Jérôme Crassous
email: jerome.crassous@univ-rennes1.fr

Patrick Chasle

Arnaud Saint-Jalmes Juliette Pierre

Benjamin Dollet

Synchronized Diffusive Wave Spectroscopy: Principle and Application to Sound Propagation in Aqueous Foams

Keywords: numbers: 42.25.Dd Wave propagation in random media, 78.35.+c Brillouin and Rayleigh scattering; other light scattering, 62.20.F-Deformation and plasticity 83.80.Iz Emulsions and foams

We present an experimental method to measure oscillatory strains in turbid material. The material is illuminated with a laser, and the speckle patterns are recorded. The analysis of the deformations of the optical pathlength shows that the speckle patterns are modulated at the strain frequency. By recording those patterns synchronously with the strain source, we are able to measure the amplitude and the phase of the strain. This method is tested on the specific case of an aqueous foam where an acoustic wave propagates. The effects of material internal dynamics and of heterogeneous deformations are also discussed.

Soft materials are commonly used in the food, cosmetics and pharmaceutical industries; this is in part due to the wide range of texture and rheology which can be encountered when dealing with gels, pastes, concentrated colloidal solutions, foams or emulsions. Together with these mechanical aspects, the ability to encapsulate and deliver chemicals provides some increased interest in such materials. As well, the non-trivial and often dispersive nature of wave propagation in such materials is also another specificity which can be optimized to get original thermal or acoustical macroscopic properties. The drawbacks of such a high potentiality in applications are the structural and dynamical complexity of such soft materials; they are disordered, often opaque, and generally driven in a out-of-equilibrium state as they are formed. This results in time evolution (aging) and complex intrinsic dynamical mechanisms, with possible intermittency and heterogeneity in space and time. Understanding these evolutions inside the materials remains a generic and important issue. It is for instance important to determine the microscopic origins of the intrinsic rearrangements, and how they can be coupled and superimposed onto rearrangements induced by external forcing. As well, transport properties and wave propagation in such disordered and amorphous materials need to be investigated, both on fundamental and practical standpoints. Numerous techniques to scan these materials have been developed, especially light scattering methods, taking advantage of being non-intrusive. When dealing with turbid media, diffusive wave spectroscopy (DWS) is well suited, as it can monitor the internal dynamics in highly diffusive samples [START_REF] Pine | Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit[END_REF][START_REF]Dynamic Light Scattering: The Method and Some Applications[END_REF]. This technique has been improved in different ways to better resolve the space and time fluctuations, to reduce the measurement timescales, and to get more information on the homogeneity of the dynamics [START_REF] Kirsch | [END_REF][4][5][6][7][8][START_REF] Bandyopadhyay | Speckle-visibility spectroscopy: A tool to study time-varying dynamics[END_REF]. Despite these improvements, the optimization of existing light scattering methods or the design of new ones remains an active axis of research.

As a typical example of soft, opaque and aging materials, aqueous foams -dispersions of gas into a liquidhave been used as model systems to test and demonstrate the efficiency of DWS [START_REF] Durian | Scaling behavior in shaving cream[END_REF][START_REF] Durian | Multiple light-scattering probes of foam structure and dynamics[END_REF]. With time, DWS actually became a major tool for investigating foams and has provided important insights on foam properties at the scale of the bubbles, especially when it was coupled to macroscopic rheology [START_REF] Hohler | Multiple light scattering as a probe of foams and emulsions[END_REF][START_REF] Hohler | [END_REF]. However, and despite their wide use in industries and active academic studies [START_REF] Prud | Foams: Theory, Measurements, and Applications[END_REF][START_REF] Cantat | Foams -Structure and Dynamics[END_REF], various issues on aqueous foams remain open. These pending problems mostly concern (i) the time destabilization of a foam and how this can be controlled by the physicochemical parameters, and (ii) the rheology of foams and its specificities when compared to other soft glassy materials. In that respect, new progress requires techniques to follow how the bubble diameter D and the foam liquid fraction φ l evolve in time; in fact, as a consequence of drainage and coarsening, these two crucial quantities can hardly be kept constant, as the bubble diameter increases with time and the initial liquid content of the foam decreases with time. Optical and electrical methods can be used to monitor these aging effects, but the whole evolution of D and φ l can still not be simply inferred with these techniques. More recently, the acoustic properties of aqueous foams have also been widely investigated, with the aim to design original methods to probe foam properties [START_REF] Kann | Sound waves in foams[END_REF][START_REF] Salem | Propagation of ultrasound in aqueous foams: bubble size dependence and resonance effects[END_REF][START_REF] Pierre | A technique for measuring velocity and attenuation of ultrasound in liquid foams[END_REF][START_REF] Pierre | Acoustic characterization of liquid foams with an impedance tube[END_REF][START_REF] Pierre | Resonant acoustic propagation and negative density in liquid foams[END_REF][START_REF] Pierre | Sound propagation in liquid foams: Unraveling the balance between physical and chemical parameters[END_REF]. The propagation of sound in foams turns out to be quite complex, with non-trivial effects, like the occurrence of negative density [START_REF] Pierre | Resonant acoustic propagation and negative density in liquid foams[END_REF]. Though promising, the experimental approach based on transducers add also some experimental limitations due to the mismatch of acoustic impedance between the transducer and the foam; hence, the injected acoustic wave depends on the foam properties itself. As a consequence, measuring all the sound features into a foam remains tricky. As an alternative, the direct measurement of the acoustic de-

A C C E P T E D M A N U S C R I P T 2
formation (amplitude and phase) at any given location is another approach to extract the sound velocity and its attenuation. Along this direction, we previously showed that the acoustic deformation can be detected by DWS [START_REF] Erpelding | Investigating acoustic-induced deformations in a foam using multiple light scattering[END_REF]. This was a first attempt to use light scattering techniques to investigate the sound propagation into a foam.

The method described in [START_REF] Erpelding | Investigating acoustic-induced deformations in a foam using multiple light scattering[END_REF] allows only to obtain the amplitude of the acoustic waves. The phase of the wave may be obtained by synchronizing the acquisition of scattered light with the acoustic signal. This has been done by Wintzenrieth et al [START_REF] Wintzenrieth | Laser-speckle-visibility acoustic spectroscopy in soft turbid media[END_REF]. These authors used a method based on the visibility of the speckle pattern [START_REF] Bandyopadhyay | Speckle-visibility spectroscopy: A tool to study time-varying dynamics[END_REF]. The variations of the phase difference between the beginning of time integration and the harmonic excitation produces a variation of the visibility. The relative phase between the excitation and material deformation may then be obtained.

Following those previous works, we propose here another DWS experimental scheme where the deformation amplitude and phase can be inferred from synchronized measurements and the combination of four partial correlation functions. The system chosen to make this proof of concept consists in an aqueous foam, where the shear arises from an acoustic forcing. This method is tested on the acoustics propagation into a liquid foam and compared to previous measurements.

In this article, we first describe this DWS scheme, named "Synchronized DWS", and present the mathematical formalism -valid for any diffusive system under a sinusoidal shear deformation -showing that the shear amplitude and phase of this deformation can be derived by measuring four different correlation functions, monitored synchronously with the deformation. Then, we explain how this can be tested by doing experiments on foams under an acoustic forcing. Various results are presented, either at a given location for different imposed amplitude and phase, or while scanning the foam as a function of the distance from the source. Further experimental tests, discussions and comparisons are given in the last section.

II. SYNCHRONIZED DIFFUSING WAVE SPECTROSCOPY A. Principle of the method

Diffusing wave spectroscopy is a experimental tool which has been successfully used for concentrated colloidal suspensions, emulsions, foams or granular materials. The principle of DWS is to record multiply scattered coherent light, and to monitor the time evolution of this scattered light, in terms of correlation functions. Shortly speaking, the correlation of the scattered intensity arises from interference between many photon paths. If a system is at rest, the interference pattern is frozen, and the scattered intensity does not show temporal evolution. If scatterers move inside the sample, interference pattern fluctuates, and the intensity correlation function decreases with time. We consider here the case of a physical system of scatterers which is periodically sheared at frequency T . We plot in Fig. 1a a sinusoidal shear deformation. Fig. 1b shows an optical path joining some scatterers. Since they are displaced into the sheared zone, the path is also periodically deformed. Let t 0 be a time at which the strain vanishes. The paths at times t 0 +T /4 and t 0 + 3T /4 are symmetrically sheared. This shear induce a phase shift along this ray, thus a loss of correlation of the scattered light between these two times. The amplitude of the shear may then be related to this loss of correlation. Because γ(t 0 ) = γ(t 0 + T /2), the paths at times t 0 and t 0 + T /2 are identical. The system appears frozen, and the intensity of the scattered line is perfectly correlated. Hence, the time t 0 may be deduced from the maximum of correlation of speckle patterns acquired at time t and t + T /2. The phase difference between the shear at a given point of the material and the source of the shear may then be estimated. Therefore, in principle, by a synchronized monitoring at times t, t + T /4, t + T /2 and t+3T /4, one can derive the amplitude and the phase of the deformation. The derivation of the relevant mathematical combinations allowing us to get these quantities from the partial correlations is given below. The principle of parallel lock-in detection that we use is not new and has been used in detection of ultrasonic modulation such as described in [START_REF] Lévêque | Ultrasonic tagging of photon paths in scattering media:?parallel speckle modulation processing[END_REF][START_REF] Yao | Theoretical and exper-imental studies of ultrasound-modulated optical tomography in biological tissue[END_REF], but to our knowledge never used with DWS. In the following, we note l * the transport mean free path into the material, f = 1/T the frequency of the strain modulation and ω = 2πf . The length of a photon path into the sample is noted s. We consider here a parallel detection of the scattered light. For this a camera is used as sensor, and the intensity of many pixels are measured simultaneously. We note I(t) the array of scattered intensity acquired at a time t. We compute the normalized correlation function of the scattered intensity:

g I (t, t + τ ) = I(t)I(t + τ ) -I 2 I 2 -I 2 , ( 1
)
where • is here an average on the pixels of the camera. The electronic noise of the camera is removed following a procedure explained in [START_REF] Djaoui | Probing creep motion in granular materials with light scattering[END_REF]. The normalization of the correlation function ensured that g I (t, t) = 1 whatever the contrast of the image. From the Siegert relation g

I (t, t + τ ) = |g E (t, t + τ )| 2
we obtain the normalized correlation function of the scattered electric field

E : g E (t, t + τ ) = (1/I 0 ) E * (t) • E(t + τ ) .
The normalization constant I 0 is the mean scattered intensity.

The autocorrelation function of the scattered electric field may be decomposed as a sum on paths of length s [START_REF] Pine | Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit[END_REF][START_REF]Dynamic Light Scattering: The Method and Some Applications[END_REF]:

g E (t, t + τ ) = s P (s) exp ∆φ s (t, t + τ ) ds. (2)
In (2), P (s) is the normalized path length distribution with s P (s)ds = 1. The complex exponential function is averaged on all paths of length s, and ∆φ s (t, t + τ ) is the phase shift for a path of length s. We drop in the following the two times t and t + τ in equations. Such paths may be decomposed in s/l * independent segments of length l * . It then follows that ∆φ s = s/l * j=1 ∆φ j , with ∆φ j the phase variation of the segment number j between times t and t + τ . Since ∆φ s is the sum of many independent variables, it is a Gaussian random variable, and then:

exp(∆φ s ) = exp - 1 2 ∆φ 2 s = exp   - 1 2 s/l * j=1 ∆φ 2 j   . (3)
In (3), • is an average on all orientations of the segments, and we also assume that ∆φ j = 0, i.e. there is no dilatation of compression of the medium. If the deformation is homogeneous, ∆φ 2 j does not depend on the number of the segment, and s/l * j=1 ∆φ 2 j = s ∆φ 2 /l * . For small enough phase shifts, exp s ∆φ 2 /2l * 1s ∆φ 2 /2l * and (2) becomes: g E (t, t + τ ) s P (s)[1s ∆φ 2 /2l * ]ds. After integration we obtain:

g E (t, t + τ ) 1 -A ∆φ 2 (t, t + τ ) , (4)
with A a constant depending on P (s). Following the approach detailed in numerous studies [27? -29] we now relate ∆φ 2 to the deformation of the material. We consider a segment joining the points r and r + l * e with e the unit vector joining the two points as shown on Fig. 1c. The displacements at time t are A(r, t) and A(r+l * e, t), and the new distance between the two points is l * 1 + (e • ∇)A(r, t) • e . The variation of the phase between the two times t and t + τ is then k times the difference of length:

∆φ = kl * (e • ∇) A(r, t + τ ) -A(r, t) • e. ( 5
)
For a harmonic displacement with a polarization along the unit vector a, we can write A(r, t) = [α(r) cos(ωt) + β(r) sin(ωt)]a. The phase variation is then:

∆φ 2kl * (e • a) sin(ωτ /2) -e • ∇α(r) sin(ωt + ωτ /2) + e • ∇β(r) cos(ωt + ωτ /2) . (6)
For simplicity, we suppose that ∇α(r) and ∇β(r) are parallel to the same unit vector n. We will justify this assumption for our experiments in Sec. IV C. We may then write:

∇α(r) = γ(r) cos Ψ 0 (r) n (7a) ∇β(r) = -γ(r) sin Ψ 0 (r) n, (7b)
with γ(r) the amplitude and Ψ 0 (r) the phase of the deformation. Performing average on segment orientations:

∆φ 2 4k 2 l * 2 η(a, n)γ 2 (r) sin 2 (ωτ /2) × sin 2 (ωt + ωτ /2 + Ψ 0 (r)) (8)
with η(a, n) = (e • a) 2 (e • n) 2 e . For transverse waves η(a, n) = 2/15. Combining with (7), we finally obtain:

γ 2 (r) sin 2 (ωτ /2) × sin 2 (ωt + ωτ /2 + Ψ 0 (r)) C × [1 -g E (t, t + τ )], (9)
with C a constant depending on geometry and of optical constants.

C. Synchronized acquisition

The correlation functions are now measured at four different combinations of times t(mod T ) and t + τ (mod T ):

g (1) = g E (0, T /2) (10a) g (2) = g E (T /4, 3T /4) (10b)
g (3) = g E (0, T /4) (10c)

g (4) = g E (T /4, T /2). (10d)
With ( 9), we have:

A C C E P T E D M A N U S C R I P T 4 C × [1 -g (1) ] = γ 2 (r) sin 2 [Ψ 0 (r) + π/2] (11a) C × [1 -g (2) ] = γ 2 (r) sin 2 [Ψ 0 (r) + π] (11b) C × [1 -g (3) ] = 1 2 γ 2 (r) sin 2 [Ψ 0 (r) + π/4] (11c) C × [1 -g (4) ] = 1 2 γ 2 (r) sin 2 [Ψ 0 (r) + 3π/4], (11d)
and then:

γ 2 (r) = C × 2 -g (1)
-g (2) , (12a) cot 2Ψ 0 (r) = g (1) -g (2) 2 -g (1) -g (2) / g (3) -g (4) 2 -g (3) -g (4) . (12b)

The amplitude and the phase of the shear may then be simply obtained with the above combinations of correlation functions, all measured synchronously with the harmonic excitation. The preceding formalism is in principle applicable to every scattering medium which is periodically sheared. In order to test this formalism, we performed experiment on aqueous foams, in which we apply a sinusoidal deformation by an external acoustic forcing. In our geometry, the strain occurs because there is a displacement field generated by the acoustic wave into the bulk, and no acoustic displacement at the glass walls [START_REF] Erpelding | Investigating acoustic-induced deformations in a foam using multiple light scattering[END_REF]. This creates a periodically sheared layer near the lateral glass boundaries. The structure of this sheared layer will be discussed in Sec. IV C.

The experimental setup is drawn on Fig. 2. A cylindrical glass container (diameter 19 cm, height 50 cm) is filled with a liquid foam. A loudspeaker is placed above the cylinder, and generates a acoustic wave at a frequency f . The acoustic wave emitted by the loudspeaker is partially reflected by the foam surface, and partially transmitted within the foam. The sheared layer is illuminated with the beam of a continuous laser (633 nm, 15 mW). The beam is slightly expanded to a diameter of a few millimeters and illuminates the foam. The scattered light is recorded with a CSMOS camera (Photon-Focus MV1-D1312-160-CL) operating at a frequency 4f : sequences of images at 4f are acquired in a burst mode. The beginning of the acquisition sequence is triggered synchronously to the loudspeaker excitation. A delay between the trigger and the first acquired image may be added in order to imposed a given phase shift ψ (imp) 0

. All the experiments presented here have been performed at frequency f = 800 Hz and the exposure time of every image is 11 µs. The number of pixels of each image is N p = 13120.

The liquid foam is made using the method described in [30]: it provides large quantities of homogeneous foam, with initial bubble size of the order of 100 microns in diameter. The production rate is 0.1 L/s, so that our 50-cm high cell is filled in 1 min. The gas used is C 2 F 6 , to slow down the coarsening [31]. Experiments are performed after waiting times between 30 mn to 5 hours, corresponding to bubble diameter of 200 to 700 microns. For the experimental results shown here, we used sodium dodecyl sulfate (SDS) as surfactant, with a concentration equal to 10 times the surfactant critical micelle concentration (cmc). The initial liquid fraction is φ l 5%. Complementary tests were made using a more complex chemical formulation, providing a high interfacial viscoelasticity [START_REF] Golemanov | Surfactant mixtures for control of bubble surface mobility in foam studies[END_REF].

B. Computations of correlation functions

The raw data are a numbered succession of images of N p = 13120 pixels acquired at intervals 1/4f = 312.5 µs. Because the light intensity levels are low, we need to carefully remove the electronic noise of the sensor. We define the normalized intensity correlation function between two images n and m as:

g n,m I = I m I n -I m I n -a elec -b elec δ nm I 2 n -I n 2 -a elec -b elec (13)
We noted I n the intensity vector of N p pixels of the image n, and • designs here an average on all the pixels. We checked that the electronic noise i n is such that

i n i m = a elec + b elec δ nm .
The values of a elec and b elec are determined by an independent measurement, and we checked that for a well aged foam at rest, we get g n,m n I = 0 and g n,n+1 I = 1. For a cycle of oscillation n, we compute the quantities

I (n) = 1 2 (g 4n,4n+2 I + g 4n+2,4n+4 I ) (14b) g (2)
I (n) = 1 2 (g 4n+1,4n+3 I + g 4n+3,4n+5 I ) (14c) g (3)
I (n) = 1 2 (g 4n,4n+1 I + g 4n+1,4n+4 I ) (14d) g ( 4
)
I (n) = 1 2 (g 4n+1,4n+2 I + g 4n+2,4n+5 I ). ( 14e
)
If we suppose a scattering medium where the dynamics are only due to the acoustic wave (i.e. no internal dynamics), we have for i = 0:

g (i) = g (i) I (4n), ( 15
)
where the g (i) are the quantities defined in [START_REF] Durian | Scaling behavior in shaving cream[END_REF]. The interest of computing g In the following, we will average g (i) on 250 cycles of oscillations, i.e. on sequences of acquisition 0.31 s.

C. Amplitude and phase measurements

In this Section, we demonstrate that we can determine the imposed variation of amplitude and phase -at a given location -from our model of combinations of correlations functions.

The amplitude of the strain is obtained from (12a) as: γ 2 (r) = C × 2 -g (1) -g (1) . We perform experiments where the amplitude of the strain is varied. For this, we change the level of excitation of the loudspeaker. In our experiments, we remain always below 90 dB of acoustic level in air, hence the pressure amplitude in air is below 1 Pa, and it is even lower in foam because only a fraction of acoustic energy is transmitted to the foam. Hence, we remain in the regime of linear acoustics. Indeed, since foam is mostly made of gas, the order of magnitude of its bulk modulus is given by the atmospheric pressure, 10 5 Pa, and deviations from linear acoustics are expected only when the pressure amplitude of the acoustic wave becomes a significant fraction of the bulk modulus.

FIG. 4. Symbols: 1 -(g (1) + g (2) )/2 as a function of the amplitude of excitation of the acoustic wave. The straight line is of slope 2.

Fig. 4 shows the evolution of 1 -(g (1) + g (2) )/2 as the function of the excitation amplitude. Every symbol correspond to one measurement of duration 0.31 s. We see that the decorrelation increases with the amplitude of the acoustic excitation. The straight line is line of slope 2, showing that 1 -(g (1) + g (2) )/2 varies as γ 2 at least at small amplitudes. This is in agreement with (4). It should be remained that (4) has been obtained in the limit of small phase shifts, and deviations to the γ 2 are expected at large strain amplitudes.

The phase of the strain is obtained from (12b). In order to test this relation, we proceed as follow: we fix the amplitude of the acoustic wave, and we begin to acquire images with a given phase shift ψ (imp) 0 (see Sec. III A). Fig. 5a shows the evolution of g (i) as a function of the imposed phase shift ψ (imp) 0

. We see that the correlation functions evolves with the imposed phase shift. As it may be seen from ( 9) and [START_REF] Durian | Scaling behavior in shaving cream[END_REF], advancing the imposed phase of π/2 has the same effect of the permutations of g (1) with g (2) and of g (3) with g (4) , reflecting the ωt + ψ 0 dependence of (9). The phase is obtained from (12b) as: 1) -g (2) 2 -g (1) -g (2) / g (3) -g (4) 2 -g (3) -g (4) (16) The unwrapped phase Ψ 0 calculated from the data of Fig. 5a is plotted on Fig. 5b. As it may be seen, the phase of the acoustic wave is measured with high precision. This shows that the phase of the strain may be extracted from DWS synchronized with the strain source with great accuracy.

Ψ 0 = 1 2 arccot g (

D. Application to the measurement of phase velocity in a foam

Building on the previous experimental proofs of concept at a single position, we investigated how the phase evolve inside a foam as a function of the distance of propagation into our cylindrical cell. This is the relevant experiment in terms of foam acoustics, as it should provide information which can be compared to previous ones. In practice, the laser and the camera are therefore translated of a distance ∆x = 2 mm between successive measurements. The ageing time of the foam is here 45 mn. This is a short enough time to avoid drainage and to prevent liquid fraction variations in the scanned part of the foam [START_REF] Saint | Time evolution of aqueous foams: drainage and coarsening[END_REF].

FIG. 6. Sound phase as a function of the distance of propagation: comparison between the measured phase (symbol) and the model of Eq. ( 17).

Fig. 6 shows the evolution of the phase as a function of the depth. The phase shift is roughly 4π, corresponding to two acoustic wavelengths. In this experiment, the bottom "wall" is the top surface of the drained liquid in the bottom of the glass cylinder. It is located at a the distance H = 202 mm. We see that, far from the bottom of the foam, the phase evolves linearly with the distance; however, small oscillations of the phase occurs as the surface of the drained liquid is approached. Rather than only focusing on the linear regime away from the bottom, we can take into account all these features by including interferences between the propagating and reflected wave into the cylinder. Let u i (x) = u 0 exp[-(jk a + β a )x] be the incident acoustic wave, with u 0 the amplitude, k a the wave vector of the acoustic wave and β a the attenuation coefficient. The reflected wave is u r (x) = Ru 0 exp (jk a + β a )x with R the complex reflection coefficient. We set that, at the bottom, the drained liquid is a perfectly reflecting surface, which yields the boundary condition: u r (H)+u i (H) = 0. This assumption comes from the fact that the acoustic impedance Z = ρc of a foam is orders of magnitude lower than that of the liquid, because both ρ and c are much lower in foam than liquid. It follows that R = e -2(jka+βa)H , and that the argument of u = u r + u i is:

arg u = -jk a x -arctan e -2βa(H-x) sin 2k a (H -x) 1 + e -2βa(H-z) cos 2k a (H -x)
.

(17) The plain line of Fig. 6 shows the evolution of arg(u) as the function of the distance as predicted by [START_REF] Salem | Propagation of ultrasound in aqueous foams: bubble size dependence and resonance effects[END_REF]. The free parameters are k a , β a and a constant phase which is added to arg(u). The shown adjustment is obtained with k a = 0.09 mm -1 and β a = 0.009 mm -1 . The value of the velocity is thus v = ω/k a = 56 m/s. These values fully agree with the previous studies. For the velocity, it is expected to have a value following the Wood's law, valid

A C C E P T E D M A N U S C R I P T
for these bubble sizes and frequencies [START_REF] Pierre | A technique for measuring velocity and attenuation of ultrasound in liquid foams[END_REF][START_REF] Pierre | Acoustic characterization of liquid foams with an impedance tube[END_REF]. Indeed, the Wood's law predicts a velocity of 55 m/s for φ l =0.05. Although we have not monitored the variation of liquid fraction, the fact that this value is so close to the experimental value also suggests that drainage has not modified much the profile of liquid fraction over the height of the foam probed in Fig. 6. Also, Pierre et al. [START_REF] Pierre | Acoustic characterization of liquid foams with an impedance tube[END_REF] have shown by acoustic measurements in an impedance tube that at 800 Hz, the attenuation coefficient equals 8 ± 1 m -1 for SDS foams, a value insensitive (at this frequency) to the liquid fraction, which is in excellent agreement with our measurement.

IV. REMARKS ON THE METHODS AND ON THE EXPERIMENTAL TESTS

Following the experimental tests demonstrating the feasibility of measuring the amplitude and the phase of a acoustic wave propagating into a foam, we want to point out a few other remarks on this synchronized DWS method.

A. Corrections of internal dynamics

We want here to give some information about the sensitivity of the determination of the correlation functions. The first point to address is the effect of the internal dynamics of the scattering medium on the correlation functions. Fig. 3 shows the evolutions of the correlation functions g (i)

I with time. The fluctuations are due to the internal dynamics of the system. Indeed, it is well known that reorganizations occurs in foam which create variations on path lengths [START_REF] Durian | Scaling behavior in shaving cream[END_REF][START_REF] Durian | Multiple light-scattering probes of foam structure and dynamics[END_REF]. When those fluctuations of correlations are small compared to the decorrelations due to the acoustic wave, their effects may be safely neglected. However, in the case of very small strains, their effects must be taken into account. A simple way consists in considering that the internal and the acoustic waves dynamics are uncorrelated. Defining ∆φ int (t, t + τ ) the variation of phase due to the internal dynamic, (4) becomes:

g E (t, t + τ ) 1 -A ∆φ 2 (t, t + τ ) + ∆φ 2 int (t, t + τ ) , (18)
with ∆φ(t, t + τ ) the phase shift due to the acoustic wave. Since ∆φ(t, t + T ) = 0, we have g E (t, t + T ) 1 -A ∆φ 2 int (t, t + T ) . If the internal dynamic is due to many independent rearrangements which occurs at a constant rate between t and t + T , we expect that ∆φ 2 int (t, t + τ ) = (τ /T ) ∆φ 2 int (t, t + T ) , and then:

1 -A ∆φ 2 (t, t + τ ) (19)
g E (t, t + τ )+ τ T 1 -g E (t, t + T )) .
Since all the correlation functions g

I with i = 0 are measured on a the same mean delay τ = T /2, we may re-move the internal dynamics by computing a "corrected" value:

g (i =0) I;corr = g (i =0) I (4n) + 1 2 1 -g (0) I (4n) . (20)
I as a function of an imposed phase shift. Curves are sinusoidal guidelines. Color codes are the same as for Fig. 3 The effect of such a correction is striking on a small amplitude measurement. Fig. 7 shows a measurement where the phase is controlled and the amplitude of the acoustic wave is very small. If the internal dynamics is not corrected, one can hardly detect the evolutions of g (i) with the imposed phase. However as far as the internal dynamics is corrected using [START_REF] Pierre | Resonant acoustic propagation and negative density in liquid foams[END_REF], the variations are clearly visible. This shows that acoustic propagation may be probed even if the internal dynamic dominates the variations of path lengths.

B. Sensitivity and comparison with the stroboscopic method

We want here to quantify the uncertainties on the determination of the amplitude and of the phase. We focus on the noise on measurements during 250 oscillations cycles. Due to the multispeckle scheme used here, the measurement of correlation functions are averaged on many coherence areas. We record images of 13120 pixels, and the coherence area of ≈ 4 pixels. We then have ≈ 3000 coherence areas on every image. Because the scattering medium used here has a internal dynamics, the speckle pattern evolves slowly. The typical timescale of this evo-

A C C E P T E D M A N U S C R I P T 8
lution may be measured in a experiment where no oscillations take place, and we found an evolution time ≈ 0.1 s, which is 1/3 of the experiment duration. With both the time and the multispeckle averages, one phase and amplitude measurement is averaged on ≈ 3×3000 realizations.

The noise for the phase determination is estimated as the difference between the measured and the imposed phase in a experiment where the phase is imposed. We found a typical noise of 0.02 rad, which does not seem to depend strongly on the amplitude of oscillation. The standard deviations on the values of 1 -(g (1) + g (2) )/2 are typically of order 10 -3 when signals are uncorrected from internal dynamics and of 2 × 10 -4 when the signals are corrected. We may then expect to measure 1 -g E on typically 3 orders of magnitude.

An alternative method to characterize mechanical wave in light diffusing medium has been proposed recently by Wintzenrieth et al [START_REF] Wintzenrieth | Laser-speckle-visibility acoustic spectroscopy in soft turbid media[END_REF]. When a scattering medium is submitted to a strain modulation, the contrast of the time-averaged speckle pattern is lowered compared to contrast of the same static medium. This has been used to detect ultrasonic waves in optical tomography measurements [START_REF] Zemp | Stochastic explanation of speckle contrast detection in ultrasound-modulated optical tomography[END_REF]. By synchronizing the beginning of the light acquisition with the acoustic wave, and by measuring the visibility of the speckle pattern, the phase of the strain modulation may be obtained [START_REF] Wintzenrieth | Laser-speckle-visibility acoustic spectroscopy in soft turbid media[END_REF]. A quantitative comparison between this method and the method reported in this study is not straightforward. Such a comparison requires quantitative models for the different sources of noises, for instance noises due to internal dynamics of the scattering medium, or noise due to sensors, and this analysis is far from being trivial. Nevertheless, we may notice that the visibility methods correspond to measurements of correlation functions integrated over time. If g E (t) is the electric field correlation function the visibility is

V (T ) = 1 T T 0 2(1 -t τ )|g E (t)| 2 dt [9]
. It is then easy to show that g E (t) is related to the second time derivative of the visibility:

|g E (t)| 2 = 1 2 d 2 [V (t)t 2 ] dt 2
. Generally speaking, a time derivative is a source of noise. Hence, we may expect that synchronized acquisitions, which avoid such derivatives, allow to obtain correlation functions with a better signal-to-noise ratio. This is in agreement with the fact that we are able to measure 1 -g E on typically 3 orders of magnitude, while Wintzenrieth et al. [START_REF] Wintzenrieth | Laser-speckle-visibility acoustic spectroscopy in soft turbid media[END_REF] obtains a dynamical range for 1 -g E of one order of magnitude. This is also confirmed by numerical simulations where we compared correlations functions obtain directly by correlation of signal, and by correlation functions obtained by time-derivative of visibility. However, only an experimental comparison of the two methods on different experimental systems may quantitatively confirm these differences.

C. Structure of the sheared layer

The method explained in this paper permits to measure the amplitude and the phase of a sheared zone. We discuss in this subsection the origin and the structure of the shear created by an acoustic wave near a solid surface which is perpendicular to the propagation direction of the acoustic wave. In a previous paper [START_REF] Erpelding | Investigating acoustic-induced deformations in a foam using multiple light scattering[END_REF], we have considered the experimental situation of an acoustic wave propagating into a foam. The wave propagates parallel to the wall. Because of the non-slip boundary condition at the boundary, the acoustic displacement cancels at the wall. The variation of the displacement with the distance from the wall occurs in a viscoelastic boundary layer, which depends on the rheology of the material. We treat the foam as a continuous visco-elastic fluid, with ρ the density and G = G 0 exp j∆ the visco-elastic modulus of the material. Let u(z, t) = Re[u(z)e iωt ] be the acoustic displacement, and u 0 = lim z→∞ u(z) the displacement far from the wall. The force balance writes:

ρ ∂ 2 U (z, t) ∂t 2 = G ∂ 2 U (z, t) ∂z 2 , (21)
with U (z, t) = u(z, t) -u 0 . The solution of ( 21) is:

U (z, t) = U 0 exp (jωt) exp (κz), (22)
with U 0 + u 0 the amplitude of displacement at z = 0 and κ = κ 0 exp jϕ. We have κ 0 = ω ρ/G 0 and ϕ = (π -∆)/2. The strain is γ = ∂U (z, t)/∂z = U 0 κ exp (jωt) exp (κz), and we obtain:

|γ(z)| = κ 0 exp [-κ 0 cos(ϕ)z] (23a) Ψ 0 (z) = ϕ + κ 0 sin(ϕ)z. (23b)
In this model, the amplitude and the phase of the strain depend on z. As explained in [START_REF] Erpelding | Investigating acoustic-induced deformations in a foam using multiple light scattering[END_REF], it is this sheared layer that is probed with light scattering. In Sec. II, we made the hypothesis that the deformation is homogeneous into the volume probed by the light. Using this hypothesis, every term of the sum s/l * j=1 ∆φ 2 j of phase shift used in (3) is the same: ∆φ 2 . The deformation being in fact heterogenous, we must consider average values of ∆φ 2 on volumes V s probed by paths of length s:

s/l * j=1 ∆φ 2 j = (s/l * ) ∆φ 2
Vs . Because long paths probe larger volumes than short paths, the volume V s depends on s.

The fact that the phase of the strain is heterogeneous has an interesting consequence. Indeed, let us consider a segment of the random walk located at a distance z from the wall. The variance of the phase shift (8) depends on z:

∆φ 2 (z) ∝ γ 2 (z) sin 2 (ωτ /2) sin 2 [ωt + ωτ /2 + Ψ 0 (z)]. ( 24
)
Since Ψ 0 depends on z, ∆φ 2 (z) cannot be canceled simultaneously at every z. It follows that the correlation function g (i) with i = 0 cannot be equal to one. This is what is observed on the Fig. 5a: the maximum values of the correlation functions are not 1. Complementary experiments with foam of high interfacial viscoelasticity [START_REF] Golemanov | Surfactant mixtures for control of bubble surface mobility in foam studies[END_REF] exhibit higher values of correlation recovery. This property may be used as a useful non-destructive method to Finally, we can justify the assumption on the displacement field made to derive (7) from (6). At the frequency of 800 Hz, the thickness ξ = 1/κ 0 cos(ϕ) of the sheared layer is about 2 mm [START_REF] Erpelding | Investigating acoustic-induced deformations in a foam using multiple light scattering[END_REF], whereas the acoustic wavelength in the foam is λ a = 2π/k a = 6 cm (see Sec. III D). Hence, ξ/λ a 1, and to a good approximation, the displacement field in the sheared layer writes : A(r, t) = [α(z) cos(ωt)+β(z) sin(ωt)]e x , with e x the unit vector in the direction of propagation. Hence, ∇α and ∇β are both along e z .

V. CONCLUSION

We have investigated the situation of a turbid media undergoing a periodical shear, and wondered if and how the amplitude and the phase of this deformation could be locally measured by light scattering. We have proposed a new approach -named here "synchronized DWS"which requires to acquire four different correlations functions. Then by combining these correlations, the amplitude and the phase can be derived, at any locations. This approach has been successfully tested by experiments on foams, where a sinusoidal shear is obtained as an acoustic wave is propagating. In a first set of tests, we have found an excellent agreement between the imposed forcing and the measurements. These first results fully validated the principles and our formalism. Further experiments allowed us to scan a foam as a function of the distance of propagation of the sound. It turns out that we have been able to monitor the phase of the deformation along a few wavelengths. The full analysis -including in-terference effects at the bottom of the vessel -allowed us to quantify the phase velocity and the sound attenuation. The obtained values are in excellent agreement with previous measurements, and definitively confirms that this approach based on the measurement by DWS of the acoustic deformation is relevant. Moreover, we have shown that possible internal dynamics and heterogeneity in space do not prevent these types of measurements, as they can also be taken into account.

In the future, these results can be pursued along different routes. For instance, this method may be used to get information about the shear layer in a direction perpendicular to the displacement. We saw in Sec. IV C that the structure of this sheared layer depends on the rheological properties of the material. Correlation data should then permit to obtain informations about high frequency rheological properties with λ a l * . A deeper understanding will be required to clarify the links between the correlation data and the viscoelasticity of the material. As well, measurements can be done not only in the direction of propagation, but also in the orthogonal one. It is thus possible to create a 2D mapping of the amplitude and of the phase; this might be especially relevant in the cases where sound could be diffracted by obstacles or slits.

FIG. 1 .

 1 FIG. 1. (a) A sinusoidal shear of displacement γ. Time t0 is such that γ(t0) = 0. (b) Snapshots of a portion of optical path (full line) on some scatterers (black circle). The zone is periodically sheared and the path periodically deformed. (c) Variation of a segment joining two points r and r + l * e. A is the displacement field of the scatterers.

3 B

 3 . Link between the intensity correlation function and material deformation

  FIG.2. Schematic drawing of the setup. A cylindrical glass cell is filled with a liquid foam. A loudspeaker generates an acoustic wave. A laser illuminates the foam and the scattered light is detected by a camera. A lens is placed to expand the beam. The camera and the laser may be translated along the z direction.

I

  (n) and of the somewhat tricky definitions of g(i =0) I(n) is to allow some corrections of the scattering medium dynamic. This will be explained in Sec. IV A.

FIG. 3 .

 3 FIG. 3. Correlations functions of the scattered intensities g

I

  (n) as a function the number n of the oscillation cycle. Colors are i = 0: purple, 1: black, 2: red, 3: green and 4: blue.

Fig. 3

 3 Fig. 3 shows the evolution of the function g

I

  (n) as a function of the cycle of oscillation n. In this experiment the value of the acoustic excitation is kept constant, with a fixed phase. g (0) I is close to 1, the fluctuations being due to the intrinsic dynamics of the foam (coarsening events). The values of g (i =0) I fluctuate around their mean values, and the values depend on the partial correlations functions number i.

6 FIG. 5 .

 65 FIG. 5. (a) Variations of g (i) as a function of an imposed phase shift. i = 1: black, 2: red, 3: green and 4: blue. Symbols are results from measurements and continuous curves are sinusoids of period π for eyes guidelines. (b) Computed phase shift as a function of the imposed one. Symbols are measurements and the line is the linear fit with a slope 1.

FIG. 7 .

 7 FIG. 7. Symbols: uncorrected (top) and corrected (bottom) values of g

  of ϕ and will be discussed in a forthcoming paper.

ACKNOWLEDGMENTS

We acknowledge funding support from Agence Nationale de la Recherche in the frame of the SAMOUSSE project (ANR-11-BS09-001, coordinated by Florence Elias). We thank all the participants of this project for fruitful discussions. We also thank the GdR "Mousses et Émulsions" for providing another network for discussions.


Fei Wang

Yinglong Li

Anyuan Deng

Xiujie Xu

Xingwu Zhang

professor, Engang Wang
email: egwang@mail.neu.edu.cn

Continuous casting process of Incoloy800HT superalloy and its quality improvement with electromagnetic fields

Keywords: Superalloy, Continuous casting, Electromagnetic field, Solidification

The superalloy is generally produced in ingot casting mode, which generally brings a lower productivity rates, high costs and some casting defects. In this paper, the billets of Incoloy800HT superalloy are fabricated in a vertical pilot continuous caster with different frequency electromagnetic field, which is respectively applied on the mould zone and secondary cooling zone of continuous caster, and their effects were investigated at different process parameters. The research results show that electromagnetic stirring (EMS) can effectively restrain the dendrites growth and increase the ratio of equiaxed grains, and reduce the shrinkage porosity and segregation in the central of billets. The surface quality of billets also have a greatly improved as applied a high frequency electromagnetic field on the mould. The electromagnetic fields become the key techniques to control the internal and external quality of Incoloy800HT billets.

Moreover, the mechanism of electromagnetic fields is analyzed based on the examination of billets.

Introduction

Incoloy800HT is a single-phase austenitic solid solution Ni-based superalloy, which is extensively used in high temperature environments due to its advantages in high strength and corrosion resistance at high temperatures, such as steam generator tubes, reformer tubes, and gas turbines [START_REF] Donachie | Superalloys a technical guide[END_REF][START_REF] Daris | Metallurgical processing and properties of superalloys[END_REF][START_REF] David | Nickel, cobalt, and their alloys[END_REF][START_REF] Dehmolaei | [END_REF] .

In order to decrease the production cost of the conventional casting of remelted superalloy ingots, a continuous casting process is being developed to replace the conventional casting. So a series of developments in the continuous casting of superalloys have been carried out. However, due to the alloy's wider brittle range [5,6] and solidification condition, some seriously internal and external quality issues of the continuously cast Incoloy800HT superalloy have been revealed, such as coarse column grains, cracks, segregation, coarse surface, etc.

Electromagnetic force generated by different frequency electromagnetic field can be used to control the solidification process for improving internal and external quality of the billets. Therefore, the aim of the present study is to investigate the effect of the combination of high frequency electromagnetic field and EMS on the internal and external quality of Incoloy800HT superalloy in the continuous casting process.

Experimental procedure

The chemical composition of Incoloy800HT used in the present study, given in mass percents, is: 0.08% C, 0.52% Si, 0.80% Mn, 0.023% P, 0.002%, 20.13% Cr, 30.88% Ni, 0.52% Ti, 0.28% Al and rest Fe. The Incoloy800HT bars were melted in a medium frequency induction furnace with a protective argon atmosphere. The melt was heated to 1425℃ and then poured into the vertical continuous caster to obtain two 1200mm in length square billets. A high frequency electromagnetic field device and a rotary electromagnetic stirrer were respectively applied on the mould zone and secondary cooling zone of continuous caster. A schematic illustration for the experiment device was shown in Fig. 1, and the casting condition was listed in Table 1.To evaluate the influence of the electromagnetic field, all continuous casting parameters, including casting temperature, casting speed and cooling water flows, were held constant. and a uniformly solidified shell is formed as well as oscillation marks are obviously suppressed, which greatly improve the surface quality of Incoloy800HT billet.

Result and discussion

Effect of high frequency electromagnetic field on the surface quality of Incoloy800HT superalloy square billets

Effect of EMS on the solidification structure of Incoloy800HT billets

Fig. 3(a) and (b) show the solidification structure of Incoloy800HT billets with and without EMS, it can be seen that when EMS is applied, the ratio of equiaxed grain increased from 2.45% to 41.45%, and the average equiaxed grain size refine remarkably from 10.83mm to 1.28mm.

The dendrite morphologies at the various regions in the cross section can display the different solidification stages in Fig. 3(c)~(h). At the beginning of the solidification, it is observed in Fig. 3(c) that large numbers of equiaxed dendrites in the chill layer without EMS, whose growth directions are parallel to the temperature gradient, grow into unidirectional columnar dendrites towards the center of the billet, as shown in Fig. 3(d). Because of the high temperature gradient at the solidification front, the unidirectional columnar dendrites continuous grow up until the formation of few coarse equiaxed dendrites in the center of the billet. With the application of EMS, it is the same manner of the chill zone and the unidirectional columnar dendrites formation at the beginning of solidification in Fig. 3(f). However, with the evolvement of the solidification, the unidirectional columnar dendrites is prevented and plenty crossed dendrites emerge, presented in Fig. 3(g), and the columnar dendrites become less with no obvious orientation.

In the center of the billet, a large number of fine equiaxed dendrites are formed and grow up, as shown in Fig. 3(h).

This phenomenon can be explained that the severe forced convection caused by EMS can generate the fragmentation of the dendrites, which is the remelting of the dendrite arms at its roots by thermal gradients and solute enrichment. The Applying EMS can generate the forced convection to break the columnar dendrites for preventing interdendritic bridging, and promote the solidification feeding. Simultaneously, the forced convection improves the heat transfer to reduce the thermal stress, which results in suppressing the internal crack formation.

The segregation index is used to analysis the carbon segregation distribution. Fig. 5 shows that the positive segregation of C elements reaches the maximum 1.49 in the center of the billet without EMS, while the maximum C segregation index of the billet with EMS is only 1.16, so the centerline segregation of the billet without EMS is rather serious. This result show that more uniform carbon distribution and less segregation can be obtained and the concentration gradient of solute elements are significantly reduced by applying EMS. It is considered that the forced convection generated by EMS constantly scours the solute-rich liquid in the mushy zone and accelerates the transport of the solute elements, which reduces the solute-enrichment degree at the solidification front and homogenizes the molten pool composition.

Conclusions

(1) The application high frequency electromagnetic field in the continuous casting process produces the high quality surface of Incoloy800HT billet. The oscillation marks and some surface defects are remarkably suppressed and the external quality of the Incoloy800HT billet is obviously improved.

(2) By applying EMS in the continuous casting process of Incoloy800HT billet, the macrostructure is significantly refined. The fraction of the equiaxed grain increases from 2.45% to 41.45%, and the equiaxed grain size decreases from 10.83mm to 1.28mm.

(3) The application of EMS for Incoloy800HT billet can restrain the formation of shrinkage porosity, internal cracks and centerline segregation. The internal quality of the Incoloy800HT billet is remarkably improved.

Fig. 2

 2 Fig. 2 shows the appearance of the Incoloy800HT billets with and without high frequency electromagnetic field, respectively. As shown in Fig. 2(b), the surface quality of the Incoloy800HT billet under high frequency electromagnetic field is obviously improved that oscillation marks are suppressed and surface defects can be eliminated.The reason is that high frequency electromagnetic field applied in the mold not only generate a electromagnetic force to reduce contact pressure on the mold, which results in a decreased friction force between the melt and the mold, but also produce Joule heating to heat the meniscus. As a result, the mold flux consumption is increased dramatically,

Fig. 4 Fig. 5 C

 45 Fig. 4 Solidification structure of the Longitudinal section of Incoloy800HT billets

Acknowledgment

This work was financially supported by the National Nature Science Foundation of China (No.50834009), the Key Project of the Ministry of Education of China (No. 311014) and the Programme of Introducing Talents of Discipline to Universities (the 111 Project of China, No. B07015).


Dan Mou

Yubo Zuo
email: zuoyubo@epm.neu.edu.cn

Qingfeng Zhu

Lei Li

Jianzhong Cui

Study on the macrosegregation behaviour of 2524 alloy flat ingot solidified under the influence of electromagnetic field

Keywords: electromagnetic field, DC casting, macrosegregation, 2524 alloy

The flat ingots of 2524 alloy were prepared by direct chill (DC) casting process with the application of a low frequency electromagnetic field and the macrosegregation behaviour of this alloy was investigated. The experimental results showed that there are an obvious positive segregation near to the surface and a negative segregation in the centre area of the ingot. Cu shows the highest segregation tendency among the main elements of Cu, Mg and Mn. Ti shows a different segregation trend opposite to that of Cu. The application of electromagnetic field do not have significant effect on the segregation near to the ingot surface. However, with the application of electromagnetic field, the negative centreline segregation in the centre area of the ingot was evidently reduced. This paper presents these results and corresponding discussions.

Fig. 1 Schematic of the LFEC process

The chemical composition at different positions was measured by using a direct reading spectrometer. The flat ingot was machined layer by layer from the surface to the centre (along the thickness direction) for the composition measurement.

3 Results and discussions 3.1 Macrosegregation of DC cast ingot Fig. 2 shows the concentration distribution of Cu, Mg, Mn and Ti from the surface to the centre (along the thickness direction) of DC cast ingot. Different elements show different macrosegregation tendencies. For Cu, Mg, there is a negative (solute-depleted) segregation in the centre adjoined by a positive (solute-rich) segregation approximately at mid-thickness with a solute depletion at subsurface followed by a strong positive segregation at the surface. The macrosegregation of Cu is more serious than that of Mg. The distribution of Mn is uniform without obvious macrosegregation. The distribution of Ti exhibits a exactly different tendency from that of Cu. It shows a centreline positive segregation and a negative segregation at the surface. Fig. 2 Macrosegregation of DC cast 2524 alloy ingot It is well known that the solidification of alloys is accompanied by a certain degree of microsegregation of alloying elements due to rejection of element (K<1) during grain growth and due to the non-equilibrium nature of solidification, resulting in the composition difference between liquid and solid phases. If, subsequently, relative movement between the liquid and the solid occurs, the segregation can appear on a macro-scale, then the macrosegregation is formed. Therefore the partition coefficient, K, plays a very important role in the formation of macrosegregation. The partition coefficients of Cu, Mg, Mn and Ti are 0.17, 0.43, 0.90 and 9.0 respectively. Partition coefficient of Mn is 0.90 which is close to 1, therefore Mn shows more uniform distribution without serious macrosegregation. Partition coefficient of Cu is 0.17, so Cu shows a higher macrosegregation tendency than Mg and Mn. Ti with K > 1 exhibits an exactly different segregating tendency, which is opposite to the trend of Cu and Mg. For element of Cu, the copper concentration at the ingot surface can reach about 9%. The surface macrosegregation is mainly caused by exudation of interdendritic melt due to solidification shrinkage and the formation of air gap between the shell and the mould induced by the global solidification contraction of the ingot. The transport of interdendritic elements enriched melt to the surface leads to positive macrosegregation at the ingot surface, and consequently results in negative segregation in subsurface through which the interdendritic melt flow has taken place. Mg shows a macrosegregation tendency similar to Cu. Ti shows a results opposite to Cu due to its partition coefficient is much larger than 1. In the case of centreline macrosegregation [3,10] , there are several mechanisms relating to thermo-solutal convection, free floating grains, shrinkage and deformation induced flow, and forced convection. These factors make contributions to the formation of negative macrosegregation in the centre of ingot.

Macrosegregation of DC cast ingot under the influence of electromagnetic field

With the application of electromagnetic field, the macrosegregation tendency get changed. The results are shown in Fig. 3. As discussed in 3.1, the segregation tendency of Mg and Mn is not very serious, here the segregation tendency of only Cu and Ti was studied under the influence of electromagnetic field. The electromagnetic field did not show significant effect on the surface segregation for both Cu and Ti. The ingots prepared with DC and LFEC process have obvious segregation near to the surface. However the LFEC process shows a obvious effect on the centreline segregation. With the application of electromagnetic field, both the negative segregation of Cu and the positive segregation of Ti in the centre of the ingots are evidently reduced. Fig. 3 Comparison of macrosegregation of ingots prepared by DC and LFEC processes Fig. 3 only shows the concentration distribution along a line from the surface to the centre of the ingot (thickness direction). In order to more clearly observe the effect of electromagnetic field on the macrosegregation, a contour picture was platted by measuring the composition over the entire quarter of the cross section of the ingot. The contour picture of the concentration of Cu is shown in Fig. 4. Conventional DC LFEC process Fig. 4 The contour picture of the concentration of Cu It can be seen from Fig. 4 that the negative segregation in the centre area of conventional DC cast ingot is significantly reduced with the application of LFEC process, and the distribution of Cu in the ingot becomes more uniform. In the LFEC process the alternative current generates a time varying magnetic field in the melt, which, in turn, gives rise to an induced current in the melt and/or ingot. Therefore, the melt is subjected to electromagnetic body forces caused by the interaction between the induced current and the magnetic field. The Lorentz force can be expressed as Eq.

(1) [6,7] .

2 B 2 1 )B B ( 1 B J F          (1)
where B and J are the magnetic induction intensity and current density generated in the melt, μ is the permeability of the melt. The first term on the right hand of Eq. ( 1) is a rotational component which results in a forced convection and a flow in the melt. The forced convection results in uniform temperature field, reduced sump depth [11] and in consequence uniform and refined microstructure [12] . It is accepted that the shrinkage induced flow contributes to the formation of negative centreline segregation [10] . Grain refinement can decrease the permeability of the mushy zone and in consequence reduce the shrinkage-induced flow. With the reduction of the sump depth, the solidification front during LFEC process becomes much flatter, resulting in the reduced shrinkage induced flow. Therefore the grain refinement and reduced sump depth make contributions to the reduced centreline segregation. Floating grains also contribute to negative centreline segregation [13] . Uniform and refined microstructure resulted from the application of LFEC process, does not show obvious floating grains. With the reduction of floating grains, the negative centreline segregation could be weakened.

Conclusions

(1) The main elements in the flat ingot of 2524 alloy show a typical macrosegregation with a positive segregation at the surface and a negative segregation in the centre of the ingot. Cu shows the highest segregation tendency among the main elements of Cu, Mg and Mn. Ti shows a different segregation trend opposite to that of Cu.

(2) The electromagnetic field does not show significant effect on the surface segregation of DC cast 2524 alloy. However the LFEC process shows an obvious effect on the centreline segregation. With the application of electromagnetic field, the negative segregation of Cu and the positive segregation of Ti in the centre of the ingots are evidently reduced.

  surface of the ingot (mm)

  t a n c e f r o m t h e s u r f a c e o f t h e i n g o t ( m m ) DC L F E C , 5 0 A

Acknowledgment

This work was financially supported by the National Natural Science Foundation of China (51374067), the outstanding young scholars growth plan in the colleges and universities of Liaoning Province, China (LJQ2014032) and the National Basic Research Program of China (2012CB619506).


Jianrong Gao
email: jgao@mail.neu.edu.cn

Jia Liu

Andrew Kao

Koulis Pericleous

Dendritic growth velocities in undercooled melts under static magnetic fields

Keywords: Dendritic growth, Undercooling, Static magnetic fields, Thermoelectric magnetohydrodynamics

Dendritic growth in undercooled melts has been an interesting topic for metallurgists, physicists and mathematicians. In recent years, attention has been focused on the effects of melt flow on dendritic growth. Significant thermoelectric currents form in undercooled growth due to the presence of relatively large thermal gradients. Numerical simulations showed that the application of a static magnetic field exerts a complex influence on melt flow due to Lorentz force, damping and thermoelectrically driven convection, affecting growth kinetics in undercooled metallic melts. To verify the simulated results, bulk melts of high purity nickel were undercooled using the glass fluxing technique under static magnetic fields of up to 6 T. A high-speed camera was used for in situ monitoring of the recalescence process of the undercooled samples. The dendritic growth velocities at different melt undercoolings were calculated by simulating the recorded images of the recalescence process. The measured data confirms the predicted effect of heat and mass transport through thermoelectric magnetohydrodynamics flow on dendritic growth.

Introduction

Dendritic growth is often observed in solidification of undercooled metallic melts. It determines the final grain sizes and solute segregation patterns of metal castings [1]. Fundamentally, it represents a non-linear and a non-equilibrium process [2]. For these reasons, it has aroused common research interest in the fields of metallurgy, materials physics and computational mathematics. Since the pioneer work by Ivantsov in late 1940's [3], theoretical efforts have been made to predict the relationships between melt undercooling, the tip radius and tip velocity of a growing equiaxed dendrite (see Ref. [4] and references therein). In recent years, the effect of melt flow on dendritic growth aroused novel research interest because it is largely responsible for a discrepancy between theory and experiment for low undercoolings [5][6]. Magnetic fields are commonly used as a tool for controlling of melt flow in metallic melts. An alternating current (AC) magnetic field with high frequency can produce intensive melt flow known as electromagnetic stirring [7], whereas a static magnetic field typically introduces electromagnetic damping forces and thus can effectively reduce or remove fluid flow [8,9]. However, the role of the static magnetic field is not limited to damping, especially close to the solid front. The interaction of the static magnetic field with natural and inherent thermoelectric currents produces the phenomenon of thermoelectric magnetohydrodynamics (TEMHD) [10][11][12] leading to intensive melt flow around the primary tip, and secondary or higher order arms of a dendrite growing at significant undercoolings. Such opposing effects of the static magnetic field provide a cheap way for quantitative terrestrial studies of the effect of melt flow on dendritic growth when compared with space experiments [5]. Dendritic growth kinetics in pure nickel has been intensively studied over the past decades (see a review in Ref. [START_REF] Gao | Solidification of Containerless Undercooled Melts[END_REF]). An impurity effect has been considered to account for the remaining discrepancy between the theory of dendritic growth and the experimental data at low undercoolings [6]. A recent experimental study on elemental nickel of 99.99% purity revealed a U-shaped magnetic field dependence at low melt undercoolings [START_REF] Gao | [END_REF]. However, the effect of impurities on the dendritic growth velocities in the presence of TEMHD is unclear. This paper presents numerical simulations of the damping and thermoelectric effects of the static magnetic fields during melting and solidification of a glass-fluxed metallic sample, followed by measured data of dendritic growth velocities of nickel of higher purity under static magnetic fields and finally a comparison between the prediction of the numerical simulations and the experimental data.

Numerical Models

Numerical simulations were carried out to simulate the melt flow during natural cooling of an inductively melted spherical nickel sample of 6 mm in diameter under a static magnetic field. The details of the method can be found elsewhere [8]. It was found that the imposition of a static magnetic field of 0.5 T or more can damp melt flow in the nickel sample effectively. In the absence of a static magnetic field, the AC magnetic field used for induction melting produces strong turbulent flow of the magnitude of 0.1-1 m/s. As illustrated in Fig. 1, the turbulent flow is suppressed and the flow velocity is reduced to less than 0.01 m/s under the influence of a 6 T static magnetic field. There is a thermal gradient along the z direction, namely the direction of the static magnetic field. This gradient can be attributed to radiation cooling of the sample in the absence of electromagnetic stirring. The calculated gradient is in reasonable agreement with a measured gradient of 2.5 K/mm on an inductively melted Ni-Sn eutectic sample of the same size. The numerical simulation of TEMHD flow during dendritic growth from an undercooled melt is illustrated in Fig. 2. The figure shows the complex TEMHD flow structure that forms in the presence of an arbitrarily low static magnetic field. TEMHD creates flow circulations about the growth direction of the primary tip. For tangential tips, the flow is tilted and the corresponding flow patterns become complex, which grow in a direction normal to the static magnetic field. Such flow patterns will have different influences on the dendritic tip kinetics (tip radius and tip velocity) and eventually lead to very complex growth morphology [10,11]. In general, the TEMHD flow is localized and the flow structure and magnitude are highly dependent on the thermophysical properties of the crystalline material, on the direction and intensity of the magnetic fields and on the growth conditions of the dendrite (undercooling and chemical composition) as well. Fig. 2: Simulated flow structure of TEMHD around an equiaxed dendrite growing from an undercooled melt under an arbitrarily low static magnetic field (taken from ref. [11]).

In-situ Observations

Electromagnetic levitation is a popular method for high undercooling of a bulk melt. A levitated sample usually rotates and needs to be cooled using an inert gas jet. Glass fluxing offers access to comparable undercoolings of non-reactive metallic melts. But, it allows samples to be cooled without the use of the noble inert gas. The cost of the measurement is reduced and the experimental time is shortened as only a single or a few samples are required [START_REF] Gao | Solidification of Containerless Undercooled Melts[END_REF]. In the present work, it was combined with induction melting for measurements of dendritic growth velocities in undercooled melts under static magnetic fields. As shown in Fig. 3, the experimental set-up used has four key parts: a radio frequency vacuum induction melting furnace, a superconducting magnet, a high-speed camera, and a single-color pyrometer. The superconducting magnet has a room-temperature cylindrical bore of 300 mm in diameter and offers static magnetic fields of intensities up to 6 T. The high-speed camera was not focused directly onto the sample surface, but was focused onto an image of the sample projected into a prism at a distance of about 0.7 m (see Fig. 3b). The camera has a maximum frame rate of 125,000 fps and a two-dimensional resolution of 100× 100 m 2 (128 × 32 pixel). This resolution is sufficient for measurements of growth velocities ranging from 0.1 m/s to 100 m/s. The pyrometer was used for monitoring the surface temperature of the sample at a sampling rate of 100 Hz with an accuracy of ± 6 K. The sample was nickel of 99.999% purity with a mass of 1.0 g. Before the measurements, the vacuum chamber of the induction melting furnace was evacuated to a pressure of 5×10 -3 Pa, and backfilled with argon of 99.999% purity to a pressure of 5×10 4 Pa. The measurements were started with no static magnetic field at first. The sample was heated, melted and overheated inductively under the protection of the argon atmosphere. The overheating of the sample was carefully controlled by tuning the power to the coil to produce a desired undercooling during the subsequent cooling. After the sample was held in the overheated state for one or more minutes, the heating power was reduced to about 14% of the initial value to let the sample cool at a rate of about 20 K/s. Crystal nucleation in the undercooled sample was not controlled using an external trigger. Very often nucleation occurred on the lower surface of the sample. Recalescence followed due to rapid release of latent heat. The advancing of the recalescence front on the sample surface was monitored and recorded using the high-speed camera. The melting and solidification cycle was repeated 20 to 40 times to produce a wide spectrum of undercooling. After the measurements under no static magnetic field, the superconducting magnet was ramped to a magnetic field of 1 T, 2 T, 3 T, 4 T, 5 T and 6 T in sequence. Under each magnetic field, the same measurements were conducted by repeating the melting and solidification cycle of the sample at least 20 times. The recorded images were analyzed using a Pov Ray software program (V 3.6) to determine dendritic growth velocities during recalescence. The details of the method for image analysis can be found elsewhere [START_REF] Gao | Solidification of Containerless Undercooled Melts[END_REF]. The measured growth velocities are plotted in Fig. 4 as a function of undercooling. The data measured under each static magnetic field shows a power law before a critical undercooling of T crit = 165 K is achieved. The growth kinetics shows a negative deviation from the power law at higher undercoolings. Such observations are in agreement with our recent measurements on a pure nickel sample of lower purity [START_REF] Gao | [END_REF]. To investigate the effect of melt convection on the dendritic growth kinetics, the measured data at undercoolings below 165 K was fitted to different power laws and normalized with respect to a maximum for a given undercooling. The normalized growth velocities are shown in Fig. 5 as a function of the intensity of the static magnetic fields. For undercoolings below 100 K, the normalized growth velocities decline slightly or remain constant with increasing intensity of the static magnetic fields. They peak up at a critical magnetic field of 4 T and show a declining tendency at higher static magnetic fields. The dependences of the normalized growth velocities become indistinguishable for undercoolings of 100 K or above (in consideration of a total error of about 20 % in the measurements and in the power law fittings). Such a complex dependence is different from the U-shaped dependence observed for the normalized growth velocities of the nickel sample of lower purity [START_REF] Gao | [END_REF]. Despite this difference, the undercooling range where the static magnetic fields have a clear effect on dendritic growth velocities is essentially the same.

Discussion and Concluding Remarks

The present measurements show complex effects of the static magnetic fields on dendritic growth velocities of pure nickel. The constant or slightly reduced growth velocities at low and high field sides can be attributed to the dominance of the damping effect over the TEMHD effect. The peak growth velocities observed at the critical magnetic field of 4 T can be related to the strongest TEMHD flow near the dendritic tip. These observations are in agreement with the earlier numerical simulation of the TEMHD flows during dendritic growth [11].

The present results also suggest that there is an effect of impurities on the dendritic growth velocities of pure nickel.

The lower impurity level of the present nickel samples leads to the complex magnetic field dependence of the dendritic growth velocities with respect to the U-shaped dependence observed in the lower purity sample. The complex magnetic field dependence reflects the intrinsically complex TEMHD flows in dendritic growth. The higher impurity level of the previous nickel sample in recent measurements [START_REF] Gao | [END_REF] may further increase the intrinsic complexity of the TEMHD phenomenon during dendritic growth from the undercooled melt. TEMHD flow is highly dependent on the local Seebeck coefficients at the solid/liquid interface. Impurities, which have a tendency to congregate at the interface, may modify these values significantly, in effect acting as semiconductor-like dopants [START_REF] Garandet | [END_REF]. The higher impurity level of the previous sample [START_REF] Gao | [END_REF] brings about a clear and remarkable depression of the growth velocities at low fields, which may be due to secondary TEMHD flows that have not yet been considered. But fundamentally this difference is rooted in interactions between solute rejection and melt convection. On the other hand, the higher impurity level of the previous sample [START_REF] Gao | [END_REF] would also modify the intensities of the TEMHD flows by changing thermophysical/thermoelectric properties of liquid and solid phases. The critical magnetic field will be dependent on the thermophysical/thermoelectric properties. Thus, this second impurity effect may be responsible for the increase of the critical magnetic field. For a better understanding of the impurity effect, analytical and numerical modellings of the melt flow effect and the impurity effect on dendritic growth are under the way.

Fig. 1 :

 1 Fig. 1: Simulated flow velocity and temperature in a nickel sample inductively melted under a 6 T static magnetic field along the z direction. The r and z are distances away from the center of the sample in m. Temperature is in K.

Fig. 3 :

 3 Fig. 3: Bird's eye view (a) and schematic diagram (b) of experimental set-up used for measurements of dendritic growth velocities under static magnetic fields.

Fig. 4 :

 4 Fig. 4: Measured dendritic growth velocities of pure nickel as a function of undercooling. The dotted line shows a critical undercooling of 165 K for deviations from a power law.

Fig. 5 :

 5 Fig. 5: Normalized dendritic growth velocities of pure nickel as a function of the intensity of static magnetic fields at undercoolings below 165 K. The curves are a guide to the eye.

Acknowledgment

The work is financially supported by the National Natural Science Foundation of China (51071043 and 51211130113), the Fundamental Research Funds for Central Universities (N09050901 and N130509001), and the Royal Society International Exchanges Scheme -2011 China Costshare (NSFC). The authors thank D. M. Herlach, P. K. Galenko and D. V. Alexandrov for helpful discussion of experimental data. The authors are indebted to V. Bojarevics for offering the computer code for magnetohydrodynamics modeling. The authors are grateful to C. Yang, Y. J. Zhang, X. T. Deng, J. C. Jin, D. Xiang and H. L. Zhao for assistance in experimental work. The authors also thank S. Binder for providing computer program for image analysis.


G H Kim

S H Kwon

Y M Won

C H Lee

Enhancement of slab internal quality by electromagnetic stirring of molten steel

Keywords: electromagnetic stirring, slab, solidification, internal quality

Internal defects in slab, such as centerline segregation, porosity and micro structure, affect to crack, tearing, surface defect, and mechanical discontinuity in plate. Electromagnetic stirring (EMS) is applied for a long time to achieve better internal quality of slab, especially with regard to the most demanding products. Removing the segregation and the porosity in a centerline of slab is quite difficult even if we apply the EMS and the soft reduction due to mush zone and narrow channel of liquids. Several sets of strand EMS were positioned in the region of bow section to stir liquid, and they were operated to generate several flow patterns. This work carried out optimization of EMS such as system configuration, design of flow patterns, stirrer position configuration, and stirring strength to enhance the internal quality of slab. Strong stirring of the molten steel to the wide range in front of crater end is a quite effective to enhance the internal quality of slab in addition to the reduction technology.

Introduction

Centre segregation and centre porosity are usually the main defect in continuously casted slabs, and these can be a major obstacle to produce high strength steel grades with qualified mechanical properties. Many technologies [1], such as a soft reduction and an electromagnetic stirring (EMS), are applied in strand region to overcome the internal quality problem. In spite of applying these technologies, the internal quality cannot be reached to the level of demanded quality. Thus, POSCO developed an innovative heavy strand reduction technology, PosHARP, in several years ago and improved the internal quality dramatically. Strong strand EMS was also adapted on that strand to enhance the internal quality in stable and uniform at the same time. This paper presents the results of installation and application of EMS in POSCO GY32 continuous casing machine.

Installation of heavy strand reduction segment and strand EMS

Soft reduction just avoids the fluid flow of solute-enriched liquid by pressing slightly the continuously cast slab at the end of solidification. On the other hand, PosHARP compresses the slab at high reduction rate in the middle stage of solidification, as shown in Fig. 1, using several rolls equipped on the segment in horizontal region of continuous casting machine. Compressing the slab results to squeeze solute-enriched liquid existing in the mid-thickness region of slab to upstream where a large amount of liquid still exists and homogenized. At the same time, both solidified shells contact each other at the centerline of slab. All these actions result in the negative segregation, which is not harmful for the internal quality of slabs and prevents the formation of shrinkage cavity at the centerline of slab.

Fig. 1: Installation region of strand EMS and heavy reduction segment

Soft or heavy reduction of slab thickness plays important role to improve the internal quality. But, in some case, the uniformity of segregation distribution along the centre line is poor and the effect of the reduction is unstable even though the reduction technology was applied. Thus, the strand EMS was installed in upstream side segment compare to the reduction segment to enhance distribution uniformity and to achieve stable effect by stirring the squeezed liquid. Fig. 2 is an operation window of strand EMS. Travelling direction and time of magnetic field for each in-roll EMS can be controlled independently to generate various mode of liquid flow in strand. As shown in the macrostructure of slab center, thick centerline segregation is observed in slab applied soft reduction only. On the other hand, segregation is hardly observed in slab applied PosHARP and EMS. It was also clearly confirmed in the EPMA results. While soft reduction slab has about 1.04 Mn segregation degree, PosHARP slab shows negative segregation because the solute-enriched liquid was squeezed to upstream. Also, applying POSHARP technology, the solidified shells of slab contact at the centerline and formation of shrinkage cavity reduces remarkably. Thus, center porosity of PosHARP slab is much less than that of Soft reduction slab.

Conclusion

Heavy reduction technology improved internal quality in significant and strand EMS has a role to enhance the uniformity and the stability of centerline quality. Flow patterns in the S-EMS installed region are critical to enhance the internal quality of slab. Optimization of flow pattern, EMS position is needed according to steel grade.

References [1]

The Making, Shaping and Treating of Steel, "Casting Volume", AISE Steel Foundation, Pittsburgh (2003)

Fig. 2 :

 2 Fig. 2: Operation window of strand electromagnetic stirrer installed in POSCO GY32 continuous casing machine Flow pattern control Since divided roll type strand EMS was installed in segments of caster strand, several patterns of flow was designed such as double roll, quadruple roll, and multiple roll. Fig 3 shows one of the simulated flow patterns with strand EMS operation. Alternate operation, forward and reverse, achieved more uniform enhancement of internal quality in direction of slab width compare to continuous operation. Electric current was applied in EMS coil to generate a flow pattern of liquid as shown in right bottom part of Fig. 3, forward during 15 seconds, stop in 2 second, and reverse during 15 seconds. Maximum velocity of melt is 0.053m/s at the left edge of slab in the end of forward current flow with casting speed of 0.8m/min. According to the experimental results, this condition mixed the melt to break a solidification bridge in the center line of slab.


X L Wang

N Wu

M S Liu

W B Dai

Y H Yan

X Zhao
email: zhaox@mail.neu.edu.cn

Effect of electric current densities on microstructure and mechanical properties of a Cu-Zn alloy

Keywords: electric current pulses, microstructure, mechanical properties, current densities

As an instantaneous high energy input method, the electric current pulses treatment (ECP) has been extensively applied in materials science and engineering. In this work, by changing the current densities, the effect of ECP on the microstructures and the mechanical properties in a Cu-Zn alloy is investigated. The results show that the elongation of samples treated after ECP is greatly improved without a sharp decrease of the tensile strength. And with current density increasing at j max =12.99kA/mm 2 , the comprehensive mechanical properties is improved. The possible reason can be ascribed to the increased dislocation mobility and the crack healing induced by ECP.

Introduction

Since 1963, when Troitskii and Likhman first reported that moving electrons in a metal crystal may interact with dislocations [1], the following researches have indicated that high current density electric current pulses (ECP) influences the behavior of materials. Conrad et al. proposed that ECP could enhance the nucleation rate of recrystallization and refined the grain size of a cod-worked copper by accelerating the dislocations mobility [2][3][4][5]. Qin et al. demonstrated in theory that ECP could increase nucleation rate by decreasing the thermodynamic barrier during recrystallization or phase transformation (liquid-solid and solid-state) [6]. Recently, Zhou et al. obtained ultrafine recrystallized grains in a cold-rolled brass by ECP treatment [7]. With the further investigation on the application of ECP, Dai et al. proposed that the electric current direction also played a great role on the recrystallized nucleation rate [8]. Wang et al. further found that the recrystallized grains induced by ECP nucleate randomly, but with an oriented growth [9]. However, the aim to optimize the materials' microstructure is to improve the mechanical properties. Up to now, though lots of studies have been carried out about the effect of ECP on materials' microstructures, a few reports are about the corresponding the mechanical properties. In this work, the relationship between the microstructural evolution and the mechanical properties due to the application of ECP is investigated.

Experimental details

A 33% reduction in thickness direction of a cold-rolled commercial Cu-Zn alloy sheet with a composition of Cu 63.8 mass% and Zn 36.2 mass% was used as the research object in this study. By using the electrospark discharge technique, dog-bone-shaped samples with 10 mm gage length, 5 mm width, and 1 mm thick were prepared, and the sizes of the two ends were much larger than the size of the gage part. During the ECP process, the two ends of each sample were put into copper electrodes. Thus, the current density was much higher in the gage part than in the two ends. Then the temperature rise of the two ends was very small and could be regarded as room temperature. Due to the cooling effect of the two cool ends, a higher cooling rate could be obtained in the gage part of the sample during cooling. The single ECP was produced through a discharge of capacitor banks under ambient conditions, and its waveform was detected to be a damped oscillation wave using a Rogowski coil and a TDS3012 digital storage oscilloscope (Tektronix, Beaverton, Oregon). After ECP treatment, these flat samples were divided into four groups, respectively, denoted A, B , C and D, among which samples of type A did not undergo any further treatment after cold rolled, the others were treated with ECP using current density 12.50kA/mm 2 , 12.70kA/mm 2 and 12.99kA/mm 2 respectively. Each group includes four standard specimens, three for uniaxial tensile test and one for microstructure observation. To detect the microstructure characteristic, a JEOL JSM-7100F SEM (JEOL, Akishima, Japan) was used. The tensile tests at room temperature were conducted to examine mechanical properties using an Instron 1195-5500R test machine with a cross-head speed of 1mm/min.

Results and discussion

The Cu-Zn alloy selected in this study is a dual phase brass (α+β phases). During current passing, the temperature increment can be calculated as 550K, 574K, and 594K, respectively for the samples B, C and D. Apparently, the temperature caused by ECP are lower than the phase transformation temperature (953K). Therefore, the microstructural evolution shown in Fig. 1 can be resulted from the formation of recrystallization caused by ECP. Fig. 1 shows the SEM morphologies of specimens A, B, C and D. Fig. 1(a) shows lots of coarse grains randomly distribute. Also massive sliding traces and some deformation twins appeared in the primary α-phase grains of the coldrolled Cu-Zn alloy. The coarse β grains distribute at the triple junctions of α grains. After the ECP treatment, the refined recrystallized α grains are preferentially formed at grain boundary, sliding traces and other defect areas, as shown in Fig. 1(b). With the current density increasing, the recrystallized grain growth of α-phase is taken place and the grain sizes become homogeneous. Especially, with the grains growing up, lots of annealing twins are formed and the deformed microstructures almost disappeared in Fig. 1(d). However, it can be observed that there is no significant change in the grain size distribution for β phase. To clarify the effect of electric current on the mechanical properties, Fig. 2 plots the evolution of the mechanical properties at the different current densities. Worthy to mention that during the mechanical test, each group includes three specimens, and the data shown in Fig. 2 are the average values of the three specimens. It can be found that the tensile strength of the cold-rolled Cu-Zn alloy is significantly decreased from 477MPa to about 400MPa for the ECP treated specimens. While for the ECP treated specimens, with the ECP current densities increased, the tensile strength and the elongation of the cold-rolled Cu-Zn alloy have a saddle point for samples C with j max =12.70kA/mm 2 . For samples D with j max =12.99kA/mm 2 , the tensile strength and the elongation rate are higher than others. The fracture surfaces of samples A-D after tensile tests are shown in Fig. 3. The dimples and cleavage modes are found on the fracture surface of the samples treated before ECP, while for electric-current-pulsed samples, the plastic dimples become more homogeneous. Especially, the cleavage modes almost disappeared in the electric-current-pulsed samples, especially as that shown in Fig. 3(d) for samples D.

From the above mentioned, it can be found that the deformed microstructure vanished gradually and recrystallized grains were obtained, which increases the materials' ductility. Because the Joule heating caused by ECP could provide temperature and energy conditions for recrystallization, the application of ECP treatment would enhance the mobility of the dislocations. The drift electrons can exert a force on dislocations when high density electric pulses are passing through the specimen [4]. The force is named after electron wind force, and it is proportional to current density. Due to the effect of electron wind force, the mobility of dislocation will be increased during ECP treatment [7], It is also well-known that the glide and climb of dislocation and migration of atoms are important for the static recrystallization process, thus ECP treatment can produce more advanced stage of recrystallization and enhance the nucleation rate of recrystallization with the current density increasing. In addition, the ECP treatment has a selective effect. When the high density electric pulses are passing through a metal sample, due to the larger local resistivity and the stronger detour of the electric current, the Joule heating and the transient thermal compressive stress are stronger in the defectiveness area. Then the change of the temperature in the area with a defect is higher than other sides. Because of existence of these defects, inhomogeneous physical field in a metal is generated. Under these effects, the microcrack can be closured or healed [10]. Therefore, the ECP treatment is an effective method to heal the damage, which is also an important influence on the improvement of the mechanical properties.

The above results indicate that the difference of the mechanical properties can be resulted from the different microstructure induced by different current densities. Obviously, the improvement of mechanical properties should be ascribed to the homogeneous distribution of the grain size after the ECP treatment. In addition, an optimum combination of ductility and strength in the cold-rolled Cu-Zn alloy could be achieved by the ECP treatment.

Conclusions

(1) The improvement of the mechanical properties induced by ECP can be ascribed to the different effect of electric current density on the microstructural evolution. With increasing current density, a degree of recrystallization is increased. The effect of ECP includes not only the thermal effect, but also the electric current special effect.

(2) The ECP treatment has an important effect on the damage healing in cold-rolled Cu-Zn alloy, which gives a significant increase in total elongation.

Fig. 1 :

 1 Fig. 1: Microstructural evolution of the samples treated: (a) cold-rolled, and ECP treated with (b) j max =12.50kA/mm 2 , (c)j max =12.70kA/mm 2 , (d) j max =12.99kA/mm 2 .

Fig. 2 :

 2 Fig. 2: Relationship between the mechanical properties and the current densities (a) the tensile stress, (b) the elongation rate.

Fig. 3 :

 3 Fig. 3: SEM fractographs of the samples (a) cold-rolled, and treated with ECP at (b) j max =12.50 kA /mm 2 , (c) j max =12.70 kA /mm 2 , (d) j max =12.99 kA /mm 2 .

Acknowledgment

This work was supported by the National Nature Science Foundation of China, Grant No. 51471047, the 111 project of China, Grant No. B07015, and the Fundamental Research Funds for the Central Universities, Grant No. N130418001.