SU1388784A1 - Method of determining poissonъs ratio - Google Patents

Abstract

The invention relates to acoustic methods for measuring the physical parameters of solids. The aim of the invention is to improve the accuracy by eliminating the error in determining the speed of propagation of various types of waves through the use of plane longitudinal and surface waves. On sample I, the emitter 2 of a plane elastic wave and the receiver 3 are installed, whose linear dimension along the wave front is not less than the size of the emitter 2. Plane longitudinal and surface waves are excited and their propagation time is measured. The distance between the radiator 2 and the receiver 3 is changed and the propagation time of the longitudinal and surface oscillations is measured again. Using the measured values, the Poisson's ratio of the sample material 1 is determined. 2 Il. (L

Description

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The invention relates to acoustic methods for measuring the physical parameters of solids and can be used in determining the Poisson's ratio, for example, mountain populations,

The aim of the invention is to improve the accuracy by eliminating the error in determining the speed of propagation of various types of waves.

Figure 1 shows the installation of ultrasonic (US) transducers on the sample when determining the Poisson's ratio; Fig. 2 illustrates the graphical dependence of the Poisson's coefficient jU on the value of the coefficient K. The method for determining the Poisson's ratio is as follows.

tp. tR2 R,

(0.874 + 1

.12f /) j

The method for determining the Poisson ratio is as follows.

A radiating transducer 2 of a plane elastic wave is installed on the flat surface of the rock sample under study 1, i.e. a transducer whose linear dimensions in the direction perpendicular to the direction of propagation of the radiated wave exceeds the length of this wave, for example, the transducer П113-0,1-С60-00 1 from the set of the UD2-16 device At distance 1. from the radiating converter 2 in parallel The receiver transducer 3 is installed to it, for example, similar to the radiating one. Converter 2 excites plane longitudinal and surface waves in sample 1, which, having overcome the distance 1 ,, arrives at converter 3. Transducer 3 transforms acoustic oscillations into an electrical signal entering the time interval measuring unit, with which time is measured -t p the propagation of longitudinal waves and the time t p of propagation of longitudinal surface waves. The choice of identical linear dimensions of transducers 2 and 3 along the wave front provides the highest signal-to-noise ratio, which allows fixing time t p and tj with great accuracy. The transducer 3 is then rearranged so that the acoustic oscillations,

At the same time, plane longitudinal and surface waves are excited in the test sample. A receiving transducer with a linear size along the wave front, not smaller than the size of the emitting converter, is received by ultrasonic vibrations that have passed a specified distance in the sample, and the time tp is measured

and t propagation, longitudinal and surface waves, respectively. The distance between the radiating and receiving transducers is changed, the oscillations that have passed the modified distance in the sample are received by the receiving transducer, and the time t p and t d for the propagation of longitudinal and surface waves, respectively, are measured. Determine the coefficient // Poisson from the expression

.2l. 2 (1 - | uM (l

b)

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40

45

50

55

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2 and 3, the distance passes, and the time tp of propagation of longitudinal waves and the time t of propagation of surface waves are measured again. Calculate the parameter

K (tp,) / (t,),

as a result of the application of which the absolute systematic error of measurement of time intervals is excluded, and the Poisson coefficient | u is determined from the expression

(2.5088-2Kb (2.6612-2K) fx + + (2k -0.43) / 1 (+ (, 7639) 0.

When determining the coefficient | U of Poisson, there is no error associated with the measurements of the bases and the precise installation of the transducers, since the bases are not measured, and the transducers are installed at arbitrary points. The accuracy of the determination is influenced mainly by the methodological error of measuring the propagation times of the longitudinal and surface waves, which, using modern ultrasonic devices, does not exceed 0.5–1%.

The calculation of the / from the third degree equation is laborious and the dependence fx f (K) constructed in accordance with this equation, shown in Fig. 2, allows us to simplify the definition of | U.

You can use a simplified formula to determine the Poisson's JL coefficient.

 2 56-0 25bK-K l7T2-0,

which in the range of 0.15, 40, performed for most rocks, gives an error relative to the third-degree equation of 1.5%.

From the point of view of improving the signal / interference ratio, it is advisable that the first entry of the surface wave in time is separated from the first half-wave of the longitudinal oscillations. For example, if at a working frequency of 200 kHz, the duration of the first half-wave (longitudinal oscillations) is 2.5 MCS, then for a material with a longitudinal wave propagation velocity of 4000 m / s, the minimum distance between the transducers is 10 mm. To obtain the accuracy of measurements of time intervals in the range of 1% using modern serial equipment, for example, an ultrasonic device UD2-16 with a measurement error of time intervals within 6t 0.005t + 0.1 MKS, it is obvious that the difference in time intervals between the first and second measurements MI must exceed 20 µs. In this service tp and t

RI

- - (0.874 + 1.12ju) Ri R,

the time of passage of a given initial distance by longitudinal and surface waves, respectively;

Also, the minimum distance between the two positions of the receiving transducer at longitudinal wave propagation speeds of 2000–5000 m / s should be, respectively, 40–100 mm

Formula l and h, about brea

The method of determining the Poisson's ratio, which consists in exciting a volumetric and surface acoustic oscillations with a radiating transducer in the sample under test, accepts the oscillations passed through the specimen by the receiving transducer, measures the time of passage of the oscillations of a given distance, and taking into account the measured time, determines the Poisson coefficient that differs the fact that, in order to increase the accuracy, after measuring time at a given distance, the distance between the radiating and receiving zovatel mi, further measured passage time wobbles of this distance, as oscillations using flat longitudinal and surface waves, reception is performed converter with a linear dimension of the wave front is not smaller than the size of the emitting transducer, and the coefficient, and Poisson determined from expression

1-2

2 С -7)

R,"

-R4

transit time of the modified distance by longitudinal and surface waves, respectively.

Compiled by V. Gondarevsky Editor T. Parfenova. Tehred M. HodanychKopjJBKTop L. Patay

Order 1575/46

Circulation 847

VNIIPI USSR State Committee

on; s, elam inventions and discoveries 113035, Moscow, Zh-35, Raushsk nab., d. A / 5

FIG. 2

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Claims (2)

Claim The method for determining the Poisson's ratio, which consists in the fact that both volumetric and surface acoustic vibrations are excited by the emitting transducer in the test sample, receive the vibrations transmitted by the receiving transducer ¹ , measure the transit time by the oscillations of a given distance and, taking into account the measured time, determine the Poisson's ratio, characterized in that , in order to improve accuracy, after measuring time at a given distance, the distance between the radiating and receiving transducers is changed shifters further measured transit time fluctuations in this distance, are used as the oscillation plane longitudinal and surface waves, reception is performed with a linear transducer for measuring wave front, not smaller size of the emitting transducer, and the Poisson ratio μ is determined from the expression I - 2 y ~ 2 (ϊ7ό (ϊ7) ’the transit time of the altered distance by longitudinal and surface waves, respectively.