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Ultrasounds Back-Scattering Measurements for New Anisotropy Indicator Construction J. MOYSAN, G. CORNELOUP. Laboratoire de Caractérisation Non Destructive Université de la Méditerranée - IUT GMP Avenue Gaston Berger - 13625 Aix en Provence Cédex - France Contact

ABSTRACT

The present paper refers to the improvement of ultrasonic testing applied to anisotropic material. A better knowledge of anisotropy is often a great help for accurate nondestructive evaluation. Indeed the exact understanding of ultrasounds path (refraction angle) depends on the knowledge of the anisotropic behaviour. Furthermore Signal to Noise Ratio greatly varies with wave refraction angle.
Our bibliographic work led us to conclude that no technical solutions exist for the in-situ measurement of materials anisotropy. Many possibilities have been developed in laboratories, all of them using velocity of propagation. Such a measure is not always simple or even possible as you need to know one distance precisely.
We propose an approach based on the attenuation of ultrasounds. To be close to real testing conditions, natural backscatterring is used instead of artificial reflectors. This implies choosing ultrasounds frequencies in order to reduce absorption phenomena and rise scattering. Modelling shows that the only measurement that can be made is the product of the attenuation coefficient multiplied by the velocity of propagation. This is an indicator to characterise anisotropy. To obtain more precise information strong hypotheses on the symetry of the material under investigation are made.
Transversely isotropic material is considered in this study. Presentation is limited to a few promising results obtained in an austenitic V-weld. Experimental measurements are made with the immersion technique and transverse waves are used. This paper presents how to take into account the surface echo to obtain a correct estimation of our anisotropy indicator.
Keywords : ultrasound, weld, scattering, attenuation, signal processing

INTRODUCTION

The study consists in developing an inverse method making it possible to evaluate the principal direction of elasticity of transverse isotropic materials. The experimental methods based on ultrasonic velocity measurements are suited to such an evaluation but their implementation on site is delicate because they require the existence and the measurement of a precise geometrical dimension. An aim of the study is to cancel this obligation. The work will concern the analysis of the ultrasonic field backscattered by the medium. This field is closely dependent on the material microstructure and thus on its preferential orientation, if it exists. One will show the possibilities offered by the analysis of the backscattered signal in metallic materials with granular structure.

Firstly we present the types of structures which we plan to characterize. Then we are interested in the attenuation of the waves in the solids in order to analyze the scattering effect more particularly. We propose a model of backscattered signal which we validate by an experimentation on real parts. Finally we conclude on the potential of the method and on the prospects for the continuation of the study.

STEEL GRAIN STRUCURE IN CASE OF MULTIPASS WELDING

Among austenitic stainless steel parts, one finds multipass manual metal arc welds. The technique consists in depositing metal on a support by the intermediary of a succession of weld beads. During multipass manual metal arc welding, the parameters such as scanning rate, angle of the filler rod, welding intensity and voltage influence the form of the bath of fusion and the distribution of the variation in temperature. Solidification is then directed [BAIK 77].

The growth of the microstructure occurs in the form of fine dendrites in the direction of the maximum variation in temperature. The crystallographic direction [100] of the elementary pattern for austenite is parallel with the average direction of dendrites. In the axis of dendrites, the crystallographic direction [100] is privileged and in their perpendicular plan all the crystallographic directions are equiprobable. The material thus textured is a transversely isotropic system whose principal axis of symmetry coincides with the axis of dendrites. Its matrix of rigidity has five independent constants which can be estimated starting from the three cubic elastic constants of a single cubic crystal, austenite steel being f.c.c [OGI 85].

ULTRASONIC WAVES ATTENUATION

During its propagation in a real medium, an ultrasonic wave sees its amplitude decreasing. This phenomenon is dependent on the structure of the medium and on its mechanical behavior. One distinguishes two types of attenuation: attenuation by absorption (a _a) and scattering (a_s).

(1)

Absorption is due to the inelastic behavior of the propagation medium. It converts the vibratory mechanical energy into heat. This type of behavior is dominating in viscoelastic homogeneous materials such as amorphous polymers. For polycrystalline metallic materials absorption is generally neglected versus the scattering. The attenuation by absorption increases with the frequency.

If the propagation medium has heterogeneities, there is presence of scattering. Thus polycrystals scatter. Each grain constitutes an acoustic impedance discontinuity. An incidental acoustic wave sees its energy gradually degraded during its propagation. Each grain generates a diffraction, a reflexion and a refraction of the transient wave. In an isotropic polycrystal, the scattering is a function of the frequency and the average size of heterogeneities. In the case of single-phase polycristalline material whose grains are equiaxed, one defines expressions of the attenuation scattering coefficient for three frequential regions, depending on the concerned acoustic phenomena. In our study we more particularly analyze the Rayleigh scattering region. This region corresponds to the range of frequencies generally used in ultrasonics inspection which covers 500 KHz to 20 MHz.

RAYLEIGH SCATTERING REGION

Several authors work on the modelling of the scattering coefficient for polycristalline media [AHM 92] [HIR 86]. The equation of motion (2) is solved using the perturbation method. Numerical calculations are based upon three assumptions : the crystal is weakly anisotropic, all grains have same shape and size, probability of having material constants is the same for each grain.

(2)

where x: position variable, C_ijkl (x): elastic constants, w: wave pulsation, u: displacement amplitudes

Hirsekorn's work [HIR 86] enables to obtain velocities and scattering coefficients for a textured polycristal.Values are given for the three propagation modes (SH waves, SV waves and compressionnal waves).
The framework of the study is the following : slowly evoluating material (Born approximation), scatterers are defined as spheres, all grains have the same orientation [100].

In his publications Ahmed [AHM 92] gives an elliptic shape to material grains. His results apply to all frequencies. His conclusions on the evolution of scattering coefficients or celerities are the same as those of Hisekorn. These results allow to approximate the evolution of scattering coefficients in the Rayleigh region. We are mainly interested in the evolution of the scattering coefficients of SV waves as this mode can be generated alone provided that incidence angle is beyond the first critical angle. In case of real parts, distribution of grain size, variations in orientation, non-monochromatic wave, lead to less important evolution as it is proved by Neuman's experimental results [NEU 89].

BACKSCATTERED NOISE

Research described previously evaluates the acoustic parameters of a textured material such as celerities and the scattering coefficients of the three existing modes of propagations in anisotropic solids. This research does not provide an expression of the backscattered field. It is necessary to find a model able to represent the signal of noise received by a transducer when it measures acoustic response of a material. Work is here very different from classical ultrasonic testing as grain noise brings the searched information. Saniie proposes such a model in the case of an isotropic polycrystalline material tested in 0° incidence by a normal pulser/receiver probe [SAN 88]. The received signal is the convolution of the impulse response of the transducer by the transfer function of the inspected part (fig 1).

Fig 1a: Scattering in polycristal material	Fig 1b: Grain scattering model
Fig 1: Saniie's modelling representation.

Considering Rayleigh scattering, each grain is viewed as a single scatterer in an homogeneous surrounding medium. There is a reflection at the grain boundary depending on the grain cross section and on its impedance difference with surrounding medium. Backscattered signal results from many reflected echoes. Depth positions in the sample gives a temporal delay to reflected echoes. Given the incident beam diameter and a time interval for the observation, the received signal corresponds to the inspection of a limited volume V containing a total number M of scatterers. Thus during its propagation, the incident wave sees its amplitude decreasing and furthermore each reflected wave is attenuated during its backpropagation. Globally behavior of the material is represented by a decreasing function of time. The amplitude decay has an exponential form. If we neglect absorption effect, the exponential decay depends on scattering coefficient a_s. Saniie writes :

(3)

where,s_dk : grain scattering cross section, t_k : temporal position of the scatterrer k, M : total number of scatterers within the range cell V, C : wave celerity.

The impulse response of the transducer is comparable with one broad band pulse whose spectrum of amplitude is of Gaussian form. This is one classical modelling to represent signals generated by normal transducers. If one is interested in one moment t Î [t-e,t+e] such as e is weak in comparison with the period of the pulse, the response is written:

(4)

so R is the resulting modulus of the sum of scattered signals, f is the resulting phase.

Insofar as it is possible to determine the distribution of the scatterers and their positions in the sample, the distributions of the amplitude R and the phase f can be given. In reality, one never knows the distribution of the size of the grains in the material nor their position. However, if it is supposed that the position and the volume of the scatterers are independent, their law of distribution is identical in all volume V, the number of diffusers in V is high then, the amplitude R and the phase f respectively have a Rayleigh probability density function and a uniform distribution [COUL 84 ].

Consequently, the envelope of the real signal of noise has a Rayleigh distribution balanced by exponential decreasing utilizing the scattering attenuation coefficient. The variance of this distribution is all the more low since the variance of the sections of scatterers is low. If the microstructure does not spatially evolve, the signal is stationary and ergodic. In this case Saniie shows the average envelope of the signal of scattered noise is proportional to exponential decreasing.

(5)

EXTENSION TO OBLIQUE INCIDENCE TESTING

The purpose of the present work is to extend Saniie's modelling in order to allow to make full use of signals obtained in oblique incidence testing. Figure 3 describes the experimental configuration of an immersion testing with oblique incidence. It appears clearly that the tilted beam penetrates gradually in the sample. We suppose a perfectly plane interface and a cylindrical ultrasonic beam in water, one notes T time necessary to the complete penetration of the beam.

Fig 3: Oblique incident beam modification at a water/steel interface.

We chose to use normal transducers in order to limit the effects of focusing and defocusing which could occur with a focused transducer due to the anisotropy of the polycrystal. A normal transducer generates a wave assumed to be plane and whose acoustic pressure varies according to the space position. These variations have an effect on the shape of the signal in the case of non null incidence. In order to construct a model of the average envelope of the noise, we integrate these evolutions via the distribution of the acoustic pressure on a section of the beam, via its evolution along its axis, and we neglect the divergence of the beam (approximately 2° for compressionnal waves in water and 1° for SV in steel).

To obtain a simple approximation of the shape of the average envelope of the noise signal we use very classical models. Thus, the beam generated by a normal transducer can be considered cylindrical from the surface of the transducer to a distance equal to the near field limit. For a more precise approach it would be possible to characterize the real behavior of the transducer.

The amplitude of the received signal is proportional to the acoustic pressure, it is maximum at the near field limit then decreases according to a law inversely proportional to the distance. The origin of times is taken on the section of the beam, it corresponds to the point of intersection between the shortest generator of the beam with surface (fig. 3). It is generally taken on the beam axis because the acoustic pressure is maximum there and one thus associates the beam with its axis. In order to simplify our expressions, we chose, after experimental checking, to represent the variation of pressure on a section of the beam by a gaussian curve with standard deviation equals to D/8. Discretizing the beam, the average envelope is obtained by a simple summation of several decreasing exponential curves, linearly delayed depending on incidence i values and weighted by acoustic pressure distribution. We obtain in a continuous form :

(6)

where p_LCP is the pressure at the near field limit, D is the transducer diameter, C is the ultrasonic celerity, l is the wavelength

Neglecting acoustic pressure decay along the beam axis (so K(t) is equal to 1) compared to the attenuation in material, the envelope averaging is then simply a decreasing exponential function after the time 2.T. The signal processing is easy, using an interpolation algorithm we obtain the product : attenuation coefficient multiplied by ultrasonic celerity. Modelling [HIR 86] and experimental trials [NEU 89] indicate that attenuation variations are far greater than celerity variations, so this product should be a good indicator of attenuation variation. Knowing the variations of this product, we will be able to find the specific incidence for which the ultrasonic beam is not deviated. It means that phase and group velocities and also corresponding refracted angles are identical.

CALCULATION OF THE ATTENUATION COEFFICIENT FROM NOISE SIGNALS

The attenuation coefficient is calculated from the average envelope of the signal. The method is based on the assumption that noise signals correspond to a stationary and ergodic process. This makes it possible to consider two methods of calculation of envelope averaging. The first solution is space averaging of envelopes of various uncorrelated signals (stationarity). The second solution is temporal averaging of an envelope of a signal (stationnarity and ergodicity). Preliminary, signal filtering is necessary to obtain the envelope, it is carried out by Hilbert transform.

In the case of space averaging it is necessary to obtain N uncorrelated signals, the data are obtained on a square surface with a recovering effect of a quarter of the transducer diameter. After the envelope processing of N signals, one calculates for each time value t the average amplitude of N envelopes. The estimate of the average envelope is all the more precise since the number of signals is large and the variance of the distribution of the amplitudes of the envelope is low (low difference in volume of heterogeneities).

In the case of time domain averaging, the data is simply one signal. The average is calculated on a sliding temporal window of temporal length t containing N samples of the envelope of the rectified signal. The larger the value of t, the better the estimate can be. The variance of the distribution of the envelope amplitudes must also be low to obtain accurate results. This mode of calculation presents the disadvantage of truncating the signal in its two ends, the signal length is reduced by half the size of the sliding window on each extremity. So the accuracy of the approximation by exponential decreasing allowing the estimate of the product a_d.C is somewhat faded.

In experimental configuration (null incidence or not), we previously showed that, after a given time 2.T the average envelope of the signal can be approximated by a decreasing exponential. A simple linear regression after logarithmic processing makes it possible to estimate by a least square function, the value of the attenuation coefficient a _d weighted by the propagation velocity of the wave generated in the part:

(7)

In the remainder of the paper, the product a_d.C is normalized by the ultrasonic celerity of SV waves in isotropic steel (C=3230 m.s^-1).

In order to compare the performances of each processing (spatial and time domain averaging), noise signals were simulated (null incidence). Our results show that the averaging offers a better precision on the approximation of the attenuation and this whatever configurations are considered. The time domain averaging presents too much uncertainty so we do not plan to exploit it. The randomness of the noise leads to estimate the true value of the attenuation. It is obvious that it approaches the true value as well as possible when the conditions of noise generation are optimal (a large number of diffusers and low standard deviation).

EXPERIMENTS

In order to check the preferred orientation of dendrites, we carried out a metallographic analysis of our part. Various samples, cut out in selected plans, are observed after an electrolytic attack with 10% oxalic acid. This examination reveals the orientation of the microstructure obtained with the multipass manual metal arc welding. The orientation is estimated, by simple measurement on a micrography, to be approximately 27°. Moreover, one such examination makes it possible to consider the average thickness of dendrites which is about tenth of millimetre. For frequencies varying from 1 to 20 MHz we are then ensured to be in Rayleigh scattering region

Experimental procedure consists in acquiring several signals for various incidence. As we use immersion technique and we want to generate only SV waves in our sample, incidence limits are obtained by Snell's law by supposing the material to be isotropic in order to take a reference celerity C_SV=3230 m.s^-1. We obtain an incidence range : iÎ[15°,28°], both sides of the normal to the interface. One side is referenced as "dendrite direction", the second as "opposite direction". Consequentlty there is an undetermined zone, where two wave modes propagate together, which could not be useful for the evaluation of the attenuation coefficient. This angular sector corresponds to refracted angles between -34° and +34° (fig. 4).

Fig 4: Experimental configuration.

Fig 5: Results of attenuation measurement.

For each incidence, a series of signals is acquired. The spacing between measurements is equal to a quarter of the probe diameter for obtaining uncorrelated data. Then, the calculation of the averages of the signals envelopes and their approximation by exponential decreasing enable to estimate the value of the normalized attenuation coefficients.

The simplicity of this procedure however is compromised by the existence of an unforeseen phenomenon related to the interface, returning our results vague. A traditional problem with which are confronted test operators is the presence of an echo of interface which comes to disturb the signal in a zone close to surface. Indeed, the interface has an imperfect surface quality which generates diffraction echoes [BIL 82 ]. We previously showed that incidence examination implies that there is another disturbance whose duration is at least equal to 2.T if perfectly cylindrical beam is considered. In practice, normal transducers generate a divergent beam which leads to increase time 2.T, adding diffraction effect on the surface and pulse duration, the double of duration has been observed (4.T). The approximation of our signals by decreasing exponential curve has then to be carried out apart from this disturbed zone.

Data acquisition on the anisotropic part is carried out for incidences of 16° to 28° in the two configurations "dendrite direction" and "opposite direction" (fig. 4). Figure 5 presents the evolution of the measured attenuation according to the incidence after space averaging on 36 signals per incidence. The step of incidence is 2°. The central frequency of the transducer is 10MHz. In order to free ourselves from the surface disturbance, or at least to reduce this disturbance, a solution would be to carry out a polishing of the interface of the sample.

The same procedure was applied to an isotropic part (ferritic steel). Attenuation ceofficient values are about 12 Neper/m ± 0,5. For the anisotropic part and in the same experimental conditions, evolution of the attenuation definitely is more important. Indeed, attenuation varies between 12 and 37 Neper/m. One can detect the existence of a minimum for an incidence of 20° in dendrite direction and there is a maximum for an incidence of 22° in the opposite direction. We can conclude that the behavior of the part is anisotropic. It is a question from now to determine its principal direction of elastic symmetry.

The assumption of a transverse isotropic symmetry of our material authorizes us to use the evolutions of the attenuation coefficient provided by the model of Hirsekorn [HIR 86]. Moreover we suppose that the evolution of the attenuation coefficient is dominating on the celerities variations. It means that the product a_d.C is the image of the variations of the attenuation. It remains from now to determine the principal direction by identification of the extrema which correspond to directions of propagation of transverse waves for which the beam is not deviated. Two properties related to symmetry are thus used : propagation velocities of SV waves along the axis of dendrites and normal to dendrites are equal, and propagation velocity of SV waves at 45° to the longitudinal axis of dendrites is minimal.

With our experimental setting it is probable to succeed in revealing at least two extrema even if the incidence range produces an undetermined zone (fig. 4). In the best case there are two minima of attenuation corresponding to a propagation at 0° and 90° to the longitudinal axis or there are two maxima corresponding to a propagation at 45°. We obtain a system with two equations from Snell law and we have two unknown factors : the refracted angle and the celerity as we assumed from models that celerity is identical at 0° and 90° angle. In a less favorable case there are one maximum and one minimum in the attenuation curve. They correspond respectively to propagations at angles 0° or 90° and angles 45°. With a 27° dendrite direction we are in an unfavourable case. Indeed, we observe the presence of a minimum and a maximum of attenuation. The problem is unsolvable in practice as the problem becomes a system with two equations and three unknown factors (two equations from Snell law connecting the incidences in water (known) to the refracted angles and waves celerities (C₄₅ and C_0/90)). However, knowing the principal axis of symmetry that we estimated at 27°, it is possible to check the coherence of our results.
Logically the minimum in figure 5 corresponds to a propagation along the dendrites longitudinal axis and the maximum corresponds to a propagation at 45° to this axis. SV waves thus refract respectively at 27° and -18°. Snell law enables us to calculate associated celerities. One finds then celerities equal to 1970 m.s^-1 at 0° to the axis of the dendrites and 1200 m.s^-1 at 45°:
These values are erroneous for a steel. Our results do not correspond to our forecasts. The evolutions of the standardized attenuation do not correspond to our forecasts and prevent us from validating the proposed procedure. However, the curve of figure 5 shows well an anisotropic behavior of the part obtained by multipass manual metal arc welding, a behavior really different from those of the isotropic sample. This problem is inevitably related to an unknown physical phenomenon in connection with this real part. One can think that the angle of 27° of dendrites measured by micrography is not constant despite the precautions observed during welding process. There can also be a 3D orientation of dendrites. Investigations on other parts or another experimental setup should bring a response to these imperfect conclusions.

CONCLUSION

The development of a method based on the attenuation appears interesting to solve an inverse problem of characterization of transversaly isotropic structure whose axis of symmetry is not known. Knowing this axis allows ultrasonic testing in better condition. To avoid the need of reflectors to measure attenuation we chose to use the backscattering of ultrasonic waves. It enables us to propose a procedure of nondestructive evaluation simple to be used on site. Voluntarily restricted to textured austenitic steels, our study showed that the attenuation measurement can apply, in its principle, to any type of heterogeneous materials provided that the absorption of the ultrasonic waves is negligible relatively to the attenuation by scattering.
The validation of the results could not be carried out in an absolute way but the existence of an anisotropic behavior is clearly highlighted.
The continuation of the study should bring answers by looking further into the experimentation. The sample we used is thick and strongly attenuates transverse waves. Consequently, it was not possible to make celerity measurements and refraction angle measurements. So our results of attenuation could not be compared with other results. Failing to obtain this information, if we do not modify the experimental setup it becomes essential to obtain measures in the undetermined zone to have more understanding of the phenomenon. An inspection on both sides, preferably polished, is to be envisaged. The complete evolution of the attenuation will help to validate or not our forecasts. The development of an in situ procedure imposes access to only one side. It is a real challenge to study the effect of coupling between compressional waves and shear waves on the noise signal. This would make possible to cover the whole of the directions of propagation in the part.

REFERENCES

1. [AHM 92] Ahmed S., Thompson R. B., Effect of preferred grain orientation and grain elongation on ultrasonic wave propagation in stainless steel, in Review of Progress in Quantitative Nondestructive Evaluation, Vol. 11, edited by D. O. Thompson and D. E. Chimenti (Plenum, New York, 1992), p.1999-2006
2. [BAI 77] BAIKIE B. L. YADD D., Oriented structures and properties in type 316 stainless steel metal, Int. Conf. Solidification and Casting, Metals Society, Sheffield Univ, 1977, p. 438 - 443.
3. [BIL 82] de BILLY M., QUENTIN G., Backscattering of acoustic waves by randomly rough surfaces of elastic solids immersed in water , J. Acoust. Soc. Am. 72 (2), August 1982, p.591-601
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6. [HIR 86] HIRSEKORN S., Directionnal dependence of ultrasonic propagation in textured polycrystals, J. Acoust. Soc. Am. 79 (5), May 1986, p.1269-1279
7. [NEU 89] NEUMANN A. W. E., On the State of the art of the inspection of austenitic welds with ultrasound, Int. J. Pres. Ves. & Piping 39, 1989, p.227 - 246
8. [OGI 85] OGILVY J. A, A model for elastic wave propagation in anisotropic media with application to ultrasonic inspection through austenitic steel, British Journal of NDT, n°1, vol 27, 1985, p.13-21
9. [SAN 88] SANIIE J., WANG T., BILGUTAY N.M., Statistical evaluation backscattered ultrasonic grain signals, J. Acoust. Soc. Am. 84 (1), July 1988, p.400-408

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