Method for measuring elastic properties using ultrasound

Abstract

A method measuring elastic properties using ultrasound of a part made of a material having a curved surface, includes: emission of bundles of ultrasound waves in a direction of a point of impact on the part's surface to generate waves within the part; knowing a thickness d of the part at the point of impact in a first direction D.sub.1 and a thickness d2 in a second direction forming an angle determined with respect to the first direction, taking a first measurement t1 of time taken by the longitudinal waves transmitted to travel d1 from the point of impact, and taking a second measurement t2 of the time taken by the transverse waves to travel d2 from the point of impact; and determining the Young's modulus and/or Poisson's ratio of the material based on the longitudinal velocity VL=d1/t1 and transverse velocity VT=d2/t.

Claims

1. A method for determining elastic properties of a spherical part, comprising; positioning an emitting transducer in a first position, the emitting transducer operating also as a receiver in said first position; emitting beams of ultrasound waves towards a point of impact on a surface of the spherical part so as to generate waves within the spherical part, the beams of ultrasound waves being emitted through a coupling fluid; determining a diameter d.sub.1 of the spherical part at a first point of impact forming an angle of incidence with a first direction D.sub.1 and a length of a cord d.sub.2 in a second direction D.sub.2forming an angle with respect to the first direction D.sub.1; providing a measurement of the transmission time t.sub.R of ultrasound waves to travel from the emitting transducer in said first position to the first point of impact; providing a first measurement t.sub.1 of a time taken by longitudinal ultrasound waves transmitted to travel the distance d.sub.1 the first point of impact based on the first position; displacing the emitting transducer to a second position with a second point of impact, in such a way to bring the beam to a top of the spherical part and to maintain the angle of incidence with the first direction D.sub.1 producing waves forming the angle with the first direction D.sub.1; providing a second measurement t.sub.2 of the time taken by transverse ultrasound waves transmitted to travel the length of a cord d.sub.2 from the second point of impact, given that for the measurement of t.sub.2 , the transmission time t.sub.R of the waves through the coupling fluid is corrected for displacement of the transducer to the second position, the transmission time t.sub.m in both the spherical part and the coupling fluid until a receiving transducer that is different from the said emitting transducer is measured, and the corrected time t.sub.R is then subtracted from the time t.sub.m; and determining a Young's modulus and/or a Poisson's ratio of a material of the part based on a longitudinal velocity V.sub.L=d.sub.1/t.sub.1 and a transverse velocity V.sub.L=d.sub.2/t.sub.2.

2. The method according to claim 1, wherein the material of the part is isotropic.

3. The method according to claim 2, wherein the material is metal or ceramic.

4. The method according to claim 1, wherein the angle 45 .

5. The method according to claim 1, wherein the coupling fluid is water.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) The invention will be better understood, and its other aims, details, features and advantages will become more clearly apparent on reading the detailed explanatory description that follows, of embodiments of the invention given as purely illustrative and non-limiting examples, with reference to the appended diagrammatic drawings.

(2) In these drawings

(3) FIG. 1 is a diagrammatic illustration of the position in reflection mode of an ultrasound transducer relative to a sphere to be analysed and the two successive reflections of the longitudinal ultrasound wave on the sphere;

(4) FIG. 2 shows the trace on an oscilloscope of the variation in the signal produced by the transducer in the case shown in FIG. 1 with the interface echo and the reflection on the bottom of the sphere;

(5) FIG. 3 is a diagram, not to scale, showing the two successive positions of an transmitting transducer for producing a transverse wave propagating at 45 towards a receiving transducer disposed laterally relative to the transmitter on the sphere;

(6) FIG. 4 shows an embodiment of the assembly using focused transmitting and receiving transducers;

(7) FIG. 5 is the illustration of the trace of the signal emitted by a transducer and reflected on the surface of the sphere;

(8) FIG. 6 is the illustration of the trace of the signal transmitted from the transmitting transducer to the receiving transducer;

(9) FIG. 7 shows the change in the calculated velocity of the transverse wave as a function of the angle of incidence.

DETAILED DESCRIPTION OF THE INVENTION

(10) To illustrate the invention, the method has been applied to the examination of a stainless steel sphere. In the example developed here, the sphere has the following features: diameter=19.050 mm; mass=28.1865 g; density =7,789.2 kg/m.sup.3 Measurement of the velocity of propagation of the longitudinal wave

(11) A transducer 2 is plunged into a coupling fluid 3, which is water, with the sphere 1. The transducer, such as the Panametrics V322-6 10 MHz transducer with a focal length of 6 inches, is connected electrically to a workstation for controlling and for receiving signals, which is not shown. It is placed in transmit-receive mode and is oriented along the axis passing through the centre of the sphere.

(12) From the graph of the amplitude of the ultrasound wave produced as a function of time, as shown in FIG. 2, the propagation time t.sub.L1 of said wave is seen between the transducer 2 and the interface at the surface of the sphere on one side and the propagation time t.sub.L2 between the transducer 2 and the bottom of the sphere seen from the transducer.

(13) The propagation times identified on the graph in FIG. 2 are as follows:
t.sub.L1=205.517 s
t.sub.L2=211.897 s

(14) The velocity of propagation of the longitudinal wave V.sub.L is therefore the ratio of twice the diameter of the sphere over the travel time:
V.sub.L=2diameter/(t.sub.L1t.sub.L2)
which, in the example, is
38.1010.sup.3/6.38010.sup.6=5,971.8 m/s. Measurement of the velocity V.sub.T of the transverse wave

(15) The principle used is that of the propagation of a transverse wave V.sub.T in a direction D.sub.2 forming a given angle relative to the direction D.sub.1 of the longitudinal transmission wave by mode conversion in accordance with the principles of the Snell-Descartes laws.

(16) The correct angle of incidence producing the propagation of a transverse wave forming the angle , and the travel time t.sub.2 in the sphere for this transverse wave are determined. The angle chosen is 45.

(17) The method is described with reference to FIG. 3; in this drawing, the sensors and the ball are not to scale, the ball is dilated relative to the sensors. For the measurement of t.sub.2, separate measurements are taken of the transmission time t.sub.R of the waves through the coupling fluid and then of the transmission time t.sub.m in both the part and the coupling fluid, and the time t.sub.R, where necessary corrected, is then subtracted from the time t.sub.m.

(18) The emitting transducer 2 is disposed in a coupling fluid with the sphere, a receiving transducer 4 like the transducer referenced I3-1004-R, 10 MHz 1 0.25, is disposed laterally at the intersection of the direction D.sub.2 with the sphere.

(19) The velocity of propagation of the transverse wave is thus the ratio of the distance d.sub.2 separating the point of impact of the ultrasound wave and the intersection with the sphere in this direction D.sub.2: d.sub.2=R2.sup.1/2

(20) According to a first step, a measurement is taken of the precise travel time t.sub.R of the wave, for the given angle , from the surface of the sensor to the normal to the sphere. The coupling fluid ensures that there is no superposition of echoes.

(21) By placing the transducer in transmit-receive mode, the maximum amplitude of the reflected signal is determined. This maximum amplitude indicates that the signal is normal to the sphere at the angle concerned. As we are in transmit-receive mode, the travel time is half the time measured on the oscilloscope screen.

(22) The sensor is then displaced horizontally, in such a way as to bring the beam to the top of the sphere. The displacement is calculated as a function of the radius R of the sphere Rtg

(23) In this second step, the travel time t.sub.m of the wave to the receiving transducer 4 is measured.

(24) The velocity of the transverse wave is the ratio of the distance d.sub.2 travelled by that wave to the time t.sub.2 taken to travel it. The measurement of the travel time has to be adjusted because of the fact that, as the transducer has been moved horizontally, the wave travels a shorter distance.

(25) The adjustment of the path A in terms of time t.sub.A is expressed as follows:
t.sub.A=R(1cos)/cosV.sub.water
where V.sub.water is the velocity of propagation in water.

(26) As the measured time t.sub.m is the sum of the time (t.sub.Rt.sub.A) corresponding to the path from the transducer to the surface of the sphere, and the time t.sub.2 taken to travel along the length of the chord d.sub.2, the travel time t.sub.2 is therefore expressed as follows:
t.sub.2=t.sub.m(t.sub.Rt.sub.A)

(27) The velocity of the transverse wave is the ratio of the path of travel d.sub.2=R2 to the time taken to travel this distance: V.sub.T=d.sub.2/t.sub.2

(28) For an angle of 19, the following values are obtained (time measured with a digital oscilloscope accurate to 1 ns): V.sub.water=1 486.5 m/s 2t.sub.R=202.63 s (FIG. 5) t.sub.m=105.02 s (FIG. 6) displacement: Rtg=3.279 mm t.sub.A=R(1cos)/cosV.sub.water=0.3692 s d=2R=13.470 mm V.sub.T=3 306.2 m/s

(29) The value 19 of the angle is an estimate. In order to obtain the correct value for the angle , measurements are taken around this estimate. Thus, the operation above is repeated for values of the angle included in the range between 17 and 23.

(30) The calculated velocity values are repeated

(31) at 17 V.sub.T=3 323.7 m/s at 18 V.sub.T=3 326.1 m/s at 19 V.sub.T=3 306.2 m/s at 20 V.sub.T=3 284.4 m/s at 21 V.sub.T=3 304.8 m/s at 22 V.sub.T=3 302.3 m/s at 23 V.sub.T=3 314.5 m/s

(32) The curve obtained and reproduced in FIG. 7 has a point of minimum velocity; the velocity corresponding to the minimum point is associated with the shortest path of travel relative to the distance separating the two transducers.

(33) Thus V.sub.T=3 284.4 m/s

(34) The values obtained for the transmission velocities of the sound wave make it possible to calculate the characteristic parameters of the part.

(35) Calculation of the mechanical characteristics of a steel ball =7 789.2 kg/m.sup.3 V.sub.L=5 971.8 m/s V.sub.T=3 284.4 m/s E=V.sub.T2(3V.sub.L.sup.24V.sub.T.sup.2)/(V.sub.L.sup.2V.sub.T.sup.2)=215.6 GPa v=0.5(V.sub.L.sup.22V.sub.T.sup.2)/(V.sub.L.sup.2V.sub.T.sup.2)=0.283

(36) Calculation of the mechanical characteristics of a ball made of silicon nitride Si.sub.3N.sub.4 =3 166.5 kg/m.sup.3 V.sub.L=11 202 m/s V.sub.T=6 041.8 m/s E=V.sub.T2(3V.sub.L.sup.24V.sub.T.sup.2)/(V.sub.L.sup.2)=299.3 GPa v=0.5(V.sub.L.sup.22V.sub.T.sup.2)/(V.sub.L.sup.2V.sub.T.sup.2)=0.295

(37) It should be noted that to enable an accurate measurement to be taken, it is desirable to use a receiving transducer 4 with a very short focal length and therefore a small radius of curvature, which enables the ball to be centred, so that its axis coincides perfectly with the geometric axis of the transducer, the preferred configuration is shown in FIG. 4.