·Table of Contents ·Materials Characterization and testing | Ultrasounds Back-Scattering Measurements for New Anisotropy Indicator ConstructionJ. MOYSAN, G. CORNELOUP.Laboratoire de Caractérisation Non Destructive Université de la Méditerranée - IUT GMP Avenue Gaston Berger - 13625 Aix en Provence Cédex - France Contact |
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.
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].
(1) |
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.
(2) |
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].
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) |
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) |
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) |
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) |
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.
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 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).
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 (C_{45} 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.
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