Method for analyzing orientation state of filler in resin molded article

Abstract

A method for analyzing the orientation state of a filler in a resin molded article, the method comprising: a slice image acquisition step for acquiring, in a predetermined direction, a slice image of at least a portion of a resin molded article molded from a resin composition containing a filler at a predetermined ratio; a power spectrum image acquisition step in which one or more slice images are selected from among the slice images, and a power spectrum image is acquired by performing Fourier transform on the selected slice images; and an orientation state analysis step in which, on the basis of the power spectrum images, the orientation state of the filler in each of the power spectrum images is analyzed and numeralized.

Description

Technical Field

[0001] The present invention relates to a method for analyzing the orientation state of a filler in a resin molded product. Background Art

[0002] Conventionally, in order to shorten the design cycle of resin products (resin molded products) and reduce the cost of trial production, attempts have been made to introduce numerical analysis methods in the design of various resin products instead of mechanical strength tests of various resin products.

[0003] Problems when numerical analysis is not used include the need to prepare enough prototypes for the test and the inability to repeat the test due to time constraints in the resin product design period when the mechanical strength test involves the destruction of the resin product and its prototype.

[0004] Therefore, in the design site of resin products, it has become an important issue to use numerical analysis methods to replace mechanical strength tests of resin products.

[0005] In particular, resin products prepared using resin compositions containing fillers such as fibrous fillers need to predict strength by taking into account the orientation of fillers such as fibrous fillers. However, when strength prediction considering the orientation of fillers cannot be fully performed, it is difficult to distinguish whether the reason lies in the prediction accuracy of the fiber orientation state or the accuracy of the method for predicting physical property values ​​based on the fiber orientation. Therefore, the prediction accuracy based on numerical analysis is worrying.

[0006] As a method for analyzing the orientation of the filler, there can be cited a method using X-ray CT as described in Patent Documents 1 and 2. In contrast, there can be cited a method in which, instead of using X-ray CT, a cross section is physically formed by cutting or the like, and the orientation angle and orientation degree are calculated from an image taken by SEM or the like, as described in Non-Patent Document 1.

[0007] Prior art literature

[0008] Patent Literature

[0009] Patent Document 1: Japanese Patent Application Publication No. 2012-002547

[0010] Patent Document 2: Japanese Patent No. 5844921

[0011] Non-patent literature

[0012] Non-patent document 1: Fiber orientation in injection-molded composites: A comparison of theory and experiment RANDY S.BAY Et al. POLYMER COMPOSITES, AUGUST 1992, Vol. 13, No. 4 Summary of the invention

[0013] Problems to be solved by the invention

[0014] The problems of the method described in Patent Document 1 include: a large amount of time is required in the binarization process and when obtaining the orientation angle and orientation degree, and it is difficult to set the threshold value when binarizing the image, and the orientation angle and orientation degree vary depending on the image measurement method and the threshold setting method. Therefore, as a numerical analysis method, it is difficult to verify the analysis accuracy of the fiber orientation obtained by Autodesk, Moldflow Insight, etc.

[0015] Furthermore, the method described in Patent Document 2 has the problem that a lot of time is required to fit the virtual cylinder, and there are concerns about the calculation accuracy of the orientation degree and orientation angle in a bent state of the fibers.

[0016] Furthermore, the method described in Non-Patent Document 1 has the following problems: a lot of time is required to prepare a sample for cross-sectional observation, the clarity in the cutting direction needs to be increased, and the resolution in the cutting direction is poor.

[0017] The present invention has been made in view of the above-mentioned conventional problems, and an object of the present invention is to provide an analysis method capable of analyzing the orientation state of a filler in a resin molded product containing a filler such as a fibrous filler simply and with practical accuracy.

[0018] Solutions to Solve Problems

[0019] The present inventors have conducted intensive research to solve the aforementioned problems and have found that, for images of resin molded products obtained by X-ray CT, time-consuming image processing and data processing are omitted, and the orientation tendency of fillers in resin molded products can be analyzed with practical accuracy and processing time, thereby completing the present invention.

[0020] One aspect of the present invention for solving the above-mentioned problems is as follows.

[0021] (1) A method for analyzing the orientation state of a filler in a resin molded product comprises:

[0022] a slice image obtaining step of obtaining a slice image in a predetermined direction of at least a portion of a resin molded product molded by a resin composition containing a filler at a predetermined ratio;

[0023] a power spectrum image acquisition step of selecting one or more slice images from the slice images and acquiring a power spectrum image by performing Fourier transform on the selected slice images; and

[0024] The orientation state analysis step is to analyze and quantify the orientation state of the filler in the power spectrum image based on the power spectrum image.

[0025] (2) According to the method for analyzing the orientation state of fillers in a resin molded product described in (1) above, in the orientation state analysis step, the following formula 1, the following formula 2 and the following formula 3 are used to calculate the two-dimensional tensor T shown in the following formula 4 from the brightness of a pixel at any position in the power spectrum image.

[0026] [Calculation formula 1]

[0027]

[0028] [In equations 1 to 4, F(x, y) represents the density of a pixel at the x-position and y-position of an image, and x and y represent the horizontal and vertical positions of the pixel, respectively.]

[0029] (3) According to the method for analyzing the orientation state of fillers in resin molded products described in (2) above, in the orientation state analysis step, the eigenvalues ​​a, b and eigenvectors are calculated from the two-dimensional tensor T, the orientation degree is calculated from the eigenvalues ​​a and b, and the orientation angle is calculated from the eigenvectors.

[0030] (4) According to the method for analyzing the orientation state of a filler in a resin molded article described in (3), in the orientation state analysis step, a relative orientation degree represented by the following equation 5 is obtained from the two components of the characteristic values ​​a and b.

[0031] Relative orientation degree = a / b...Formula 5

[0032] [In Formula 5, the characteristic values ​​a and b are a≥b.]

[0033] (5) According to the analytical method for the orientation state of the filler in the resin molded product described in (3), the X-direction component intensity DX shown in the following equation 6 and the Y-direction component intensity DY shown in the following equation 7 are obtained using the components XX and YY in the above equation 4.

[0034] [Calculation formula 2]

[0035]

[0036] Effects of the Invention

[0037] According to the present invention, it is possible to provide a method for analyzing the orientation state of a filler in a resin molded product containing a filler such as a fibrous filler simply and in a short time with practical accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of an X-ray CT measuring device.

[0039] Figure 2 This is a diagram showing the entire image of a resin molded product captured by an X-ray CT device.

[0040] Figure 3 The diagram shows a slice image of a resin molded product captured by an X-ray CT device.

[0041] Figure 4 Yes Figure 3 (a) A power spectrum image obtained by performing Fourier transform on the image shown, and (b) a diagram showing a state where the power spectrum image is arranged on coordinates.

[0042] Figure 5 It is a description of Figure 3 (a) A power spectrum image obtained by Fourier transforming the image shown; and (b) a diagram showing a method of deriving the orientation angle.

[0043] Figure 6 It is a perspective view showing the shape of the resin molded product used in Examples.

[0044] Figure 7 Yes means Figure 5 An example of eigenvalues ​​(a, b), orientation angles, and principal eigenvectors in a power spectrum image is shown.

[0045] Figure 8 This is a graph showing an example of the distribution of the orientation angle of the fibrous filler with respect to the position in the wall thickness direction of the resin molded product.

[0046] Fig. 9 This is a graph showing an example of the distribution of the degree of orientation of the fibrous filler with respect to the position in the wall thickness direction of the resin molded product.

[0047] Fig.10 It is a graph showing the relative position of the Y-direction component intensity distribution with respect to the wall thickness direction of the resin molded product.

[0048] Fig.11 It is a graph showing the correlation between the average value of the Y-direction component strength and the tensile strength.

[0049] Fig.12 Yes Figure 3 The image shown is a binarized image.

[0050] Fig.13 Yes Fig.12 The image shown is a diagram of a power spectrum image obtained by performing Fourier transform.

[0051] Fig.14 This is a graph showing the distribution of the orientation angle of the fibrous filler with respect to the position in the wall thickness direction of the resin molded product when the X-ray CT image is binarized.

[0052] Fig.15 This is a graph showing the distribution of the degree of orientation of the fibrous filler with respect to the position in the wall thickness direction of the resin molded product when the X-ray CT image is binarized. DETAILED DESCRIPTION

[0053] The method for analyzing the orientation state of fillers in a resin molded product of the present embodiment (hereinafter sometimes referred to as "the analysis method of the present embodiment") is characterized in that it comprises: a slice image acquisition step, which acquires a slice image in a specified direction of at least a portion of a resin molded product molded by a resin composition containing fillers in a specified proportion; a power spectrum image acquisition step, which selects one or more slice images from the slice images and acquires a power spectrum image by performing Fourier transform on the selected slice images; and an orientation state analysis step, which analyzes and digitizes the orientation state of the filler in the power spectrum image based on the power spectrum image.

[0054] Before describing the analysis method of this embodiment, the resin molded product to be analyzed is first described. The resin molded product is molded by a resin composition containing a resin material and a filler, and includes a resin part and a filler part. The resin material contained in the resin part and the filler contained in the filler part are described below.

[0055] [Resin material]

[0056] In the analysis method of this embodiment, various conventionally known resin materials can be used to prepare the resin molded product to be analyzed. In addition, a resin mixture obtained by blending a plurality of resins is also included in the above-mentioned resin material.

[0057] [filler]

[0058] As described above, the resin molded product contains fillers in a predetermined ratio. The type of filler is preferably an inorganic filler that allows for a clear boundary between the resin and the filler and has a low X-ray transmittance. Examples of conventionally known inorganic fillers include fibrous fillers, granular fillers, plate-like fillers, and the like.

[0059] Preferred fibrous fillers include, for example, glass fibers, asbestos fibers, silica fibers, silica / alumina fibers, alumina fibers, zirconia fibers, boron nitride fibers, silicon nitride fibers, boron fibers, potassium titanate fibers, and inorganic fibrous substances such as fibers of metals such as stainless steel, aluminum, titanium, copper, and brass.

[0060] In addition, examples of powdery fillers include silicon dioxide, quartz powder, glass beads, ground glass fibers, glass balls, glass powder, calcium silicate, aluminum silicate, kaolin, talc, clay, diatomaceous earth, silicates such as wollastonite, iron oxide, titanium oxide, zinc oxide, antimony trioxide, metal oxides such as aluminum oxide, metal carbonates such as calcium carbonate and magnesium carbonate, metal sulfates such as calcium sulfate and barium sulfate, and others include ferrite, silicon carbide, silicon nitride, boron nitride, and various metal powders.

[0061] Examples of the plate-like filler include mica, glass flakes, and various metal foils.

[0062] The resin composition may further include a resin composition to which additives such as a nucleating agent, a colorant, an antioxidant, a stabilizer, a plasticizer, a lubricant, a release agent, and a flame retardant are added to impart desired properties.

[0063] In this embodiment, the resin molded product can be obtained by a conventionally known molding method, such as compression molding, transfer molding, injection molding, extrusion molding, blow molding, and other various molding methods.

[0064] Among them, the resin molded product containing fibrous fillers has large anisotropy in physical properties due to the orientation state of the filler. As a result, if the orientation of the fibrous filler is not analyzed with higher precision, the analysis results cannot be used for the evaluation of physical properties. Therefore, in the conventional method, when the resin molded product containing fibrous fillers is used as the analysis object, more time and energy are spent to improve the analysis accuracy. On the other hand, the analysis method of the present embodiment can properly analyze the tendency of the orientation state of the filler even if the resin molded product containing fibrous fillers is used as the object, without spending energy for improving the analysis accuracy. Therefore, even if the resin molded product containing fibrous fillers is used as the object, the analysis results can be used for the prediction of physical properties. In the case where glass fibers are also contained in the above-mentioned fibrous fillers, especially if the orientation state of the filler is not analyzed with high precision, the analysis results cannot be used for the prediction of physical properties. The analysis method of the present embodiment can properly analyze the tendency of the orientation state of the filler even if the resin molded product containing glass fibers is used as the object, without spending energy for improving the analysis accuracy.

[0065] In addition, when the content of filler is high, fillers overlap in a complex manner in the resin product and interfere with each other seriously. As a result, the analysis accuracy is greatly reduced in the conventional method, and the analysis results cannot be used for prediction of physical properties. On the other hand, the analysis method of the present embodiment can easily and appropriately analyze the orientation state tendency of the filler even if the content of filler is high, so even if the resin molded product with a high content of filler is used as the object, the analysis results can be used for prediction of physical properties.

[0066] [Other ingredients]

[0067] In the present embodiment, the resin composition further contains additives such as a nucleating agent, a colorant, an antioxidant, a stabilizer, a plasticizer, a lubricant, a release agent, and a flame retardant to impart desired properties to the resin composition.

[0068] [Method for producing resin molded article]

[0069] The resin molded article according to the present embodiment can be obtained by a conventionally known molding method, such as compression molding, transfer molding, injection molding, extrusion molding, blow molding, and the like.

[0070] <Analysis method of orientation state of filler in resin molded product>

[0071] The analysis method of the present embodiment includes a slice image acquisition step, a power spectrum image acquisition step, and an orientation state analysis step. Hereinafter, each step of the analysis method of the present embodiment will be described in more detail.

[0072] [Slice image acquisition steps]

[0073] The slice image acquisition step is a step of acquiring one or more slice images at predetermined intervals in a predetermined direction for at least a portion of a resin molded product molded by a resin composition containing a filler at a predetermined ratio.

[0074] One or more slice images are obtained at a specified interval in a specified direction for at least a portion of the resin molded product. "At least a portion" means that the obtained resin molded product as a whole can be used as the object for analyzing the orientation state of the filler, or a portion of the resin molded product can be used as the object for analyzing the orientation state of the filler. For example, when the orientation state in the resin molded product is the same, if the orientation state is analyzed for only a portion, the other portions can be regarded as having the same orientation state as the analyzed portion. In addition, when fragile portions such as welding portions are known in advance and only the physical properties of the portion are to be evaluated, one or more slice images of the portion are obtained, so that the purpose can be achieved even without obtaining a slice image of the entire portion. According to the analysis method of this embodiment, the tendency of the orientation state of the filler in the resin molded product can be easily analyzed with high precision, and as a result, the physical properties of the resin molded product can be easily predicted.

[0075] Furthermore, when it is necessary to predict and identify the desired measurement location, a resin molded product is cut out from the resin molded product to be subjected to the slice image acquisition, and a resin test piece for obtaining the slice image is prepared as needed. Furthermore, if it is not necessary, the entire resin molded product may be used as a resin test piece without cutting out the test piece from the resin molded product.

[0076] There is no particular limitation on the method of obtaining the slice image, and the following methods can be used: Figure 1 The X-ray CT apparatus 1 is provided with: an X-ray irradiation unit 11 for irradiating X-rays toward the resin test piece 2; an X-ray detection unit 12 for detecting X-rays transmitted through the resin test piece 2 as projection data; a sample stand 13 for holding the resin test piece 2; and a unit for moving the sample stand 13 up and down ( Figure 1 Movement in the direction of the arrow in the figure) and rotational movement ( Figure 1 a rotation drive unit 14 for moving in the direction of the blank arrow in FIG. 1 ); and an image processing unit 15 for reconstructing projection data in multiple angular directions as slice images.

[0077] The X-ray irradiation unit 11 is a part for irradiating X-rays toward the resin test piece 2. As long as it can irradiate X-rays, there is no particular limitation, and a conventionally known X-ray irradiation device can be used. For example, an X-ray tube, etc. can be listed. The X-ray irradiation unit 11 can adjust the irradiation conditions of the X-rays irradiated toward the resin test piece 2. Examples of the X-ray irradiation conditions include tube current, X-ray irradiation time, etc. In the analysis method of this embodiment, the X-ray irradiation conditions are not particularly limited, and can be appropriately changed according to the shape of the resin test piece that is the object, the type of resin contained, etc.

[0078] The X-ray detection unit 12 is a part that converts X-rays transmitted through the resin test piece 2 into electric signals and detects the signals as projection data. The X-ray detection unit 12 is disposed to face the X-ray irradiation unit 11 with the resin test piece 2 interposed therebetween.

[0079] The sample stand 13 is a portion for holding the resin test piece 2 so that the resin test piece 2 is irradiated with X-rays. The sample stand 13 is disposed between the X-ray irradiation unit 11 and the X-ray detection unit 12.

[0080] The rotation drive unit 14 is a part for moving the sample stage 13 up and down and rotating it to irradiate the resin test piece 2 with X-rays from multiple angles. The rotation drive unit 14 is connected to the sample stage 13. The rotation drive unit 14 can irradiate X-rays from multiple directions to various positions in the resin test piece 2. As a result, various projection data of X-rays that pass through the resin test piece 2 from various angles can be obtained.

[0081] The image processing unit 15 is a part that reconstructs the projection data in multiple angular directions as slice images. The image processing unit 15 is connected to the X-ray detection unit 12. The projection data detected by the X-ray detection unit 12 is sent to the image processing unit 15, and the slice images are obtained by performing conventionally known image processing. Conventionally known image processing methods refer to methods such as: performing one-dimensional Fourier transform on the projection data in each direction, synthesizing them to produce a two-dimensional Fourier transform image, and performing inverse Fourier transform on them to obtain a reconstructed image.

[0082] The slice image obtained by the above method is a slice image at a predetermined interval in a predetermined direction in the resin molded product. "Prescribed interval" refers to the range in which the lightness and darkness are averaged when the slice image is obtained. The interval of the slice image is not particularly limited and can be implemented by appropriately changing it according to the measurement object, etc., but in order to properly analyze the orientation state of the filler in the resin molded product containing fibrous fillers, the interval of the slice image is less than the average diameter of the filler, and when the average diameter is unknown, it is preferably less than 20 μm. In addition, the "prescribed direction" is a direction perpendicular to the image surface of the slice image, and the prescribed direction can be set to a desired direction.

[0083] An example of the slice image obtained in the above manner is shown in Figure 2 , 3 .exist Figure 2 , 3 A monotonous image is shown in . Figure 2 For the entire test piece, Figure 3To take out one of the slice images. The darker part is the part of the resin molded product that is easy to transmit X-rays, and the whiter part is the part of the resin molded product that is not easy to transmit X-rays. The slice image contains the resin part and the filler part. Generally, the resin part is easier to transmit X-rays than the filler part. Therefore, in Figure 3 In the image, the black part tends to represent the resin, and the white part tends to represent the filler. In addition, as described below, the slice image also contains a noise pattern, so it cannot be simply said that the part represented by black is the resin part and the part represented by white is the filler part.

[0084] Since the resin portion and the filler portion have different X-ray absorption rates, an image with shades can be obtained. Moreover, in the case of obtaining a slice image of the resin test piece 2 composed of multiple materials with different X-ray absorption rates, the X-ray absorption rate changes discontinuously across the boundary between the resin portion and the filler portion. Therefore, discontinuous (rapid) changes also appear in the projection data obtained by the X-ray detection unit 12. As a result, high-frequency components caused by discontinuous changes appear in large quantities in the one-dimensional Fourier transform image. Due to the numerical calculation error caused by this high-frequency component, a virtual image (noise image) called an artifact appears in the reconstructed image obtained from the image processing unit 15.

[0085] This noise map is also included in the slice image. This noise map becomes a big obstacle in analyzing the orientation state of fillers using the slice image using the traditional method. This is because the traditional method is a method of analyzing the orientation state of fillers one by one. Therefore, in the method of patent document 1, a threshold is set within the range of brightness of the image, the image is binarized, and the image is divided into two areas of the resin part and the filler part, and then the power spectrum is calculated.

[0086] As mentioned above, X-ray CT images are Figure 3 The image shown in the figure includes a white part, a black part, and a gray part. In the method described in Patent Document 1, for each pixel, when the image density of the pixel is above an appropriately set image density threshold, white is binarized to black when the image density of the pixel is below the image density threshold.

[0087] However, in order to attribute the gray part to the resin part or the filler part, a threshold value needs to be set, but depending on the threshold value, the volume fraction of the resin part may be different from the actual volume fraction. In addition, the noise processing method based on the clarity of the image and image processing sometimes depends on the operator's subjectivity. As a result, it is different from the actual volume fraction, which may have an adverse effect on the calculation accuracy of the orientation degree and orientation angle.

[0088] Therefore, in this embodiment, a power spectrum image is acquired as follows, and the orientation state of the filler is analyzed based on the power spectrum image.

[0089] [Steps to obtain power spectrum image]

[0090] The power spectrum image acquisition step is a step of selecting one or more slice images from the slice images acquired in the slice image acquisition step, and acquiring a power spectrum image by performing Fourier transform on the selected slice images.

[0091] An example of a power spectrum image is shown in Figure 4 (a). Figure 4 The power spectrum image shown in (a) is Figure 3 The power spectrum is obtained by Fourier transforming the two-dimensional image shown.

[0092] [Orientation state analysis steps]

[0093] The orientation state analysis step is a step of analyzing and digitizing the orientation state of the filler in the power spectrum image based on the power spectrum image obtained by the power spectrum image acquisition step. According to the analysis method of this embodiment, since the orientation state tendency is analyzed for each two-dimensional image, the orientation state tendency of the entire analysis range can be captured extremely well and accurately with the length resolution of one pixel of X-ray CT. In particular, in the wall thickness direction, for example, in the past, there were about 10 sheets per 1 mm, and the thickness of one sheet was also inaccurate, but in this embodiment, there are 100 sheets per 1 mm, so the resolution is greatly improved.

[0094] In the orientation state analysis step, in order to quantify the orientation state of the filler, the following formula 1, the following formula 2, and the following formula 3 are used, from Figure 4 The two-dimensional tensor T shown in the following equation 4 is obtained by calculating the brightness of a pixel at any position in the power spectrum image represented by the grayscale shown in (a).

[0095] [Calculation 3]

[0096]

[0097] [In equations 1 to 4, F(x, y) represents the density of a pixel at the x-position and y-position of an image, and x and y represent the horizontal and vertical positions of the pixel, respectively.]

[0098] The eigenvector and eigenvalues ​​a and b are obtained from the component values ​​of the obtained two-dimensional tensor T. As a calculation method, it can be easily calculated / installed in the numerical calculation library of the Jacobi method and the programming language Python. In addition, a and b in the equation 5 described later can be obtained by combining the program.

[0099] For an example of a method for deriving the orientation angle of a filler, refer to Figure 5 to explain. Figure 5 (a) represents the power spectrum image, Figure 5 (b) represents coordinates used to explain the method of deriving the orientation angle. Figure 5 As shown in (b), the Y direction of the image is taken as the flow direction (FD), when it is near 90°, it is the flow direction (FD), and when it is 0° or 180°, it is the flow perpendicular direction (TD). By combining the obtained eigenvectors and eigenvalues, the one with the higher eigenvalue becomes the principal vector, and the direction represented by the principal vector is calculated from each component of the vector and used as the orientation angle. The angle can be easily calculated from the values ​​of each component of the vector V1x, V1y by the Atan2 function of Excel, Visual C#, etc. In addition, in Figure 4 (a) and Figure 5 In (a), the power spectrum image is the same, but in Figure 4 In (a), an ellipse is given. Figure 5 The arrows are given in (a), which is different from each other.

[0100] Next, an example of a method for deriving the orientation degree of a filler is described. The orientation degree can be represented as a relative orientation degree by the ratio of the major axis to the minor axis of the brightness of an elliptical distribution. For example, Figure 4 The power spectrum image shown in (a) is captured as an ellipse, which is Figure 4 In addition, Figure 4 When the major axis of the ellipse shown in (b) is a and the minor axis is b, the orientation degree is expressed by the following formula 5.

[0101] Relative orientation degree = a / b··Formula 5

[0102] Determined from the power spectrum image Figure 4 The threshold of brightness of the elliptical region such as (b) is not uniquely determined, so the values ​​of a and b are biased, and as a result, the orientation degree is not constant. However, in this embodiment, as described above, a and b can be obtained according to the calculation program. In this way, the values ​​of a and b are uniquely determined, and a constant orientation degree can be calculated.

[0103] In addition, the major diameter a is the eigenvalue of the principal vector, and the minor diameter b is the eigenvalue in the perpendicular direction of the principal vector. In addition, the degree of orientation can also be expressed as an eigenvalue or a component of a two-dimensional tensor T. The method for deriving the orientation function is not particularly limited, and conventionally known methods can be used.

[0104] In addition, only the distribution of orientation degree and orientation angle cannot be used to obtain the correlation with the physical property values ​​such as elastic modulus and strength in the flow direction and perpendicular direction of the flow. Therefore, the X-direction component intensity DX shown in Formula 6 and the Y-direction component intensity DY shown in Formula 7 are obtained by using the components XX and YY of the two-dimensional tensor T calculated from each image through Formula 4. And by obtaining the average value in the wall thickness direction, the orientation intensity in each direction represented by the image is obtained.

[0105] [Calculation 4]

[0106]

[0107] As described above, in the analysis method of this embodiment, the binarization process of the X-ray CT image can be omitted, so that the analysis can be performed in a short time. In addition, the setting of the threshold value which is difficult to set in the binarization and the setting of the threshold value for determining the brightness of the elliptical area are unnecessary, and as a result, the deviation of the calculation results of the orientation angle and the orientation degree can be suppressed.

[0108] Example

[0109] Hereinafter, the present embodiment will be described in more detail with reference to examples, but the present embodiment is not limited to the following examples.

[0110] [Example 1]

[0111] (Slice image acquisition step)

[0112] The shape of the resin molded article used in the examples is Figure 6 The flat plate 20 shown in FIG. 1 has four types of thicknesses of 1 mm, 2 mm, 3 mm, and 4 mm. These resin molded products are prepared by injection molding. The shapes of the resin molded products and the molding conditions during injection molding are as follows. Figure 6 The case where the thickness is 2.00 mmt is shown in FIG.

[0113] Shape: 80.00mm in length, 80.00mm in width, 1.00, 2.00, 3.00, 4.00mm in thickness

[0114] Resin: Polybutylene terephthalate resin containing 15% by mass of glass fiber

[0115] Mold temperature: 60℃

[0116] Resin temperature: 260℃

[0117] Filling rate: 17.3cm 3 / s

[0118] Holding pressure: 49MPa, 5sec

[0119] Cooldown: 7 seconds

[0120] Next, each of the above-mentioned resin molded products was cut into a resin test piece with a width of 12.5 mm and a length of 20 mm, and a slice image was obtained. The imaging device used was a commercially available X-ray CT device (ScanXmate-D090SS270 manufactured by COMSCANTECNO Co., Ltd.). The imaging conditions are as follows. In addition, among the obtained slice images, the slice image with a thickness of 2 mmt is shown in Figure 3 .

[0121] Voltage: 50kV

[0122] Tube current: 150μA

[0123] Pixel size: 10.6μm

[0124] (Steps for obtaining power spectrum image)

[0125] The power spectrum image was created by continuously performing Fourier transform on each image using a program manufactured by Polyplastics Co., Ltd. The created power spectrum image is shown in Figure 4 .

[0126] (Orientation analysis steps)

[0127] The two-dimensional tensor T represented by equation 4 is calculated from the power spectra of the above-mentioned power spectrum images using equations 1, 2, and 3. The component with the largest value among the obtained XX, YY, and XY is set to 1 to find the ratio of each component. As an example, the components of the two-dimensional tensor T are XX=0.32468, YY=1, and XY=-0.14789.

[0128] The X-direction component intensity DX is 0.245, and the Y-direction component intensity DY is 0.755.

[0129] From the obtained two-dimensional tensor T, eigenvalue decomposition is performed to obtain the eigenvalue and the corresponding eigenvector. At the same time, the relative orientation degree a / b is obtained from the eigenvalue (a, b) and the above formula 5. Figure 5 The angles, relative orientations, eigenvalues, and eigenvectors (main eigenvectors) in the images shown are shown in Table 1. Figure 7 .

[0130]

Table 1

[0131]

[0132] The stacking direction of the pixels is taken as the wall thickness direction, and the distribution of the orientation angle and orientation degree is obtained from the eigenvalues ​​and eigenvectors. Figure 8 ,9 .

[0133] In addition, the Y-direction component intensity DY corresponding to the flow direction is obtained from the obtained two-dimensional tensor T, and the distribution in each wall thickness is obtained. The relative position of the Y-direction component intensity distribution with respect to the wall thickness direction is shown in Fig.10 .exist Fig.10 In the figure, the horizontal axis represents the relative position in the wall thickness direction, 0 represents the surface, 0.5 represents the center, and 1 represents the surface on the opposite side. The vertical axis represents the relative value of the Y-direction component intensity. Fig.10 In the figure, the dashed line represents a wall thickness of 1 mm, the solid line represents a wall thickness of 2 mm, the dotted line represents a wall thickness of 3 mm, and the single-dot chain line represents a wall thickness of 4 mm.

[0134] In addition, the average value of the obtained Y-direction component strength distribution was obtained for each wall thickness and compared with the tensile strength of the test piece. The correlation between the average value of the Y-direction component strength distribution and the tensile strength is shown in Fig.11 .

[0135] It was found that the average value of the Y-direction component strength and the tensile strength have a good correlation. This shows the influence of filler orientation on material properties, and makes material design and product design easier by analyzing the elastic modulus and strength.

[0136] [Reference Example 1]

[0137] The analysis was performed in the same manner as in Example 1 except that the binarization process was performed before the power spectrum image acquisition step. The binarization process was performed using the image processing software ImageJ (developer Wayne Rashand). The binarized image is shown in Fig.12 , the power spectrum image after Fourier transformation is shown in Fig.13 , the orientation angle distribution in the wall thickness direction is shown in Fig.14 , the orientation degree is shown in Fig.15 In the case of Reference Example 1, the orientation degree is close to 1, and most of the analyzed image range is close to the result of random orientation. Figure 8 , 9 ), with high degree of orientation, more accurately reproduces Figure 2 , 3 The orientation state of the central part of the product shown. According to the analysis method of this embodiment, it is confirmed that the orientation state of the filler can be analyzed very accurately. In addition, since binarization processing is not required, the analysis time is also short. Specifically, Example 1 without binarization processing can shorten the analysis time by about 30 minutes compared with Reference Example 1 with binarization processing.

[0138] Description of symbols

[0139] 2 Resin test piece

[0140] 11 X-ray irradiation department

[0141] 12 X-ray inspection unit

[0142] 13. Sample table

[0143] 14 Rotation drive unit

[0144] 15 Image Processing Unit

[0145] 20 tablets.

Claims

1. A method for analyzing the orientation state of a filler in a resin molded product, characterized in that: have: a slice image obtaining step of obtaining a slice image in a predetermined direction of at least a portion of a resin molded product molded by a resin composition containing a filler at a predetermined ratio; A power spectrum image acquisition step, which selects one or more slice images from the slice images and acquires a power spectrum image by performing Fourier transform on the selected slice images; as well as The orientation state analysis step is to analyze and quantify the orientation state of the filler in the power spectrum image based on the power spectrum image.

2. The method for analyzing the orientation state of fillers in a resin molded product according to claim 1, characterized in that: In the orientation state analysis step, the following equation 1, the following equation 2, and the following equation 3 are used to obtain a two-dimensional tensor T shown in the following equation 4 from the brightness of a pixel at any position in the power spectrum image: [Calculation formula 1] In Formulas 1 to 4, F(x, y) represents the density of a pixel at an X position and a Y position of an image, and x and y represent the horizontal and vertical positions of the pixel, respectively.

3. The method for analyzing the orientation state of fillers in a resin molded product according to claim 2, characterized in that: In the orientation state analysis step, eigenvalues ​​a, b and eigenvectors are obtained from the two-dimensional tensor T, the orientation degree is obtained from the eigenvalues ​​a and b, and the orientation angle is obtained from the eigenvectors.

4. The method for analyzing the orientation state of fillers in a resin molded product according to claim 3, characterized in that: In the orientation state analysis step, the relative orientation degree shown in the following equation 5 is obtained from the two components of the characteristic values ​​a and b: Relative orientation degree = a / b...Formula 5 In Formula 5, the characteristic values ​​a and b satisfy a≥b.

5. The method for analyzing the orientation state of fillers in a resin molded article according to claim 3, characterized in that: Using the components XX and YY in the above formula 4, the X-direction component intensity DX shown in the following formula 6 and the Y-direction component intensity DY shown in the following formula 7 are obtained: [Calculation formula 2]

Images