0.003 wt.%), P (< 0.003 wt.%), S (< 0.0025 wt.%), Cr (< 0.005 wt.%), Ti (0.001 wt.%), Al (< 0.003 wt.%) and B (< 0.0017 wt.%). The experimental results are compared with those obtained on a high purity iron substrate (99.98 wt.%, the principal impurities being Si, Mn, Cr and Ti). Before the experiments, the substrates were polished up to 1 µm. The average surface roughness Ra obtained was less than 8 nm. During the annealing treatment described before, the iron -silicon substrates became covered with tiny particles (FeSi0.03, FeSi0.06, FeSi0.08, FeSi0. 1, FeSi0.15) or films (FeSi0.25, FeSi0.5) (Table 2, Figures 6b and6c). Si was detected in these particles and films by Energy Dispersive Spectroscopy (EDS Princeton Gamma-Tech in a Field Emission Gun Scanning Electron Microscope FEG-SEM LEO 1530). The Iron surface exhibits a strong faceting, varying from one grain to the other, and a thermal grooving of grain boundaries. A few rare globular shaped particles can be observed (Figure 6a).

Thermodynamic calculations show that iron oxides are completely reduced under the annealing conditions chosen and silicon is oxidized into SiO2 [START_REF] Huin | [END_REF] . The surfaces studied will then be pure metallic iron for the Iron samples and metallic iron partly or completely covered with SiO2 particles or films for the iron-silicon substrates. An image analysis procedure is used to estimate the percentage in surface area covered by silica fsilica for the Fe-Si alloys after annealing. fsilica varies from 0.2 to 100 %.

The average roughness Ra and maximum roughness Rt measured by Atomic Force Microscopy (AFM Digital Instruments Nanoscope IIIA) or 3D optical surface profiler (ZYGO, NView 6K) are given in Table 2 for each sort of sample. The average roughness Ra is less than 8 nm. The grain-boundary grooves formed on Iron substrates (given by Rt values) do not cause any distortion of the triple line. In all cases, the samples can be presumed to be smooth for the wettability experiments [START_REF] Eustathopoulos | Wettability at High Temperatures[END_REF] . The effect of the Wenzel's roughness (Eq. 5) will therefore be presumed to be negligible.

Ra (nm) 2 ± 1 2 ± 1 2 ± 1 8 ± 1 7 ± 1 3 ± 1 4 ± 1 5 ± 1 4 ± 1

Final contact angles

This part of the study is focused on the final contact angle " J reached at the end of the spreading as a function of the surface area fraction covered by silica from pure iron to pure silica (Table 2). In Figure 7, the experimental points obtained are represented by red squares and compared to the Cassie contact angle (Eq. 7) estimated in two cases: • The drop can penetrate between the silica particles or films and be in contact with the Fe2Al5Znx formed and silica. At equilibrium, the apparent contact angle is related to the Young contact angles on Fe2Al5Znx and silica and to the Wenzel roughness -$ . As the average roughness Ra and the maximum roughness Rt are low, the samples can be presumed to be smooth for the wettability experiments, i.e. -$ = 1. The equilibrium contact angle is then given by: /01" % = 1 -5 K6L6M* /01" Fe2Al5Zn+ + 5 K6L6M* /01" K6L6M* (11) where " Fe2Al5Zn+ and " K6L6M* are the Young contact angles on Fe2Al5Znx and silica respectively and 5 K6L6M* is given in Table 2. The Cassie contact angle is represented by the blue curve in Figure 7.

• Conversely, the drop can remain in contact with an air / substrate composite surface. Assuming that the contact angle in air is " TUV = 180°, the apparent contact angle is then related to 5 K6L6M* and " K6L6M* only:

/01" % = -1 + 5 K6L6M* + 5 K6L6M* /01" K6L6M* (12) The Cassie contact angle obtained is represented by the pink curve in Figure 7. In our experiments, pure iron is wetted by liquid Zn-Al alloy (0.2 wt.%) saturated in iron with a contact angle of about 22°. This contact angle is of the same order of magnitude as the measurements found in the literature for the iron / zinc system at short contact times 23) . Silica is not wetted by the Zn-Al alloy used. The high contact angle obtained (157°) is of the same order of magnitude as the contact angle measured for zinc on vitreous silica (133° to 500°C 24) ). The final contact angle increases with the surface area fraction covered by silica. This is in good agreement with previous results found in the same experimental conditions, i.e. wetting by Zn -Al (0.2 wt.%) alloy of Fe /Si substrates annealed under a N2 / H2 atmosphere at low dew point 26) . The authors showed that the higher the silicon content in the alloy, the higher the final contact angle. However, they did not measure the corresponding surface area fraction of silica as we did.

The contact angles measured for the iron / silica substrate with fsilica = 34% are very different from each other: among the six angles measured for this system, three are high (about 150°) and three are low (about 40°). It therefore seems that the transition between wetting and non-wetting corresponds to surface area fractions covered by silica of about 34% with the experimental conditions used here.

For surface area fractions covered by silica below this limit of 34%, the Fe / SiO2 substrates are wetted by the liquid metal with a contact angle lower than the Cassie contact angle estimated on Fe2Al5Znx / SiO2 substrates. The explanation might be that the initial wetting of the liquid metal drop is forced by the kinetic energy of the droplet. The droplet is then receding before reaching its final position. In our experiments, the surface defects are the oxide particles which are less wetted than metallic iron by liquid Zn -Al and represent barriers for advancing and receding liquid front. Moreover, the formation of the interfacial product (Fe2Al5Znx) creates a complementary barrier to receding of the liquid. Thus, the final contact angle is then a receding contact angle close to the contact angle measured on the better wetted parts of the surface (here Fe2Al5Znx formed on metallic iron).

For surface area fractions covered by silica more than 34%, the final contact angle is close to the Cassie contact angle calculated on air / SiO2 substrates. This means that, in this case, bubbles are trapped in between the silica particles or films (no intimate contact between metallic iron and liquid alloy is created).

CONCLUSION

Wetting refers to the study of how a liquid deposited on a solid (or liquid) substrate spreads out. To begin with, the main features of wetting were defined, namely the surface energy, the triple line, the static and dynamic contact angles and the contact angle hysteresis. Then, simple models used to predict the equilibrium contact angle in the case of ideal surfaces (Young's equation) and rough or heterogeneous surfaces (Wenzel's and Cassie's equations) were presented.

Wetting can be studied at the laboratory scale by means of the dispensed drop technique, in which a liquid droplet is released on a solid sample and its spreading is filmed using a high-speed camera. This technique was described in detail together with the parameters characteristic of the wetting which can be determined, e.g. the impact velocity of the droplet on the solid substrate, the spreading diameter, the left and right contact angles, the contact angle hysteresis.

Two examples of studies performed by means of the dispensed drop technique were presented in the field of hot-dip galvanizing:

1) The forced wetting of a partly oxidized steel by liquid Zn -Al was investigated. The spreading of the liquid metal droplet as a function of its initial kinetic energy was observed and filmed. The final contact angle decreases significantly when the kinetic energy of the droplet is increased. The experimental results can be related to the reactions occurring at the interface between the steel and the molten metal at very short contact time.

2) Wetting experiments were performed to measure the final contact angle of a liquid Zn -Al droplet as a function of the surface area fraction covered by silica (for heterogeneous surfaces composed of silica particles or films and iron) at short contact time. The spreading of the liquid metal droplet strongly depends on the surface area fraction covered by silica. The transition between wetting and non-wetting was found for surface area fractions covered by silica of about 34% with the experimental conditions used here. The final contact angles obtained were compared to Cassie's equation. This shows that, for fsilica < 34%, the final contact angle is a receding contact angle on iron parts of the surface and for fsilica > 34% bubbles are trapped in between silica particles or films due to a high non-wetting contact angle.

Figure 1 :

 1 Figure 1: A small droplet in equilibrium on a) a flat horizontal surface (Young contact angle " = " # ), b) a rough surface (Wenzel contact angle " = " $ ) and c) an heterogeneous surface (Cassie contact angle " = " % ).

Figure 2 :Figure 3 :

 23 Figure 3: Spreading of a liquid lead droplet on SiO2 at 450°C. The initial spreading is followed by a dewetting and a rebound of the liquid metal droplet.

Figure 4 :

 4 Figure 4: a) FEG-SEM and b) AFM images of the steel surface after annealing, c) FEG-SEM image of Fe2Al5Znx formed at the interface between solid metal and liquid Zn-Al (after preferential dissolution of the solidified drop).

Figure 5 :

 5 Figure 5: Effect of the initial kinetic energy of the zinc alloy droplet on the evolution of the dimensionless spreading diameter D/D0 (left) and the contact angle (right) as a function of time.

  P stands for small discrete SiO2 particles; (b) F for SiO2 films.

Figure 6 :

 6 Figure 6: FEG-SEM images of the substrate surface after the annealing treatment for a) Iron, b) FeSi0.08 and c) FeSi0.25 alloys. The FeSi0.08 alloy is covered with globular SiO2 particles and the FeSi0.25 alloy surface is completely covered by a SiO2 film.

Figure 7 :

 7 Figure 7: Final contact angles (red squares) between liquid Zn-Al and iron / silica substrates as a function of the surface area fraction covered by silica. The experimental points are compared with the Cassie contact angles estimated for the drop in contact with silica and air (pink curve) or silica and Fe2Al5Znx (blue curve)

Table 1 :

 1 Average composition of the IF Ti steel studied (wt.%)

	C	Si	Mn	P	Al	Cr	Ti	B	S	N	V	As	Cu	Ni	Sn
	0.002	0.009	0.117	0.013	0.027	0.017	0.074	0.0001 0.008	0.005	0.002	0.002	0.018	0.023	0.004

Table 2 :

 2 Characterization of the substrates after the annealing treatment (surface area fraction covered by silica fsilica, average surface roughness Ra, maximum roughness Rt)

		Iron	FeSi0.03 FeSi0.06 FeSi0.06 FeSi0.08 FeSi0.1	FeSi0.15 FeSi0.25 FeSi0.5
	Si (wt.%)	0.0002	0.032	0.057	0.061	0.077	0.097	0.150	0.245	0.485

ACKNOWLEDGEMENTS

The authors are extremely grateful to the staff of CentraleSupélec for their valuable assistance (N. Ruscasiser, A. Ollivier, J. Diawara, J. Trubuil). They extend their thanks to Jean-Michel Mataigne for fruitful discussions.