Semi-automatic for ultrasonic measurement of texture

A method for measuring texture of metal plates or sheets using non-destructive ultrasonic investigation includes measuring the velocity of ultrasonic energy waves in lower order plate modes in one or more directions, and measuring phase velocity dispersion of higher order modes of the plate or sheet if needed. Texture or preferred grain orientation can be derived from these measurements with improved reliability and accuracy. The method can be utilized in production on moving metal plate or sheet.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a method of measuring texture in metal 
plates or sheets, and particularly, pertains to a method of utilizing 
ultrasound to measure texture. The invention also pertains to a method for 
the prediction of mechanical formability of metal plates using ultrasound. 
2. Problems in the Art 
It would be greatly advantageous to be able to quickly and accurately 
discern texture in relatively thin plate and sheet material during its 
production. With such information, the manufacturing process could be 
efficiently controlled to produce a product of desired texture 
characteristics, or to correct texture deficiencies within a short time of 
when they occur. Knowledge of this texture is important, for example, in 
predicting the capability of the metal to be formed into parts of complex 
shape. 
Previously, texture analysis required periodic sampling of the continuously 
produced sheet or plate material, and then utilization of x-ray or neutron 
diffraction techniques. Not only does this require destructive analysis 
from the periodically excised samples, such processes are time consuming 
and therefore cannot be used to immediately correct or change the 
production processes. Furthermore, x-ray processes give data only 
regarding the near surface of the material. Even though the material being 
analyzed is relatively thin sheet or plate, the texture characteristics 
can change drastically through its cross-section. The neutron processes 
provide information about the entire thickness of the material. However, 
the samples must be taken to a neutron source to perform the analysis. 
Therefore, the accuracy of these currently used processes is not as 
reliable or convenient as is desired. 
Therefore, a real need exists for improvement regarding the monitoring and 
estimation of texture in sheet or plate materials such as rolled metal 
plate. It has previously been known that certain properties and inferences 
of texture can be derived from the analysis of received ultrasonic energy 
after it has been passed through the material. In particular, it has been 
discovered that texture might be inferred from measuring the differences 
in speed of ultrasonic energy in different directions through the 
material. 
However, this knowledge has applied to thick metal pieces in which the wave 
properties are uninfluenced by the part surfaces. They must be modified to 
be applied to metal plates and sheets, which is the geometry often 
encountered when one wishes to control texture. 
The present inventors have worked with theoretical foundation for such 
non-destructive texture estimation. However up until the present 
invention, the theoretical bases for valid and accurate texture estimation 
had not been discovered. In fact, previous published works on the matter 
had been incorrect in the assumptions and theory for certain parts of the 
analysis. 
It is therefore a principal object of the present invention to improve over 
or solve the deficiencies and problems in the art. 
Another object of the present invention is to provide a method of 
ultrasonic measurement of texture which provides efficient and accurate 
estimates of texture in plate or sheet material. 
A further object of the present invention is to provide a method as above 
described which is non-destructive to the material being analyzed. 
Another object of the present invention is to provide a method as above 
described which can be easily adapted to be used in the area of and during 
production of the material. 
Another object of the present invention is to provide a method as above 
described which does not require complex, time-consuming, or impractical 
processes or equipment to derive accurate texture estimations. 
A further object of the present invention is to provide a method as above 
described which utilizes ultrasound as an interrogating medium. 
These and other objects, features, and advantages of the invention will 
become more apparent with reference to the accompanying specification and 
claims. 
SUMMARY OF THE INVENTION 
A method of ultrasonic measurement of texture utilizes advances in 
mathematical and theoretical understanding of measurement of the 
anisotropy of ultrasound wave velocities through a plate material, along 
with advances in technology and instrumentation, to allow accurate, 
reliable and efficient non-destructive estimation of texture in such 
material. The process can be easily adapted to be used directly in the 
manufacturing environment to give feedback in a matter of minutes to 
control manufacturing and to monitor output. 
The method measures the velocity of ultrasonic energy carried by low order 
plate modes of the material in one or more directions. Utilizing 
mathematical theory for describing texture in metal plate, the velocity 
measurements can be used to solve for the texture. In some cases, however, 
the answers may be erroneously influenced by certain idealizations in the 
theory. To complete the texture characterization under those conditions, 
the velocity of higher order plate modes regarding the ultrasonic waves is 
also measured. Information from such measurements provides an alternate 
scheme to provide the information needed for mathematical estimation of 
texture. 
The low order modes in which velocities are measured are S.sub.o and 
SH.sub.o, in the preferred embodiment of the invention. The higher order 
modes include the SH.sub.n modes. The invention therefore allows accurate 
estimation of texture without having to utilize the commonly used 
destructive x-ray or neutron diffraction techniques. Additionally, the 
method can be in continuous operation and give quick "in-process" 
feedback. The manufacturing process can therefore be adjusted to change or 
correct texture characteristics according to desire. The value of such an 
in-process method is enormous to the rolled metal-plate industry. The 
application of the invention can also be applied to similar materials.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
With reference to the drawings, a preferred embodiment of the present 
invention will now be described. It is to be understood that this 
description is not by way of limitation to the invention, but is for 
purposes of understanding the invention and disclosing one preferred way 
in which it can be carried out. 
To aid in an understanding of the invention, FIG. 1 schematically depicts a 
rolled metal plate 10. Arrows 1, 2, and 3 depict the rolling, transverse, 
and thickness directions, respectively, of plate 10. Any reference to the 
"plane" of plate 10 refers to the plane defined by directions 1 and 2. It 
can thus be seen that in the preferred embodiment, the invention can be 
utilized on rolled metal plate 10 to determine characteristics such as 
texture and preferred orientation of grain. With such knowledge, 
characteristics such as hardness, grain size, ductility, strength and 
formability can be estimated. It is important to understand that the 
present invention allows the determination of these texture 
characteristics "in-process"; that is, contrary to conventional methods of 
destructive x-ray or neutron diffraction, the present invention allows 
non-destructive evaluation as the plate is being produced, and directly on 
the plate production line. The advantages of this much quicker, local, 
non-destructive method are many. 
The present invention thus requires the generation and introduction of 
appropriate ultrasonic energy into plate 10. It then also requires the 
ability to receive the transmitted ultrasonic energy and to precisely 
deduce the velocity of propagation. In some cases, the velocity will be 
frequency dependent, and this dispersion must be taken into account. The 
preferred embodiment of the invention thus requires appropriate means and 
methods to send, receive, and process the ultrasound for these purposes. 
One embodiment for doing so is disclosed by S. J. Wormley and R. B. 
Thompson, entitled "A Semi-Automaic System for Ultrasonic Measurement of 
Texture," in Review of Progress in Quantitative Non-destructive 
Evaluation, 6A, D. O. Thompson and D. E. Chimenti, Eds. (Pleum Press, N.Y. 
1987), p. 951 by Wormley and Thompson, and hereby incorporated by 
reference. 
The central concept of the present invention is to utilize non-destructive 
ultrasonic interrogation to derive the preferred grain orientation (also 
called texture) of a metal plate or sheet from measurements of anisotropy 
of ultrasonic wave speeds through the material. The fundamental basis for 
measuring ultrasound velocity is disclosed in R. B. Thompson, J. F. Smith, 
and S. S. Lee, "Inference of Stress and Texture from the Angular 
Dependence Ultrasonic Plate Mode Velocities", Non-Destructive Evaluation 
of Microstructure for Process Control, H. N. G. Wadley, Editor (ASM. Metal 
Park, Ohio 1985), pp. 73-80; and R. B. Thompson, S. S. Lee, and J. F. 
Smith, "Angular Dependence of Ultrasonic Wave Propagation in a Stressed 
Orthorhombic Continuum: Theory and Application to the Measurement of 
Stress and Texture", J. Acoust. Soc. Amer., 80, 921-931, September 1986), 
both of which are incorporated by reference herein. 
The preferred orientation of grains (texture) in a metal plate is described 
by the series 
##EQU1## 
where .epsilon.=cos .theta., W is a distribution function describing the 
probability that a grain will have a particular orientation, .theta., 
.psi., .phi., are Euler angles defining crystallite orientation, and 
Z.sub.1mn are generalized Legendre functions. W.sub.1mn are constant 
coefficients which can be derived in plates such as rolled metal plate 10 
by measuring ultrasonic velocities when the variable letter term "1" of 
W.sub.1mn is less than or equal to the number 4. 
While this general relationship was disclosed in the above cited articles, 
certain incorrect assumptions and mathematical analysis were utilized 
which did not and cannot accurately derive the desired texture 
characteristics. 
The present invention therefore accurately and reliably derives texture in 
a rolled metal plate utilizing equation (1) and the following steps. 
The Voigt procedure to compute the average elastic constants of a 
polycrystal of a cubic material described by a crystallite orientation 
distribution function (CODF) leads to the following result: 
##EQU2## 
where in the Voigt approximation, the isotropic elastic moduli are defined 
as L=C.sub.11.degree.-C.degree./ 5, P=C.sub.12 .degree.+C.degree./5, 
T=C.sub.44 .degree.+C.degree./5, the elastic anisotropy is defined as 
C.degree.=C.sub.11 .degree.-C.sub.12 .degree.-2C.sub.44 .degree. and 
C.sub.11 .degree., C.sub.12 .degree., and C.sub.44 .degree. are the single 
crystal elastic constants of cubic crystallites. For these equations, it 
is assumed that plate 10 is homogeneous and has macroscopic orthotropic 
(orthorhombic) symmetry defined by the three mutually perpendicular mirror 
planes which can be associated with directions 1, 2, and 3 in FIG. 1. 
Equations 2 show that the elastic constants of cubic polycrystals are 
defined by only three coefficients of the CODF expansion; namely, 
W.sub.400, W.sub.420, and W.sub.440. When the single crystal contants are 
known, the Voigt averaging procedure can be used (in cases where plate 10 
has weak anitropy). Only these three orientation distribution coefficients 
(ODC's) need to be measured to fully specify the texture to the fullest 
degree possible, utilizing linear ultrasonic measurements. 
Texture can induce variations in these ODC's to change the anisotropy in 
wave speed. Wave speed anisotropies can also be induced by the presence of 
stress, as is discussed in the printed publication entitled "Inference of 
Stress & Texture from the Angular Dependence Ultrasonic Plate Mode 
Velocities" identified previously. While the present application can be 
applied to plate 10 having stress effects, for purposes of the preferred 
embodiment, it will be assumed that all stress effects have been 
eliminated from the data via the previous art and the characterization of 
texture will be a prime consideration. 
Recently, advances have been made in the theoretical understanding of the 
relationship between the speeds of the waves in plates and the ODC's 
(W.sub.1mn). Also, recent developments in measuring equipment (such as 
development of electromagnetic acoustic transducers (EMAT's)) allow 
ultrasonic velocity measurements to be made rapidly with no couplant. 
EMAT's are ideally suited to real time measurements in actual production 
environments; that is, directly in the process line for rolled metal plate 
10. The invention can therefore be used for direct non-destructive 
contemporaneous in-process control. 
It has been found that the preferred EMAT probe geometries include the use 
of meander coil and periodic permanent magnet geometries. 
In the preferred embodiment of the invention, unknown ODC's W.sub.400, 
W.sub.420 and W.sub.440 are deduced. Coefficients W.sub.420 and W.sub.440 
are deduced from variations of wave velocities in the plane of plate 10, 
as determined by the elastic constant anisotropy. In principle, W.sub.420 
could be determined from the difference of C.sub.11 and C.sub.22 as 
deduced from a comparison of the velocities of longitudinal waves 
propagating in the rolling and transverse directions, directions 1 and 2 
in FIG. 1, respectively. However, such simplistic ideas do not give 
quantitatively correct results as discussed below. The significance of the 
new art will be first put in perspective by a comparison to prior 
knowledge. 
Prior art has shown that W.sub.4mn can be measured in different thicknesses 
of plate 10 as follows: For thick plates, for which it is possible to 
resolve in time the echoes of shear waves propagating through the 
thickness, W.sub.420 can be determined from the relative arrival times of 
signals polarized along directions 1 and 2 (rolling and transverse) in 
FIG. 1. This amounts to a comparison of C.sub.44 and C.sub.55. Precise 
knowledge of the plate thickness is not essential since it is the same for 
both polarizations. The properties of the material are averaged through 
the thickness for the particular volume of plate through which the 
ultrasonic beam passes. Parameters W.sub.420 and W.sub.440 both can be 
deduced from the angular dependence of the Rayleigh wave (elastic surface 
wave) velocity on the plane of plate 10. Separation of the two is made 
possible by the different angular variations (COS 2.theta. and COS 
4.theta.) of the variations governed by the two coefficients. The plate 10 
is sampled to a thickness equal to the penetration of the Rayleigh wave 
(approximately one wavelength). The results are independent of thickness 
as long as the lower surface of plate 10 does not interact with the 
Rayleigh wave. W.sub.440 can also be deduced from the angular variation of 
the velocity of surface skimming horizontally polarized shear waves. The 
material properties are sensed in a near-surface region, although the 
penetration depth is somewhat greater than for Rayleigh waves, and depends 
upon the details of the experimental geometry. 
For thinner plates, somewhat different considerations are involved. The 
velocities of longitudinal waves propagating along the rolling and 
transverse direction may be affected by the boundaries of the plate 
surfaces. It may be difficult to resolve echoes of signals propagating 
through the thickness of plate 10. Also, Rayleigh waves and surface 
skimming horizontally polarized shear waves may be influenced by the 
proximity of plates 10's lower surface, as these solutions assume a medium 
bound by only one surface. 
As revealed herein, these difficulties are overcome by analyzing the 
received data in terms of the guided elastic modes of plate 10. In one 
preferred embodiment, coefficients W.sub.400, W.sub.420 and W.sub.440 are 
deduced from the speeds of the SH.sub.o and S.sub.o modes propagating in 
the plane of the plate. By referring to FIG. 3, it can be seen that the 
phase velocity (.omega./k) of the S.sub.o mode is essentially constant at 
low frequencies, as indicated by the essentially constant slopeof that 
portion of the dispersion curve. It is in this region that the 
measurements are preferred to be made. 
By referring to FIG. 2, it can be seen that the angular dependence of 
ultrasonic wave speeds of these SH.sub.o (horizontally polarized shear) 
and S.sub.o (extensional) modes of plates 10 can be used. Both the 
SH.sub.o and S.sub.o wave speeds are measured at 0.degree., 45.degree. and 
90.degree. with respect to rolling direction 1 (in FIG. 1). The angular 
dependences of these speeds has the same functional form as that of plane 
waves, but the parameters are modified by the differences between the 
plane wave and plate solutions. The recognition of this difference is an 
important aspect of this invention. Reference is taken to R. B. Thompson, 
S. S. Lee and J. F. Smith, "Relative Anisotropies of Plane Waves and 
Guided Modes in Thin Orthorhombic Plates: Implication for Texture 
Characterization", Ultrasonics, 1987, Vol. 25, May, pp. 133-137, which is 
incorporated by reference herein. The formulae relating velocities to the 
W.sub.400, W.sub.420 and W.sub.440 coefficients are: 
##EQU3## 
Examination of Equations (3a-3e) show that W.sub.420 and W.sub.440 are 
predicted from differences in measured velocities while W.sub.400 depends 
on the sums of measured velocities. Thus W.sub.420 and W.sub.440 can be 
determined from angular determinations of velocities while W.sub.400 
depends on the absolute velocity. Because of this difference, practical 
difficulties sometimes are encountered on the determination of W.sub.400. 
The inference of W.sub.400 from absolute measurements depends on the 
absolute accurcy of the computation of polycrystalline average elastic 
constants. Since the accuracy of those computations is considerably better 
for relative variations than for absolute values, this additional 
potential for significant error also exists. Moreover, when attempting to 
deduce W.sub.400 from S.sub.o mode measurements, the data must also be 
corrected from the slight frequency dependence of the S.sub.o mode 
velocity at low frequencies. These may not be limiting factors for alloys 
of simple metallurgical structure, but may cause greater problems for more 
complex alloys. 
Therefore, the present invention includes alternate procedures for 
determining W.sub.400 from the phase velocity dispersion of the higher 
order plate modes. In one approach, one deduces the elastic constants 
C.sub.44, C.sub.55 and C.sub.66 from the data and calculates W.sub.400 in 
terms of the differences in these elastic constants. This eliminates the 
possible errors in both velocity measurement and computation of 
polycrystalline average elastic constants as would occur in attempting to 
determine W.sub.400 from absolute velocity measurements. In another 
approach, one examines the degree of splitting of the dispersion curves 
for two modes which would normally be tangent in the untextured case (see 
FIG. 3). These two approaches are described in greater detail below. 
The speeds of the higher order horizontally polarized shear modes, denoted 
SH.sub.n in FIG. 3, depend only on C.sub.44, C.sub.55 and C.sub.66 when 
the waves are propagating along the rolling and transverse directions 
denoted by the 1 and 2 axes in FIG. 1. If these constants can be 
determined by fitting measured velocity data to the theory, examination of 
Eq. (2) shows that enough information is available to determine the three 
unknown coefficients. 
In one embodiment, one observes the frequency of waves which can be excited 
by a transducer having a fixed periodicity, which defines the wavelength 
of the waves at that frequency. One has thus specified one point 
(.omega.,k) on the dispersion curve. C.sub.44, C.sub.55, and C.sub.66 can 
be determined by analyzing the results of several such measurements in 
terms of the dispersion curves of the plate modes. The thickness of plate 
10 is not particularly critical for C.sub.44 and C.sub.55 as they depend 
on thickness and similar waves. However, thickness must be precisely known 
for determining C.sub.66, as these methods average the elastic properties 
through the thickness of plate 10 over the path transversed by the 
ultrasonic waves. 
A strong motivation for use of this approach is in the determination of 
W.sub.400, when it cannot be obtained from absolute measurements of the 
velocity of the S.sub.o mode as discussed in the previous embodiment. 
Utilizing equations 2(g)-2(i) and the elastic constants C.sub.44, and 
C.sub.55 and C.sub.66 deduced by measuring the phase velocity dispersion 
of the higher order plate modes of plate 10, it follows that: 
##EQU4## 
Utilizing this step, the problems of utilizing absolute measurements are 
overcome since determination of W.sub.400 now depends on relative values 
of C.sub.44 +C.sub.55 -2 C.sub.66. However, it is essential to precisely 
know the thickness of the plate because of the aforementioned dependence 
of C.sub.66 on this parameter. 
In the other preferred embodiment depending on the dispersion curves of the 
higher order plate modes, concentration is focused on the point at which 
the SH.sub.1 and S.sub.o mode dispersion curves are tangent, as 
illustrated in FIG. 3. This is the behavior that is characteristic in an 
isotropic plate (W.sub.400 =W.sub.420 =W.sub.440 =0). However, when 
anistropy is present, this tangency no longer occurs. The SH.sub.1 and 
S.sub.o mode dispersion curves either overlap, with two points of 
intersection, or do not cross at all. Modeling of ultrasonic wave 
propagation is anistropy plates having elastic constants described by Eq. 
(2) shows that W.sub.400 can be quantitatively inferred from measurements 
of the degree of overlap or lack thereof. This technique has the 
additional advantage of not requiring a precise knowledge of the plate 
thickness, since the dispersion curves of both modes are shifted in a 
similar fashion by thickness changes. 
An instrument suitable for the experimental measurement of the properties 
of these modes in this region has been disclosed by R. B. Thompson and C. 
F. Vasile, "An Elastic-wave Ellipsometer for Measurement of Material 
Property Variations", Appl. Phys. Lett. 34, 128-130 (1979). 
Operation of the invention can be advantageous in many applications. It can 
be used in process control of sheet metal production and quality control 
of incoming materials for aerospace, automotive, packaging, and many other 
processes and industries. 
Experimental results have shown that the present invention compares 
favorably with x-ray diffraction. 
Table I below shows the experimental results for W.sub.440 utilizing the 
present method for aluminum and copper sheet or plate, as compared to 
x-ray diffraction results. 
TABLE I 
______________________________________ 
Comparison of W.sub.440 Predicted by X-ray 
and Ultrasonic Techniques 
X-ray SH.sub.o Ultrasonics 
S.sub.o Ultrasonics 
______________________________________ 
Aluminum 
-0.00362 -0.00594 -0.00583 
Copper -0.00319 -0.00302 -0.00288 
______________________________________ 
In Table I, the samples used were 1100 aluminum and commercially pure 
copper. With regard to copper, the values of W.sub.440 deduced from the 
two ultrasonic modes are in good agreement with the x-ray diffraction 
data. With respect to the aluminum, the two ultrasonic values are in 
agreement but differ from the x-ray value by a considerable margin, nearer 
50%. 
Both x-ray and ultrasonic techniques predicted considerably smaller values 
for W.sub.420 for those samples. 
FIGS. 4-7 presents a comparison of x-ray and ultrasonic pole figures for 
plate reduced to 84%, and the same plate after annealing for 0.5 hours at 
300.degree. C. Although the ultrasonic pole figures do not contain the 
same degree of detail, the general structure of the texture and its change 
with annealing are clearly revealed. The ultrasonic figures (FIGS. 5 and 
7) show only the first few terms in the series equation 1 which results in 
the lesser detail. 
For further comparison, FIGS. 8 and 9 qualitatively compare the modulus 
difference (C.sub.44 -C.sub.55 ; which is proportional to W.sub.420) as a 
function of thickness reduction to the normalized intensity of what are 
referred to as the (111) and (200) poles as determined by x-rays. The 
evolution of the texture is indicated in a similar manner by each 
parameter. 
FIGS. 4-9 therefore show the general good agreement between the present 
invention and x-ray diffraction. The advantages of the present invention 
over x-ray diffraction techniques provides a real and valuable advance in 
the art. 
The included preferred embodiment is given by way of example only, and not 
by way of limitation to the invention, which is solely described by the 
claims herein. Variations obvious to one skilled in the art will be 
included within the invention defined by the claims. 
The present invention can be utilized for measuring textures of 
polycrystals of various crystallite symmetries. This can include, but is 
not limited to cubic metals such as copper, aluminum, and iron. It can 
also include materials of hexagonal crystal symmetry, including but not 
limited to titanium, zirconium, and similar metals.