JPH0618403A - Measuring method of porosity and pore size in solid material - Google Patents

Abstract

PURPOSE:To calculate the porosity and pore size of a solid material accurately according to a specific formula pertaining to pore properties in the solid material by utilizing an ultrasonic wave. CONSTITUTION:A pair of ultrasonic sensors are set up at both ends of a solid material, while an ultrasonic wave is transmitted out of the sensor on one side and the response waveform is detected by the sensor on the other. In succession, the detected waveform is subjected to reverse convoluted integral processing by comparison with the response waveform obtained out of a solid material sample piece of the same material, where no pore exists at all, and thereby a pore function to be expressed in an equation I is found out. In this equation, tp shows propagation delay time in the pore function, tw is half-value width of each pore, H a peak value of the pore function, respectively. A graph, using axis of abscissa for the time, axis of ordinate for the pore function respectively, is drawn up, finding out tp, tw and H from this graph. In addition, porosity psi and means pore radius (r) are found out of functional equations II and III of pore properties. In the equations, Vp shows sound velocity of an incident wave, Vc the sound velocity of a bypass wave (a wave advancing along a pore surface), L a propagation distance of wave motion, respectively. With this constitution, the porosity and the pore radius can be sought without being swayed by material quality, form and measuring conditions.

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 porosity or pore diameter using ultrasonic waves. More specifically, according to the present invention, an input / output sensor is attached to a solid material, ultrasonic waves are emitted, and the response waveform is analyzed, so that the porosity of the pores existing inside the material can be obtained without destroying the material. , A method for measuring the average pore diameter.

[0002]

2. Description of the Related Art Conventionally, as a method of measuring the porosity of a solid material, for example, a method of determining the porosity by the specific gravity measurement by the Archimedes method or a method of determining the porosity by the specific gravity measurement by the X-ray absorption coefficient method has been put into practical use. ing. However, the former method by the Archimedes method cannot measure the local porosity of the subject, and has the drawbacks that the measurement is complicated and the accuracy is low, and the method by the X-ray absorption coefficient method is also available. In the above, there is a drawback in that a large-scale device is required, it is impossible to inspect an actual material, the device is extremely expensive, and the pore diameter cannot be measured.

On the other hand, as a method of non-destructively measuring the porosity of a solid material using ultrasonic waves, attention is paid to the fact that the speed of sound of ultrasonic waves hits the pores and slows down, and its relationship with the attenuation rate. Has reported a method for obtaining porosity ("Non-destructive inspection", Vol. 36, No. 3, pages 201 to 205).

However, this method cannot accurately measure the porosity and the average pore diameter because the quantitative relationship between the pore distribution characteristics and the ultrasonic wave propagation characteristics is insufficient, and the same pores are not measured. Even if it is a distribution, the measurement result varies depending on the material, shape, and measurement conditions of the material, so it cannot be universally applied, and it has the drawback that pores of 0.1 mm or less cannot be detected. It has not been.

[0005]

SUMMARY OF THE INVENTION The present invention utilizes ultrasonic waves to destroy the porosity of a solid material without being affected by the material or shape of the material, or the measurement conditions. The purpose of the present invention is to provide a method that can measure the pore diameter and the pore size.

[0006]

Means for Solving the Problems The inventors of the present invention have conducted extensive studies on a method of non-destructively evaluating pore characteristics in a solid material using ultrasonic waves. First, the incident waveform of ultrasonic waves We proposed a method to determine the porosity and pore diameter of solid materials by using a specific function called the stomatal response function obtained by performing stochastic processing on the waveform after passing through the material and Proceedings of the Conference (A), Vol. 57, No. 536, pp. 760-803], and as a result of further research, use specific relational expressions that clarify various relations regarding the pore physical properties of solid materials. It was found that a more accurate measurement value can be obtained, and the present invention has been completed based on this finding.

That is, according to the present invention, when the porosity or pore radius of a solid material is measured using ultrasonic waves, (a)
Place a pair of ultrasonic sensors on both sides of the solid material sample,
The ultrasonic wave is emitted from one sensor and the response waveform is detected by the other sensor. (B) The detected waveform is compared with the response waveform obtained from a solid material sample of the same material with no pores. The inverse convolution integral processing by the comparison of

[Equation 4] (However, t _p is the propagation delay time of the stomatal function, t _w is the half-value width of the stomatal function, and H is the peak value of the stomatal function). (C) The horizontal axis represents time, and the vertical axis represents the above. create a graph with pore function, the propagation delay time from the graph (t _p), the half-value width (t _w) and the peak value of the pore function pore function (H) to obtain the, and (d) the propagation delay time (t _p), the half-value width (t _w) or peak value of the pore function pore function (H) and the porosity using the relation expression between stomatal physical data to calculate the ([psi) or pore radius (r) A characteristic measuring method is provided.

Next, a specific embodiment of the present invention will be described. First, as shown in FIG. 1, a transmitting sensor 2 and a receiving sensor 3 for ultrasonic waves are arranged on both sides of a solid material sample 1. Then, ultrasonic waves are output from the ultrasonic oscillator 4, and the waveforms caught by the transmission sensor 2 and the transmission sensor 3 are recorded in the digital oscilloscope 5. The information thus obtained is then processed by the personal computer 6 for measurement control and analysis and output as desired data.

The above formula (I) shows the correlation between the ultrasonic parameters and the stomatal parameters, and is derived as follows.

That is, if the internal structure of the porous body is replaced with a model in which pores are distributed at a constant area ratio on N cross sections divided at equal intervals, direct waves (waves that reach without hitting the pores) The probability F (t) of a wave that arrives with a delay of j · Δt time from the equation is F (t) = φ ^j · (1−φ) ^Nj · _N C _j , (j = 0, 1,
2, ..., N) (II) (where φ is the area ratio of the pores in one cross section, N is the cross-sectional area, and Δt is the direct wave generated when the wave collides with one pore and detours. a propagation time difference, which depends on the pore geometry, for example in the case of spherical pore Δt = r · (π-2V C / V P) / (2V C) (III) in the case of disc-shaped pores Delta] t = r / V _C , and _N C _j is represented by a combination number that selects j sheets from N sheets.

Here, the present inventors have obtained a pore function h (t).
With the formula h (t) = F (j · Δt) · Δt ⁻¹ = φ ^j · (1-φ) ^Nj · _N C _j · Δt ⁻¹ , (j = 0, 1,
2, ..., N) (IV). As a result of further experimentation, the present inventors have found that not all of the waves that hit the pores are detour waves, but some of them disappear as scattered waves, although they are extremely small. Therefore, if the probability of the wave that hits the pores and propagates as a detour wave without being scattered and lost is Z _C , the probability that these waves are detour waves among all the waves that are incident on one cross section is Z _C · φ. Further, the proportion of direct waves that do not hit the pores remains (1-φ). Therefore, the formula (IV) can be rewritten as h (t) = (Z _C · φ) ^j · (1-φ) ^Nj · Δt ⁻¹ (V).

[0012] Next, in this form as it is, since it takes time to calculate and the correlation equation between the parameters cannot be obtained, the present inventors utilize probability statistics to calculate the above equation (V) as It was decided to approximate by the following equation (if N is 10 or more, sufficient approximation is possible, and if N is infinite, the equal sign holds).

[0013]

[Equation 5]

However, a = N · φ σ ² = N · φ · (1-φ) (VII).

In the above formula (VI), the following permutation is carried out to obtain formula (I).

[0016]

[Equation 6]

[0017] As is apparent from the form of equation (I), pore function h (t) takes a peak value H when t = t _p, t
= T _p ± t _w, the probability density function is H · e ^−1/2 .

Next, the horizontal axis is time t, and the pore function h
A graph is created with (t) as the vertical axis, as shown in FIG.

[0019] The shape of the graph, the porosity of the solid material, as shown in FIG. 3 has a correlation with the pore radius, propagation delay time (t _p), the half width of pore function (t _w ) and the peak value (H) of the pore function have the following relationship with the pore parameter.

[0020]

[Equation 7]

[0021]

[Equation 8]

[0022]

[Equation 9]

These expressions (IX), (X) and (X
I) can be derived as follows.

That is, considering a model in which the pores are arranged in the solid at equal intervals with a pitch p, the porosity ψ and the pore diameter r
A pore area rate phi, between the section number N, N = L / p φ = πr 2 / p 2 ψ = (4πr 3/3) / p 3 the relationship is established. By clearing the p from these equations, N = (4π / 3ψ) -1/3 · L / r φ = π a ^{(4π / 3ψ) -2/3 (XII} ). Moreover, in the sintered body such as ceramics,
Since the pore shape can be regarded as a spherical shape, Δt is Δt = r · (π−2V _c / V _p ) / (2V _c ) (III) as described above, and t _p is t as described above. _p = [a + σ ² · In (Z _c )] · Δt. Here, it is known from the experimental result that Z _c takes a value extremely close to 1, so In (Z _c ) becomes a value close to zero. Therefore, it can be approximated as t _p = a · Δt. In this equation, the above equations (VII) and (I
Substituting II), t _p = N · φ · (π−2V _c / V _p ) · r / (2V _c ). By further substituting the equation (XII), the equation (IX) is derived.

Further, by substituting the expressions (VII) and (III) into the second expression of the expression (VIII), tw = σΔt = {Nφ (1-φ)} ¹ / 2 { (Π-2 (V _c /
V _p )} · r / (2V _c ), and the formula (XI
By substituting and substituting I), the formula (X) is derived.

Further, in the third equation of the equation (VIII), if In (Z _c ) is set to zero, then H = Z _c ^a / {Δt · σ (2π) ^1/2 }. By substituting equations (VII) and (III) into this equation,

[Equation 10] Further, by substituting the formula (XII) into this formula and rearranging the formula, the formula (XI) is derived.

Therefore, the porosity ψ and the average pore radius r
Can be obtained according to the following equation based on the numerical values of the propagation delay time t _p and the half-value width t _w of the stomatal function.

[0028]

[Equation 11] as well as

[Equation 12]

Note that these mathematical formulas are derived as follows. That is, the mathematical expression (XIII) is derived by rearranging the mathematical expression (IX) with respect to ψ.

Further, the from Equation _{(VIII), (t w /} t p) 2 = σ 2 / {a + σ 2 · In (Z c)} 2 is guided, In (Z _c) zero, as described above since the value close to, it can be approximated as ^{_{(t w / t p) 2}} = σ 2 / a 2. This equation, by substituting the formula _{(VII) (t w / t} p) 2 = (1-φ) / (N · φ) is obtained. Substituting the mathematical formula (XII) into this formula and rearranging it,

[Equation 13] And rearranging this equation for r,

[Equation 14] Is obtained. Further, in this formula, the above formula (XIII)
By substituting and rearranging, the formula (XIV) is derived.

Although the above method is based on the inverse analysis, the pore parameters are sequentially exchanged to calculate the pore function, and the convolution integral is performed on the material of the same material having no pores with the function. It is also possible to obtain the porosity and the pore diameter by the forward analysis of finding the pore parameters that match the observed waveforms.

[0032]

EFFECT OF THE INVENTION The ultrasonic pore detection method of the present invention is much simpler than the conventional method. It is possible to measure the variation of the pore distribution. Not only the porosity but also the average diameter of the pores is measured. Capable of detecting pores of the order of several microns (conventionally about 100 microns), it does not depend on the sensitivity characteristics of the sensor used or the adhesive conditions, and can be measured with simple correction even if the material or shape of the object is different. It has features that data can be compared and the device can be constructed at low cost. For example, measurement of porosity and pore diameter of various porous materials including ceramic sintered bodies, detection of hydrogen damage in petrochemical plant equipment materials. It can be applied to product quality evaluation.

[0033]

EXAMPLES Next, the present invention will be described in more detail by way of examples.

Example An example in which the present method is applied to the non-destructive detection of the porosity and the average pore size of the pores remaining inside the ceramic will be shown.

As the samples, four kinds of alumina sintered bodies (sheet thickness: about 15 mm) produced by changing the powder particle size and the sintering temperature were used. Table 1 shows the results of actual measurement of the porosity and average pore size of these samples by the conventional Archimedes method and microscopic image analysis (binarization method), respectively. Fig. 4 shows the observed waveform of ultrasonic waves detected by this method. Sample 1 has a porosity of 0.2%, and the results of analyzing the pore functions of Samples 2 to 4 by considering this sample as a reference sample having no pores are shown in FIG. Table 2 shows the porosity and average pore diameter obtained from this function. This detected value corresponds well with the measured value by the alternative method shown in Table 1.

[0036]

[Table 1]

[0037]

[Table 2]

[Brief description of drawings]

FIG. 1 is a schematic view of an example of a measurement system for carrying out the method of the present invention.

FIG. 2 is a graph showing a pore function h (t).

FIG. 3 is a diagram showing an example of a relationship between a porosity and a pore radius of a solid material and an ultrasonic wave propagation waveform.

FIG. 4 is a diagram showing an ultrasonic observed waveform of each alumina sintered body in the example.

FIG. 5 is a graph showing the results of analyzing the stomatal function from FIG.

Claims (3)

[Claims] 1. When measuring the porosity or pore radius of a solid material using ultrasonic waves, (a) a pair of ultrasonic sensors are arranged on both sides of a solid material sample, and ultrasonic waves are emitted from one of the sensors. , And detect the response waveform with the other sensor. (B) Reverse convolution of the detected waveform with the response waveform obtained from a solid material sample of the same material with no pores. After integration processing, the equation (However, t _p is the propagation delay time of the stomatal function, t _w is the half-value width of the stomatal function, and H is the peak value of the stomatal function). (C) The horizontal axis represents time, and the vertical axis represents the above. create a graph with pore function, the propagation delay time from the graph (t _p), the half-value width (t _w) and the peak value of the pore function pore function (H) to obtain the, and (d) the propagation delay time (t _p), the half-value width (t _w) or peak value of the pore function pore function (H) and the porosity using the relation expression between stomatal physical data to calculate the ([psi) or pore radius (r) Characteristic measuring method. 2. A propagation delay time (t _p), the half width of pore function (t _w) or peak value of the pore function (H) and [2 Number] relational expression between stomatal physical properties [Where ψ is the porosity, V _P is the speed of sound of the incident wave (longitudinal wave),
The measurement method according to claim 1, wherein V _C is a sound velocity of a detour wave (a wave traveling along the surface of the pores), and L is a propagation distance of the wave. 3. A propagation delay time (t _p), the half-value width (t _w) and Equation 3] is a relational expression between stomatal physical properties of pores function (Where r is the average pore radius, L is the wave propagation distance, and V is the
The measurement method according to claim 1, wherein _C is the detour wave sound velocity, and V _P is the incident wave sound velocity.