JPH0797089B2 - Hardness measuring method for hardened steel by X-ray diffraction using Gaussian curve - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for measuring the hardness of an as-quenched steel material and a steel material quenched at various temperatures after quenching by X-ray diffraction.

[Problems to be Solved by Prior Art and Invention]

In the following description, the as-quenched steel material and the steel material that has been tempered at various temperatures after quenching are referred to as hardened steel for the sake of convenience.

Generally, hardness measurement of hardened steel is indispensable for judging hardenability and evaluation of strength of hardened steel.

Hardness measurement using a hardness meter such as Vickers hardness which has been widely used conventionally requires cutting out a test piece from a material and polishing a portion to be measured, which requires a lot of labor and cost.

Therefore, two studies have clarified the relationship between the half-value width of the diffraction line and the hardness of the hardened steel, focusing on the fact that the width of the diffraction line due to X-rays remarkably widens when the structure of the steel becomes altensite by quenching. Seen three times.

Here, the diffraction line is a curve showing the relationship between the diffraction angle x and the X-ray intensity y as shown in FIGS. Diffraction angle x
Is the angle between the direction of X-rays incident on the material and the direction of X-rays diffracted from the material.

In FIG. 1, a portion a where the X-ray intensity is low at the foot of the diffraction line
The baseline ae that connects E and e is called the background of diffraction lines (represented by BG).

The half-value width B is the width of the diffraction line at a height half the height of the diffraction line above BG, as described in FIG. It is often used.

However, in the hardness measurement by the half width, it is necessary to measure the X-ray intensity of the entire diffraction line as shown in FIG. 2 and FIG. With respect to hardened steel having such a wide range of diffraction lines, it is difficult to accurately obtain the diffraction line background required for measuring the half width, and it has not been put to practical use yet.

The present invention solves the drawbacks of the hardness measurement by the hardness meter and the hardness determination by the diffraction line half width as described above, and there is no need to make a small test piece for measurement by the hardness meter at all. A non-destructive hardness measurement method that does not damage products and structures, and can measure the hardness without contacting the object to be measured as long as it can irradiate X-rays. Hardness measurement by X-ray diffraction using a Gaussian curve It provides a method.

[Means for Solving the Problems]

 The gist of the present invention will be described.

Some test pieces were prepared by cutting out a part of the as-quenched steel material and the tempered steel material at various temperatures after quenching,
The hardness of each of these test pieces is determined by a known hardness measuring method such as Vickers hardness, and each test piece is irradiated with X-rays to show the relationship between the diffraction angle and x and the X-ray intensity y. 50-80% of the height of this diffraction line
When the above area is approximated by a Gaussian curve represented by the following equation (1) and this Gaussian curve is considered as a normal probability density function represented by the following equation (2), the standard deviation of the following equation (1) Since α corresponds to the standard deviation σ of the following equation (2), the following equation (4) is derived, and the standard deviation α of the following equation (4) is calculated by using the constant a of the following equation (1) as a minimum of two. After the constant a obtained by the least squares method is transformed into a simple formula, it is determined by substituting it in a of the following formula (4) to obtain the following formula (5). The standard deviation α of the following equation (1) for each test piece determined by the following equation (5) and the hardness of each test piece obtained by the above-mentioned known hardness measuring method are plotted on the vertical axis and the horizontal axis, respectively. To obtain a relationship between the standard deviation α and known hardness, that is, a calibration curve, and to obtain the same value as the heat-treated steel material. Gauss characterized in that the object to be measured of the material is irradiated with X-rays to obtain the standard deviation α in the same manner as described above, and the standard deviation α of the object to be measured is applied to the calibration curve to obtain the hardness of the object to be measured. The present invention relates to a method for measuring the hardness of hardened steel by X-ray diffraction using a curve.

Note (1) Formula y = C exp (−ax ² + bx) (a> 0, C> 0) where C, a and b are constants, x is a diffraction angle, and y is an X-ray intensity.

Formula (2) However, σ and μ are the standard deviation and the average value of the normal probability density function, respectively.

Formula (4) Equation (5) However, T _i = 12t _i ² −n ² +1 , K is a constant, Σ is a sum of i = i to n, 1n is a natural logarithm, y _i is a measurement value of X-ray intensity, and c is each measurement point related to the diffraction line ( The interval between the diffraction angles x of the bending angle x _i and the X-ray intensity y _i , that is, the step width, and n represents the number of measurement points of the X-ray intensity y.

[Work]

The present invention derives a simple formula in which the standard deviation α of the Gaussian curve fitted near the peak of the diffraction line can be calculated in a short time, and the standard deviation α is used to evaluate the spread of the diffraction line accompanying the heat treatment of the hardened steel. A method for measuring the hardness of hardened steel by
It utilizes that the standard deviation α corresponds well with the hardness measured by the hardness meter.

〔Example〕

A method of obtaining the standard deviation α of the Gaussian curve used for the hardness measurement of the present invention will be described. It has been clarified that the vicinity of the diffraction line peak can be approximated by a Gaussian curve represented by the following equation.

y = C exp (−ax ² + bx) (a> 0, C> 0) (1) where C, a and b are constants, x is the diffraction angle, and y is the X-ray intensity.

The standard deviation α of the Gaussian curve as a value for evaluating the spread of the diffraction line proposed in the present invention is obtained by using the Gaussian curve of the equation (1) as a normal probability density function However, σ and μ are the standard deviation and the average value of the normal probability density function, respectively. Considering that, it is a value corresponding to the standard deviation σ of this normal probability density function.

If the coefficients of x ^{2 in} equations (1) and (2) are equal,
The following equation holds between σ in equation (2) and the constant a in equation (1).

It is a well known fact that the spread of a normal probability density function is represented by its standard deviation σ.

Therefore, if the Gaussian curve of equation (1) that approximates the diffraction line is considered to be the normal probability density function of equation (2), then σ of equation (2)
The value corresponding to Can express the spread of the diffraction line approximated by a Gaussian curve. Therefore, this Is the standard deviation of the Gaussian curve. If this is represented by α, the standard deviation of the Gaussian curve α is Becomes

The diffraction line that can be approximated by the Gaussian curve is near the peak of the diffraction line, but the range of the diffraction line that can be approximated by the Gaussian curve depends on the material of the test piece.

Therefore, the maximum value of the X-ray intensity of the diffraction line is y
_It is assumed that each point of Ry _{max and} above can be well approximated by a Gaussian curve when _max is set and R is a constant.

The value of R depends on the material and is approximately 0.5 to 0.85.
It has been clarified by the inventor's past research that the value of is taken.

However, for many materials, each point of at least 0.8y _max is well approximated by a Gaussian curve, so here R
Although the case where R is selected to 0.8 will be described, it goes without saying that the same applies when R is selected to another value.

Next, a method of specifically determining the standard deviation α of the Gaussian curve of the equation (4) will be described.

As Figure 4 now, 0.8y _max over n number of points (x _1,
y ₁ ), (x ₂ , y ₂ ), ..., (x _n , y _n ) is applied to the Gaussian curve of equation (1) using the least squares method to obtain the constant a.
By substituting this into the equation (4), the standard deviation α of the Gaussian curve showing the spread of the diffraction line is calculated.

The calculation formula of this α is quite complicated, but if various calculation techniques are applied to this and it is made into the simplest form, However, T _i = 12t _i ² −n ² +1 , K is a constant, Σ is a sum of i = i to n, 1n is a natural logarithm, y _i is a measurement value of X-ray intensity, and c is each measurement point related to the diffraction line ( The interval of x of the diffraction angle of the bending angle x _i , the X-ray intensity y _i , that is, the step width, and n represents the number of measurement points of the X-ray intensity y.

Becomes

In FIGS. 1 to 3, the original diffraction line consists of the X-ray intensity above the background (BG). The standard deviation α of the Gaussian curve when BG is corrected (that is, BG is subtracted) to obtain this original diffraction line, the BG intensity y _b is subtracted from y instead of using the X-ray intensity y as it is. Value y−y _b
Can be calculated by using.

However, since the spread of the diffraction line can be evaluated and the hardness can be measured with sufficient accuracy even from α in Eq. (5) when BG is not corrected, here, α when BG correction is omitted will be described. Needless to say, α in the case of correcting can be obtained by a similar method.

When the steel is quenched, that is, rapidly cooled from a high temperature, the structure of the steel usually undergoes martensitic transformation, the steel becomes hard, and the diffraction line broadens as shown in FIG. However, since the S35C steel shown in Fig. 2 has a low carbon content (about 0.35%), the structure did not undergo martensitic transformation due to such rapid cooling, so the sharp diffraction line as shown in Fig. 2 was obtained. It has a low hardness.

Hereinafter, FIGS. 5 to 8 will be described.

Here, an example is described in which the standard deviation α of the Gaussian curve is measured using an X-ray stress measurement device that uses chromium (Cr) Kα X-rays that is often used for residual stress measurement of steel materials. Α can be similarly measured using a source or an X-ray diffractometer.

FIG. 5 illustrates how to take each point of the X-ray intensity y in the vicinity of the diffraction line peak in order to quickly measure the standard deviation α of the Gaussian curve.

When measuring the X-ray intensity, the X-ray incident angle, that is, the angle formed by the normal line of the surface of the object to be measured and the direction of the incident X-ray may be any value, but the X-ray intensity is as strong as possible. Normally, 0 ° is used as the incident angle.

An X-ray detector for measuring y may scan from a side with a small diffraction angle x to a side with a large diffraction angle x, or may scan in the opposite direction. Since scanning is performed from the angle side to the low angle side, here, from the high angle side to the low angle side, as shown in FIG. 5, A, B, C, ..., P, Q, R are sequentially scanned. The case will be described.

First, the peak position of the diffraction line of unstressed steel is about 156
Since it is ゜, about 159 ゜ on the higher angle side than this 1
The X-ray detector is scanned from the position A of 60 ° to the low angle side at a constant interval (step width) c, and the X-ray intensity y is measured as shown in FIG.

The measured y is input to the personal computer via the interface, which determines the maximum value y _max of y.

Further, the X-ray intensity y is continuously measured, and y passes through the peak.
When 0.8y _max or less, the X-ray detector automatically stops and y
End the measurement of.

At the same time, n points C of 0.8y _max or more in FIG.
The standard deviation α of the Gaussian curve is calculated from P and Q by the equation (5) by the personal computer.

Since these values are calculated within 1 second by the personal computer, the time for obtaining α is almost equal to the time for measuring each point of the X-ray intensity in FIG.

FIG. 6 is a principle diagram of an automatic measuring device using a personal computer for rapidly and accurately carrying out the measuring method of the present invention.

1 is an X-ray generator.

The incident X-ray r emitted from the X-ray tube 2 is applied to the measurement object 3.

The X-ray intensity y diffracted by the measurement object 3 is measured by the X-ray detector 4.

The X-ray detector 4 is scanned by the pulse motor 5 along an arc centered on the surface of the measurement object 3, measures the X-ray intensity y at a predetermined diffraction angle position x, and sends it to the X-ray counter 6. send.

The X-ray intensity y measured by the X-ray counter 6 is sent to the personal computer 9 via the interface 8,
Calculate α according to a pre-loaded program.

As shown in FIG. 5, drive control of the X-ray detector 4 for efficient and rapid measurement of data is performed by the personal computer 9 via the interface 8 of the pulse motor drive controller 7.

The display 10 is used to display the programs and calculation results of the personal computer 9.

The printer 11 and plotter 12 are used for recording and graphing measured data and results.

The mini-floppy disk 13 is used for recording and storing programs and data.

Of the elements constituting the apparatus shown in FIG. 6, the portions from the X-ray generator 1 to the X-ray calculator 6 are newly manufactured, or the conventionally well-known X-ray stress measuring device, X-ray diffracting device, etc. Can be used.

However, in order to quickly and automatically measure the standard deviation α of the Gaussian curve, the devices from the pulse motor drive control device 7 to the mini floppy disk 13 in FIG. 6 must be newly added.

Among these, the devices from the personal computer 9 to the mini floppy disk 13 are the main body of a commercially available personal computer and its peripheral devices.

An apparatus equipped with such a personal computer is a programmable program capable of recombining an optimum program according to a desired value or measurement condition, as compared with a known X-ray stress measurement apparatus or X-ray diffraction apparatus having a built-in microcomputer. It has the advantage of being a device.

FIG. 7 shows a flowchart for obtaining the standard deviation α of the Gaussian curve by the personal computer using the method shown in FIG.

In FIG. 7, C, Pt, c, x ₀ is the preset time (second) (measurement time of X-ray intensity y _i ), the step width, and the initial value of the diffraction angle, that is, the x coordinate for starting the measurement.

R in FIG. 7C is usually set to 0.8.

When the X-ray intensity y _i becomes less than R y _max in α, α is immediately calculated by the personal computer and the measurement ends, so the X-ray intensity y _i required for the calculation can be measured quickly without wasting, and the half width The measurement is completed in about 1/5 of the measurement time.

If necessary, the measurement results can be plotted on a plotter as shown in FIG.

Finally, an example in which the standard deviation α of the Gaussian curve and the hardness Hv are measured for various hardened steels will be described.

FIG. 8 shows the Vickers hardness Hv (test load 500 g) and standard deviation α of the Gaussian curve of the test piece of the machine structural carbonized steel S45C as-quenched and the test piece tempered at various temperatures after quenching.
That is, the relationship, that is, the calibration curve is shown.

This figure shows that α corresponds fairly well with hardness Hv, and that Hv can be obtained from α using this figure.

〔The invention's effect〕

As described above, the present invention approximates the vicinity of the peak of the diffraction line of the hardened steel test piece with a Gaussian curve, evaluates the spread of the diffraction line accompanying heat treatment with the standard deviation of this Gaussian curve, and the same kind as this test piece Since it is a Gaussian hardness measurement method for measuring the hardness of the steel material by using the relationship between the standard deviation and the hardness, which is obtained in advance using the test piece of the steel material described above, that is, the calibration curve, the conventional half width It has the following advantages over the hardness measurement by.

(1) Since the present invention only needs to measure the X-ray intensity only near the peak of the diffraction line, the measurement time can be greatly reduced (about 1/5 of half-width measurement).

(2) Generally, hardened steel has a wide range of diffraction lines, and it is difficult to accurately obtain the background (BG) of the diffraction lines necessary for measuring the half width, but the present invention does not need to obtain BG. Therefore, the hardness can be accurately measured even for hardened steel having a wide range of diffraction lines.

Further, the present invention has the following advantages over the hardness measurement by the hardness meter which has been most widely used in the past.

(1) Non-destructive, non-contact hardness measurement can be performed.

(2) The automation of the measurement using a personal computer is easy, and the hardness can be measured in an extremely short time by using this and the equation (5) for obtaining the standard deviation of the Gaussian curve derived in the present invention.

(3) The hardness can be measured even for a large structure or an object that cannot be measured by a hardness meter such as a notch or fillet having a non-planar shape.

[Brief description of drawings]

The drawings show one embodiment of the present invention. FIG. 1 is an explanatory view of the method for obtaining the half width B, and FIGS. 2 and 3 show quenched carbon steel S35C for machine structural use and carbon tool steel SK3. Diffraction line diagram, Fig. 4 is a schematic diagram of a Gaussian curve fitted to the n points near the diffraction line peak using the least squares method, and Fig. 5 is an example of the diffraction line of carbon steel S45C for machine structure. FIG. 6 is a diagram showing how to take each point of the X-ray intensity y for obtaining the standard deviation α of the Gaussian curve, FIG. 6 is a principle diagram of the apparatus of the present invention, and FIG. 7 is a personal computer for obtaining the standard deviation α of the Gaussian curve. FIG. 8 is a flowchart of a computer, and FIG. 8 is a diagram showing the relationship between the standard deviation α of S45C and the Vickers hardness Hv of a steel material that has been quenched and tempered at various temperatures after quenching.

Claims (1)

[Claims] 1. Test pieces are produced by cutting out a part of the as-quenched steel material and a steel material that has been tempered at various temperatures after hardening, and the hardness of each of these test pieces is determined by a known hardness such as Vickers hardness. These test pieces are irradiated with X-rays by the measuring method, and the diffraction line of each test piece showing the relationship between the diffraction angle and x and the X-ray intensity y is obtained, and the height of this diffraction line is 50-80. When a region of% or more is approximated by a Gaussian curve represented by the following equation (1) and this Gaussian curve is considered as a normal probability density function represented by the following equation (2), the standard of the following equation (1) Since the deviation α corresponds to the standard deviation σ of the following equation (2), the following equation (4) is derived, and the standard deviation α of the following equation (4) is set to the minimum of the constant a of the following equation (1). After the constant a obtained by the least square method is transformed into a simple equation, the following (4) It is determined by substituting into the equation a to obtain the following equation (5), and the standard deviation α of the following equation (1) and the known hardness for each test piece determined by the following equation (5) The hardness of each test piece obtained by the measuring method is plotted on the vertical axis and the horizontal axis, respectively, to create a relationship between the standard deviation α and the known hardness, that is, a calibration curve, and subsequently, the heat-treated steel material. X on the same object as
The standard deviation α is obtained by irradiating a ray in the same manner as described above, and the standard deviation α of the object to be measured is applied to the calibration curve to obtain the hardness of the object to be measured X using a Gaussian curve.
Hardness measurement method for hardened steel by line diffraction. (1) Formula y = C exp (−ax ² + bx) (a> 0, C> 0) where C, a and b are constants, x is a diffraction angle, and y is an X-ray intensity. Formula (2) However, σ and μ are the standard deviation and the average value of the normal probability density function, respectively. Formula (4) Equation (5) However, T _i = 12t _i ² −n ² +1 , K is a constant, Σ is a sum of i = i to n, 1n is a natural logarithm, y _i is a measurement value of X-ray intensity, and c is each measurement point related to the diffraction line ( The interval of x of the diffraction angle of the bending angle x _i , the X-ray intensity y _i , that is, the step width, and n represents the number of measurement points of the X-ray intensity y.