Method for analyzing the orientation of fillers in resin molded products

Abstract

To provide an analysis method that can simply and with practical accuracy analyze an orientation state of a filler in a resin molded product containing the filler, such as a fibrous filler.SOLUTION: An analysis method of an orientation state of a filler in a resin molded product includes: a slice image obtaining step which obtains slice images in a predetermined direction of at least a part of the resin molded product obtained by molding a resin composition containing the filler at a predetermined rate; a power spectrum image obtaining step which obtains a power spectrum image by selecting one or more slice images from the slice images and performing Fourier transform on the selected slice images; and an orientation state analysis step which analyzes and digitizes an orientation state of the filler in each power spectrum image based on the power spectrum image.SELECTED DRAWING: None

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, for the purpose of shortening the design period of resin products (resin molded products) and reducing the prototype cost, attempts to substitute numerical analysis methods for mechanical strength tests and the like of various resin products have been adopted at the design sites of various resin products.

[0003] Problems when not using numerical analysis methods include the need to prepare test pieces for the number of tests when the mechanical strength test involves the destruction of resin products or their prototypes, and the inability to repeat the test due to time constraints in the design of resin products. Therefore, substituting numerical analysis methods for mechanical strength tests and the like of resin products has become an important issue at the design sites of resin products.

[0004] In particular, for resin products made using a resin composition containing a filler such as a fibrous filler, it is necessary to predict the strength considering the orientation of the filler such as the fibrous filler. However, when the strength prediction considering the filler orientation cannot be sufficiently performed, it is difficult to determine whether the cause lies in the prediction accuracy of the fiber orientation state or the accuracy of the method for predicting physical property values from the fiber orientation. Therefore, the prediction by numerical analysis is of concern in terms of accuracy.

[0005] As a method for analyzing the orientation of this filler, there is a method using X-ray CT as described in Patent Documents 1 and 2. On the contrary, there is a method that does not use X-ray CT, physically forms a cross-section by cutting or the like, and calculates the orientation angle and orientation degree from image photography such as SEM as described in Non-Patent Document 1.

Prior Art Documents

Patent Documents

[0006] [Patent Document 1] Japanese Patent Publication No. 2012-002547 [Patent Document 2] Patent No. 5844921 [Non-patent literature]

[0007] [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 [Overview of the project] [Problems that the invention aims to solve]

[0008] The problems with the method described in Patent Document 1 include the fact that the binarization process and the determination of the orientation angle and degree of orientation require a considerable amount of time, and that setting a threshold is difficult when binarizing the image, resulting in the orientation angle and degree of orientation changing depending on the image measurement method and the threshold setting method. Therefore, it has been difficult to verify the accuracy of fiber orientation analysis obtained using numerical analysis methods such as Autodesk's Moldflow Insight.

[0009] Furthermore, the problems with the method described in Patent Document 2 are that it takes a considerable amount of time to fit the virtual cylinder, and there are concerns about the accuracy of calculating the degree of orientation and orientation angle when the fibers are curved.

[0010] Furthermore, the problems with the method described in Non-Patent Document 1 include the fact that it requires a great deal of time to prepare samples for cross-sectional observation, and that it necessitates a wide range of resolution in the cutting direction, resulting in poor resolution in the cutting direction.

[0011] The present invention has been made in view of the above-mentioned conventional problems, and its objective is to provide an analytical method that can analyze the orientation state of fillers in resin molded products containing fillers such as fibrous fillers in a simple and practical manner. [Means for solving the problem]

[0012] As a result of diligent research to solve the aforementioned problems, the inventors have discovered that it is possible to analyze the orientation trend of fillers in resin molded products with practical accuracy and processing time, without requiring time-consuming image processing and data processing of images of resin molded products obtained by X-ray CT, and have completed the present invention.

[0013] One embodiment of the present invention that solves the aforementioned problems is as follows. (1) A slice image acquisition step in which slice images are acquired in a predetermined direction for at least a portion of a resin molded product obtained by molding a resin composition containing a filler in a predetermined proportion, A power spectral image acquisition step involves selecting one or more slice images from the aforementioned slice images and obtaining a power spectral image by applying a Fourier transform to the selected slice images. An orientation state analysis step, based on the power spectrum image, analyzes and quantifies the orientation state of the filler in the power spectrum image, A method for analyzing the orientation state of fillers in a resin molded product, comprising the following characteristics.

[0014] (2) The method for analyzing the orientation state of a filler in a resin molded product as described in (1), wherein in the orientation state analysis step, a two-dimensional tensor T shown in the following equation 4 is obtained from the brightness of a pixel at an arbitrary position in the power spectral image using the following equations 1, 2, and 3.

[0015]

number

[0016] (3) The method for analyzing the orientation state of a filler in a resin molded product according to (2) above, wherein in the orientation state analysis step, eigenvalues a, b and eigenvectors are obtained from the two-dimensional tensor T, and the degree of orientation is obtained from the eigenvalues a, b, and the orientation angle is obtained from the eigenvectors.

[0017] (4) The method for analyzing the orientation state of a filler in a resin molded product according to (3) above, wherein in the orientation state analysis step, the relative degree of orientation shown in the following Mathematical Formula 5 is obtained from the two components of the eigenvalues a, b. Relative degree of orientation = a / b ··· Mathematical Formula 5 [In Mathematical Formula 5, the eigenvalues a, b satisfy a ≥ b.]

[0018] (5) The method for analyzing the orientation state of a filler in a resin molded product according to (3) above, wherein the X-direction component intensity DX shown in the following Mathematical Formula 6 and the Y-direction component intensity DY shown in the following Mathematical Formula 7 are obtained using the components XX and YY in Mathematical Formula 4. [Number] [Advantages of the Invention]

[0019] According to the present invention, it is possible 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. [Brief Description of the Drawings]

[0020] [Figure 1] It is a schematic diagram of an X-ray CT measuring device. [Figure 2] It is a diagram showing an entire image of a resin molded product photographed by an X-ray CT device. [Figure 3] It is a diagram showing a slice image of a resin molded product photographed by an X-ray CT device. [Figure 4] Figure 3 shows (a) the power spectral image and (b) the power spectral image arranged in coordinates, obtained by applying a Fourier transform to the image shown in Figure 3. [Figure 5] This figure illustrates the method for deriving (a) the power spectral image and (b) the orientation angle, obtained by applying a Fourier transform to the image shown in Figure 3. [Figure 6] This is a perspective view showing the shape of the resin molded product used in the example. [Figure 7] Figure 5 shows an example of eigenvalues ​​(a, b), orientation angle, and principal eigenvectors in a power spectral image. [Figure 8] This graph shows an example of the distribution of orientation angles of fibrous fillers relative to their position in the thickness direction of a resin molded product. [Figure 9] This graph shows an example of the distribution of the degree of orientation of fibrous filler relative to the position in the thickness direction of a resin molded product. [Figure 10] This graph shows the Y-direction intensity distribution with respect to relative position in the thickness direction of a resin molded product. [Figure 11] This graph shows the correlation between the average strength of the Y-direction component and the tensile strength. [Figure 12] This image shows the same image as Figure 3, but after being binarized. [Figure 13] This figure shows the power spectral image obtained by applying a Fourier transform to the image shown in Figure 12. [Figure 14] This graph shows the distribution of the orientation angle of the fibrous filler relative to the position in the thickness direction of the resin molded product when X-ray CT images are binarized. [Figure 15] This graph shows the distribution of the degree of orientation of fibrous filler relative to the position in the thickness direction of a resin molded product, when X-ray CT images are binarized. [Modes for carrying out the invention]

[0021] The method for analyzing the orientation state of fillers in a resin molded product according to this embodiment (hereinafter sometimes abbreviated as "the analysis method of this embodiment") is characterized by comprising: a slice image acquisition step of acquiring slice images in a predetermined direction for at least a part of a resin molded product made by molding a resin composition containing fillers in a predetermined proportion; a power spectrum image acquisition step of selecting one or more slice images from the slice images and acquiring a power spectrum image by applying a Fourier transform to the selected slice images; and an orientation state analysis step of analyzing and quantifying the orientation state of the fillers in the power spectrum image based on the power spectrum image.

[0022] Before describing the analysis method of this embodiment, let's first describe the resin molded product to be analyzed. The resin molded product is made by molding a resin composition containing a resin material and a filler, and includes a resin portion and a filler portion. The resin material included in the resin portion and the filler included in the filler portion will be described below.

[0023] [Resin materials] In the analysis method of this embodiment, the resin molded product to be analyzed can be manufactured using various conventionally known resin materials. Resin mixtures, which are blends of multiple resins, are also included in the above-mentioned resin materials.

[0024] [Filling material] As described above, the resin molded product contains a filler in a predetermined proportion. The preferred type of filler is an inorganic filler that clearly defines the boundary between the resin and the filler and has low X-ray transmittance. Conventionally known inorganic fillers include fibrous fillers, granular fillers, and plate-shaped fillers. 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 materials such as stainless steel, aluminum, titanium, copper, and brass. Furthermore, examples of granular fillers include silica, quartz powder, glass beads, milled glass fiber, glass balloons, glass powder, calcium silicate, aluminum silicate, kaolin, talc, clay, diatomaceous earth, silicates such as wollastonite, metal oxides such as iron oxide, titanium oxide, zinc oxide, antimony trioxide, and alumina, metal carbonates such as calcium carbonate and magnesium carbonate, metal sulfates such as calcium sulfate and barium sulfate, as well as ferrite, silicon carbide, silicon nitride, boron nitride, and various metal powders. Other examples of plate-shaped fillers include mica, glass flakes, and various metal foils.

[0025] The above resin compositions also include resin compositions to which additives such as nucleating agents, colorants, antioxidants, stabilizers, plasticizers, lubricants, mold release agents, and flame retardants have been added to impart desired properties.

[0026] In this embodiment, the resin molded product can be obtained by conventionally known molding methods. Examples of conventionally known molding methods include compression molding, transfer molding, injection molding, extrusion molding, blow molding, and various other molding methods.

[0027] Among these, resin molded products containing fibrous fillers exhibit significant anisotropy in physical properties depending on the orientation of the filler. As a result, unless the orientation of the fibrous filler is analyzed with higher precision, the analysis results cannot be used to evaluate physical properties. Therefore, with conventional methods, when analyzing resin molded products containing fibrous fillers, it takes more time and effort to improve the analysis accuracy. On the other hand, the analysis method of this embodiment can appropriately analyze the trend of the orientation state of the filler without requiring extra effort to improve the analysis accuracy, even when targeting resin molded products containing fibrous fillers. Therefore, even when targeting resin molded products containing fibrous fillers, the analysis results can be used to predict physical properties. In particular, when glass fibers are included among the fibrous fillers, the orientation state of the filler must be analyzed with high precision, otherwise the analysis results cannot be used to predict physical properties. The analysis method of this embodiment can appropriately analyze the trend of the orientation state of the filler without requiring extra effort to improve the analysis accuracy, even when targeting resin molded products containing glass fibers.

[0028] Furthermore, when the filler content is high, the fillers overlap in a complex manner within the resin product and interfere significantly with each other. As a result, conventional methods suffer a significant decrease in analytical accuracy, making it impossible to use the analysis results to predict physical properties. On the other hand, the analytical method of this embodiment can easily and appropriately analyze the orientation trend of the fillers even when the filler content is high. Therefore, even when targeting resin molded products with a high filler content, the analysis results can be used to predict physical properties.

[0029] [Other ingredients] In this embodiment, the resin composition also includes resin compositions to which additives such as nucleating agents, colorants, antioxidants, stabilizers, plasticizers, lubricants, mold release agents, and flame retardants have been added to impart desired properties.

[0030] [Method for manufacturing resin molded products] The resin molded product according to this embodiment can be obtained by conventionally known molding methods. Examples of conventionally known molding methods include compression molding, transfer molding, injection molding, extrusion molding, blow molding, and various other molding methods.

[0031] <Method for analyzing the orientation of fillers in resin molded products> The analysis method of this embodiment includes a slice image acquisition step, a power spectrum image acquisition step, and an orientation state analysis step. Each step of the analysis method of this embodiment will be described in more detail below.

[0032] [Slice image acquisition step] The slice image acquisition step is a step of acquiring one or more slice images at predetermined intervals in a predetermined direction of at least a portion of a resin molded product obtained by molding a resin composition containing a filler in a predetermined proportion.

[0033] One or more slice images are acquired at predetermined intervals in a predetermined direction for at least a portion of the resin molded product. "At least a portion" means that the entire resin molded product may be used as the target for analyzing the orientation state of the filler, or only a portion of the resin molded product may be used as the target for analyzing the orientation state of the filler. For example, if the orientation state within the resin molded product is uniform, analyzing the orientation state of only a portion allows other parts to be assumed to have the same orientation state as the analyzed portion. Also, if weak parts such as weld areas are known in advance and it is desired to evaluate the physical properties of only those parts, the objective can be achieved by acquiring one or more slice images of those parts without acquiring slice images of the entire product. According to the analysis method of this embodiment, the trend of the orientation state of the filler within the resin molded product can be easily analyzed with high accuracy, and as a result, the physical properties of the resin molded product can be easily predicted.

[0034] Furthermore, if necessary, such as when the area to be measured is known in advance, a resin test piece for obtaining the slice image may be prepared by cutting out a portion of the resin molded product from which the slice image will be acquired. If it is not necessary, the entire resin molded product may be used as the resin test piece without cutting out a test piece from it.

[0035] The method for acquiring slice images is not particularly limited, but they can be acquired using an X-ray CT apparatus 1 as shown in Figure 1. The X-ray CT apparatus 1 comprises an X-ray irradiation unit 11 for irradiating a resin test piece 2 with X-rays, an X-ray detection unit 12 for detecting X-rays transmitted through the resin test piece 2 as projection data, a sample stage 13 for holding the resin test piece 2, a rotation drive unit 14 for moving the sample stage 13 up and down (movement in the direction of the arrow in Figure 1) and rotating it (movement in the direction of the white arrow in Figure 1), and an image processing unit 15 for reconstructing projection data in multiple angular directions as slice images.

[0036] The X-ray irradiation unit 11 is the part that irradiates the resin test piece 2 with X-rays. It is not particularly limited as long as it can irradiate with X-rays, and conventionally known X-ray irradiation devices can be used. For example, an X-ray tube can be used. The X-ray irradiation unit 11 can adjust the irradiation conditions of the X-rays irradiated onto the resin test piece 2. Examples of X-ray irradiation conditions include tube current and X-ray irradiation time. 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 target resin test piece, the type of resin contained in it, etc.

[0037] The X-ray detection unit 12 is the part that converts the X-rays that have passed through the resin test piece 2 into electrical signals and then detects them as projection data. The X-ray detection unit 12 is positioned opposite the X-ray irradiation unit 11 with the resin test piece 2 in between.

[0038] The sample stage 13 is a part that holds the resin test piece 2 so that X-rays are irradiated onto the resin test piece 2. The sample stage 13 is positioned between the X-ray irradiation unit 11 and the X-ray detection unit 12.

[0039] The rotary drive unit 14 is the part that moves the sample stage 13 up and down and rotates it to irradiate the resin test piece 2 with X-rays from multiple angular directions. The rotary drive unit 14 is connected to the sample stage 13. The rotary drive unit 14 allows X-rays to be irradiated from multiple directions to various positions within the resin test piece 2. As a result, projection data can be obtained for the X-rays that have passed through the resin test piece 2 from various angles.

[0040] The image processing unit 15 is the part that reconstructs projection data from multiple angular directions as slice images. The image processing unit 15 is connected to the X-ray detection unit 12. Projection data detected by the X-ray detection unit 12 is sent to the image processing unit 15, and slice images are obtained by performing conventionally known image processing. Conventional known image processing methods include, for example, a method in which projection data from each direction is subjected to a one-dimensional Fourier transform, these are combined to create a two-dimensional Fourier transform image, and this is then subjected to an inverse Fourier transform to obtain a reconstructed image.

[0041] The slice images obtained by the method described above are slice images taken at predetermined intervals in a predetermined direction within the resin molded product. The "predetermined interval" is the range over which the grayscale is averaged when obtaining the slice images. The interval of the slice images is not particularly limited and can be changed as appropriate depending on the object to be measured, but in order to properly analyze the orientation state of the filler in a resin molded product containing fibrous filler, it is preferable that the interval of the slice images be less than or equal to the average diameter of the filler, or 20 μm or less if the average diameter is unknown. The "predetermined direction" is the direction perpendicular to the image plane of the slice image, and the predetermined direction can be set to any desired direction.

[0042] Examples of slice images obtained as described above are shown in Figures 2 and 3. Figures 2 and 3 show monochrome images. Figure 2 shows the entire test specimen, and Figure 3 shows a slice image of one of them. Darker areas are parts of the resin molded product that are more easily transmitted by X-rays, while whiter areas are parts of the resin molded product that are less easily transmitted by X-rays. The slice image includes both the resin and filler parts. Generally, the resin part is more easily transmitted by X-rays than the filler part. Therefore, in Figure 3, the black parts tend to represent the resin, and the white parts tend to represent the filler. However, as shown below, the slice image also contains noise patterns, so it cannot be simply said that the parts represented by black are the resin parts and the parts represented by white are the filler parts.

[0043] Because the resin portion and the filler portion have different X-ray absorption rates, an image with varying shades is obtained. Furthermore, when obtaining a slice image of a 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. As a result, discontinuous (steep) changes also appear in the projection data obtained by the X-ray detection unit 12. Consequently, high-frequency components caused by the discontinuous change appear significantly in the one-dimensional Fourier transform image. Due to numerical calculation errors caused by these high-frequency components, a virtual image (noise pattern) called an artifact appears in the reconstructed image obtained from the image processing unit 15. This noise pattern is also included in the slice image. This noise pattern is a major obstacle when analyzing the orientation state of the filler material using slice images with conventional methods. This is because conventional methods analyze the orientation state of each individual filler material. Therefore, in the method of Patent Document 1, a threshold is set within the range of brightness and darkness of the image, the image is binarized, and after dividing it into two regions, the resin portion and the filler portion, the power spectrum is obtained.

[0044] As shown in Figure 3 above, an X-ray CT image is an image containing white areas, black areas, and gray areas. In the method described in Patent Document 1, each pixel is binarized so that if the image density of the pixel is above an appropriately set image density threshold, it is displayed as white, and if the image density of the pixel is below the image density threshold, it is displayed as black. However, when assigning the gray areas to the resin and filler portions, it is necessary to set thresholds, but depending on the thresholds, the resin portion may differ from the actual volume fraction. Also, the image clarity and noise reduction methods used in image processing may depend on the subjective judgment of the operator. As a result, it is expected that this may differ from the actual volume fraction and negatively affect the accuracy of the calculation of orientation degree and orientation angle. Therefore, in this embodiment, as shown below, a power spectral image is acquired, and the orientation state of the filler is analyzed based on the power spectral image.

[0045] [Power spectrum image acquisition step] The power spectrum image acquisition step involves selecting one or more slice images from the slice images acquired in the slice image acquisition step, and then applying a Fourier transform to the selected slice images to acquire a power spectrum image.

[0046] An example of a power spectrum image is shown in Figure 4(a). The power spectrum image shown in Figure 4(a) is the power spectrum obtained by applying a Fourier transform to the two-dimensional image shown in Figure 3.

[0047] [Orientation state analysis step] The orientation state analysis step is a step in which the orientation state of the filler in the power spectrum image is analyzed and quantified based on the power spectrum image acquired in the power spectrum image acquisition step. According to the analysis method of this embodiment, since the orientation state trend is analyzed for each 2D image, the orientation state trend of the entire analysis range can be captured with extremely high resolution and accuracy within the length of one pixel of an X-ray CT. In particular, in the thickness direction, for example, conventionally, there were about 10 images per 1 mm and the thickness of each image was inaccurate, whereas in this embodiment, the resolution is greatly improved to 100 images per 1 mm.

[0048] In the orientation state analysis step, to quantify the orientation state of the filler, the two-dimensional tensor T shown in Equation 4 is obtained from the brightness of pixels at any position in the grayscale power spectrum image shown in Figure 4(a), using Equations 1, 2, and 3 below.

[0049]

number

[0050] From the obtained 2D tensor T, we can find the eigenvectors and eigenvalues ​​a and b. This can be easily calculated and implemented using the Jacobi method or numerical computation libraries such as Python. Furthermore, a program can be written to calculate a and b in equation 5 below.

[0051] An example of a method for deriving the orientation angle of a filler will be explained with reference to Figure 5. Figure 5(a) shows a power spectrum image, and Figure 5(b) shows coordinates for explaining the method of deriving the orientation angle. As shown in Figure 5(b), the Y direction of the image is taken as the flow direction (FD), and when it is near 90° it is the flow direction (FD), and when it is 0° or 180° it is the direction perpendicular to the flow (TD). In the combination of the obtained eigenvectors and eigenvalues, the one with the higher eigenvalue becomes the principal vector, and the direction indicated by the principal vector is calculated from each component of the vector to become the orientation angle. The angle can be easily calculated from the component values ​​V1x, V1y of the vector using the Atan2 function in Excel, Visual C#, etc. Note that in Figure 4(a) and Figure 5(a), the power spectrum images are the same, but they differ in that an ellipse is added in Figure 4(a) and an arrow is added in Figure 5(a).

[0052] Next, an example of a method for deriving the degree of orientation of a filler will be explained. The degree of orientation can be expressed as a relative degree of orientation, as the ratio of the major axis to the minor axis of the lightness distributed in an elliptical shape. For example, the power spectrum image shown in Figure 4(a) is treated as an ellipse, and this ellipse is represented by coordinates as shown in Figure 4(b). Then, if the major axis of the ellipse shown in Figure 4(b) is a and the minor axis is b, the degree of orientation is given by the following equation 5. Relative degree of orientation = a / b ... Formula 5 Since the brightness threshold that defines the elliptical region shown in Figure 4(b) from the power spectral image is not uniquely determined, there is variation in the values ​​of a and b, and as a result, the degree of orientation is not constant. However, in this embodiment, as described above, it is possible to determine a and b from a calculation program. In this way, the values ​​of a and b are uniquely determined, and a constant degree of orientation can be calculated. The major axis 'a' is an eigenvalue of the principal vector, and the minor axis 'b' is an eigenvalue perpendicular to the principal vector. The degree of orientation may also be expressed as an eigenvalue or as 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.

[0053] Furthermore, the distribution of orientation degree and orientation angle alone does not provide a correlation with physical properties such as elastic modulus and strength in the flow direction and perpendicular to the flow direction. Therefore, using the components XX and YY of the two-dimensional tensor T calculated from each image using Equation 4, the X-direction component strength DX shown in Equation 6 and the Y-direction component strength DY shown in Equation 7 are determined. Then, by calculating the average value in the thickness direction, the orientation strength in each direction shown in the image can be obtained.

number

[0054] As described above, the analysis method of this embodiment eliminates the need for binarization of X-ray CT images, thus allowing for analysis in a shorter time. Furthermore, it eliminates the need to set thresholds, which were difficult to set in binarization, and the need to set brightness thresholds to define the elliptical region. As a result, it is possible to suppress variations in the calculation results of the orientation angle and orientation degree. [Examples]

[0055] The embodiment will be described in more detail below with reference to examples, but this embodiment is not limited to the following examples.

[0056] [Example 1] (Slice image acquisition step) The resin molded products used in the examples were flat plates as shown in Figure 6, with four thicknesses: 1 mm, 2 mm, 3 mm, and 4 mm. These resin molded products were manufactured by injection molding. The shapes of the resin molded products and the molding conditions during injection molding are shown below. Shape: 80mm (height), 80mm (width), 1, 2, 3, 4mm (thickness) Resin: Polybutylene terephthalate resin containing 15% by mass of glass fiber Mold temperature: 60℃ Resin temperature: 260℃ Filling rate: 17.3cm 3 / s Holding pressure: 49 MPa, 5 sec Cooling time: 7sec

[0057] Next, resin test pieces measuring 12.5 mm in width and 20 mm in length were prepared from each of the above-mentioned resin molded products, and slice images were acquired. A commercially available X-ray CT scanner (ScanXmate-D090SS270, manufactured by Comscan Techno Co., Ltd.) was used for imaging. The imaging conditions are shown below. Of the obtained slice images, those with a thickness of 2 mmt are shown in Figure 3. Voltage: 50kV Tube current: 150μA Pixel size: 10.6 μm

[0058] (Power spectrum image acquisition step) The power spectral images were created by applying a continuous Fourier transform to each image using a program manufactured by Polyplastics Co., Ltd. The created power spectral images are shown in Figure 4.

[0059] (Orientation state analysis step) Using the power spectra of each of the above power spectrum images, the two-dimensional tensor T shown in Equation 4 was calculated using Equations 1, 2, and 3 described above. Of the obtained XX, YY, and XY, the component with the largest value was set to 1, and the ratio of each component was determined. As an example, the components of the two-dimensional tensor T were XX=0.32468, YY=1, and XY=-0.14789. The X-direction component intensity DX was 0.245, and the Y-direction component intensity DY was 0.755.

[0060] Eigenvalue decomposition was performed on the obtained two-dimensional tensor T to obtain eigenvalues ​​and their corresponding eigenvectors. In addition, the relative orientation degree a / b was determined from the eigenvalues ​​(a, b) and equation 5 described above. Examples of angles, relative orientation degrees, eigenvalues, and eigenvectors (principal eigenvectors) in the image shown in Figure 5 are shown in Table 1 and Figure 7.

[0061] [Table 1]

[0062] The orientation angle and degree of orientation were determined from the eigenvalues ​​and eigenvectors, with the pixel stacking direction defined as the thickness direction. The orientation angle and degree of orientation at positions in the thickness direction are shown in Figures 8 and 9.

[0063] Furthermore, the Y-direction component intensity DY, corresponding to the flow direction, was determined from the obtained two-dimensional tensor T, and its distribution at each wall thickness was determined. Figure 10 shows the Y-direction component intensity distribution with respect to the relative position in the wall thickness direction. In Figure 10, the horizontal axis represents the relative position in the wall thickness direction, with 0 representing the surface, 0.5 representing the center, and 1 representing the opposite surface. The vertical axis represents the relative value of the Y-direction component intensity. Also, in Figure 10, the dashed line represents the graph for a wall thickness of 1 mm, the solid line for a wall thickness of 2 mm, the dotted line for a wall thickness of 3 mm, and the dashed line for a wall thickness of 4 mm.

[0064] Furthermore, the average value of the obtained Y-direction component strength distribution was calculated for each wall thickness and compared with the tensile strength of the test specimen. Figure 11 shows the correlation between the average value of the Y-direction component strength distribution and the tensile strength. A good correlation was observed between the average value of the Y-direction component strength and the tensile strength. From this, the influence of filler orientation on material properties can be understood, and material design and product design will be facilitated from the analysis of elastic modulus and strength.

[0065] [Reference example 1] The analysis was performed in the same manner as in Example 1, except that binarization was performed before the power spectrum image acquisition step. Image processing software ImageJ (developed by Wayne Rashand) was used for the binarization process. Figure 12 shows the image after binarization, Figure 13 shows the power spectrum image after Fourier transform, Figure 14 shows the orientation angle distribution at the thickness direction, and Figure 15 shows the degree of orientation. In Reference Example 1, the degree of orientation was close to 1, and the majority of the analyzed image range was close to random orientation. In contrast, in Example 1 (see Figures 8 and 9), the degree of orientation was high, and the orientation state of the central part of the product shown in Figures 2 and 3 was reproduced more accurately. It was confirmed that the analysis method of this embodiment can analyze the trend of the orientation state of the filler with great accuracy. Moreover, since binarization is not required, the analysis time is also shortened. Specifically, Example 1, which did not undergo binarization, was able to shorten the analysis time by about 30 minutes compared to Reference Example 1, which underwent binarization.

Claims

1. A slice image acquisition step of acquiring slice images in a predetermined direction for at least a portion of a resin molded product obtained by molding a resin composition containing a filler in a predetermined proportion, A power spectral image acquisition step involves selecting one or more slice images from the aforementioned slice images and obtaining a power spectral image by applying a Fourier transform to the selected slice images. An orientation state analysis step, based on the power spectrum image, analyzes and quantifies the orientation state of the filler in the power spectrum image, It has, A method for analyzing the orientation state of a filler in a resin molded product, wherein in the orientation state analysis step, a two-dimensional tensor T shown in the following equation 4 is obtained from the brightness of a pixel at an arbitrary position in the power spectral image using the following equations 1, 2, and 3. [Math 1] [In formulas 1-4, F(x,y) represents the pixel density at the X and Y positions of the image, where x and y represent the horizontal and vertical positions of the pixel, respectively.]

2. A method for analyzing the orientation state of a filler in a resin molded product according to claim 1, wherein in the orientation state analysis step, eigenvalues ​​a, b and eigenvectors are obtained from the two-dimensional tensor T, the degree of orientation is obtained from the eigenvalues ​​a, b and the angle of orientation is obtained from the eigenvectors.

3. The method for analyzing the orientation state of a filler in a resin molded product according to claim 2, wherein in the orientation state analysis step, the relative degree of orientation shown in the following formula 5 is determined from the two components of the eigenvalues ​​a and b. Relative degree of orientation = a / b ...Equation 5 [In equation 5, the eigenvalues ​​a and b satisfy the condition a ≥ b.]

4. A method for analyzing the orientation state of a filler in a resin molded product according to claim 2, wherein the component strength DX in the X direction shown in the following formula 6 and the component strength DY in the Y direction shown in the following formula 7 are determined using the components XX and YY in the above formula 4. [Math 2]

Images