JP2016109516A - Method for estimating fracture strength of material and rubber composition - Google Patents

Abstract

PROBLEM TO BE SOLVED: To evaluate estimate durability performance by estimating fracture strength of a tire without sampling a rubber sample from a tire or performing a durability evaluation test, and to provide a highly durable tire.SOLUTION: A fracture-strength estimation method for a material includes: a first step of scanning a fracture surface of the material, measuring a position (X, y) and a height z(x, y) of the fracture surface, and digitizing a state of the fracture surface; a second step of calculating distances between respective positions using heights z of the position (x, y), a position (x+1, y), a position (x, y+1), and a position (x+1, y+1), and measurement intervals between the respective positions; a third step of calculating an area among four points using Heron's formula; and a step of determining whether or not a ratio obtained from surface roughness of the fracture surface and the measurement area is equal to or more than a threshold and estimating the fracture strength of the material.SELECTED DRAWING: Figure 1

Description

The present invention relates to a method for predicting the breaking strength of a material and a rubber composition.

One of the fracture analysis methods for materials is fracture surface analysis (fractography). This is a technique for evaluating the characteristics against the destruction of the material from the form of the fracture surface when the material is broken.

In brittle fracture, plastic deformation hardly occurs until fracture occurs, so the molecular chain does not stretch and breaks instantaneously, and there is almost no slip between the molecular chains. Therefore, the fracture surface is characterized by being relatively flat. On the other hand, since the ductile fracture is accompanied by a large plastic deformation until the fracture, the crack grows while slipping between the molecular chains. Therefore, the fracture surface is characterized by unevenness and roughness. In addition, a characteristic pattern is generated depending on the mode of destruction, and the progress direction of the destruction can be analyzed therefrom.

Such fracture surface analysis has been mainly performed in the field of metals, but in recent years, research is also being advanced in the field of polymer materials. A technique generally used for analysis of a fractured surface is morphological observation using the naked eye, an optical microscope, or a scanning electron microscope (SEM) (Patent Document 1 and Non-Patent Document 1).

However, morphological observation using the naked eye, an optical microscope, or a scanning electron microscope (SEM) has a problem that it is difficult to make a determination without a certain level of skill. In addition, because it is a qualitative evaluation method, it is easily influenced by the subjectivity of the observer, and there is a problem that it is not possible to determine the difference in fine roughness, etc., and it is not possible to investigate the correlation with physical properties and performance. is there.

JP 2014-118544 A

Journal of Japan Rubber Association, Vol. 55 (1982) no. 2, p82-103

It is an object of the present invention to predict the breaking strength of a tire and evaluate the durability performance without collecting a rubber sample from a material, for example, a tire and performing a durability evaluation test, and to provide a highly durable tire. Objective.

That is, the present invention
A first step of scanning the fracture surface of the material, measuring the position (x, y) and height z (x, y) of the fracture surface, and quantifying the state of the fracture surface;
Expressions (1) to (5) using the height z of the position (x, y), position (x + 1, y), position (x, y + 1), position (x + 1, y + 1) and the measurement interval p between the positions. Further, the distance a (x, y) between each position (the distance between the position (x, y) and the position (x + 1, y)), b (x, y) (the position (x + 1, y) and the position (x + 1, y + 1). ), C (x, y) (distance between position (x + 1, y + 1) and position (x, y + 1)), d (x, y) (position (x, y) and position (x, y + 1) ), E (x, y) (distance between position (x, y) and position (x + 1, y + 1)),
Triangle area S ₁ (x, y) (position (x, y), position (x + 1, y), position (x + 1, y + 1)) calculated using the Heron formula shown in equations (6) to (9) ), S ₂ (x, y) (the area of position (x, y), position (x, y + 1), and position (x + 1, y + 1)) is added by equation (10) to obtain 4 points. A third step of calculating an area A (x, y) between, and
Including the step of performing the first to third steps on the entire fractured surface and determining whether the ratio An / A obtained from the surface roughness An and the measurement area A of the fractured surface obtained by the equation (11) is equal to or greater than a threshold value. The present invention relates to a method for predicting the fracture strength of a material.
a (x, y) = [{z (x + 1, y) −z (x, y)} ² + p ² ] ^1/2 (1)
b (x, y) = [{z (x + 1, y + 1) −z (x + 1, y)} ² + p ² ] ^1/2 (2)
c (x, y) = [{z (x, y + 1) −z (x + 1, y + 1)} ² + p ² ] ^1/2 (3)
d (x, y) = [{z (x, y) −z (x, y + 1)} ² + p ² ] ^1/2 (4)
e (x, y) = [{z (x + 1, y + 1) −z (x, y)} ² + p ² + p ² ] ^1/2 (5)
s ₁ (x, y) = (a + b + e) / 2 (6)
s ₂ (x, y) = (c + d + e) / 2 (7)
S ₁ (x, y) = {s ₁ × (s ₁ −a) × (s ₁ −b) × (s ₁ −e} ^1/2 (8)
S ₂ (x, y) = [s ₂ × (s ₂ −c) × (s ₂ −d) × (s ₂ −e)} ^1/2 (9)
A (x, y) = S ₁ + S ₂ (10)
An = ΣA (x, y) (11)

The present invention also provides:
A first step of scanning the fracture surface of the tire, measuring the position (x, y) and height z (x, y) of the fracture surface, and quantifying the state of the fracture surface;
Expressions (1) to (5) using the height z of the position (x, y), position (x + 1, y), position (x, y + 1), position (x + 1, y + 1) and the measurement interval p between the positions. Further, the distance a (x, y) between each position (the distance between the position (x, y) and the position (x + 1, y)), b (x, y) (the position (x + 1, y) and the position (x + 1, y + 1). ), C (x, y) (distance between position (x + 1, y + 1) and position (x, y + 1)), d (x, y) (position (x, y) and position (x, y + 1) ), E (x, y) (distance between position (x, y) and position (x + 1, y + 1)),
Triangle area S ₁ (x, y) (position (x, y), position (x + 1, y), position (x + 1, y + 1)) calculated using the Heron formula shown in equations (6) to (9) ), S ₂ (x, y) (the area of position (x, y), position (x, y + 1), and position (x + 1, y + 1)) is added by equation (10) to obtain 4 points. A third step of calculating an area A (x, y) between, and
The first step to the third step are performed on the entire fractured surface, and a tire in which the ratio An / A obtained from the surface roughness An and the measurement area A of the fractured surface obtained by the equation (11) is 1.55 or more is manufactured. The present invention relates to a rubber composition.
a (x, y) = [{z (x + 1, y) −z (x, y)} ² + p ² ] ^1/2 (1)
b (x, y) = [{z (x + 1, y + 1) −z (x + 1, y)} ² + p ² ] ^1/2 (2)
c (x, y) = [{z (x, y + 1) −z (x + 1, y + 1)} ² + p ² ] ^1/2 (3)
d (x, y) = [{z (x, y) −z (x, y + 1)} ² + p ² ] ^1/2 (4)
e (x, y) = [{z (x + 1, y + 1) −z (x, y)} ² + p ² + p ² ] ^1/2 (5)
s ₁ (x, y) = (a + b + e) / 2 (6)
s ₂ (x, y) = (c + d + e) / 2 (7)
S ₁ (x, y) = {s ₁ × (s ₁ −a) × (s ₁ −b) × (s ₁ −e} ^1/2 (8)
S ₂ (x, y) = [s ₂ × (s ₂ −c) × (s ₂ −d) × (s ₂ −e)} ^1/2 (9)
A (x, y) = S ₁ + S ₂ (10)
An = ΣA (x, y) (11)

By using the prediction method of the present invention, durability performance can be evaluated by predicting the breaking strength of a material (tire) without collecting a rubber sample from a material, for example, a tire and conducting a durability test. And a highly durable material (tire) can be provided.

It is a coordinate diagram showing the positional relationship between a position (x, y) on a material fracture surface and a height z (x, y) at that position and a proximity position that is separated by a measurement interval p. It is the figure which plotted An / A with respect to the tensile strength about the tensile strength of the sample of each Example and a comparative example. It is the figure which plotted Ra (micrometer) with respect to the tensile strength about the tensile strength of the sample of each Example and a comparative example.

The method for predicting the fracture strength of the material of the present invention is:
A first step of scanning the fracture surface of the material, measuring the position (x, y) and height z (x, y) of the fracture surface, and quantifying the state of the fracture surface;
Expressions (1) to (5) using the height z of the position (x, y), position (x + 1, y), position (x, y + 1), position (x + 1, y + 1) and the measurement interval p between the positions. Further, the distance a (x, y) between each position (the distance between the position (x, y) and the position (x + 1, y)), b (x, y) (the position (x + 1, y) and the position (x + 1, y + 1). ), C (x, y) (distance between position (x + 1, y + 1) and position (x, y + 1)), d (x, y) (position (x, y) and position (x, y + 1) ), E (x, y) (distance between position (x, y) and position (x + 1, y + 1)),
Triangle area S ₁ (x, y) (position (x, y), position (x + 1, y), position (x + 1, y + 1)) calculated using the Heron formula shown in equations (6) to (9) ), S ₂ (x, y) (the area of position (x, y), position (x, y + 1), and position (x + 1, y + 1)) is added by equation (10) to obtain 4 points. A third step of calculating an area A (x, y) between, and
Performing the first step to the third step on the entire fracture surface, and determining whether the ratio An / A obtained from the surface roughness An and the measurement area A of the fracture surface obtained by the equation (11) is equal to or greater than a threshold value. It is characterized by including.

a (x, y) = [{z (x + 1, y) −z (x, y)} ² + p ² ] ^1/2 (1)
b (x, y) = [{z (x + 1, y + 1) −z (x + 1, y)} ² + p ² ] ^1/2 (2)
c (x, y) = [{z (x, y + 1) −z (x + 1, y + 1)} ² + p ² ] ^1/2 (3)
d (x, y) = [{z (x, y) −z (x, y + 1)} ² + p ² ] ^1/2 (4)
e (x, y) = [{z (x + 1, y + 1) −z (x, y)} ² + p ² + p ² ] ^1/2 (5)
s ₁ (x, y) = (a + b + e) / 2 (6)
s ₂ (x, y) = (c + d + e) / 2 (7)
S ₁ (x, y) = {s ₁ × (s ₁ −a) × (s ₁ −b) × (s ₁ −e} ^1/2 (8)
S ₂ (x, y) = [s ₂ × (s ₂ −c) × (s ₂ −d) × (s ₂ −e)} ^1/2 (9)
A (x, y) = S ₁ + S ₂ (10)
An = ΣA (x, y) (11)

In the first step, the fracture surface of the material is scanned, the height z (x, y) at the position (x, y) of the fracture surface is measured, and the state of the fracture surface is digitized. The material is preferably a rubber material, and can be suitably applied particularly to a tire. Further, the fracture surface is not particularly limited, and examples thereof include a fracture surface caused by a chipping fracture surface, a wear surface, a tensile fracture, an impact fracture, a torsion fracture, and the like. The area A of the fracture surface to be measured is not particularly limited, but is preferably 0.25 to 0.50 μm ² , more preferably 0.35 to 0.40 μm ² .

Although the measuring method of a fracture surface is not specifically limited, A contact-type or non-contact-type surface roughness meter is mentioned. More specifically, the contact type includes a surface roughness meter using an atomic force microscope and a probe, and the non-contact type includes a laser measurement type surface roughness meter and a confocal laser microscope. . It is preferable to use a confocal laser microscope because it can accurately measure unevenness on a minute surface.

The resolution in the vertical and horizontal directions during measurement (that is, the measurement interval p between each position) is preferably 500 μm or less, more preferably 50 μm or less, and even more preferably 1 μm or less. If it is larger than 500 μm, it becomes larger than the irregularity cycle of the fracture surface, and there is a possibility that accurate measurement cannot be performed. The resolution in the height direction (that is, the height z) is preferably 5 μm or less, more preferably 0.5 μm or less, and still more preferably 0.01 μm or less. If it is larger than 5 μm, it becomes larger than the height of the unevenness of the fracture surface, and there is a possibility that accurate measurement cannot be performed.

In the second step, the height z and the measurement interval p of the position (x, y), the position (x + 1, y) close to the position (x, y), the position (x, y + 1), and the position (x + 1, y + 1) are set. Using the expressions (1) to (5), the distance between each position, that is, the distance a (x, y) between the position (x, y) and the position (x + 1, y),
Distance b (x, y) between position (x + 1, y) and position (x + 1, y + 1),
Distance c (x, y) between position (x + 1, y + 1) and position (x, y + 1),
Distance d (x, y) between position (x, y) and position (x, y + 1),
Distance e (x, y) between position (x, y) and position (x + 1, y + 1)
Is calculated. Here, the relationship between the four positions is shown in the coordinate diagram of FIG.

In the third step, the triangular area S ₁ (x, y) (position (x, y) and position (x + 1, y)) calculated using the Heron formula shown in equations (6) to (9) (Area with position (x + 1, y + 1)), S ₂ (x, y) (area with position (x, y), position (x, y + 1) and position (x + 1, y + 1)) is added by equation (10). By combining them, the area A (x, y) between the four points is calculated.

In the fourth step, the first to third steps are performed on the entire fractured surface, and whether the ratio An / A obtained from the surface roughness An and the measurement area A of the fractured surface obtained by Equation (11) is equal to or greater than a threshold value. Determine. The threshold value is determined in advance based on the market evaluation of the material. When it is higher than the threshold, it is determined that the durability against destruction is high, and when it is low, the durability against destruction is low. In the case of a tire, the threshold is preferably 1.55 or more, and more preferably 1.60 or more.

Moreover, the measuring device for the fracture strength of the material of the present invention is:
Measuring means for scanning the fracture surface of the material and measuring the height z (x, y) at the position (x, y) of the fracture surface to quantify the state of the fracture surface;
Expressions (1) to (5) using the height z of the position (x, y), position (x + 1, y), position (x, y + 1), position (x + 1, y + 1) and the measurement interval p between the positions. Further, the distance a (x, y) between each position (the distance between the position (x, y) and the position (x + 1, y)), b (x, y) (the position (x + 1, y) and the position (x + 1, y + 1). ), C (x, y) (distance between position (x + 1, y + 1) and position (x, y + 1)), d (x, y) (position (x, y) and position (x, y + 1) ), E (x, y) (a distance between position (x, y) and position (x + 1, y + 1)),
Triangle area S ₁ (x, y) (position (x, y), position (x + 1, y), position (x + 1, y + 1)) calculated using the Heron formula shown in equations (6) to (9) ), S ₂ (x, y) (the area of position (x, y), position (x, y + 1), and position (x + 1, y + 1)) is added by equation (10) to obtain 4 points. Means for calculating an area A (x, y) between, and
Means for performing the first to third steps on the entire fracture surface and determining whether the ratio An / A obtained from the surface roughness An and the measurement area A of the fracture surface obtained by the equation (11) is equal to or greater than a threshold value. It is characterized by including. With this measuring device, the breaking strength of the material can be predicted.

Examples of the rubber material that can be evaluated according to the present invention include a material obtained from a rubber composition in which a filler such as carbon black and silica, a vulcanizing agent, a vulcanization accelerator, and the like are blended with a rubber component.

Examples of rubber components include natural rubber (NR), modified natural rubber such as epoxidized natural rubber (ENR), isoprene rubber (IR), butadiene rubber (BR), styrene butadiene rubber (SBR), butyl rubber (IIR), Brominated product of isobutylene-p-methylstyrene copolymer, acrylonitrile-butadiene rubber (NBR), chloroprene rubber (CR), ethylene-propylene rubber (EPM), ethylene-propylene-diene copolymer rubber (EPDM), styrene-isoprene Rubber, styrene-isoprene-butadiene rubber copolymer rubber (SIBR), isoprene-butadiene rubber, chlorosulfonated polyethylene (CSM), acrylic rubber (ACM, ANM), epichlorohydrin rubber (CO, ECO, GECO), polysulfide rubber ( T), silicone Beam (Q), fluororubber (FKM), and urethane rubber (U) may be used.

Diene rubbers include natural rubber (NR), modified natural rubber such as epoxidized natural rubber (ENR), isoprene rubber (IR), butadiene rubber (BR), styrene butadiene rubber (SBR), and acrylonitrile butadiene rubber (NBR). ), Chloroprene rubber (CR), styrene-isoprene-butadiene copolymer rubber (SIBR), and the like. These diene rubbers may be used alone or in combination of two or more.

You may mix | blend carbon black, such as furnace black, acetylene black, thermal black, channel black, and graphite, with a rubber composition. The compounding quantity of carbon black is 150 mass parts or less normally with respect to 100 mass parts of rubber components, and 10-150 mass parts is preferable. If the amount is less than 10 parts by mass, sufficient reinforcing properties tend not to be obtained. If the amount exceeds 150 parts by mass, heat generation increases, rolling resistance deteriorates, workability deteriorates, and wear resistance performance decreases. There is a tendency. As for this compounding quantity, 20-120 mass parts is more preferable.

Silica, for example, dry process silica, wet process silica, and the like may be blended in the rubber composition. The amount of silica is preferably 5 parts by mass or more, more preferably 10 parts by mass or more, still more preferably 20 parts by mass or more, particularly preferably 30 parts by mass or more, and most preferably 45 parts by mass with respect to 100 parts by mass of the rubber component. More than part by mass. When the amount is less than 5 parts by mass, it becomes difficult to obtain a rolling resistance reduction effect and a wet grip improvement effect by using silica. The amount of silica is preferably 150 parts by mass or less, more preferably 100 parts by mass or less, and still more preferably 80 parts by mass or less. When it exceeds 150 parts by mass, it is difficult to process because there is too much silica.

A well-known silane coupling agent can be used with silica. As the silane coupling agent, conventional ones that have been conventionally used can be used. 0.5-20 mass parts is preferable with respect to 100 mass parts of silica, as for a coupling agent compounding quantity, 1.5-15 mass parts is more preferable, and 2.5-10 mass parts is still more preferable. If the blending amount of the silane coupling agent is less than 0.5 parts by mass, the effect of improving the silica dispersion by adding the silane coupling agent cannot be sufficiently obtained, and the wear resistance and fracture energy tend to be reduced. If the amount exceeds 20 parts by mass, the effect cannot be obtained for the cost increase, and further, the reinforcement and wear resistance may be lowered.

As process oils, synthetic oils, mineral oils such as paraffinic process oils, naphthenic process oils, and aromatic process oils are used. Vegetable oils include castor oil, cottonseed oil, sesame oil, rapeseed oil, soybean oil, palm oil, palm oil, peanut oil, rosin, pine oil, pineapple, tall oil, corn oil, rice bran oil, bean flower oil, sesame oil, olive oil , Sunflower oil, palm kernel oil, coconut oil, jojoba oil, macadamia nut oil, safflower oil, tung oil and so on.

The anti-aging agent is not particularly limited as long as it is a heat-resistant anti-aging agent, a weather-resistant anti-aging agent and the like and is usually used in rubber compositions. For example, a naphthylamine type (phenyl-α-naphthylamine etc.), diphenylamine System (octylated diphenylamine, 4,4′-bis (α, α′-dimethylbenzyl) diphenylamine, etc.), p-phenylenediamine system (N-isopropyl-N′-phenyl-p-phenylenediamine, N- (1, 3-dimethylbutyl) -N′-phenyl-p-phenylenediamine, N, N′-di-2-naphthyl-p-phenylenediamine, etc.); 2,2,4-trimethyl-1 Quinoline antioxidants such as polymers of 2,2-dihydroquinoline; monophenols (2,6-di-tert-butyl-4-methylphenol, Phenol aging prevention such as tyrenated phenol), bis, tris, polyphenol (tetrakis- [methylene-3- (3 ′, 5′-di-t-butyl-4′-hydroxyphenyl) propionate] methane, etc.) Agents.

The rubber composition is used for tire cap treads and the like. A tire is manufactured by a normal method using the rubber composition. That is, a rubber composition containing various additives as necessary is extruded in accordance with the shape of the cap tread at an unvulcanized stage, molded by a normal method on a tire molding machine, Bonding together with the tire member forms an unvulcanized tire. This unvulcanized tire can be heated and pressurized in a vulcanizer to produce a tire.

The present invention will be specifically described based on examples, but the present invention is not limited to these examples.

Production Example According to the following composition, chemicals other than sulfur and a vulcanization accelerator were kneaded using a 1.7 L Banbury mixer manufactured by Kobe Steel. Next, using an open roll, sulfur and a vulcanization accelerator were added to the kneaded product and kneaded to obtain an unvulcanized rubber composition. Next, the obtained unvulcanized rubber composition was press vulcanized with a 2 mm thick mold at 170 ° C. for 15 minutes to obtain a vulcanized rubber composition (vulcanized rubber sheet).

Further, the obtained unvulcanized rubber composition is molded into a tread shape, and bonded together with other tire members on a tire molding machine to form an unvulcanized tire, which is vulcanized at 150 ° C. for 30 minutes, and tested. Tires (size: 11R22.5) were manufactured.

(Combination)
SBR: NS116R manufactured by Zeon Corporation (Solution-polymerized SBR, bound styrene content: 23% by mass, Tg: -21 ° C.) (see Table 1 for the blending amount)
BR: BR150B manufactured by Ube Industries, Ltd. (see Table 1 for blending amount)
Carbon black: Seast N220 manufactured by Mitsubishi Chemical Corporation (N ₂ SA: 114 m ² / g) (20 parts by mass)
Silica: Ultrasil VN3 (N ₂ SA: 175 m ² / g) (50 parts by mass) manufactured by EVONIK-DEGUSSA
Silane coupling agent: Si69 (bis (3-triethoxysilylpropyl) tetrasulfide) (5 parts by mass) manufactured by EVONIK-DEGUSSA
Process oil (aromatic oil): Process X-140 (aromatic process oil) manufactured by Japan Energy (20 parts by mass)
Paraffin wax: Nippon Seiwa Co., Ltd. Ozoace 0355 (1 part by mass)
Anti-aging agent: Nocrack 6C (N- (1,3-dimethylbutyl) -N′-phenyl-p-phenylenediamine) (1 part by mass) manufactured by Ouchi Shinsei Chemical Industry Co., Ltd.
Stearic acid: Stearic acid manufactured by NOF Corporation (2 parts by mass)
Zinc oxide: Zinc flower No. 1 (2 parts by mass) manufactured by Mitsui Mining & Smelting Co., Ltd.
Sulfur: Powder sulfur manufactured by Tsurumi Chemical Co., Ltd. (2 parts by mass)
Vulcanization accelerator: Noxeller NS (chemical name: N-tert-butyl-2-benzothiazylsulfenamide) manufactured by Ouchi Shinsei Chemical Industry Co., Ltd. (1 part by mass)
Was used.

Examples 1-3 and Comparative Examples 1-2
The tires obtained in the production examples were mounted and the appearance of the tires after running in the market was observed. Durability was evaluated with good as a tread chip and good as a bad.

<Fracture surface evaluation>
From the prepared rubber sheet having a thickness of 2 mm, a tensile test was performed using a No. 3 dumbbell according to JIS K6251 to produce a fracture surface. At that time, the breaking strength (TB) and the elongation at break (EB) (%) were measured, and the tensile strength of each formulation was obtained from the composition of Example 1 with the numerical value of TB × EB / 2 as the tensile strength. The tensile strength of the piece was taken as 100 and indicated as an index. The larger the index, the better the breaking strength.

<Fracture surface evaluation>
In the first step fracture surface evaluation, the fracture surface formed by tensile fracture is height at position (x, y) using a confocal laser microscope ("VK9500" manufactured by Keyence Corporation) as a surface roughness meter. z (x, y) was measured and digitized. The resolution p in the vertical and horizontal directions was 0.69 μm, and the measurement area A was 0.37 μm ² . At the same time, arithmetic average roughness Ra was also measured according to JIS B0601-2001.

Based on the value obtained by the second step quantification and the measurement interval p between each position, the distances (a (x, y) (a (x, y) ( Distance between position (x, y) and position (x + 1, y)), b (x, y) (distance between position (x + 1, y) and position (x + 1, y + 1)), c (x, y) ( Distance between position (x + 1, y + 1) and position (x, y + 1)), d (x, y) (distance between position (x, y) and position (x, y + 1)), e (x, y) ( The distance between the position (x, y) and the position (x + 1, y + 1))) was calculated.
a (x, y) = [{z (x + 1, y) −z (x, y)} ² + p ² ] ^1/2 (1)
b (x, y) = [{z (x + 1, y + 1) −z (x + 1, y)} ² + p ² ] ^1/2 (2)
c (x, y) = [{z (x, y + 1) −z (x + 1, y + 1)} ² + p ² ] ^1/2 (3)
d (x, y) = [{z (x, y) −z (x, y + 1)} ² + p ² ] ^1/2 (4)
e (x, y) = [{z (x + 1, y + 1) −z (x, y)} ² + p ² + p ² ] ^1/2 (5)

Third step A square area S ₁ (x, y) formed by connecting these four points (area of position (x, y), position (x + 1, y), and position (x + 1, y + 1)) , S ₂ (x, y) (the area of position (x, y), position (x, y + 1), and position (x + 1, y + 1)) is the Heron formula expressed by equations (6) to (10). Sought by.
s ₁ (x, y) = (a + b + e) / 2 (6)
s ₂ (x, y) = (c + d + e) / 2 (7)
S ₁ (x, y) = {s ₁ × (s ₁ −a) × (s ₁ −b) × (s ₁ −e} ^1/2 (8)
S ₂ (x, y) = [s ₂ × (s ₂ −c) × (s ₂ −d) × (s ₂ −e)} ^1/2 (9)
A (x, y) = S ₁ (x, y) + S ₂ (x, y) (10)

The 4th process 1st-3rd process was performed on the whole fracture surface, and surface roughness An of the fracture surface was computed by adding together like a formula (11).
An = ΣA (x, y) (11)

Table 1 shows the market evaluation, An / A, and Ra (μm) of each tire.

FIG. 2 is a diagram in which An / A is plotted against the tensile strength of the samples of the examples and comparative examples, and FIG. 3 is a diagram in which Ra (μm) is plotted against the tensile strength. The correlation coefficient between tensile strength and An / A was 0.979, and the correlation coefficient between tensile strength and Ra (μm) was 0.447. It was found that neither the tensile strength nor the market evaluation of the tire could be reproduced only by the information (Ra) of the unevenness of the fracture surface.

However, the surface area ratio An / A of the fracture surface could be related to the fracture strength of the rubber composition. Further, the surface area ratio An / A of the fracture surface has a correlation with the tire market evaluation result, and it was found that if An / A is 1.55 or more, the durability of the tire in the market can be maintained.

Claims (2)

A first step of scanning the fracture surface of the material, measuring the position (x, y) and height z (x, y) of the fracture surface, and quantifying the state of the fracture surface;
Expressions (1) to (5) using the height z of the position (x, y), position (x + 1, y), position (x, y + 1), position (x + 1, y + 1) and the measurement interval p between the positions. Further, the distance a (x, y) between each position (the distance between the position (x, y) and the position (x + 1, y)), b (x, y) (the position (x + 1, y) and the position (x + 1, y + 1). ), C (x, y) (distance between position (x + 1, y + 1) and position (x, y + 1)), d (x, y) (position (x, y) and position (x, y + 1) ), E (x, y) (distance between position (x, y) and position (x + 1, y + 1)),
Triangle area S ₁ (x, y) (position (x, y), position (x + 1, y), position (x + 1, y + 1)) calculated using the Heron formula shown in equations (6) to (9) ), S ₂ (x, y) (the area of position (x, y), position (x, y + 1), and position (x + 1, y + 1)) is added by equation (10) to obtain 4 points. A third step of calculating an area A (x, y) between, and
Including the step of performing the first to third steps on the entire fractured surface and determining whether the ratio An / A obtained from the surface roughness An and the measurement area A of the fractured surface obtained by the equation (11) is equal to or greater than a threshold value. A method for predicting the fracture strength of materials.
a (x, y) = [{z (x + 1, y) −z (x, y)} ² + p ² ] ^1/2 (1)
b (x, y) = [{z (x + 1, y + 1) −z (x + 1, y)} ² + p ² ] ^1/2 (2)
c (x, y) = [{z (x, y + 1) −z (x + 1, y + 1)} ² + p ² ] ^1/2 (3)
d (x, y) = [{z (x, y) −z (x, y + 1)} ² + p ² ] ^1/2 (4)
e (x, y) = [{z (x + 1, y + 1) −z (x, y)} ² + p ² + p ² ] ^1/2 (5)
s ₁ (x, y) = (a + b + e) / 2 (6)
s ₂ (x, y) = (c + d + e) / 2 (7)
S ₁ (x, y) = {s ₁ × (s ₁ −a) × (s ₁ −b) × (s ₁ −e} ^1/2 (8)
S ₂ (x, y) = [s ₂ × (s ₂ −c) × (s ₂ −d) × (s ₂ −e)} ^1/2 (9)
A (x, y) = S ₁ + S ₂ (10)
An = ΣA (x, y) (11) A first step of scanning the fracture surface of the tire, measuring the position (x, y) and height z (x, y) of the fracture surface, and quantifying the state of the fracture surface;
Expressions (1) to (5) using the height z of the position (x, y), position (x + 1, y), position (x, y + 1), position (x + 1, y + 1) and the measurement interval p between the positions. Further, the distance a (x, y) between each position (the distance between the position (x, y) and the position (x + 1, y)), b (x, y) (the position (x + 1, y) and the position (x + 1, y + 1). ), C (x, y) (distance between position (x + 1, y + 1) and position (x, y + 1)), d (x, y) (position (x, y) and position (x, y + 1) ), E (x, y) (distance between position (x, y) and position (x + 1, y + 1)),
Triangle area S ₁ (x, y) (position (x, y), position (x + 1, y), position (x + 1, y + 1)) calculated using the Heron formula shown in equations (6) to (9) ), S ₂ (x, y) (the area of position (x, y), position (x, y + 1), and position (x + 1, y + 1)) is added by equation (10) to obtain 4 points. A third step of calculating an area A (x, y) between, and
The first step to the third step are performed on the entire fractured surface, and a tire in which the ratio An / A obtained from the surface roughness An and the measurement area A of the fractured surface obtained by the equation (11) is 1.55 or more is manufactured. Rubber composition that can be made.
a (x, y) = [{z (x + 1, y) −z (x, y)} ² + p ² ] ^1/2 (1)
b (x, y) = [{z (x + 1, y + 1) −z (x + 1, y)} ² + p ² ] ^1/2 (2)
c (x, y) = [{z (x, y + 1) −z (x + 1, y + 1)} ² + p ² ] ^1/2 (3)
d (x, y) = [{z (x, y) −z (x, y + 1)} ² + p ² ] ^1/2 (4)
e (x, y) = [{z (x + 1, y + 1) −z (x, y)} ² + p ² + p ² ] ^1/2 (5)
s ₁ (x, y) = (a + b + e) / 2 (6)
s ₂ (x, y) = (c + d + e) / 2 (7)
S ₁ (x, y) = {s ₁ × (s ₁ −a) × (s ₁ −b) × (s ₁ −e} ^1/2 (8)
S ₂ (x, y) = [s ₂ × (s ₂ −c) × (s ₂ −d) × (s ₂ −e)} ^1/2 (9)
A (x, y) = S ₁ + S ₂ (10)
An = ΣA (x, y) (11)

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