JP3245606B2 - Measurement method of particle dispersion amount and particle size of solid material - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring the volume fraction or particle size of dispersed particles contained in a solid material using ultrasonic waves. More specifically, the present invention measures the volume fraction and the average diameter of the dispersed particles contained in the material by oscillating ultrasonic waves in the solid material and analyzing the response waveform without destroying the material. How to do it.

[0002]

2. Description of the Related Art Conventionally, as a method of measuring the amount of dispersed particles of a solid material, a wet method, that is, a method of quantitatively analyzing a sample collected by a drill has been put to practical use. However, since this method is a destructive inspection, it can be applied only to a sampling inspection of a product. Further, since the measurement is complicated and time-consuming, it has been practically impossible to measure the variation in the particle distribution inside the solid material in detail.

[0003] On the other hand, although not intended for measurement of dispersed particles, as a method of non-destructively measuring the reinforcing fiber content of a solid material using ultrasonic waves, the sound speed of ultrasonic waves is reduced to the fiber content. Paying attention to the fact that it increases in proportion, a method of calculating the fiber content from the relationship between the two has been reported (Proceedings).
edings of the third Japan
international SAMPE symp
osium, December 1993, vol. 2,2276
~ 2281).

[0004]

However, the above report does not elucidate the cause of the increase in the speed of sound, and simply finds out from the experimental results of a specific material that the sound speed and the fiber content are in a linear relationship. (Actually, it seems that the fiber content and the sound velocity seem to have a linear relationship at first glance, but in fact, the inventors have found that the fiber content and the sound velocity have a linear relationship with the inverse propagation time. Is found). For this reason, since the measurement results differ depending on the material, shape, type of fibers and particles contained in the base material, and the characteristics of the ultrasonic sensor and the measuring device used, universal application is not possible. Also, there is no mention of a method for detecting fiber dimensions. For these reasons, the method of detecting dispersed particles using ultrasonic waves has not been put to practical use yet.

[0005] The present invention utilizes ultrasonic waves to cut (non-destructively) solid materials without breaking or breaking them.
An object of the present invention is to provide a practical method capable of measuring the volume fraction and particle size of dispersed particles inside a material without being affected by the material and shape of the material, the measurement conditions, and the like.

[0006]

Means for Solving the Problems The inventors of the present invention have studied a method for non-destructively evaluating the pore distribution characteristics in a solid material, and have studied the ultrasonic waves propagating in the solid material and the physical properties of the pores. A specific relational expression that clarifies various relations was derived, and a method of measuring porosity and pore size using this relational expression was proposed (Japanese Patent Laid-Open No. 6-18403). After that, in order to apply it to the non-destructive detection of dispersed particles, further studies were conducted.As a result, waves that have a significant effect on the ultrasonic propagation characteristics of solid materials travel along the pore surface in the case of pores It was a diffracted wave, but in the case of the dispersed particles, it was found to be a transmitted wave passing through the particles. Based on this knowledge, as a result of repeated experiments and theoretical analyses, a specific relational expression relating to ultrasonic waves and dispersed particles was found, and a method for detecting the amount of dispersed particles and the particle diameter was invented. More specifically, the above relational expression has a general form that can be widely applied even if the material, shape, and measurement conditions of the material are different.

That is, according to the present invention, when measuring the amount of particle dispersion or particle size of a solid material using ultrasonic waves, (a) a pair of ultrasonic sensors are arranged on both sides of the solid material, Oscillating short pulse ultrasonic waves and detecting the response waveform with the other sensor, (b)
Alternatively, a sensor is arranged on the surface of the solid material to oscillate a short pulse ultrasonic wave to detect a reflected waveform from the bottom surface of the solid material. (C) The sound speed of the detected ultrasonic wave is measured and ) And the volume ratio (分散) of the dispersed particles are in a constant relationship, and the volume ratio (分散) of the dispersed particles is calculated. (D) The detected waveform is the same as that containing no particles. Deconvolution integration by comparison with the detection waveform obtained from the solid material specimen of the material

[Equation 11] (However, t _p takes a peak value of tissue response function time,
_tw is the half value width of this function, and H is the tissue response function expressed by the peak value of this function). (e) Time (t _p ) at which the amplitude of the tissue response function takes a peak value, peak value The half width (t _w ) of the tissue response function at the height of exp (− ／) times of [or the peak value (H) of the tissue response function]
And calculating a volume ratio (ψ) or a particle radius (r) of the dispersed particles using a relational expression between the dispersion particle distribution characteristics (volume ratio and particle diameter).

Next, the present invention will be described in detail. First, as shown in FIG. 1, an ultrasonic transmitting sensor 2 and a receiving sensor 3 are arranged on both sides of a solid material specimen 1 and an ultrasonic oscillator is provided. 4, an ultrasonic short pulse is output, the ultrasonic wave oscillated by the transmission sensor 2 is detected by the reception sensor 3, and recorded on the digital oscilloscope 5. The waveform signal thus obtained is then processed by a personal computer 6 for measurement control and analysis, and is output as desired data. By repeating the measurement and analysis while scanning the transmission / reception sensor on the specimen, the distribution state of the dispersed particles can be measured.

In the above measuring method, instead of using a pair of transmitting and receiving sensors to measure the ultrasonic wave propagated through the specimen, a single transmitting / receiving sensor is used to measure the reflected wave from the bottom surface of the specimen. Good.

The above-mentioned formula I represents the correlation between the ultrasonic parameter and the dispersed particle parameter, and is derived as follows.

As shown in FIG. 2, consider a model in which particles having a radius r are arranged at regular intervals inside a solid material. When the ultrasonic wave hits one particle, it passes through the inside of the particle,
A propagation time difference Δt represented by the following formula II occurs between the wave traveling directly without hitting the particle (direct wave). Δt = 4r (1 / V _p −1 / V _m ) / 3 (II) where 4r / 3 is the average transmission distance when the ultrasonic wave passes through one spherical particle, and V _p the speed of sound when the ultrasound is transmitted through the particles, the V _m is the speed of sound when propagating substrate.

Next, the probability of the ultrasonic wave reaching an arbitrary time is obtained. The model shown in FIG. 2 can be replaced with a model in which particles are distributed at an area ratio φ in N cross sections perpendicular to the propagation direction of the ultrasonic wave (perpendicular to the paper surface in FIG. 2). A delay of jΔt time from a direct wave (a wave that arrives without hitting a particle at all) (when Δt is negative, |
jΔt | time earlier) The probability P (jΔt) of the wave to arrive is
Since it is equal to the probability of hitting a particle in j cross sections and not hitting a particle in the remaining (N−j) cross sections, P (jΔt) = φ ^j (1−φ) ^(Nj) _N C _j (j = 0, 1,2, ..., N) (III). Here, _{NC j} is the number of combinations for extracting j sheets from N sheets.

Equation (III) is expressed by plotting time on the horizontal axis and P on the vertical axis.
When (jΔt) is displayed, P (jΔt) = 1 at time zero for a material containing no particles,
At other times, it becomes a single straight line with P (jΔt) = 0,
The material containing particles has a binomial distribution in which the probability takes the maximum value at time N · φ · Δt.

Since the waveform detected by the ultrasonic sensor is obtained by measuring the pressure of the sound wave over time, it naturally corresponds to the arrival probability curve represented by the equation (III). However, the propagation waveform is affected not only by the dispersed particles, but also by the material and shape of the material, the characteristics of the ultrasonic sensor, and the like, so that the arrival probability curve represented by the equation (III) is hidden in the detection waveform. It has been done.

Therefore, the following mathematical operations are performed on the detected waveform and the arrival probability function to associate them with each other.

First, the detected ultrasonic waveform is deconvoluted and integrated with the detected waveform of a specimen containing no particles. On the other hand, the arrival probability function represented by equation (III) has 1
/ Δt. The former is defined as a measured tissue response function, and the latter as a theoretical tissue response function. By this operation, the tissue response function of the specimen containing no particles becomes a single impulse in which the time width is infinitely small, the height is infinite, and the product of the time width and height is 1 in the former, and in the latter, The width is Δt and the height is 1 /
It becomes a single impulse of Δt. Therefore, when Δt is sufficiently small, that is, when the particle diameter is sufficiently small, they match. If the same mathematical operation is performed on the detection waveform and arrival probability function when particles are included, the resulting measured and theoretical tissue response functions should naturally match. Therefore, the distribution characteristics of the dispersed particles can be estimated by examining which theoretical tissue response function the measured tissue response function corresponds to.

As described above, the theoretical tissue response function h
(T), since it is multiplied by 1 / Delta] t in the formula (III), h (t) = P (jΔt) / Δt = φ j (1-φ) (Nj) N C j · Δt -1 (j = 0,1,2, ..., N) (IV), where t is the propagation time of the ultrasonic wave, but normalized to the propagation time of the specimen containing no particles as zero. ing.

In this form, it is a discrete function,
In addition, since it takes a very long time to calculate and a correlation between parameters cannot be obtained, it is considered to approximate the discrete function by a continuous function. Using stochastic statistics, a discrete variate having a binomial distribution can be approximated by a Gaussian function, and φ ^j (1−φ) ^(Nj) _N C _j = σ ⁻¹ (2π) ^{−1 / 2} exp {-(ja) ² / (2 σ ² )} (V) holds in a sufficiently large range of N. However, a ^{a = N · φ σ 2 =} N · φ · (1-φ), a mean value, sigma ² represents the variance.

By substituting equation (V) into equation (IV) and performing the following substitution, equation (I) is derived. _{j = t / Δt t p =} a · Δt = N · φ · Δt t w = σ · Δt = {N · φ · (1-φ)} 1/2 · Δt (VI) H = 1 / {σ · (2π) ^1/2・ Δt｝ = {2π ・ N ・ φ ・
^{(1-φ)} -1/2 /} Δt Equation As is apparent from the form of (I), the theoretical tissue response function h (t) takes a H a maximum at t = t _p, t = t
a Gaussian function as a H · exp (-1/2) when the _p ± t _w.

Next, a graph is created with the horizontal axis being time t and the theoretical tissue response function h (t) being on the vertical axis, as shown in FIG.

The shape of this graph has a correlation with the volume fraction and the particle size of the dispersed particles contained in the solid material as shown in FIG. 4, and the time when the tissue response function takes a peak value ( t _p), the half-value width (t _w) and the peak value of the tissue response function of the tissue response function (H) has the following relationship between the dispersion particle parameters.

(Equation 12)

(Equation 13)

[Equation 14] These equations (VII), (VIII) and (IX) can be derived as follows.

That is, considering a model in FIG. 2 in which dispersed particles are arranged at regular intervals at a pitch p in a solid, from the geometrical relationship, the particle volume ratio φ, the particle radius r and the cross-sectional area N, and particle area ratio phi, between the propagation distance L, N = L / p φ = πr 2 / p 2 ψ = (4πr 3/3) / p 3 the relationship is established. By clearing the p From these relations, N, phi is N = a ^{(4π / 3ψ) -1/3 L /} r φ = π (4π / 3ψ) -2/3 (X).

Further, Delta] t, as mentioned above, is _{Δt = 4r (1 / V p} -1 / V m) / 3 (II).

By substituting the equations (X) and (II) into the equation (VI), the equations (VII), (VIII) and (IX) are derived.

When formulas (VII), (VIII) and (IX) are rearranged for the volume ratio (率) and the particle size (r) of the dispersed particles,

(Equation 15)

(Equation 16) as well as

[Equation 17] Is obtained.

Formulas (XI), (XII) and (XII)
I) is an expression representing the correlation between the volume fraction (ψ) of the dispersed particles, the particle diameter (r), and the waveform parameter of the tissue response function. Time when this function takes the peak value (t _p )
Is measured and substituted into the mathematical expression (XI), whereby the volume ratio of the dispersed particles can be calculated. Further, by measuring the pulse half width (t _p ) or the peak value (H) of this function and substituting it into equation (XII) or (XIII),
The radius (r) of the dispersed particles can be calculated.

In the case of detecting only the volume fraction of the dispersed particles, it is possible to calculate by substituting the measured sound speed of the observed ultrasonic wave into the following equation without particularly obtaining the tissue response function.

[0028]

(Equation 18) (However, the acoustic velocity of V _p is the dispersed particles, V _m is the acoustic velocity of the substrate)
Equation (XIV) is derived as follows.

The time (t _p ) at which the tissue response function takes a peak value is determined by the propagation time (t _a ) of the ultrasonic wave when the solid material contains dispersed particles and the propagation time (t _a ) when the solid material contains no dispersed particles. equal to the time difference between t _0), in _{t p = t a -t 0 (} XV) following relationship.

On the other hand, t _a and t ₀ is equal to the value divided by the sound velocity Vm of sound velocity V and the base of each particle dispersion material the propagation distance _{L, t p = L / V} -L / V m (XVI ).

By substituting equation (XVI) into equation (XI) and rearranging, equation (XIV) is obtained.

[0032]

The method for detecting dispersed particles by ultrasonic waves according to the present invention is very simple as compared with the conventional method. It is possible to measure variations in particle distribution. It can also measure the average size of the sensor, does not depend on the sensitivity characteristics of the sensor used, requires only simple parameter changes even if the material or shape of the subject is different, and can be configured at low cost. For example, the present invention can be applied to grasping the particle distribution state of various particle dispersing materials including a ceramic particle-dispersed metal-based composite material, determining the quality of products, and the like. The conventional chemical analysis method (wet method) required two days to produce a measurement result, whereas this method provides an instant measurement result, which is effective for inspection of all products. is there.

[0033]

Next, the present invention will be described in more detail with reference to examples.

EXAMPLE This method was applied to a silicon carbide particle-dispersed aluminum alloy composite material (Al
/ SiC _p ) shows an example applied to non-destructive detection of the volume fraction and average diameter of SiC particles contained in / SiC _p ).

As specimens, four samples (□ 30 mm × t15 mm) using JIS 5083 aluminum alloy as a base material and having different particle dispersion amounts of silicon carbide (SiC) were used. Table 1 shows the results obtained by actually measuring the particle dispersion amount and the particle diameter of these samples by the conventional wet method and microscopic image analysis (binarization method). FIG. 5 shows an observation waveform of an ultrasonic wave detected by this method. The tissue response function obtained by deconvolving and integrating these observed waveforms with the observed waveform of Sample A (a sample containing no particles) is shown by a solid line waveform in FIG. 6 (for reference, the dispersed particles shown in Table 1 were used for reference). The theoretical tissue response function calculated using the parameters is indicated by the dashed line). Pulse half width t of the time t _P and the function when the tissue response function takes a peak
w was measured and substituted into the mathematical formulas (XI) and (XII) to detect the volume ratio and the particle size of the dispersed particles. Table 1 shows the results.
FIG. 7 shows a comparison with measured values obtained by another method shown in FIG. The detected values by this method correspond well with the measured values by another method. The following equation was used to convert the volume ratio into the amount of dispersion (weight ratio). ψ _wt = ψ · ρ _SiC / ｛ψ · ρ _SiC + (1-ψ) · ρ _Al ｝ where ψ _wt is the amount of dispersion of _SiC , ρ _SiC is the specific gravity of SiC (3.2), and ρ _Al is an aluminum alloy (2.65).

In the above embodiment, when only the volume ratio of the dispersed particles is measured, the volume ratio can be obtained only by measuring the sound velocity without analyzing the tissue response function. FIG. 8 is a graph of the equation (XVI) with the volume ratio (ψ) of the dispersed particles on the horizontal axis and the sound velocity (V) on the vertical axis.
The curve shown in the figure represents the theoretical relationship between ψ and V. However,
In the formula (XVI), V _P = 12000 ms ⁻¹ (Si
C), and V _p = 6350 ms ⁻¹ (sound speed of 5083 aluminum alloy). Open circles are obtained by plotting the results of measuring the SiC _p volume ratio (weight ratio is measured by a wet method and then converted to a volume ratio) and sound velocity at different measurement points in the Al / SiC _p material. Thus, the theory and the measurement show a good correspondence. Therefore, if such a graph is created in advance, the particle volume ratio of the subject can be estimated by measuring the sound velocity (V).

[0037] In likewise Example, equation by measuring the peak value H instead of measuring the pulse half width t _w (X
It is also possible to calculate the particle size from III). However, when an ultrasonic sensor of a type directly attached to the specimen is used, accurate measurement becomes difficult because the peak value H is affected by the contact state of the sensor. However, this method is practically simpler, and is recommended when non-contact measurement in water or the like is possible.

[0038]

[Table 1]

[Brief description of the drawings]

FIG. 1 shows a measuring system 1 for implementing the method of the present invention.
Schematic diagram of an example.

FIG. 2 is a model diagram for explaining the behavior of ultrasonic waves propagating through a particle dispersion material.

FIG. 3 is a graph showing a theoretical tissue response function h (t).

FIG. 4 is a diagram showing an example of the relationship between the particle dispersion amount and particle diameter of a solid material and a tissue response function.

FIG. 5 is a diagram showing observed waveforms of each Al / SiC _P sample in the example.

FIG. 6 is a diagram showing a result of analyzing a tissue response function from FIG. 5;

FIG. 7 is a graph comparing the result measured by the method according to the present invention with the result measured by another conventional method.

[8] Al / SiC _p material SiC _p volume fraction and diagrams representing the relationship between the speed of sound.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 DUT 2 Ultrasonic transmission sensor 3 Ultrasonic reception sensor 4 Ultrasonic oscillator 5 Digital oscilloscope 6 Personal computer

──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Kazuhiro Kameya 85, Hiramatsu, Susono City, Shizuoka Prefecture Mitsubishi Aluminum Co., Ltd. Technology Development Center (56) References Reference Table 3-5033312 (JP, A) (58) Field surveyed (Int. Cl. ⁷ , DB name) G01N 29/00-29/28 G01N 15/02

Claims (11)

(57) [Claims] When measuring the amount of particles dispersed in a solid material using ultrasonic waves, a pair of ultrasonic sensors are arranged on both sides of the solid material, and short-pulse ultrasonic waves are oscillated from one of the sensors. Detecting the response waveform with the other sensor, and (b) measuring the sound speed of the detected ultrasonic wave, and determining the sound speed (V) and the volume fraction of the dispersed particles (ψ) as follows: (However, the acoustic velocity _{V p} is transmitted through the dispersed particles, _{V m} is the base material
Calculating the volume fraction (ψ) of the dispersed particles by utilizing the relationship of the sound velocity at which the particles pass through (). 2. A method for measuring the amount of particles dispersed in a solid material using ultrasonic waves: (a) arranging an ultrasonic sensor for both transmission and reception on the surface of the solid material to oscillate short pulse ultrasonic waves, Detecting the reflected wave from the bottom surface of the material, (b) measuring the sound speed of the detected ultrasonic wave, and determining the sound speed (V) and the volume fraction of the dispersed particles (ψ) as follows: (However, the acoustic velocity _{V p} is transmitted through the dispersed particles, _{V m} is the base material
Calculating the volume fraction (ψ) of the dispersed particles by utilizing the relationship of the sound velocity at which the particles pass through (). 3. When measuring the amount of particles dispersed in a solid material using ultrasonic waves, (a) a pair of ultrasonic sensors are arranged on both sides of the solid material, and short pulse ultrasonic waves are oscillated from one of the sensors. Detecting the response waveform with the other sensor, and (b) performing deconvolution integration by comparing the detected waveform with a detection waveform obtained from a solid material specimen of the same material containing no particles. And the formula (Where t _p is the time to take a peak value of tissue response function, t
_w is a half value width of this function, and H is a tissue response function represented by the peak value of this function). (c) Time (t _p ) at which the amplitude of the tissue response function takes a peak value and dispersion particle distribution characteristics Calculating the volume fraction (の) of the dispersed particles by using the relational expression of the above, and a method for measuring the amount of particles dispersed in a solid material. 4. When measuring the amount of particles dispersed in a solid material using ultrasonic waves, (a) an ultrasonic sensor for both transmission and reception is arranged on the surface of the solid material to oscillate short pulse ultrasonic waves, Detecting the reflected wave from the bottom surface of the material, and (b) performing deconvolution integration by comparing the detected waveform with a detection waveform obtained from a solid material specimen of the same material that contains no particles. Equation (4) In determining the tissue response function represented, (c) the amplitude of the tissue response function using the relationship between time (t _p) and dispersion particle distribution characteristics taking a peak value, the volume ratio of the dispersed particles ([psi) Calculating the amount of dispersed particles of the solid material. 5. A relational expression for calculating a volume ratio (ψ) of dispersed particles is as follows: The method according to claim 4 or 5, wherein L is the propagation distance of the ultrasonic wave. 6. When measuring the dispersed particle size of a solid material using ultrasonic waves, (a) a pair of ultrasonic sensors are arranged on both sides of the solid material, and short pulse ultrasonic waves are oscillated from one of the sensors. Detecting the response waveform with the other sensor, and (b) performing deconvolution integration by comparing the detected waveform with a detection waveform obtained from a solid material specimen of the same material containing no particles. And the formula (C) calculating a peak value of the tissue response function, exp (−1 /
2) calculating the particle radius (r) of the dispersed particles using a relational expression between the half-width (t _w ) of the tissue response function at twice the height and the dispersed particle distribution characteristics; A method for measuring the size of dispersed particles. 7. When measuring the dispersed particle size of a solid material using ultrasonic waves, (a) an ultrasonic sensor for both transmission and reception is arranged on the surface of the solid material to oscillate short pulse ultrasonic waves, Detecting the reflected wave from the bottom surface, (b) performing deconvolution integration by comparing the detected waveform with a detection waveform obtained from a solid material specimen of the same material that does not contain any particles, and formula (Equation 7) (C) calculating a peak value of the tissue response function, exp (−1 /
2) calculating the particle radius (r) of the dispersed particles using a relational expression between the half-width (t _w ) of the tissue response function at twice the height and the dispersed particle distribution characteristics; A method for measuring the size of dispersed particles. 8. The relational expression for calculating the particle radius (r) of the dispersed particles is as follows: The method according to claim 6 or 7, wherein 9. When measuring the dispersed particle size of a solid material using ultrasonic waves, (a) a pair of ultrasonic sensors are arranged on both sides of the solid material, and short pulse ultrasonic waves are oscillated from one of the sensors. Detecting the response waveform with the other sensor, and (b) performing deconvolution integration by comparing the detected waveform with a detection waveform obtained from a solid material specimen of the same material containing no particles. And the equation (C) calculating the particle radius (r) of the dispersed particles by using a relational expression between the peak value (H) of the tissue response function and the dispersed particle distribution characteristics. A method for measuring the size of dispersed particles of a solid material. 10. When measuring the dispersed particle size of a solid material using ultrasonic waves, (a) a pair of ultrasonic sensors are arranged on both sides of the solid material, and short pulse ultrasonic waves are oscillated from one of the sensors. And the response waveform is detected by the other sensor. (B) Deconvolution integration by comparing the detected waveform with a detection waveform obtained from a solid material specimen of the same material that contains no particles And the equation (C) calculating the particle radius (r) of the dispersed particles by using a relational expression between the peak value (H) of the tissue response function and the dispersed particle distribution characteristics. A method for measuring the size of dispersed particles of a solid material. 11. The relational expression for calculating the particle radius (r) of the dispersed particles is as follows: The method according to claim 9 or 10, wherein