NDT&E International 36 (2003) 1–5 www.elsevier.com/locate/ndteint
Grain size influence on ultrasonic velocities and attenuation A. Badidi Boudaa,*, S. Lebailib, A. Benchaalaa a
Laboratoire Laboratoire de Caracte´ risation risation et d’Instrumentation, Centre de Soudage et de Controˆ Contro ˆ le, le, BP 64 Route de De´ ly ly Ibrahim, Che´ raga, raga, Algiers, Algeria b ´ des Sciences de l’inge´ nieur, Laboratoire Ge´ nie nie des Mate´ riaux, riaux, De´ partement Ge´ nie nie Mecanique, Faculte´ des nieur, USTHB, BP 32 El Alia, Bab Ezzouar, 16111 Algiers, Algeria
Received 8 January 2002; revised 24 June 2002; accepted 4 July 2002
Abstract
During the last two decades, ultrasonic testing was developed as an efficient tool for materials characterization. Acoustical waves by their passage passage through materials, materials, carry out a multitude multitude of information information contained contained in the signal on the mechanical mechanical and physical properties properties of the material under inspection. In this paper, an experimental study on steel samples has been performed to study the evolution of some ultrasonic parameters such as wave velocities and attenuation coefficients as function of the steel grains size. The experimental results obtained are discussed and analyzed in order to develop an ultrasonic non-destructive technique to grains size determination. q 2002 Published by Elsevier Science Ltd. Keywords: Ultrasonic; Grain size; Velocity; Attenuation; Scattering
1. Introduction
2. Samples choice
Technical components are designed and manufactured to bear loads (mechanica (mechanical, l, thermal, thermal, chemical) chemical) during their lifetime; lifetime; the material material property determinatio determination n by NDT is therefore from interest. Due to the propagation of an acoustical wave through material, the received signal provides several information on the mechanical or the physical properties of the explored medium. When a detailed description of the inspected volume is needed, the complexity of the ultrasonic phenomena does not allow a simple simple exploitati exploitation on of the results, results, especially especially when the structure structure is heterogene heterogeneous, ous, i.e. inhomogeneous inhomogeneous and anisotropic. Grai Grain n size size is influ influen enci cing ng mo most st of the the mech mechan anic ical al prope properti rties es and and is there therefor foree an obje object ctive ive for for materi materials als character characterizat ization. ion. We have thermall thermally y processe processed d steel steel samples whose grain size changes in length direction. We have tested three samples from the same bar. These samples have been insonified by longitudinal and shear waves. For the measurement of velocities and attenuation of the two kinds of bulk waves an immersion technique was used.
The ultrasonic measurements require a high precision, especially in the positioning of the sample relatively to its rotation rotation axis. The half cylinder cylinder shaped shaped samples samples ( Fig. 1) 1) allow allow to genera generate te the two bulk bulk modes modes (longi (longitud tudina inall and transv transvers ersal) al) by insoni insonifyin fying g a longit longitudi udinal nal wave wave under under special special angle of incidences incidences [1] [1].. For this, this, three three differ different ent steel samples, namely E24, S300PB and A60, according to AFNOR standard were thermally processed the same way. Afte Afterr quen quench chin ing, g, a grea greatt grai grain n size size grad gradie ient nt has has been been observed in the E24 steel sample, compared to those of S300PB S300PB and A60. A60. There Therefor fore, e, the E24 steel steel sample sample was characterized in details; the chemical composition is given in Table in Table 1. 1.
* Corresponding author. Tel./fax: 213-21-36-18-50. E-mail address:
[email protected] (A. Badidi Bouda).
þ
0963-8695/03/$ - see front matter q 2002 Published by Elsevier Science Ltd. PII: S 0 9 6 3 - 8 6 9 5 ( 0 2 ) 0 0 0 4 3 - 9
3. Thermal Thermal processing processing
A thermal processing device was used in order to have a continuous quenching simply simply with a suitable water water flow, and this, only on one side of the sample ( Fig. 2). 2). The principle of this this treatm treatment ent consis consists ts in heatin heating g the sample sample until until the austenisation temperature [2] [2].. When When the temper temperatu ature re is homogenously distributed, the sample is watered.
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Fig. 1. Schematic path of ultrasonic waves in the sample.
4. Grain size measurements
The grain size is determined by polishing and etching the sample and evaluating the micrograph by a suitable method [3]. To measure the average grain size, we have used the method called ‘by counting’. The image linear magnification g must be such that at least 50 grains can be counted inside the area limited by a 79.8 mm diameter circle. The average grains diameter d m in millimeters then is d m
¼ p 1m
ffiffiffi ¼
ð1Þ
where m
2
g
100
2
ð2Þ
ng ;
and n g is the total number of grains inside the circle. Grain size measurements have been made on three samples. An example is presented in Fig. 3. We can observe that the grains size is weaker on the cooled face side. By moving away from this face, the grain size increases slowly to stabilize at 40 mm distance value which corresponds to the material grain size before processing. We can therefore conclude that beyond this value the samples have not undergone notable modification in their mechanical characteristics.
Fig. 2. Thermal processing device.
6. Experimental device
The experimental device for ultrasonic measurement is sketched in Fig. 5. The generator delivers excitation pulses with an adjustable amplitude. In reception, it contains an amplifier with a large adjustable gain [4]. The probe displacement, in a water tank in X – Y plane is performed by two step by step engines controlled by a microcomputer via an interface (RS-232). The numerical scope is controlled by the microcomputer via an IEEE-488 interface. It allows a sampling in an adjustable time window. Signals collected are forwarded to the microcomputer for processing. The specimen is fixed on a goniometer and immersed in water. A computational software allows to control the different probe displacements with regard to the specimen, the sampling rate the data acquisition, processing and the visualization of obtained results.
7. Velocities and attenuations of ultrasonic waves
The experimental study of the grains size influence on the ultrasonic parameters such as the velocities and
5. Metallographical analysis
The samples were taken from the same steel bar. The metallographic analysis have shown a ferritic – perlitic structure on all the sample length. In fact we have chosen a heat treatment which maintain the same structure on all the sample lengths. Only the grain size has changed (Fig. 4). Table 1 Chemical composition Elements
Contents (%)
C Ni Mn Cr V Ti Si
0.21 0.14 0.42 , 0.10 0.002 0.002 0.14
Fig. 3. Grain size curve.
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the scattering coefficient is proportional to f 4 [15–19]
ð Þ ¼ a1 f þ a2 D3 f 4
ð5Þ
a f
where a1 is the absorption constant, a2 the scattering constant and f is the frequency. The scattering coefficient shows a high sensitivity to the variation in grain size. The following equations, respectively, give the expression of the coefficient of scattering for a longitudinal and shear wave [20,21]: For a longitudinal wave: alS
Fig. 4. Structure analysis (ferrito-perlitic).
the attenuation coefficients in polycrystalline materials requires to take into account the scattering of the ultrasonic waves. Generally, the attenuation coefficient a is a related parameter composed of the absorption coefficient aA plus the scattering coefficient a S [5–7] a
ð3Þ
¼ aA þ aS
The scattering of ultrasounds in contact with grains and interfaces in polycrystalline materials are the cause of the attenuation and create dispersive velocities. The attenuation coefficient and the velocities dispersion caused by the grains are described analytically in documentation [8– 13]. A model for the amplitude of the backscattered signal Ab ; corresponding to a given depth z, can be described for materials with homogeneous properties [14] as Ab
¼ A0aSð f Þexpð
2a f z
2
ð4Þ
ð ÞÞ
a z; f is the where A0 is the initial amplitude, a f aS z; f : In overall attenuation coefficient and aS f general, grain scattering losses are large compared to absorption losses. In the Rayleigh region (our case) where l q D (l wavelength and D grain size diameter), the absorption coefficient depends linearly on the frequency and
ð Þ¼ ð Þ ð Þ¼ ð Þ
¼
" # þ
8p3 VA2 2 375r 20 V l8
3
V l
5
V t
f 4
ð6Þ
f 4
ð7Þ
where V 1 = 6p D3 : For a shear wave:
¼
atS
¼
" # þ
6p3 VA2 3 375r 20 V t8
2
V l
5
V t
with A C 11 2 C 12 2 2C 44 Eqs. (6) and (7) reveal that the losses by scattering affect much more the shear waves than the compression waves. In the Rayleigh region, high frequency components are backscattered with larger intensity compared to low frequency components. Consequently, this situation results in an upward shift in the expected frequency of the power spectrum corresponding to the power broadband echoes. Furthermore the term exp 22a f z in Eq. (4) influences the frequency shift in a downward direction. The downward shift is dependent on the position of the scatterers relative to the probe. We have here two opposing phenomena (i.e. upward shift due to scattering and downward shift caused by attenuation). However, the sound path length z can be considered as high because of many sound path in the sample, the downward shift caused by attenuation is preponderant, and velocity is decreasing. Heterogeneities, such as pores, microcracks and grains decrease the velocity of the longitudinal wave as well as that of the transverse wave [5]. Consequently, inspection of Eq. (5) shows that the down shift frequency decreases the absorption coefficient and the scattering coefficient and thus the attenuation coefficient whereas the increase in mean grain size diameter increases the scattering coefficient.
¼
ð
ð ÞÞ
8. Ultrasonic measurements
Fig. 5. Experimental device.
Ultrasonic measurements are undertaken in immersion technique at oblique and normal angles of incidence by using a 10 MHz immersion focused probe [22]. We have chosen a focused probe because the preliminary tests performed with an unfocused probe have done a stronger scatter in the experimental results. In normal incidence and
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Fig. 6. Parameters for attenuation.
Fig. 8. Attenuation coefficient of longitudinal waves on the axis.
thereafter in oblique incidence, are measured successively the time of flight of longitudinal waves in the specimen and the amplitudes of the back-wall echoes. The parameters for the attenuation measurement are shown in Fig. 6.
11. Transverse waves velocities measurements
The principle is the same as for longitudinal waves attenuation coefficients measurement. Results are given in Fig. 9.
9. Longitudinal waves velocity measurements
The wave transit time is measured in thickness direction of the specimen. The thickness (or the radius) is mechanically measured with precision. Results are given in Fig. 7.
The amplitudes of the three first back-wall echoes are measured. The longitudinal waves attenuation coefficient aLP is a LP
¼
The transverse waves attenuation coefficient a Tp is: aTp
10. Longitudinal waves attenuation coefficients measurements
E n 2 E nþ1 1 ln R2p 2 y E nþ1 2 E nþ2
12. Transverse waves attenuation coefficients measurements
ð8Þ
¼
E n 2 E nþ1 1 ln R2p R2e E nþ1 2 E nþ2 4 y
ð9Þ
where Rp is the sample reflection coefficient at normal incidence; E , echo amplitude; y , sample thickness and R e is the sample reflection coefficient at oblique incidence. Results are given in Fig. 10.
13. Results and discussion
where E is the amplitude of the n th echo; R p, longitudinal waves reflection coefficient (sample– water) and y is the sound path length in the specimen. Results are given in Fig. 8.
By analyzing curves (Figs. 7 and 9) representing the variation of longitudinal and transverse wave velocities, we note that longitudinal velocity is high in the cooled face side. The velocity decreases until a distance of
Fig. 7. Longitudinal velocity on the axis.
Fig. 9. Transverse velocity on the axis.
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velocities and attenuation of ultrasonic waves through a steel with a variable grain size was investigated. This experimental work shows the possibility to assess the qualitative grain size of the here discussed material from its longitudinal or transverse velocity wave. However, it is important to do other experiments by increasing the frequency of the used probes. In fact, the higher the frequency is the less is the wavelength and coming into the range of the averaged grain size. In perspective, other experiments with gradients of larger grains size are necessary and frequency dependence should be the most promising tool for further investigations.
References Fig. 10. Attenuation coefficient of transverse waves on the axis.
approximately 40 mm; then increases slightly then coming to a saturation at a distance of 90 mm. The same behavior is observed for the transverse waves except that the transverse velocity gets nearly constant after the 40 mm value. Compared with Fig. 3 and the documentation of the grain size gradient, there is no strong variation of the velocities beyond this distance value. We can notice an inverse effect in the velocities composed with grain size in the cooled part. Scattering influences the velocity by the dispersion effect, i.e. higher frequencies are cancelled out by scattering a long the sound path length and velocities are decreasing [14]. On the curves representing the attenuations (Figs. 8 and 10) we notice, like with velocities, a decrease and a stabilization, but there is a large scatter in the experimental data. This scatter can be explained by diffraction due to the probes and the plane parallelism of the faces of samples which must be improved. In the Rayleigh region we have seen that the down shift frequency decreases the absorption coefficient and the scattering coefficient and thus the attenuation coefficient whereas the increase in mean grain size diameter increases the scattering coefficient. The inaccuracy of these results does not allow an exploitation at this stage of the attenuation coefficients in the characterization of the grains size by ultrasounds.
14. Conclusion
The possibility of an ultrasonic normal and oblique incidence technique in water immersion for measurement
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