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Effect of interlamellar spacing of pearlite on the attenuation of ultrasound
Effect of interlamellar spacing of pearlite on the attenuation of ultrasound B. Kopec The attenuation of ultrasound was studied in samples of pearlitic steel taken from railway wheels containing between 0.53 and 0.61% carbon. A strong dependence of ultrasonic attenuation on grain size was observed; in addition a relationship was shown between the interlamellar spacing of pearlite in the steel and the attenuation coefficient. The scattering losses in the Rayleigh zone of the pearlitic/ferritic steel were found to be proportional to the spacing of the cementite lamellae in the pearlitic structure.
The ever more stringent requirements for the materials for railway vehicle construction, particularly the wear resistance of railway wheels, are closely linked with the constantly increasing speed of railway transport systems. In the case of peaflitic steels, which are widely used for the manufacture of the railway wheels, the wear resistance depends on structural factors, especially on the amount of ferrite present and on the interlamellar spacing between the pearlite plates. From the point of view of testing such materials non-destructively, it is significant that it is these structural factors which affect the degree of attenuation of ultrasound transmitted through the material. The dependence of the attenuation coefficient of ultrasonic waves on the grain size of the material has been widely studied and reported in the literature. 1-7 Since during routine ultrasonic examination of the structural integrity of railway wheels, various characteristics of the ultrasonic attenuation coefficient are measured for the same grain size (which is measured metallographically), it was decided to analyse the effect of the cooling rate and the interlamellar spacing of pearlite on the degree of attenuation of ultrasound. The advantage of ultrasonic examination lies in the fact that it can readily be used on structures of complicated geometry and while they are in situ.
Attenuation of ultrasound in steel Two processes contribute to the attenuation of ultrasound in a polycrystaUine material such as steel; these are scattering losses, and absorption losses which are due to the conversion of mechanical wave motion energy into another energy form. The degree of ultrasonic attenuation is described by an attenuation coefficient, c~which can be divided into two components o~ = % + aa
(1)
where ~ is the scattering term and ~a the absorption term; both of which depend on the frequency. The ratio of the The author is Manager of Quality Control in ~'elez~rny a dr~tovny, Bohum[n, Czechoslovakia.
8
mean grain size,/~, to the wave length, X determines which of the two loss mechanisms predominates and also affects the frequency dependence of the scattering term. The dependence on the material structure is reflected by the degree of scattering. To determine the grain size of the material, the Rayleigh zone (in which )x < 2rrD) is used. The scattering coefficient in this zone is given by % =
(2)
a:v 4
The constant a2 expresses the scattering losses in steel materials and varies with the cube of the mean grain diameter and the square of the elastic anisotropy. The scattering losses observed in a single phase steel show considerable differences from those in a multi-phase structure. The decisive factors governing the losses in a single phase structure such as ferrite, are the elastic anisotropy and differences in the orientation of the individual grains. In pearlite, however, which is a slightly dispersed mixture of ferrite and cementite and usually has a lamellar structure, the ultrasound is scattered substantially less than is the case for individual grains of single-phase ferrite. Ultrasonic attenuation in steels depends not only on the size and mutual orientation of grains in the structure, but to a large extent on defects in the crystalline lattice I and on imperfections in the structure which are formed during the forging process. 8
Experimental methods and results Measurements of the ultrasonic attenuation in railway wheel material were carried out by the pulse echo method (using compressive ultrasound); constant acoustic coupling was used. The tests were run with a USIP-11 ultrasonic defectoscope, developed by Krautkr~imer Co (GFR), using probes of frequency 2 MHz and 4 MHz (the effective average diameter of the transducer was in both cases 23 nun). To achieve constant acoustic coupling between the sample and the probe, the latter was coupled to the sample using a constant pressure fitting; engine oil was used as the coupling medium. To
0308-9126/79/010008-04 $02.00 © 1979 IPC BusinessPress
NDT INTERNATIONAL. FEBRUARY 1979
Table 1. Details of heat treatment of attenuation samples from railway wheels Sample group
Normalizing Time at Method Grain size, temperature tempera- ofcooling D (°C) ture (mm) (hours)
1
860
4
2
860
4
Interlamellar spacing S(~m)
in furnace
0.22-0.031
1.3-1,6
in cold
0.015-0.022
0.3-0,8
air stream 3
1200
4
infurnace
0.177-0.250
0.8-1,3
4
1200
4
in cold airstream
0.177-0.250
0.3-0.8
create a uniform oil layer below the probe, the measurements were run at 3 minute intervals after coupling the sample and probe together. The railway wheel material for these measurements was selected according to carbon content; this varied from 0.53 to 0.61%, which is the range permitted by the International Railway Union (UIC) specifications. Sixteen segments about 200 mm long were cut from wheels and these segments were then divided into four groups each containing four samples with various carbon content. Each group was subjected to a different heat treatment programme in order to obtain various grain sizes in the structure and various interlammellar spacings in the pearlite constitutents. After heat treatment, samples 50 mm thick were prepared from each segment, care being taken to ensure a uniform surface quality. The various
Fig. 2 Specimen from sample group 4 (see Table 1) showing cementite lamellae in a pearlitic structure; average interlamellar spacing of pearlite ~ = O.5/~m (optical microscopy, x 1000, etched with nital)
heating and cooling procedures, together with details of the resultant structures are given in Table 1. The sample structures of the third and fourth groups described in the table are shown in Figs 1 and 2. The structure of the railway wheels is pearlitic/ferritic with a predominant pearlitic component. The grain boundaries and boundaries around the pearlitic blocks consist of a mixture of continuous and interrupted ferritic networks. The attenuation of ultrasound was measured by the difference between the amplitude of the first and second backwall echoes; a correction factor ~(d/lo) where d is the sample thickness and lo is the near field length, was applied for the deviation from linear decrease of height of the backwall echo with distance. Moreover, the loss in pulse height due to the geometry of the acoustic field between adjacent echoes was taken into consideration and the effect of the reflection coefficient was eliminated from the coupling layer. 6 From the values of the attenuation coefficient obtained from all samples, the dependence of the attenuation on the interlamellar spacing within the pearlite was plotted. Fig. 3 shows this dependence for mean grain sizes o f D = 0.022 mm and /~ = 0.177 ram, measured at 2 and 4MHz respectively and shows that in the case of/5 = 0.022 mm, both frequencies give a straight line of the same slope.
Fig. 1 Specimen from sample group 3 (see Table 1) showing cementite lamellae in a pearlitic structure; average interlamellar spacing of pearl ite S = 1.0 #m (optical microscopy, x 1000, etched with nital).
NDT I N T E R N A T I O N A L .
F E B R U A R Y 1979
The scattering losses were determined using an ultrasonic defectoscope at maximum sensitivity and following pulses on an oscilloscope. The scattering losses are characterized by the occurrence of grass representing all echoes from boundaries joining different constituents between the starting pulse and the first backwall echo. s In the case of the first and second
9
0.22
/
020
m
~
o ,8
,,M.,/
o.,4
:
/
D = 0.177 m m D : 0.022 mm
A / / ~
,
,
I
2 0.12
2M
:#
=o o.o8
•
4MHz
006
~..,,t--
~"i ~ 0.2
I 0.4
I 0.6
I 0.8
I 1.0
I 12
I 14
I I6
t ~J 1.8 2 0
Inierlomell0r spacing,S (/zm) Fig. 3 Dependence of the attenuation coefficient on the interlamellar spacing of pearlite of mean grain size O = 0.022 mm and /~ = 0.177 mm and frequency values of 2 and 4 MHz.
group of samples, where D --- 0.022 mm, (see Table 1) the scattering losses were investigated only at a probe frequency of 4 MHz. In the case of the third and fourth group of samples, where D = 0.177 mm, the scattering losses were determined at frequencies of 2 and 4 MHz. Oscillographs of selected samples of each group at a probe test frequency of 4 MHz are shown in Fig. 4. Discussion
The measurements carried out in this work have shown that attenuation of ultrasonic waves closely follows variations in the structure of the material. The well known strong dependence of the attenuation coefficient on the grain size of the material was observed, and is seen in the scattering component. In addition, the cooling rate after normalizing the sample was seen to have an effect on the attenuation coefficient; a consequence of this is that in railway wheel material, differences in the interlamellar spacing of pearlite plates can be deduced from its ultrasonic attenuation behaviour. The results obtained show the relationship between the temperature and the cooling rate during normalization and the attenuation of ultrasound. The normalization temperature to a large degree determines the grain size of the material whereas the cooling rate of the material influences the interlamellar distance between pearlite plates. Both of these factors affect, to a greater or lesser degree, the characteristics of the ultrasonic echoes in steel. For this reason, in order to determine the effect of these factors on the attenuation coefficient individually, the various heat treatment programmes were carried out in four groups of samples taken from railway wheel material as discussed above. In so far as the effect of interlamellar spacing of pearlite can be studied and thus eliminated from the investigation, it is
10
possible to allow for the effect of grain size in the heterogeneous pearlitic structures; this is done by heating all the samples to the same austenitization temperature and then, by different cooling rates, various interlamellar spacing of pearlite can be achieved at constant grain size. In homogenous austenite, if it is kept at constant temperature, pearlite is produced at a constant rate and hence has uniform inteflamellar spacing. The thickness of the individual lamellae is governed by the diffusion rate of carbon in austenite; this diffusion rate is proportional to the temperature. As the temperature decreases the austenite transforms into pearlite having a smaller spacing between cementite lamellae and thus very fine lamellar pearlite is produced. The grain size of the structure is of utmost significance in determining the degree of attenuation of ultrasound in the material. In the Rayeligh zone, the scattering component of attentuation rises with the cube of the mean grain size and so small variations in grain size result in large changes in the attenuation coefficient. In the case of constant grain size the attenuation of a peaflitic structure depends upon the interlamellar spacing of pearlite lamellae and the attenuation rises with increasing interlamellar spacing. When analyzing the proportion of pearlitic and ferritic phase in the structure of railway wheels, it has been found that if the grain size is kept constant attenuation rises as the proportion of ferrite in the structure increases. The ferritic components of the structure are significant, since during ultrasonic wave transmission the ferrite is in the form of a continuous network which encloses the pearlitic blocks and this raises considerably the attenuation. When an ultrasonic wave is transmitted through a grain of a polycrystalline ferritic/pearlitic structure with a ferritic network at the grain boundaries, the wave behaves as follows: • At the grain boundaries, the ultrasonic wave produces an echo due to the more or less developed ferritic network. Because of reflection and transformation of the wave, the amplitude of the ultrasonic wave is reduced. • As the attenuated wave is transmitted through the grain, its amplitude continues to drop. This decrease varies with the interlamellar spacing of pearlite within the grain. The scattering losses are proportional to the spacing of cementite lamellae in the peaflitic structure. Conclusions
The intedamellar spacing of peadite plays an important part in determining the yield limit and wear resistance of the pearlitic/ferritic structure of the railway wheels. In the case of heterogeneous structures containing several components, the attenuation losses of ultrasonic energy vary with the simultaneous effect of grain size and the structure of the ferritic network which surrounds these grains. The scattering losses are found to be proportional to the spacing of the cementite lamellae in a pearlitic structure. This fact can be advantageously used for investigating and analyzing the structural parameters of a pearlitic steel on the basis of attenuation of ultrasonic waves.
NDT I N T E R N A T I O N A L ,
F E B R U A R Y 1979
t
first hat, wall echo
first ~Ckwall
t
t
secm¢l beckwall echo
first backwall echo
secm~ backwall echo
first bockwalt ~
second backwall echo
seccmd I~cl~,#all e©l~
Fig. 4 Oscitlograms obtained in determining scattering losses with selected samples of each group at a testing frequency of 4 MHz; the scattering losses are characterised by grass
References
5
1
6
2 3 4
Mason, W.P. "Physical acoustics and the properties of solids' (Van Nostrand, New York, 1958) Papadakis, E.Po 'Ultrasonic attenuation and velocity in three transformation products in steel' J Appl Phys 35 (1964) pp 1474-1482 Papadakis, E.P. 'Revised grain - scattering formulae and tables" J Acoustics Soc o f A m 37 (1965) pp 703-710 Papadakis, E.P. 'Ultrasonic attenuation caused by scattering in polycrystalline metals' J o f Acoustic Soc o f A m 37 (1965) EP 711-717
NDT INTERNATIONAL.
FEBRUARY
1979
7
8
Obraz, J. 'A new method and equipment for measuring the ultrasonic attenuation caused by scattering' Seventh International Conference on ndt (Warsaw, 1973) ppaer J-01 Kopee, B. 'Ultrasonic inspection of grain size in the materials for railway wheel sets' Ultrasonics 13 No 6 (November 1975) pp 267-274 Kopec, B. 'Measurement of attenuation of ultrasound in the materials for railway axles' Proceedings o f the fifteenth International Conference on Acoustics and Ultrasound (Prague, 1976) pp 376-380 lermolov, I.N. et al 'Issledovaniezatuchivania ultrazvukovych voln pri prozvucivanii rotorav turbin' Defectoskopia No 6 (November-December 1975) pp 7-11
11
The ever more stringent requirements for the materials for railway vehicle construction, particularly the wear resistance of railway wheels, are closely linked with the constantly increasing speed of railway transport systems. In the case of peaflitic steels, which are widely used for the manufacture of the railway wheels, the wear resistance depends on structural factors, especially on the amount of ferrite present and on the interlamellar spacing between the pearlite plates. From the point of view of testing such materials non-destructively, it is significant that it is these structural factors which affect the degree of attenuation of ultrasound transmitted through the material. The dependence of the attenuation coefficient of ultrasonic waves on the grain size of the material has been widely studied and reported in the literature. 1-7 Since during routine ultrasonic examination of the structural integrity of railway wheels, various characteristics of the ultrasonic attenuation coefficient are measured for the same grain size (which is measured metallographically), it was decided to analyse the effect of the cooling rate and the interlamellar spacing of pearlite on the degree of attenuation of ultrasound. The advantage of ultrasonic examination lies in the fact that it can readily be used on structures of complicated geometry and while they are in situ.
Attenuation of ultrasound in steel Two processes contribute to the attenuation of ultrasound in a polycrystaUine material such as steel; these are scattering losses, and absorption losses which are due to the conversion of mechanical wave motion energy into another energy form. The degree of ultrasonic attenuation is described by an attenuation coefficient, c~which can be divided into two components o~ = % + aa
(1)
where ~ is the scattering term and ~a the absorption term; both of which depend on the frequency. The ratio of the The author is Manager of Quality Control in ~'elez~rny a dr~tovny, Bohum[n, Czechoslovakia.
8
mean grain size,/~, to the wave length, X determines which of the two loss mechanisms predominates and also affects the frequency dependence of the scattering term. The dependence on the material structure is reflected by the degree of scattering. To determine the grain size of the material, the Rayleigh zone (in which )x < 2rrD) is used. The scattering coefficient in this zone is given by % =
(2)
a:v 4
The constant a2 expresses the scattering losses in steel materials and varies with the cube of the mean grain diameter and the square of the elastic anisotropy. The scattering losses observed in a single phase steel show considerable differences from those in a multi-phase structure. The decisive factors governing the losses in a single phase structure such as ferrite, are the elastic anisotropy and differences in the orientation of the individual grains. In pearlite, however, which is a slightly dispersed mixture of ferrite and cementite and usually has a lamellar structure, the ultrasound is scattered substantially less than is the case for individual grains of single-phase ferrite. Ultrasonic attenuation in steels depends not only on the size and mutual orientation of grains in the structure, but to a large extent on defects in the crystalline lattice I and on imperfections in the structure which are formed during the forging process. 8
Experimental methods and results Measurements of the ultrasonic attenuation in railway wheel material were carried out by the pulse echo method (using compressive ultrasound); constant acoustic coupling was used. The tests were run with a USIP-11 ultrasonic defectoscope, developed by Krautkr~imer Co (GFR), using probes of frequency 2 MHz and 4 MHz (the effective average diameter of the transducer was in both cases 23 nun). To achieve constant acoustic coupling between the sample and the probe, the latter was coupled to the sample using a constant pressure fitting; engine oil was used as the coupling medium. To
0308-9126/79/010008-04 $02.00 © 1979 IPC BusinessPress
NDT INTERNATIONAL. FEBRUARY 1979
Table 1. Details of heat treatment of attenuation samples from railway wheels Sample group
Normalizing Time at Method Grain size, temperature tempera- ofcooling D (°C) ture (mm) (hours)
1
860
4
2
860
4
Interlamellar spacing S(~m)
in furnace
0.22-0.031
1.3-1,6
in cold
0.015-0.022
0.3-0,8
air stream 3
1200
4
infurnace
0.177-0.250
0.8-1,3
4
1200
4
in cold airstream
0.177-0.250
0.3-0.8
create a uniform oil layer below the probe, the measurements were run at 3 minute intervals after coupling the sample and probe together. The railway wheel material for these measurements was selected according to carbon content; this varied from 0.53 to 0.61%, which is the range permitted by the International Railway Union (UIC) specifications. Sixteen segments about 200 mm long were cut from wheels and these segments were then divided into four groups each containing four samples with various carbon content. Each group was subjected to a different heat treatment programme in order to obtain various grain sizes in the structure and various interlammellar spacings in the pearlite constitutents. After heat treatment, samples 50 mm thick were prepared from each segment, care being taken to ensure a uniform surface quality. The various
Fig. 2 Specimen from sample group 4 (see Table 1) showing cementite lamellae in a pearlitic structure; average interlamellar spacing of pearlite ~ = O.5/~m (optical microscopy, x 1000, etched with nital)
heating and cooling procedures, together with details of the resultant structures are given in Table 1. The sample structures of the third and fourth groups described in the table are shown in Figs 1 and 2. The structure of the railway wheels is pearlitic/ferritic with a predominant pearlitic component. The grain boundaries and boundaries around the pearlitic blocks consist of a mixture of continuous and interrupted ferritic networks. The attenuation of ultrasound was measured by the difference between the amplitude of the first and second backwall echoes; a correction factor ~(d/lo) where d is the sample thickness and lo is the near field length, was applied for the deviation from linear decrease of height of the backwall echo with distance. Moreover, the loss in pulse height due to the geometry of the acoustic field between adjacent echoes was taken into consideration and the effect of the reflection coefficient was eliminated from the coupling layer. 6 From the values of the attenuation coefficient obtained from all samples, the dependence of the attenuation on the interlamellar spacing within the pearlite was plotted. Fig. 3 shows this dependence for mean grain sizes o f D = 0.022 mm and /~ = 0.177 ram, measured at 2 and 4MHz respectively and shows that in the case of/5 = 0.022 mm, both frequencies give a straight line of the same slope.
Fig. 1 Specimen from sample group 3 (see Table 1) showing cementite lamellae in a pearlitic structure; average interlamellar spacing of pearl ite S = 1.0 #m (optical microscopy, x 1000, etched with nital).
NDT I N T E R N A T I O N A L .
F E B R U A R Y 1979
The scattering losses were determined using an ultrasonic defectoscope at maximum sensitivity and following pulses on an oscilloscope. The scattering losses are characterized by the occurrence of grass representing all echoes from boundaries joining different constituents between the starting pulse and the first backwall echo. s In the case of the first and second
9
0.22
/
020
m
~
o ,8
,,M.,/
o.,4
:
/
D = 0.177 m m D : 0.022 mm
A / / ~
,
,
I
2 0.12
2M
:#
=o o.o8
•
4MHz
006
~..,,t--
~"i ~ 0.2
I 0.4
I 0.6
I 0.8
I 1.0
I 12
I 14
I I6
t ~J 1.8 2 0
Inierlomell0r spacing,S (/zm) Fig. 3 Dependence of the attenuation coefficient on the interlamellar spacing of pearlite of mean grain size O = 0.022 mm and /~ = 0.177 mm and frequency values of 2 and 4 MHz.
group of samples, where D --- 0.022 mm, (see Table 1) the scattering losses were investigated only at a probe frequency of 4 MHz. In the case of the third and fourth group of samples, where D = 0.177 mm, the scattering losses were determined at frequencies of 2 and 4 MHz. Oscillographs of selected samples of each group at a probe test frequency of 4 MHz are shown in Fig. 4. Discussion
The measurements carried out in this work have shown that attenuation of ultrasonic waves closely follows variations in the structure of the material. The well known strong dependence of the attenuation coefficient on the grain size of the material was observed, and is seen in the scattering component. In addition, the cooling rate after normalizing the sample was seen to have an effect on the attenuation coefficient; a consequence of this is that in railway wheel material, differences in the interlamellar spacing of pearlite plates can be deduced from its ultrasonic attenuation behaviour. The results obtained show the relationship between the temperature and the cooling rate during normalization and the attenuation of ultrasound. The normalization temperature to a large degree determines the grain size of the material whereas the cooling rate of the material influences the interlamellar distance between pearlite plates. Both of these factors affect, to a greater or lesser degree, the characteristics of the ultrasonic echoes in steel. For this reason, in order to determine the effect of these factors on the attenuation coefficient individually, the various heat treatment programmes were carried out in four groups of samples taken from railway wheel material as discussed above. In so far as the effect of interlamellar spacing of pearlite can be studied and thus eliminated from the investigation, it is
10
possible to allow for the effect of grain size in the heterogeneous pearlitic structures; this is done by heating all the samples to the same austenitization temperature and then, by different cooling rates, various interlamellar spacing of pearlite can be achieved at constant grain size. In homogenous austenite, if it is kept at constant temperature, pearlite is produced at a constant rate and hence has uniform inteflamellar spacing. The thickness of the individual lamellae is governed by the diffusion rate of carbon in austenite; this diffusion rate is proportional to the temperature. As the temperature decreases the austenite transforms into pearlite having a smaller spacing between cementite lamellae and thus very fine lamellar pearlite is produced. The grain size of the structure is of utmost significance in determining the degree of attenuation of ultrasound in the material. In the Rayeligh zone, the scattering component of attentuation rises with the cube of the mean grain size and so small variations in grain size result in large changes in the attenuation coefficient. In the case of constant grain size the attenuation of a peaflitic structure depends upon the interlamellar spacing of pearlite lamellae and the attenuation rises with increasing interlamellar spacing. When analyzing the proportion of pearlitic and ferritic phase in the structure of railway wheels, it has been found that if the grain size is kept constant attenuation rises as the proportion of ferrite in the structure increases. The ferritic components of the structure are significant, since during ultrasonic wave transmission the ferrite is in the form of a continuous network which encloses the pearlitic blocks and this raises considerably the attenuation. When an ultrasonic wave is transmitted through a grain of a polycrystalline ferritic/pearlitic structure with a ferritic network at the grain boundaries, the wave behaves as follows: • At the grain boundaries, the ultrasonic wave produces an echo due to the more or less developed ferritic network. Because of reflection and transformation of the wave, the amplitude of the ultrasonic wave is reduced. • As the attenuated wave is transmitted through the grain, its amplitude continues to drop. This decrease varies with the interlamellar spacing of pearlite within the grain. The scattering losses are proportional to the spacing of cementite lamellae in the peaflitic structure. Conclusions
The intedamellar spacing of peadite plays an important part in determining the yield limit and wear resistance of the pearlitic/ferritic structure of the railway wheels. In the case of heterogeneous structures containing several components, the attenuation losses of ultrasonic energy vary with the simultaneous effect of grain size and the structure of the ferritic network which surrounds these grains. The scattering losses are found to be proportional to the spacing of the cementite lamellae in a pearlitic structure. This fact can be advantageously used for investigating and analyzing the structural parameters of a pearlitic steel on the basis of attenuation of ultrasonic waves.
NDT I N T E R N A T I O N A L ,
F E B R U A R Y 1979
t
first hat, wall echo
first ~Ckwall
t
t
secm¢l beckwall echo
first backwall echo
secm~ backwall echo
first bockwalt ~
second backwall echo
seccmd I~cl~,#all e©l~
Fig. 4 Oscitlograms obtained in determining scattering losses with selected samples of each group at a testing frequency of 4 MHz; the scattering losses are characterised by grass
References
5
1
6
2 3 4
Mason, W.P. "Physical acoustics and the properties of solids' (Van Nostrand, New York, 1958) Papadakis, E.Po 'Ultrasonic attenuation and velocity in three transformation products in steel' J Appl Phys 35 (1964) pp 1474-1482 Papadakis, E.P. 'Revised grain - scattering formulae and tables" J Acoustics Soc o f A m 37 (1965) pp 703-710 Papadakis, E.P. 'Ultrasonic attenuation caused by scattering in polycrystalline metals' J o f Acoustic Soc o f A m 37 (1965) EP 711-717
NDT INTERNATIONAL.
FEBRUARY
1979
7
8
Obraz, J. 'A new method and equipment for measuring the ultrasonic attenuation caused by scattering' Seventh International Conference on ndt (Warsaw, 1973) ppaer J-01 Kopee, B. 'Ultrasonic inspection of grain size in the materials for railway wheel sets' Ultrasonics 13 No 6 (November 1975) pp 267-274 Kopec, B. 'Measurement of attenuation of ultrasound in the materials for railway axles' Proceedings o f the fifteenth International Conference on Acoustics and Ultrasound (Prague, 1976) pp 376-380 lermolov, I.N. et al 'Issledovaniezatuchivania ultrazvukovych voln pri prozvucivanii rotorav turbin' Defectoskopia No 6 (November-December 1975) pp 7-11
11