Carbon fiber bundle, method for producing same, prepreg, and carbon fiber-reinforced composite material

Abstract

The present invention addresses the problem of providing a carbon fiber bundle and a method for producing the same, the carbon fiber bundle excelling in strand strength and strand elastic modulus, not easily experiencing single fiber breakage even when subjected to torsional deformation, and also excelling in operability.　The present invention is a carbon fiber bundle comprising a plurality of carbon fibers, wherein the strand elastic modulus E is 280 to 400 GPa, the crystallite size Lc in the carbon fibers is 1.80 to 2.60 nm, the density ρ of the carbon fibers is from 1.780 g / cm 3 to 1.830 g / cm3, and the density ρ, the crystallite size Lc, and the strand elastic modulus E satisfy relational expressions (1) and (2). (1): 1.860 ≤ ρ + 0.0333Lc ≤ 1.895, (2): 6.67 × 10-5 × (E - 207)2 + 1.60 ≥ Lc

Description

Carbon fiber bundle and its manufacturing method, prepreg, and carbon fiber reinforced composite material

[0001] The present invention relates to a carbon fiber bundle, a method for producing the same, a prepreg, and a carbon fiber reinforced composite material.

[0002] Carbon fiber bundles have high specific strength and specific modulus, and are used as reinforcing fibers for composite materials in a wide range of applications, including aerospace and space applications. Recently, they have also been used in industrial applications such as automotive components and wind power generation.

[0003] Generally, carbon fiber bundles are produced by subjecting polyacrylonitrile precursor fibers, obtained by fiberizing a polyacrylonitrile copolymer, to a flame-proofing process in which the fibers are oxidized in air at 200 to 300°C; a pre-carbonization process in which the fibers are heated in an inert atmosphere at a maximum temperature of 500 to 1,200°C; and a carbonization process in which the fibers are heated in an inert atmosphere at a maximum temperature of 1,200 to 3,000°C. When the resulting carbon fiber bundles are molded into composite materials, they are impregnated with a matrix resin while being subjected to a twisting force, such as being pulled out from a bobbin and changing direction. Applications in which carbon fiber bundles twisted and bundled into a rope-like shape are impregnated with a matrix resin have also become widespread.

[0004] Techniques for producing carbon fiber bundles with high strand strength and high strand modulus have been proposed by adjusting countless combinations of process conditions to specific ranges (Patent Documents 1 to 5). Patent Document 1 discloses carbon fibers with a strand strength of 7.6 GPa or more and a strand modulus of 240 to 440 GPa, in which resistance in the tensile direction is increased by specifying the degree of unevenness of the crack propagation section on the fracture surface of a single fiber. Patent Document 2 discloses a carbon fiber bundle with a strand strength of 7.5 GPa or more and a specific range of nonlinearity of the strand modulus, achieved by increasing the fracture toughness and shear modulus of the carbon fiber. Patent Document 3 discloses a combination of carbon fibers with a strand strength of 7.5 to 8.5 GPa and a strand modulus of 240 to 300 GPa and a specific epoxy resin, with the aim of increasing elongation. It also describes that the treatment time at the maximum temperature in the carbonization step is 20 to 60 seconds, and the heating rate in the temperature range above 1,000°C is 0.40 to 1.1°C / second, i.e., 24 to 66°C / minute. Patent Document 4 discloses a carbon fiber bundle having a crystallite size of 2.2 to 4.0 nm, which is obtained by increasing entanglement and increasing carbonization tension, thereby reducing the nonlinearity of the strand modulus with respect to strain and providing excellent shear modulus and compressive strength. Patent Document 5 discloses a method for producing carbon fibers in which a core ratio of the flame-resistant fiber is 5% or more, and high-strength carbon fibers are obtained at low cost by performing the carbonization step in a temperature range of 700 to 1,000°C with a temperature gradient of 450°C / minute or less.

[0005] JP 2017-137614 A International Publication No. 2016 / 068034 JP 2023-043149 A JP 2015-010290 A JP 2019-143287 A

[0006] However, the background art has the following problems.

[0007] Although Patent Document 1 improves the strength of the obtained carbon fiber bundle in the tensile direction, it does not mention conditions relating to a specific temperature range in the heat treatment in the carbonization step, and it was not possible to improve resistance to torsional deformation. Furthermore, as a result of the studies by the present inventors, it was considered that there is room for further study from the viewpoints of nonlinearity of elastic modulus and optimization of crystallite size.

[0008] In Patent Document 2, the carbon fiber bundles have high strength in the tensile direction and a high shear modulus, which effectively increases the 0° tensile strength of the carbon fiber composite material, but there is no mention of conditions relating to a specific temperature range in the heat treatment in the carbonization step, and the resistance to torsional deformation could not be increased. Furthermore, as a result of the inventors' studies, it was considered that there is room for further study from the viewpoints of nonlinearity of the modulus of elasticity and optimization of the crystallite size.

[0009] In Patent Document 3, although the carbon fiber bundle has an extremely high elongation in the tensile direction, the heat treatment conditions in the carbonization temperature range are mentioned only in a range including a temperature range higher than 1000° C., and it was not possible to increase the resistance to torsional deformation. Furthermore, as a result of the studies by the present inventors, it was considered that there is room for further study in terms of the nonlinearity of the elastic modulus, the mass composition ratio of nitrogen to carbon, and optimization of the crystallite size.

[0010] Although Patent Document 4 describes increasing the shear modulus, the resistance to torsional deformation is insufficient. The present inventors believe that this is because the crystallite size is too large and the shear modulus is too large.

[0011] Patent Document 5 discloses a manufacturing method for obtaining high-strength carbon fibers at low cost, in which a carbonization step for carbonizing a flame-resistant fiber having a specific core ratio involves making the temperature gradient in a specific temperature range relatively gentle, thereby obtaining carbon fibers having high strand tensile strength, but it was not possible to increase resistance to torsional deformation.

[0012] As described above, the prior art has proposed techniques for improving the mechanical properties of carbon fiber bundles, but has not disclosed a carbon fiber bundle that is excellent in operability when torsional deformation is applied to the carbon fiber bundle during advanced processing, such as in the thread guide during molding or in the molding of a rope-shaped composite material. The present invention aims to provide a carbon fiber bundle that is excellent not only in strength and strand modulus but also in operability when torsional deformation is applied during advanced processing, and that is likely to exhibit mechanical properties when made into a carbon fiber reinforced composite material, and a method for producing the same.

[0013] As a result of extensive investigations, the present inventors have found that the above-mentioned problems can be solved by setting a specific structure of the carbon fiber bundle within a certain range, and have completed the present invention as described below.

[0014] That is, the present invention and its preferred embodiments have the following configurations: [1] A carbon fiber bundle made of a plurality of carbon fibers, wherein the strand elastic modulus E is 280 GPa or more and 400 GPa or less, the crystallite size Lc of the carbon fibers is 1.80 nm or more and 2.60 nm or less, and the density ρ of the carbon fibers is 1.780 g / cm ３ 1.830g / cm or more ３ and the density ρ [g / cm ３ ], crystallite size Lc [nm], and strand modulus E [GPa] satisfy the relationships of the following formulas (1) and (2): 1.860≦ρ+0.0333Lc≦1.895 (1) 6.67×10 －５ × (E-207) ２ +1.60≧Lc (2) [2] The carbon fiber bundle according to [1], having a strand strength of 6.5 GPa or more and 8.5 GPa or less. [3] The carbon fiber bundle according to [1] or [2], wherein the mass composition ratio N / C of nitrogen to carbon in the carbon fiber is 0.0008 or more and 0.050 or less. [4] The carbon fiber bundle according to claim 1, wherein the mass composition ratio N / C[-] of nitrogen to carbon and the crystallite size Lc[nm] in the carbon fiber satisfy the relationship of the following formula (3): 12×e-D(Lc-1.67)+F≧N / C (3), where D=1.00 and F=0.015. [5] The carbon fiber bundle according to any one of [1] to [4], wherein a coefficient A calculated from an approximate formula (4) for the nonlinearity of a stress σ-strain ε curve in a resin-impregnated strand tensile test is −0.000170 or more and −0.000050 or less, ε=Aσ ２+Bσ+C ... (4) where A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [-]. [6] The carbon fiber bundle according to any one of [1] to [5], wherein the crystallite size Lc and the coefficient A calculated from the approximate formula (4) for the nonlinearity of the stress σ-strain ε curve in a resin-impregnated strand tensile test satisfy the relationship of formula (5). ε = Aσ ２ +Bσ+C ... (4) where A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [-]. 0.00621≦0.00357ρ+A≦0.00645 ... (5) [7] A carbon fiber bundle made of a plurality of carbon fibers, wherein the strand elastic modulus E is 330 GPa or more and 400 GPa or less, the crystallite size Lc of the carbon fibers is 2.40 nm or more and 2.60 nm or less, and the degree of crystalline orientation π of the carbon fibers is ００２ is 85% or more and 88% or less, and the density ρ of the carbon fiber is 1.780 g / cm ３ More than 1.800g / cm ３ and further, a coefficient A calculated from an approximate formula (4) of nonlinearity of a stress σ-strain ε curve in a resin-impregnated strand tensile test is −0.000140 or more and −0.000050 or less. ２ + Bσ + C ... (4) where A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [-]. [8] A carbon fiber having a strand modulus E of 330 GPa or more and 400 GPa or less, a crystallite size Lc of 2.40 nm or more and 2.60 nm or less, a crystalline orientation degree π002 of 85% or more and 88% or less, and a density ρ of 1.780 g / cm ３ More than 1.800g / cm ３ or less, and further, a coefficient A calculated from an approximate formula (4) of nonlinearity of a stress σ-strain ε curve in a resin-impregnated strand tensile test is −0.000140 or more and −0.000050 or less. ２+Bσ+C ... (4) where A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [-]. [9] The carbon fiber bundle according to any one of [1] to [8], wherein the mass composition ratio N / C of nitrogen to carbon in the carbon fibers is 0.0008 or more and 0.0150 or less.

[10] A carbon fiber bundle consisting of a plurality of carbon fibers, wherein the strand modulus E is 280 GPa or more and 340 GPa or less, the mass composition ratio N / C of nitrogen to carbon in the carbon fibers is 0.020 or more and 0.050 or less, the crystallite size Lc of the carbon fibers is 1.80 nm or more and 1.95 nm or less, and the density ρ of the carbon fibers is 1.805 g / cm ３ 1.830g / cm or more ３ and further, a coefficient A calculated from an approximate formula (4) for nonlinearity of a stress σ-strain ε curve in a resin-impregnated strand tensile test is −0.000170 or more and −0.000090 or less. ２ + Bσ + C ... (4) where A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [-].

[11] A carbon fiber having a strand modulus E of 280 GPa or more and 340 GPa or less, a nitrogen to carbon mass composition ratio N / C of 0.020 or more and 0.050 or less, a crystallite size Lc of 1.80 nm or more and 1.95 nm or less, and a density ρ of 1.805 g / cm ３ 1.830g / cm or more ３ and further, a coefficient A calculated from an approximate formula (4) for nonlinearity of a stress σ-strain ε curve in a resin-impregnated strand tensile test is −0.000170 or more and −0.000090 or less. ２+Bσ+C ... (4) where A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [-].

[12] The carbon fiber bundle according to [1] to [6],

[10] , or

[11] , wherein the strand elastic modulus E is 280 GPa or more and 315 GPa or less, the mass composition ratio N / C of nitrogen to carbon in the carbon fiber is 0.025 or more and 0.045 or less, and further, the coefficient A calculated from the approximation formula (4) for the nonlinearity of the stress σ-strain ε curve in a resin-impregnated strand tensile test is -0.000170 or more and -0.000145 or less. ε=Aσ ２ +Bσ+C ... (4) where A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [-].

[13] The carbon fiber bundle according to any one of [1] to [6] and

[10] to

[12] , wherein the carbon fiber has a scatterer length of 14.0 nm or more and 19.2 nm or less as measured by small-angle X-ray scattering.

[14] The carbon fiber bundle according to any one of [1] to [6] and

[10] to

[13] , wherein the coefficient A calculated from the approximation formula (4) for the nonlinearity of the stress σ-strain ε curve in a resin-impregnated strand tensile test is -0.000166 or more and -0.000095 or less. ε=Aσ ２ + Bσ + C (4) where A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [-].

[15] The density of the carbon fiber is 1.806 g / cm ３ 1.818g / cm or more ３

[16] The carbon fiber bundle according to any one of [1] to [6] and

[10] to

[14] , wherein the single fiber fineness of the carbon fiber is 0.41 dtex or more and 0.50 dtex or less.

[17] The polyacrylonitrile precursor fiber bundle is obtained by subjecting the polyacrylonitrile precursor fiber bundle to a chromatic aberration analysis using ... －１ 1453 cm for the peak intensity －１ a first flame-stabilizing step of flame-stabilizing the fiber bundle obtained in the first flame-stabilizing step for 8 to 25 minutes until the ratio of the peak intensities of the －１ The peak intensity at 1453 cm －１The ratio of the peak intensities of the two compounds is in the range of 0.70 to 0.75, and the peak intensity of the two compounds is 1370 cm in the infrared spectrum. －１ The peak intensity at 1254 cm －１ a second flame-proofing step of flame-proofing the fiber bundle obtained in the second flame-proofing step for 5 to 14 minutes until the ratio of the peak intensities of the fiber bundles to the peak intensities of the fiber bundles falls within a range of 0.50 to 0.65; a pre-carbonization step of heat-treating the flame-proofed fiber bundle obtained in the second flame-proofing step in an inert atmosphere at a maximum temperature of 300°C or more and 800°C or less; and a carbonization step of heat-treating the pre-carbonized fiber bundle obtained in the pre-carbonization step at a maximum temperature Tmax of 1,200°C or more and 2,000°C or less, wherein a maximum temperature rise rate β1 [°C / min] in the temperature rise process from 800°C to 1,000°C and a maximum temperature rise rate β2 [°C / min] in the temperature rise process from 1,000°C to the maximum temperature Tmax [°C] in the carbonization step satisfy the relationships of the following formulas (6) and (7). −200≦β1 − 0.1Tmax ≦ 0 (6) −180 ≦ β2 − 0.1Tmax ≦ 0 (7)

[18] The method for producing a carbon fiber bundle according to

[17] , wherein in the carbonization step, the maximum temperature Tmax is set to 1,700 to 2,000°C, the maximum heating rate β1 at a temperature of 800 to 1,000°C is 100°C / min or less, and the maximum heating rate β2 at a temperature from 1,000°C to the maximum temperature Tmax is 150°C / min or less.

[19] The method for producing a carbon fiber bundle according to

[17] , wherein in the carbonization step, the maximum temperature Tmax is 1,200 to 1,500°C, the maximum heating rate β1 at a temperature of 800 to 1,000°C is 60°C / min or less, and the maximum heating rate from 1,000°C to the maximum temperature Tmax is 60°C / min or less.

[20] A prepreg comprising the carbon fiber bundle according to any of [1] to

[16] and a matrix resin.

[21] A carbon fiber reinforced composite material comprising the carbon fiber bundle according to any of [1] to

[16] and a matrix resin.

[0015] According to the present invention, it is possible to provide a carbon fiber bundle that is not only excellent in strand strength and strand modulus, but also has excellent operability because single fiber breakage is unlikely to occur even when subjected to torsional deformation when subjected to advanced processing, and a method for producing the same.

[0016] In order to achieve the above object, the present invention has the following configuration: The upper and lower limits of the numerical ranges described below can be combined in any manner.

[0017] The carbon fiber bundle of the present invention is a carbon fiber bundle made of a plurality of carbon fibers, and has a strand elastic modulus E of 280 GPa or more and 400 GPa or less, a crystallite size Lc of the carbon fibers of 1.80 nm or more and 2.60 nm or less, and a density ρ of the carbon fibers of 1.780 g / cm ３ 1.830g / cm or more ３ and the density ρ [g / cm ３ ], crystallite size Lc [nm], and strand modulus E [GPa] satisfy the relationships of the following formulas (1) and (2): 1.860≦ρ+0.0333Lc≦1.895 (1) 6.67×10 －５ × (E-207) ２ +1.60≧Lc (2) Hereinafter, the above-described embodiment will also be referred to as a "first embodiment."

[0018] One particularly preferred embodiment of the carbon fiber bundle of the present invention is a carbon fiber bundle made of a plurality of carbon fibers, wherein the strand elastic modulus E is 330 GPa or more and 400 GPa or less, the crystallite size Lc of the carbon fibers is 2.40 nm or more and 2.60 nm or less, and the degree of crystalline orientation π of the carbon fibers is ００２ is 85% or more and 88% or less, and the density ρ of the carbon fiber is 1.780 g / cm ３ More than 1.800g / cm ３ Furthermore, the coefficient A calculated from the approximate formula (4) of the nonlinearity of the stress σ-strain ε curve in the resin-impregnated strand tensile test is −0.000140 or more and −0.000050 or less. ２ +Bσ+C (4) where A, B, and C are coefficients of a quadratic function of the stress σ [GPa] and the strain ε [-]. This embodiment is particularly preferable for high elastic modulus products among the carbon fiber bundles of the present invention, and hereinafter this embodiment will also be referred to as the "second embodiment."

[0019] One particularly preferred embodiment of the carbon fiber bundle of the present invention is a carbon fiber bundle made of a plurality of carbon fibers, wherein the strand elastic modulus E is 280 GPa or more and 340 GPa or less, the mass composition ratio N / C of nitrogen to carbon in the carbon fibers is 0.020 or more and 0.050 or less, the crystallite size Lc of the carbon fibers is 1.80 nm or more and 1.95 nm or less, and the density ρ of the carbon fibers is 1.805 g / cm ３ 1.830g / cm or more ３ Furthermore, the coefficient A calculated from the approximate formula (4) for the nonlinearity of the stress σ-strain ε curve in the resin-impregnated strand tensile test is −0.000170 or more and −0.000090 or less. ２ +Bσ+C (4) where A, B, and C are coefficients of a quadratic function of the stress σ [GPa] and the strain ε [-]. This embodiment is particularly preferable for a medium modulus carbon fiber bundle of the present invention, and hereinafter this embodiment will also be referred to as the "third embodiment."

[0020] The second and third aspects are included within the scope of the first aspect, and therefore, unless inconsistent, the detailed descriptions and preferred aspects of the first aspect also apply to the second and third aspects.

[0021] The carbon fiber bundle of the present invention is composed of a plurality of carbon fibers. Examples of the carbon fibers that can be used include polyacrylonitrile (PAN)-based carbon fibers, pitch-based carbon fibers, and rayon-based carbon fibers. Among these, polyacrylonitrile-based carbon fibers are preferred because they have excellent tensile strength and elastic modulus and are economically viable. Polyacrylonitrile-based carbon fibers are carbon fibers obtained by flame-proofing and carbonizing a polyacrylonitrile-based precursor fiber bundle.

[0022] In the first aspect, the mass composition ratio N / C of nitrogen to carbon of the carbon fiber is preferably 0.0008 or more and 0.050 or less. The mass composition ratio N / C of nitrogen to carbon corresponds to the amount of nitrogen atoms in the carbon fiber. By setting N / C to 0.0008 or more, more preferably 0.0010 or more, a carbon fiber bundle in which single fiber breakage due to torsional deformation is unlikely to occur can be obtained. On the other hand, by setting N / C to 0.050 or less, more preferably 0.045 or less, even more preferably 0.044 or less, and even more preferably 0.038 or less, a carbon fiber bundle that exhibits excellent rigidity when made into a carbon fiber composite material can be obtained.

[0023] In the second aspect, the mass composition ratio N / C of nitrogen to carbon of the carbon fiber is preferably 0.0008 or more and 0.0150 or less. By setting N / C to 0.0150 or less, more preferably 0.0060 or less, and even more preferably 0.0043 or less, it is possible to more effectively obtain a carbon fiber bundle having a high strand modulus and excellent rigidity when made into a composite material.

[0024] In the third aspect, the mass composition ratio N / C of nitrogen to carbon of the carbon fiber is 0.020 or more and 0.050 or less. By setting N / C to 0.020 or more, preferably 0.025 or more, more preferably 0.026 or more, and even more preferably 0.029 or more, it is possible to obtain a carbon fiber bundle having a medium elastic modulus and in which single fibers are less likely to break due to torsional deformation.

[0025] The N / C ratio can be determined by elemental analysis, which will be described later. The N / C ratio can be controlled mainly by the maximum temperature Tmax in the carbonization step; when the maximum temperature Tmax is set to 1400°C, the N / C ratio is around 0.04, and when the maximum temperature Tmax is set to 2000°C, the N / C ratio is around 0.001. In addition to the maximum temperature Tmax in the carbonization step, the N / C ratio can also be controlled by the residence time and the state in the previous step.

[0026] The crystallite size Lc of the carbon fiber in the first embodiment is 1.80 nm or more and 2.60 nm or less. By setting the crystallite size Lc to 1.80 nm or more, preferably 1.81 nm or more, and more preferably 1.83 nm or more, a carbon fiber bundle with excellent strand modulus can be obtained. On the other hand, by setting the crystallite size Lc to 2.60 nm or less, preferably 2.55 nm or less, and more preferably 2.49 nm or less, a carbon fiber bundle in which single fiber breakage due to torsional deformation is unlikely to occur can be obtained.

[0027] The crystallite size Lc of the carbon fiber in the second embodiment is 2.40 nm or more and 2.60 nm or less. By setting the crystallite size Lc to 2.40 nm or more, preferably 2.45 nm or more, more preferably 2.47 nm or more, it is possible to obtain a carbon fiber bundle having a high strand modulus, i.e., a high modulus product, which is excellent in rigidity when made into a composite material.

[0028] In the third aspect, the crystallite size Lc of the carbon fiber is 1.80 nm or more and 1.95 nm or less. By setting the crystallite size Lc to 1.95 nm or less, preferably 1.91 nm or less, and more preferably 1.88 nm or less, it is possible to obtain a carbon fiber bundle in which breakage of single fibers due to torsional deformation is unlikely to occur, particularly in a medium modulus product.

[0029] The crystallite size Lc can be evaluated by wide-angle X-ray diffraction, which will be described later. In order to control the crystallite size within the above range, it is important to increase the maximum temperature in the carbonization step and to lengthen the residence time, but since the maximum temperature also affects the density and N / C of the carbon fiber bundle, by controlling the temperature rise rate in the carbonization step, which will be described later, in addition to this, it is possible to control the crystallite size Lc while satisfying other structures.

[0030] The density ρ of the carbon fiber in the first embodiment is 1.780 g / cm ３ 1.830g / cm or more ３ The density is a parameter that indicates the microstructure of the carbon fiber bundle, and the density ρ is 1.780 g / cm ３ or more, preferably 1.785 g / cm ３ More preferably, 1.788 g / cm ３By setting the density ρ to 1.830 g / cm or more, a carbon fiber bundle with excellent strand elastic modulus can be obtained. ３ or less, preferably 1.825 g / cm ３ or less, more preferably 1.818 g / cm ３ By setting the following, it is possible to obtain carbon fibers in which single fibers are less likely to break due to torsional deformation.

[0031] The density ρ of the carbon fiber in the second embodiment is 1.780 g / cm ３ More than 1.800g / cm ３ The range of the crystallite size Lc in the second embodiment is a region where the density is likely to decrease, and in that region, the density ρ is set to 1.800 g / cm or less. ３ or less, preferably 1.795 g / cm ３ or less, more preferably 1.792 g / cm ３ By satisfying the following, a carbon fiber bundle in which breakage of single fibers due to torsional deformation is unlikely to occur can be obtained. In the second aspect, satisfying both the ranges of the coefficient A and density ρ described below is a key to obtaining a carbon fiber bundle in which breakage of single fibers due to torsional deformation is unlikely to occur.

[0032] The density ρ of the carbon fiber in the third embodiment is 1.805 g / cm ３ 1.830g / cm or more ３ The density ρ is a parameter indicating the microstructure of the carbon fiber bundle, and the density ρ is set to 1.805 g / cm ３ More preferably, 1.806 g / cm ３ By doing so, it is possible to obtain a carbon fiber bundle having an excellent strand modulus of elasticity as a medium modulus product.

[0033] The density can be measured by a method such as the Archimedes method described later. In order to control the density within the above range, it is important to increase the maximum temperature in the carbonization step, but since the maximum temperature also affects the crystallite size Lc and N / C of the carbon fiber bundle, by controlling the temperature rise rate in the carbonization step described later, the density can be controlled while satisfying other structures.

[0034] In the first embodiment, the density ρ [g / cm ３] and the crystallite size Lc [nm] satisfy the formula (1). 1.860≦ρ+0.0333Lc≦1.895 (1) ρ+0.0333Lc is preferably 1.866 or more, more preferably 1.868 or more, and even more preferably 1.869 or more. In addition, ρ+0.0333Lc is preferably 1.888 or less, more preferably 1.887 or less, and even more preferably 1.881 or less. When the relationship between the density ρ and the crystallite size Lc satisfies the formula (1), it is possible to obtain a carbon fiber bundle that has excellent strand strength and strand modulus, as well as excellent operability when subjected to advanced processing. In order to control the density ρ and the crystallite size Lc within the range satisfying the above formula (1), it is important to increase the maximum temperature in the carbonization step, but since the maximum temperature affects both the density ρ and the crystallite size Lc of the carbon fiber bundle, by controlling the temperature rise rate in the carbonization step described below in addition to this, it is possible to control the structure to satisfy formula (1).

[0035] In the first embodiment, the crystallite size Lc [nm] and the nitrogen to carbon mass composition ratio N / C [-] satisfy formula (3). 12×e-D(Lc-1.67)+F≧N / C (3) where D = 1.00, F = 0.015, and e is Napier's number. On the left side, the value of coefficient D is preferably 0.60 or less, more preferably 0.45 or less. Furthermore, the value of coefficient F is preferably 0.012 or less, more preferably 0.010 or less. A smaller Lc is preferable from the viewpoint of resistance to torsional deformation, and a larger N / C is preferable from the viewpoint of resistance to torsional deformation. When these relationships satisfy formula (3), a carbon fiber with better resistance to torsional deformation can be obtained. In order to control Lc and N / C within a range that satisfies the above formula (3), it is important to control them by the maximum temperature Tmax in the carbonization step, etc. However, since Tmax affects both Lc and N / C, by additionally controlling the rate of temperature rise in the carbonization step described below, it is possible to control them to a structure that satisfies formula (3).

[0036] In the second aspect, the degree of crystal orientation of the carbon fiber is π ００２ is 85% or more and 88% or less. ００２By making the degree of crystal orientation π 85% or more, a carbon fiber bundle with excellent strand modulus can be obtained. ００２ By making the degree of crystal orientation π 88% or less, preferably 86% or less, it is possible to obtain a carbon fiber bundle in which breakage of single fibers due to torsional deformation is unlikely to occur. ００２ can be controlled without deteriorating the operability or quality by balancing the drawing tension with the maximum temperature Tmax and the residence time in the carbonization step.

[0037] In a third aspect, the scatterer length lf of the carbon fiber measured by small-angle X-ray scattering is 14.0 nm or more and 19.2 nm or less. By setting the scatterer length lf to 14.0 nm or more, preferably 14.2 nm or more, a carbon fiber bundle with excellent strand modulus can be obtained. On the other hand, by setting the scatterer length lf to 19.2 nm or less, preferably 18.0 nm or less, more preferably 17.7 nm or less, a carbon fiber bundle in which single fiber breakage due to torsional deformation is less likely to occur can be obtained. The scatterer length lf is a parameter related to the crystalline structure inside the carbon fiber, and the results of the study of the present invention have revealed that there is a certain correlation with the crystallite size Lc.

[0038] The scatterer length can be evaluated by a microbeam small-angle X-ray scattering method using synchrotron radiation, which will be described later. With general-purpose equipment, the beam diameter of small-angle X-ray scattering (SAXS) is larger than the diameter of a carbon fiber bundle or single fiber, which causes strong total reflection components originating from the fiber surface to be superimposed, making precise analysis of the void structure, particularly at low angles, difficult. Therefore, to measure the scatterer length l f with high precision, it is important to use a microbeam with a beam diameter smaller than the single fiber diameter (4 μm or more) and to avoid strong total reflection components originating from the fiber surface.

[0039] The method for generating the microbeam is not particularly limited, and known methods such as those using focusing optical elements such as pinholes or Fresnel zone plates can be used. The full width at half maximum of the beam intensity in the vertical and horizontal directions of the microbeam is 6 μm × 2 μm or less. Total reflection is a phenomenon in which incident X-rays are completely reflected without passing through the fiber boundary surface, and because the scattering intensity is extremely high, it is superimposed on the scattering caused by the scatterer, making it difficult to analyze the length of the scatterer.

[0040] The X-ray source can be a Cu-Kα ray from a general-purpose device, but since the scattering intensity is low due to the narrow beam diameter, it is preferable to use synchrotron X-rays to obtain a sufficient signal-to-noise ratio. The microbeam is irradiated onto a single fiber to suppress total reflection, and multiple points are measured while scanning in the direction perpendicular to the fiber axis to ensure that the center is irradiated. The camera length can be determined by a known method using a standard substance such as collagen.

[0041] A two-dimensional detector must be used as the detector for measuring the scatterer length lf, since information on the scattering intensity in the azimuthal direction is required. There are no particular limitations on the type of two-dimensional detector, but a two-dimensional semiconductor detector (PILATUS, manufactured by Rigaku) ​​or an imaging plate (R-Axis VII, manufactured by Rigaku) ​​can be used. Air scattering is subtracted from the obtained two-dimensional scattering image using a known method. Free software such as Fit2d can be used to analyze the two-dimensional scattering image.

[0042] The scatterer length is determined by the half-width B of the intensity in the azimuthal direction, with reference to the method of Ran (S. Ran et al., Polymer 42 (2001) 1601-1612). ｏｂｓ , scattering vector s [nm －１ ], scatterer length lf [nm], scatterer orientation angle B φ The scatterer length lf is evaluated using the following formula (a). ｏｂｓ is calculated by fitting the intensity profile in the azimuthal direction with a Gaussian function. ｏｂｓ ２ = 1 / lf ２ ×1 / s ２ +B φ ２ ...(a).

[0043] In order to control the scatterer length lf within the above range, it is important to increase the maximum temperature in the carbonization process, but since the maximum temperature also affects the density and N / C of the carbon fiber bundle, by controlling the temperature rise rate in the carbonization process described below, it is possible to control the scatterer length lf while also satisfying other structures.

[0044] The single fiber fineness of the carbon fiber in the first embodiment is preferably 0.25 dtex or more and 0.60 dtex or less. The single fiber fineness is related to the thickness of the single fiber and is involved in the deterioration of mechanical properties due to the formation of a skin-core structure. By setting the single fiber fineness to 0.25 dtex or more, more preferably 0.30 dtex or more, and even more preferably 0.35 dtex or more, it is possible to prevent breakage of the single fiber and to generate interfiber voids in the carbon fiber bundle, which makes it easier to impregnate the carbon fiber bundle with a matrix resin when forming a prepreg. Furthermore, by setting the single fiber fineness to 0.60 dtex or less, more preferably 0.50 dtex or less, and even more preferably 0.45 dtex or less, it is possible to achieve excellent resistance to torsional deformation due to a small skin-core structure and uniform crystallite size. The single fiber fineness can be controlled by setting the single fiber fineness of the precursor fiber and the draw ratios in the flameproofing process, precarbonization process, and carbonization process.

[0045] In the third aspect, the single fiber fineness of the carbon fiber is more preferably 0.41 dtex or more and 0.50 dtex or less. By setting the single fiber fineness to 0.41 dtex or more, more preferably 0.42 dtex or more, it is possible to prevent single fiber breakage as a medium modulus product. On the other hand, by setting the single fiber fineness to 0.50 dtex or less, more preferably 0.45 dtex or less, it is possible to achieve excellent resistance to torsional deformation due to a small skin-core structure and uniform crystallite size. The single fiber fineness can be controlled by setting the single fiber fineness of the polyacrylonitrile precursor fiber bundle and the draw ratios in the flame retardation process, pre-carbonization process, and carbonization process.

[0046] The number of filaments per bundle in the carbon fiber bundle of the present invention is preferably 3,000 to 36,000, and more preferably 12,000 to 24,000. When the number of filaments is 3,000 to 36,000, the strand strength, strand modulus, and productivity of the carbon fiber bundle can all be achieved.

[0047] The strand modulus E of the carbon fiber bundle of the first embodiment is 280 GPa or more and 400 GPa or less. The strand modulus E is an amount that indicates the resistance to deformation of the carbon fiber bundle, and the larger the strand modulus E, the higher the rigidity of the carbon fiber reinforced composite material. By setting the strand modulus E to 280 GPa or more, preferably 293 GPa or more, and more preferably 302 GPa or more, it is possible to obtain sufficient rigidity as a carbon fiber reinforced composite material. On the other hand, by setting the strand modulus E to 400 GPa or less, preferably 373 GPa or less, and more preferably 365 GPa or less, it is possible to achieve an excellent balance with other properties.

[0048] The strand modulus E of the carbon fiber bundle of the second embodiment is 330 GPa or more and 400 GPa or less. Carbon fiber bundles with a strand modulus E of around 230 GPa are generally classified as standard modulus products, and those with a strand modulus E of around 300 GPa as medium modulus products. The second embodiment is positioned in a higher range. In the second embodiment, the strand modulus is a property related to the above-mentioned crystallite size and degree of crystal orientation, and is a prerequisite for manifesting the properties of a composite material. In the second embodiment, by setting the strand modulus E to 330 GPa or more, preferably 345 GPa or more, more preferably 348 GPa or more, sufficient rigidity can be obtained as a carbon fiber reinforced composite material using the carbon fiber bundle of the second embodiment.

[0049] The strand elastic modulus E of the carbon fiber bundle of the third aspect is 280 GPa or more and 340 GPa or less. In the third aspect, by setting the strand elastic modulus E to 340 GPa or less, preferably 325 GPa or less, more preferably 320 GPa or less, even more preferably 315 GPa or less, and still more preferably 309 GPa or less, the carbon fiber bundle of the third aspect has an excellent balance with other properties.

[0050] The strand modulus E can be determined from the stress-strain curve of a resin-impregnated strand tensile test of a carbon fiber bundle (JIS R7608 (2008) "Test method for resin-impregnated strands"), and the strain range for evaluating the strand modulus is 0.1 to 0.6%. The strand modulus E can be controlled by the maximum temperature in the carbonization step, etc.

[0051] In the carbon fiber bundle of the first embodiment, the crystallite size Lc [nm] and the strand modulus E [GPa] satisfy the formula (2). －５ × (E-207) ２ +1.60≧Lc (2) The second term on the left side of formula (2) is preferably 1.42, and more preferably 1.36. By making the crystallite size Lc and the strand modulus E satisfy formula (2), it is possible to obtain a carbon fiber bundle that achieves both excellent strand strength and strand modulus, and operability when subjected to advanced processing. In order to control the crystallite size Lc and the strand modulus E so as to satisfy the above formula (2), it is important to increase the maximum temperature in the carbonization step, etc., but since the maximum temperature affects both the crystallite size Lc and the strand modulus E of the carbon fiber bundle, it is possible to control the structure to satisfy formula (2) by additionally controlling the heating rate in the carbonization step described below.

[0052] The strand strength of the carbon fiber bundle of the first embodiment is preferably 6.5 GPa or more and 8.5 GPa or less. The strand strength is the strength of the carbon fiber bundle against the tensile stress. By setting the strand strength to 6.5 GPa or more, more preferably 6.7 GPa or more, and even more preferably 6.8 GPa or more, the strength of the carbon fiber reinforced composite material and the processability during advanced processing (resistance to breakage in high-tension advanced processing processes such as pultrusion and filament winding) are excellent. On the other hand, by setting the strand strength to 8.5 GPa or less, more preferably 7.2 GPa or less, and even more preferably 7.1 GPa or less, an excellent balance with other physical properties is achieved.

[0053] The strand strength can be determined by a tensile test of a resin-impregnated strand of a carbon fiber bundle (JIS R7608 (2008) "Test method for resin-impregnated strands"). The strand strength can be controlled by the maximum temperature in the carbonization step, etc.

[0054] In the carbon fiber bundle of the first embodiment, it is preferable that the value of coefficient A obtained by introducing a stress σ (GPa)-strain ε(-) curve obtained by measuring the carbon fiber bundle by a resin-impregnated strand tensile test into the following nonlinear approximation formula (4) (hereinafter referred to as formula (4)) is −0.000170 or more and −0.000050 or less. ε=Aσ ２ +Bσ+C ... (4) where A, B, and C are coefficients. Coefficient A represents the nonlinear dependence of the strand modulus of elasticity of a carbon fiber on strain. Coefficient A is found by fitting a stress-strain curve obtained by measuring a carbon fiber bundle using a resin-impregnated strand tensile test to equation (4) within a stress range of 0 to 3 GPa. As described above, the stress-strain curve of a carbon fiber bundle generally exhibits an upwardly convex curve when stress is plotted on the vertical axis and strain on the horizontal axis, and therefore coefficient A found from equation (4) takes a negative value. In other words, the closer coefficient A is to 0, the smaller the nonlinearity. The theory relating to stress and deformation in carbon fibers is explained, for example, in Patent Document 4, where coefficient A is related to the shear modulus of carbon fiber; the larger the absolute value of coefficient A, the lower the shear modulus of a carbon fiber bundle tends to be, and the smaller the absolute value of coefficient A, the higher the shear modulus of the carbon fiber bundle tends to be. Shear modulus is an index of the ease of deformation when a torsional stress is applied to a single fiber. By setting the coefficient A to −0.000170 or more, more preferably −0.000166 or more, even more preferably −0.000159 or more, and even more preferably −0.000147 or more, a carbon fiber bundle excellent in shear modulus and tensile modulus and excellent mechanical properties can be more effectively obtained. On the other hand, by setting the coefficient A to −0.000050 or less, more preferably −0.000090 or less, even more preferably −0.000098 or less, even more preferably −0.000144 or less, even more preferably −0.000145 or less, and even more preferably −0.000151 or less, a carbon fiber bundle that easily follows torsional deformation can be obtained, and breakage of single fibers during advanced processing and subsequent winding around rollers or guides can be suppressed.

[0055] In the carbon fiber bundle of the second embodiment, the value of coefficient A obtained by introducing into formula (4) a stress σ [GPa]-strain ε [-] curve obtained by measuring the carbon fiber bundle by a resin-impregnated strand tensile test is -0.000140 or more and -0.000050 or less. The coefficient A in formula (4) changes with the strand elastic modulus E, but by setting coefficient A to -0.000140 or more, preferably -0.000090 or more, more preferably -0.000085 or more within the range of the strand elastic modulus E of the second embodiment, it is possible to obtain a carbon fiber bundle of the second embodiment that is excellent in shear modulus and tensile modulus and in mechanical properties. On the other hand, by setting the coefficient A to −0.000050 or less, preferably −0.000065 or less, more preferably −0.000078 or less, a carbon fiber bundle that easily follows torsional deformation can be obtained as the second embodiment, and breakage of single fibers during advanced processing and subsequent winding around rollers or guides can be suppressed.

[0056] In the carbon fiber bundle of the third aspect, the value of coefficient A obtained by introducing the stress σ (GPa)-strain ε(-) curve, which is obtained by measuring the carbon fiber bundle by a resin-impregnated strand tensile test, into equation (4) is −0.000170 or more and −0.000090 or less. When the strand elastic modulus E is within the range of the third aspect, by making coefficient A −0.000170 or more, preferably −0.000166 or more, more preferably −0.000159 or more, and even more preferably −0.000147 or more, it is possible to obtain a carbon fiber bundle of the third aspect which is excellent in shear modulus and tensile modulus and in mechanical properties. On the other hand, by setting the coefficient A to −0.000090 or less, preferably −0.000098 or less, more preferably −0.000144 or less, even more preferably −0.000145 or less, and still more preferably −0.000151 or less, a carbon fiber bundle that easily follows torsional deformation can be obtained as the third aspect, and breakage of single fibers during advanced processing and the subsequent winding around rollers or guides can be suppressed.

[0057] The coefficient A in the formula (4) can be controlled by the draw ratio in the carbonization step, the temperature rise rate in the carbonization step, the maximum temperature in the carbonization step, and the like.

[0058] In the first embodiment, the nonlinearity coefficient A, the density ρ [g / cm ３ ] preferably satisfies formula (5). 0.00621≦0.00357ρ+A≦0.00645 (5) When the relationship between the nonlinearity coefficient A and the density ρ satisfies formula (5), the balance between the shear modulus and the tensile modulus is favorable, and carbon fibers with excellent resistance to torsional deformation can be obtained. By setting 0.00357ρ+A to 0.00621 or more, more preferably 0.00625 or more, and even more preferably 0.00626 or more, a carbon fiber bundle having a shear modulus with excellent resistance to torsional deformation can be obtained. On the other hand, by setting 0.00357ρ+A to 0.00645 or less, more preferably 0.00638 or less, and even more preferably 0.00637 or less, a carbon fiber with an excellent balance with the tensile modulus and excellent mechanical properties can be obtained. In order to control the nonlinearity coefficient A and density ρ within a range that satisfies the above formula (5), they can be controlled by the maximum temperature Tmax in the carbonization step, etc. However, since Tmax affects both the coefficient A and density ρ, it is preferable to additionally control the temperature rise rate in the carbonization step described below.

[0059] The significance of the first aspect lies in the discovery and realization of a combination of ranges of strand modulus E, density, and crystallite size Lc that could not be achieved by conventional techniques. For example, when the crystallite size is large, the strand modulus is high and single fibers tend to break easily due to torsional deformation. However, in the first aspect, by adjusting the density while keeping the crystallite size relatively large, single fiber breakage due to torsional deformation can be suppressed. On the other hand, when trying to keep the crystallite size within the range of the first aspect, it is difficult to keep both the density within the range of the first aspect by simply increasing the draw ratio or tension in the carbonization process. In the present invention, a method for controlling the heating rate in the carbonization process, which will be described later, has been discovered to achieve such a combination of parameters.

[0060] In the second embodiment, the crystallite size Lc and the degree of crystal orientation π, which could not be achieved by the prior art, are achieved. ００２The significance of this invention lies in the discovery and achievement of a combination of ranges of strand modulus, coefficient A, and density. For example, when the crystallite size is large and the strand modulus is high, single fiber breakage due to torsional deformation tends to occur easily. However, in the second embodiment, in a carbon fiber exhibiting a high strand modulus and having a relatively large crystallite size within a specific range, single fiber breakage due to torsional deformation can be suppressed by adjusting the coefficient A and density. On the other hand, when the crystallite size is within the range of the second embodiment, it is difficult to achieve both the coefficient A and density within the range of the second embodiment simply by increasing the draw ratio or tension in the carbonization process. In the present invention, in order to achieve such a combination of parameters, a method of controlling the heating rate in the carbonization process described below has been discovered.

[0061] The significance of the third aspect lies in the discovery and realization of a combination of ranges of coefficient A, strand modulus, density, crystallite size Lc, and N / C that could not be achieved by conventional techniques. For example, when the crystallite size is large and the N / C is small, the strand modulus is high and single fibers tend to break easily due to torsional deformation. However, in the third aspect, by adjusting the density and coefficient A while keeping the crystallite size relatively large and the N / C within the specific ranges of the third aspect, where N / C is relatively small, single fibers can be prevented from breaking due to torsional deformation even at high strand modulus. On the other hand, when the crystallite size Lc and N / C are within the ranges of the third aspect, it is difficult to bring both the coefficient A and density within the ranges of the present invention simply by increasing the draw ratio or tension in the carbonization process. In the present invention, a method for controlling the heating rate in the carbonization process, described below, has been discovered to achieve such a combination of parameters.

[0062] Next, a method for producing a carbon fiber bundle of the present invention, which is preferable for obtaining the carbon fiber bundle of the present invention, will be described. The method for producing a carbon fiber bundle of the present invention includes a first flame-stabilizing step of flame-stabilizing a carbon fiber precursor fiber bundle, a second flame-stabilizing step of flame-stabilizing the fiber bundle obtained in the first flame-stabilizing step, a pre-carbonization step of heat-treating the flame-stabilized fiber bundle obtained in the second flame-stabilizing step, and a carbonization step of heat-treating the pre-carbonized fiber bundle obtained in the pre-carbonization step.

[0063] (Spinning of precursor fiber bundle) Before the first flame-retardant treatment step, a polyacrylonitrile precursor fiber bundle is spinned. A polyacrylonitrile polymer is used as a raw material for producing the polyacrylonitrile precursor fiber bundle. In the present invention, the polyacrylonitrile polymer refers to a polymer in which at least acrylonitrile is the main constituent component of the polymer skeleton, and the main constituent component refers to a constituent component that accounts for 90 to 100 mass % of the polymer skeleton. In producing the polyacrylonitrile precursor fiber bundle, the polyacrylonitrile polymer preferably contains a copolymer component such as itaconic acid, acrylamide, or methacrylic acid, from the viewpoints of improving spinnability and efficiently carrying out the flame-retardant treatment.

[0064] In the production of a polyacrylonitrile precursor fiber bundle, a method for producing a polyacrylonitrile polymer can be selected from known polymerization methods. In the production of a polyacrylonitrile precursor fiber bundle suitable for obtaining the carbon fiber bundle of the present invention, the spinning dope is prepared by dissolving the above-mentioned polyacrylonitrile polymer in a solvent in which polyacrylonitrile is soluble, such as dimethyl sulfoxide, dimethylformamide, dimethylacetamide, or an aqueous solution of nitric acid, zinc chloride, and sodium rhodanide.

[0065] There is no particular limitation on the method for producing the polyacrylonitrile precursor fiber bundle used in the present invention, but preferably, dry / wet spinning is used, followed by steps such as water washing, drawing, application of an oil agent, drying and densification, and, if necessary, post-drawing, to obtain a polyacrylonitrile precursor fiber bundle.

[0066] (Dry-wet spinning) In dry-wet spinning, the polymer discharged from the nozzle is allowed to travel in the air, and then immediately introduced into a coagulation bath to coagulate the fibers.

[0067] The coagulation bath preferably contains the solvent used for the spinning dope, such as dimethyl sulfoxide, dimethylformamide, or dimethylacetamide, and a so-called coagulation promoter. The coagulation promoter may be one that does not dissolve the polyacrylonitrile polymer and is compatible with the solvent used for the spinning dope, and is preferably water.

[0068] (Water Bath Drawing Step) Following the dry / wet spinning, the fiber is drawn while being washed, preferably using a multi-stage water washing bath having a water bath temperature of 30 to 98° C. The draw ratio in the water bath drawing step is preferably 2 to 6 times.

[0069] (Oil Application Step) After the water bath drawing step, in order to prevent adhesion between the single fibers, an oil agent made of silicone or the like is applied to the yarn, preferably through an oil application step. The silicone is preferably a modified silicone, and more preferably contains an amino-modified silicone which has high heat resistance.

[0070] (Dry Heat Treatment Step) A known method can be used for the dry heat treatment. The drying temperature is preferably, for example, 100 to 200°C.

[0071] (Precursor Fiber Bundle) The single fiber fineness of the precursor fiber bundle is preferably 0.5 to 1.5 dtex. By setting the single fiber fineness of the precursor fiber bundle to 0.5 to 1.5 dtex, more preferably 0.6 to 1.0 dtex, it is possible to achieve both the strand strength and strand modulus of the carbon fiber bundle and productivity.

[0072] (Flaming process) Common to the first and second flame-resistant processes, the temperature in the process of heat-treating the precursor fiber bundle in an oxidizing atmosphere (flaming process) is preferably 220 to 300°C. If the flame-resistant treatment temperature is 220°C or higher, a flame-resistant fiber bundle having sufficient flame resistance can be produced, and if the flame-resistant treatment temperature is 300°C or lower, the heat generation rate of the flame-resistant fiber bundle does not become excessively high, so that temperature unevenness in the flame-resistant fiber bundle can be reduced and a carbon fiber bundle having excellent mechanical properties can be obtained. A known method can be used as the heat treatment method.

[0073] In the first flame-proofing step, 1370 cm in the infrared spectrum －１ The peak intensity at 1453 cm －１ The heat treatment is continued until the ratio of the peak intensities of the first and second oxide films falls within the range of 0.98 to 1.10. The flame-stabilizing time in the first flame-stabilizing step is preferably 8 to 25 minutes, more preferably 8 to 15 minutes.

[0074] Subsequently, in the second flame-stabilizing step, a fluorine-containing compound having a peak at 1370 cm in the infrared spectrum is obtained, preferably at a temperature higher than that in the first flame-stabilizing step. －１ The peak intensity at 1453 cm －１ The ratio of the peak intensities of the two compounds is within the range of 0.70 to 0.75, and the peak intensity of the two compounds is 1370 cm in the infrared spectrum. －１ The peak intensity at 1254 cm －１ The heat treatment is performed for a flame-stabilizing time of 5 to 14 minutes, preferably 5 to 10 minutes, until the peak intensity ratio falls within the range of 0.50 to 0.65. The flame-stabilizing time in the second flame-stabilizing step can be shortened by adjusting the flame-stabilizing temperature higher, but the appropriate flame-stabilizing temperature depends on the properties of the polyacrylonitrile precursor fiber bundle. In order to control the temperature at the center of the carbon fiber bundle within the aforementioned infrared spectrum range, it is preferable to set the temperature at a temperature of preferably 280 to 310°C, more preferably 280 to 300°C, and even more preferably 285 to 295°C. The flame-stabilizing temperature does not need to be constant, and may be set at multiple stages.

[0075] In both the first and second flame-stabilizing steps, it is basically preferable to set the flame-stabilizing temperature high and the flame-stabilizing time short. －１ The peak at 1370 cm is derived from alkenes, and the peak intensity decreases as the flame resistance increases. －１ Peak and 1254 cm －１ The peaks at 1.35 g / cm3 are peaks derived from the flame-resistant structures (which are thought to be derived from the naphthyridine ring and hydrogenated naphthyridine ring structures, respectively), and the peak intensity increases as the flame resistance progresses. ３ In this case, 1370 cm －１ The peak intensity at 1453 cm －１It is preferable that the ratio of the peak intensities of the obtained flame-resistant fiber bundle to the peak intensities of the －１ The peak intensity at 1254 cm －１ It is important to set the flame-stabilizing conditions so that the peak intensity ratio of the peaks is 0.50 to 0.65. The peak intensity ratio decreases as the flame-stabilizing process progresses, and the decrease is particularly large in the initial stage. However, depending on the flame-stabilizing conditions, the peak intensity ratio may not become 0.65 or less even if the time is increased, so adjustment of the conditions is necessary.

[0076] In order to achieve a balance between these two peak intensity ratios within the desired range, the conditions should basically be set by focusing mainly on reducing the amount of copolymerization component contained in the polyacrylonitrile-based polymer that constitutes the precursor fiber bundle, increasing the degree of crystalline orientation of the precursor fiber bundle, reducing the fineness of the precursor fiber bundle, and increasing the flame-proofing temperature in the latter half.

[0077] In addition to providing such a flame-resistant fiber bundle, by controlling the maximum rate of temperature rise from 800 to 1,000°C and the maximum rate of temperature rise from 1,000°C to the maximum temperature in the carbonization step described below, the strand modulus E of the carbon fiber bundle, the coefficient A of nonlinearity of the stress σ-strain ε curve in a resin-impregnated strand tensile test, N / C, crystallite size, and scatterer length lf can be controlled within the above-mentioned ranges.

[0078] (Preliminary carbonization step) Following the second flameproofing step, preliminary carbonization is performed. In the preliminary carbonization step, the flameproof fiber bundle is heated in an inert atmosphere at a maximum temperature of 300°C or higher and 800°C or lower, and the density is preferably 1.5 to 1.8 g / cm ３ By setting the maximum temperature of the pre-carbonization to 300°C or higher and 800°C or lower, the pre-carbonized fiber bundle can be carbonized in the subsequent carbonization step without being broken due to thermal decomposition.

[0079] (Carbonization Step) Following the pre-carbonization step, carbonization is carried out. In the carbonization step, the pre-carbonized fiber bundle is further heat-treated in an inert atmosphere. The maximum temperature Tmax of the heat treatment in the carbonization step is 1,200°C or higher and 2,000°C or lower. By setting Tmax to 1,200°C or higher, preferably 1,250°C or higher, and more preferably 1,300°C or higher, a carbon fiber bundle with an excellent strand modulus can be obtained. On the other hand, by setting Tmax to 2,000°C or lower, preferably 1,900°C or lower, and more preferably 1,800°C or lower, a carbon fiber in which single fiber breakage due to torsional deformation is less likely to occur can be obtained.

[0080] Regarding the relationship between Tmax and the density ρ of the carbon fiber, the density ρ is a parameter that reflects the microstructure of the carbon fiber bundle and can be changed along with the maximum temperature in the carbonization process. That is, when Tmax is around 1000 to 1500°C, the density ρ is 1.800 g / cm, which is suitable for a standard to medium modulus product. ３ When Tmax is around 1700 to 1900°C, the density ρ is 1.73 to 1.75 g / cm ３ The density tends to increase again at temperatures above this range.

[0081] In a production method suitable for producing the carbon fiber bundle of the second embodiment, Tmax is preferably 1,700° C. or higher. By setting Tmax to 1,700° C. or higher, more preferably 1,800° C. or higher, and even more preferably 1,850° C. or higher, a carbon fiber bundle having an excellent strand modulus as the second embodiment can be more effectively obtained.

[0082] In a production method suitable for producing the carbon fiber bundle of the third embodiment, Tmax is preferably 1,500° C. or less. By setting Tmax to 1,500° C. or less, carbon fibers in which single fiber breakage due to torsional deformation is unlikely to occur can be more effectively obtained as the third embodiment.

[0083] In the carbonization step, the maximum temperature rise rate β1 [°C / min] in the temperature rise process from 800°C to 1,000°C satisfies formula (6): -200 ≦ β1 - 0.1Tmax ≦ 0 (6) The left side of formula (6) is more preferably -180, and even more preferably -140. When β1 satisfies formula (6), it is possible to obtain a carbon fiber that has both high strand strength and strand modulus, and is less susceptible to breakage of single fibers due to torsional deformation.

[0084] The temperature rise rate in the present invention will be explained. When a fiber bundle passes through multiple compartments in a carbonization furnace that are controlled so that the temperature rises stepwise as it passes through the compartments, when the fiber bundle passes through a compartment at a certain temperature T1 and reaches a compartment at a higher temperature T2, the temperature difference represented by T2-T1 is divided by the time it takes the fiber bundle to pass through the compartment at temperature T1, and the average value is defined as the temperature rise rate in the temperature rise process from T1 to T2. Specifically, for example, if the fiber bundle enters a compartment at a temperature of 800°C in a carbonization furnace and takes one minute to pass through the next compartment at 1,000°C, the temperature rise rate in the temperature rise process from 800°C to 1,000°C is 200°C / min. Furthermore, when the temperature rise process from 800°C to 1,000°C spans multiple compartments, i.e., when the temperature rise from 800°C to 1,000°C occurs through multiple steps, the temperature rise rates between adjacent compartments are calculated as described above, and the largest of these is defined as the maximum temperature rise rate. Specifically, if there are three consecutive sections, with the first section set to 800°C, the second section set to 850°C, and the third section set to 1,000°C, and the fiber bundle passes between adjacent sections at a constant speed every minute, the temperature rise rate from the first section to the second section will be 50°C / min, the temperature rise rate from the second section to the third section will be 150°C / min, and the maximum temperature rise rate will be 150°C / min.

[0085] On the other hand, when a fiber bundle passes through a carbonization furnace controlled so that the temperature increases continuously, when the fiber bundle passes through a position in the carbonization furnace at a certain temperature T3 and reaches a position at a higher temperature T4, the temperature difference represented by T4-T3 is divided by the time it takes to pass from the position at temperature T3 to the position at temperature T4, and the average value is defined as the temperature difference from T3 to T4. Furthermore, if the temperature does not increase linearly, the temperature section from temperature T3 to temperature T4 is divided into 50°C intervals, and the temperature rise rate is calculated in the same manner as above, and the largest of these is defined as the maximum temperature rise rate. Specifically, when the temperature is continuously increased from 800°C to 1,000°C, if the heating rate from 800°C to 850°C is 50°C / min, the heating rate from 850°C to 900°C is 50°C / min, the heating rate from 900°C to 950°C is 50°C / min, and the heating rate from 950°C to 1,000°C is 150°C / min, the maximum heating rate will be 150°C / min.

[0086] Regarding the temperature of each compartment, when heating is performed using a heater, the temperature of the heater can be set as the temperature of the compartment.

[0087] In the carbonization step, the maximum temperature rise rate β1 in the temperature rise process from 800°C to 1,000°C is preferably 17°C / min or more and 100°C / min or less. By setting β1 to 100°C / min or less, more preferably 91°C / min or less, and even more preferably 85°C / min or less, a carbon fiber bundle that combines a high strand modulus and a property that single fibers are less likely to break due to torsional deformation can be more effectively obtained. On the other hand, by setting β1 to 17°C / min or more, excellent productivity is achieved.

[0088] In a production method suitable for producing the carbon fiber bundle of the second embodiment, β1 is preferably 70° C. / min or more and 100° C. / min or less. By setting β1 to 70° C. / min or more, the productivity in producing the carbon fiber bundle of the second embodiment is excellent.

[0089] In a production method suitable for producing the carbon fiber bundle of the third aspect, β1 is preferably 17° C. / min or more and 60° C. / min or less. By setting β1 to 60° C. / min or less, more preferably 42° C. / min or less, and even more preferably 33° C. / min or less, it is possible to more effectively obtain the carbon fiber bundle of the third aspect which satisfies both the strand modulus and the property of being less susceptible to breakage of single fibers due to torsional deformation.

[0090] In the carbonization step, the maximum temperature rise rate β2 [°C / min] in the temperature rise process from 1,000°C to the maximum temperature Tmax [°C] satisfies formula (7): -180 ≦ β2 - 0.1Tmax ≦ 0 (7) The left side of formula (7) is more preferably -160, and even more preferably -140. When β2 satisfies formula (7), it is possible to obtain a carbon fiber that has both high strand strength and strand modulus, and is less susceptible to single fiber breakage due to torsional deformation.

[0091] In the carbonization step, the maximum heating rate β2 during the heating process from 1,000°C to the maximum temperature Tmax is preferably 11°C / min or more and 150°C / min or less. By setting β2 to 150°C / min or less, more preferably 140°C / min or less, and even more preferably 135°C / min or less, it is possible to obtain carbon fibers that have both a high strand modulus and a property that makes single fibers less susceptible to breakage due to torsional deformation. On the other hand, by setting β2 to 11°C / min or more, excellent productivity is achieved.

[0092] In a production method suitable for producing the carbon fiber bundle of the second embodiment, β2 is preferably 60° C. / min or more and 150° C. / min or less. By setting β2 to 60° C. / min or more, excellent productivity is achieved in the production of the carbon fiber bundle of the second embodiment.

[0093] In a production method suitable for producing the carbon fiber bundle of the third aspect, β2 is preferably 11° C. / min or more and 60° C. / min or less. By setting β2 to 60° C. / min or less, more preferably 44° C. / min or less, and even more preferably 33° C. / min or less, it is possible to more effectively obtain the carbon fiber of the third aspect which has both a high strand modulus and a property that single fibers are less likely to break due to torsional deformation.

[0094] The temperature rise rate in the carbonization step can be controlled by adjusting the speed at which the fiber bundle is passed and the set temperature inside the carbonization furnace.

[0095] The holding time at the maximum temperature Tmax in the carbonization step is preferably 180 seconds or more and 400 seconds or less. By setting the holding time to 180 seconds or more, more preferably 200 seconds or more, and even more preferably 240 seconds or more, carbon fibers that have both a high strand modulus and high resistance to torsional deformation can be more effectively obtained. On the other hand, by setting the holding time to 400 seconds or less, more preferably 360 seconds or less, excellent productivity can be achieved.

[0096] (Oxidation Treatment Step) After the carbonization step, it is also preferable to carry out an oxidation treatment in order to improve adhesion to the matrix resin. By the oxidation treatment, oxygen-containing functional groups can be introduced into the carbon fiber bundle. As the oxidation treatment method, gas phase oxidation, liquid phase oxidation, and liquid phase electrolytic oxidation are used, but liquid phase electrolytic oxidation is preferably used from the viewpoint of high productivity and enabling uniform treatment. There is no particular specification for the method of liquid phase electrolytic oxidation, and it may be carried out by a known method.

[0097] (Sizing step) After the oxidation treatment step, it is also preferable to perform a sizing treatment to impart bundling properties to the obtained carbon fiber bundle. As the sizing agent used in the sizing step, a sizing agent having good compatibility with the matrix resin used in the composite material can be appropriately selected depending on the type of matrix resin used.

[0098] The present invention will be explained in more detail below with reference to examples, but the present invention should not be construed as being limited to these examples.

[0099] [Measurement Methods] (1) Tensile Test of Resin-Impregnated Strand of Carbon Fiber Bundle The tensile modulus of the resin-impregnated strand of the carbon fiber bundle (strand modulus E), the tensile strength of the resin-impregnated strand (strand strength), and the stress-strain curve were determined in accordance with JIS R7608 (2008) "Test Method for Resin-Impregnated Strands." The strand modulus was measured within a strain range of 0.1 to 0.6%. Test specimens were prepared by impregnating a carbon fiber bundle with the following resin composition and curing it under heat treatment conditions of 130°C for 35 minutes.

[0100] [Resin composition] 3,4-epoxycyclohexylmethyl-3,4-epoxy-cyclohexane-carboxylate (100 parts by mass) Boron trifluoride monoethylamine (3 parts by mass) Acetone (4 parts by mass).

[0101] Six strands were measured, and the arithmetic mean values ​​of the tensile modulus and tensile strength measurements were taken as the strand modulus E and strand strength of the carbon fiber.

[0102] (2) Analysis of stress-strain curves In analyzing the stress-strain curves obtained by the tensile test of resin-impregnated strands, strain ε [-] was plotted on the vertical axis and stress σ [GPa] on the horizontal axis, and coefficients A, B, and C were calculated by fitting with a quadratic function using the following formula (4). The fitting was performed for the stress-strain curve obtained by measurement in the stress range of 0 to 3 GPa. Microsoft's "Excel (registered trademark)" was used for the fitting. ε = Aσ ２ +Bσ+C (4).

[0103] (3) Crystallite size Lc and crystal orientation degree π ００２ The carbon fiber bundles to be measured were aligned and solidified using a collodion alcohol solution to prepare a measurement sample in the shape of a square pillar 4 cm long with a base having sides of 1 mm in both the vertical and horizontal directions. The diffraction pattern of the prepared measurement sample was measured using a wide-angle X-ray diffractometer (Shimadzu XRD-6100) under the following conditions: X-ray source: CuKα radiation (tube voltage 40 kV, tube current 30 mA); detector: goniometer + monochromator + scintillation counter; scanning range: 2θ = 10 to 40°; scanning mode: step scan, step unit 0.02°, counting time 2 seconds.

[0104] (Crystallite size Lc) In the obtained diffraction pattern, the apparent half-width was determined for the peak appearing around 2θ=25 to 26°, and the crystallite size Lc was calculated from this value using the following Scherrer equation: Crystallite size Lc [nm]=Kλ / β ０ cosθ ＢHowever, K: 1.0, λ: 0.15418 nm (wavelength of X-rays) β ０ :(β Ｅ ２ -β １ ２ ) １／２ β Ｅ : Apparent half-width (measured value) rad β １ : 1.046 x 10 －２ rad θ Ｂ : Bragg diffraction angle.

[0105] (Crystal orientation degree π ００２ In the obtained diffraction pattern, the crystal peak appearing around 2θ = 25 to 26° was calculated from the half-width of the intensity distribution obtained by scanning around the axis perpendicular to the fiber axis using the following formula: π ００２ = (180 - H) / 180 where H: apparent half width (deg).

[0106] The above measurement was carried out three times for the same measurement sample, and the arithmetic average was calculated as the crystallite size Lc and the degree of crystal orientation π of the carbon fiber. ００２ It was decided.

[0107] (4) Scatterer Length lf A measurement sample was prepared by fixing a single carbon fiber to be measured vertically to a paper frame with a hole cut out, 10 mm vertical and 5 mm horizontal, using a cyanoacrylate adhesive. The prepared measurement sample was measured using a microbeam X-ray from a synchrotron radiation facility (BL03XU beamline at SPring-8) under the following conditions: X-ray wavelength: 1.2 Å Beam size (vertical × horizontal): 1.0 μm × 1.0 μm Detector: PILATUS1M (Dectris) The center of the beam and the camera length were calculated for the obtained two-dimensional scattering image based on the scattering pattern of a standard substance (silver behenate). The scatterer length lf (nm) was calculated by calculating the half-width of the intensity in the azimuthal direction as B, with reference to the method of Ran (S. Ran et al., Polymer 42 (2001) 1601-1612). ｏｂｓ , the scattering vector is s (nm －１ ), the orientation angle of the scatterer is B φ was calculated from the following formula (a). ｏｂｓwas obtained by fitting the azimuthal intensity profile with a Gaussian function. The azimuthal intensity profile was obtained when the scattering vector was 0.0075 (nm －１ ) interval in the scattering vector direction. Furthermore, fitting by equation (a) was performed when the scattering vector s was 0.06 to 0.15 (nm －１ ) section. ｏｂｓ ２ = 1 / lf ２ ×1 / s ２ +B φ ２ ...(a).

[0108] (5) Mass composition ratio N / C The mass composition ratio N / C was calculated as the ratio of the nitrogen mass composition ratio N (mass%) and the carbon mass composition ratio C (mass%) of the carbon fiber bundle calculated by elemental analysis using an elemental analyzer (Vario EL Cube manufactured by Elementor). The measurement was carried out after drying the carbon fiber bundle at 120°C for 2 hours.

[0109] (6) Density of Carbon Fiber Bundle The density of the carbon fiber bundle was measured by Archimedes' method using a 1 m long carbon fiber bundle with o-dichlorobenzene as a specific gravity liquid. The measurement was carried out in a constant temperature environment of 25°C.

[0110] (7) Torsional Deformation Resistance The resistance to fracture of a carbon fiber bundle against torsional deformation was evaluated using a single fiber. A single fiber of 30 mm length with one end fixed was prepared, and the end that was not fixed was twisted by hand. Twisting was continued, and the number of twists at which the single fiber broke was measured. The number of twists was counted as one per 360° of twist angle. The number of twists at fracture corresponds to the fracture strain due to shear of the single fiber.

[0111] In Examples 1 to 17 and Comparative Examples 1 to 12 compared with these, which have a strand modulus E of 330 GPa or more, when the number of twists at break was 50 or more, the sample was judged to have particularly excellent resistance to breakage due to torsional deformation (torsional deformation resistance) (A); when the number of twists at break was less than 50 but 45 or more, the sample was judged to have excellent resistance to torsional deformation (B); and when the number of twists was less than 45, the sample was judged to have poor resistance to torsional deformation (C).

[0112] In Examples 18 to 29, which had a strand modulus E of less than 330 GPa, and Comparative Example 13 compared with these, when the number of twists at break was 52 or more, the sample was judged to have particularly excellent resistance to breakage due to torsional deformation (torsional deformation resistance) (A); when the number of twists was less than 52 but 50 or more, the sample was judged to have excellent resistance to torsional deformation (B); and when the number of twists was less than 50, the sample was judged to have poor resistance to torsional deformation (C).

[0113] (8) 2 mg of the flame-resistant fiber to be used for measuring the intensity ratio of the infrared spectrum was precisely weighed out after freeze-pulverization, thoroughly mixed with 300 mg of potassium bromide, placed in a molding jig, and pressed at 40 MPa for 2 minutes using a press to prepare a tablet for measurement. This tablet was set in a Fourier transform infrared spectrophotometer (Paragon 1000 manufactured by PerkinElmer) and measured at 1000 to 2000 cm －１ The absorbance was measured in the range of 1700 to 2000 cm to obtain a spectrum. －１ The actual measured value of the minimum absorbance of the spectrum in the range was subtracted from the spectrum so that the minimum value became zero.

[0114] Examples 1 to 28 (Production of PAN-Based Precursor Fiber Bundle) 99.0 parts by mass of acrylonitrile and 1.0 part by mass of itaconic acid were polymerized by solution polymerization using dimethyl sulfoxide as a solvent to produce a PAN-based copolymer, resulting in a spinning dope. The resulting spinning dope was discharged from a spinning nozzle in the air and introduced into a coagulation bath containing an aqueous dimethyl sulfoxide solution to coagulate a fiber bundle using a dry-wet spinning method. The fiber bundle was washed with water at 30 to 98°C by a conventional method, during which it was stretched 3.5 times. Subsequently, an amino-modified silicone oil was applied to the fiber bundle after water bath stretching, and it was subjected to a drying and densification treatment using a heated roller at 160°C by a conventional method. After reducing the number of single fibers to 12,000, it was stretched 3.7 times in pressurized steam to a total spinning draw ratio of 13 times, and then entangled to obtain a PAN-based precursor fiber bundle with a single fiber fineness of 0.7 dtex.

[0115] (Flame-resistant step) The obtained polyacrylonitrile precursor fiber bundle was subjected to a flame-resistant step using two flame-resistant furnaces, and treated in accordance with Example 1 of Patent Document 2 (WO 2016 / 068034), to obtain a flame-resistant fiber bundle.

[0116] (First flame-proofing step) The polyacrylonitrile precursor fiber bundle was passed through a first furnace at 250°C for 11 minutes. －１ The peak intensity at 1453 cm －１ The peak intensity ratio is 1.04, and the density is 1.21 g / cm ３ It was.

[0117] (Second flame-retardant process) The fiber bundle after the first flame-retardant process was passed through a second furnace at 285°C for 6 minutes to obtain a flame-retardant fiber bundle. －１ The peak intensity at 1453 cm －１ The ratio of the peak intensities is 0.72, 1370 cm －１ The peak intensity at 1254 cm －１ The peak intensity ratio is 0.62, and the density is 1.30 g / cm ３ It was.

[0118] (Pre-carbonization Step) The obtained flame-resistant fiber bundle was passed through a pre-carbonization step in an inert atmosphere at a maximum temperature of 800° C. to obtain a pre-carbonized fiber bundle.

[0119] (Carbonization step) In the carbonization step, the obtained pre-carbonized fiber bundle was divided into a plurality of temperature sections and heated stepwise, and carbonization was performed by heat treatment in an inert atmosphere under the conditions shown in Tables 1 and 3 for the maximum temperature rise rate β1 from 800°C to 1000°C, the maximum temperature rise rate β2 from 1000°C to the maximum temperature Tmax, and the maximum temperature Tmax in the carbonization step, to obtain a carbon fiber bundle. The properties of the obtained carbon fiber bundle are shown in Tables 4, 6, 7, and 9.

[0120] [Example 29] A carbon fiber bundle was obtained by carrying out a carbonization step in an inert atmosphere under the conditions shown in Table 3 in the same manner as in Example 1, except that in the production of a PAN-based precursor fiber bundle, the single fiber fineness of the polyacrylonitrile-based precursor fiber bundle was changed to 0.9 dtex. The properties of the obtained carbon fiber bundle are shown in Tables 6 and 9.

[0121] Comparative Examples 1 to 12 Carbon fiber bundles were obtained in the same manner as in Example 1, except that the conditions in the carbonization step were as shown in Table 2. The properties of the obtained carbon fiber bundles are shown in Tables 5 and 8.

[0122] Comparative Example 13 A carbon fiber bundle was obtained in the same manner as in Example 1, except that the conditions in the carbonization step were as shown in Table 3. The properties of the obtained carbon fiber bundle are shown in Tables 6 and 9.

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

Claims

1. A carbon fiber bundle consisting of a plurality of carbon fibers, wherein the strand elastic modulus E is 280 GPa or more and 400 GPa or less, the crystallite size Lc of the carbon fibers is 1.80 nm or more and 2.60 nm or less, and the density ρ of the carbon fibers is 1.780 g / cm ３ 1.830g / cm or more ３ and the density ρ [g / cm ３ ], crystallite size Lc [nm], and strand modulus E [GPa] satisfy the relationships of the following formulas (1) and (2): 1.860≦ρ+0.0333Lc≦1.895 (1) 6.67×10 －５ × (E-207) ２ +1.60≧Lc (2) 2. The carbon fiber bundle according to claim 1, having a strand strength of 6.5 GPa or more and 8.5 GPa or less.

3. The carbon fiber bundle according to claim 1, wherein the mass composition ratio N / C of nitrogen to carbon in the carbon fibers is 0.0008 or more and 0.050 or less.

4. The carbon fiber bundle according to claim 1, wherein the mass composition ratio N / C [-] of nitrogen to carbon and the crystallite size Lc [nm] in the carbon fiber satisfy the relationship of the following formula (3): 12×e-D(Lc-1.67)+F≧N / C (3), where D=1.00 and F=0.

015.

5. The carbon fiber bundle according to claim 1, wherein the coefficient A calculated from the approximate formula (4) for the nonlinearity of the stress σ-strain ε curve in a resin-impregnated strand tensile test is −0.000170 or more and −0.000050 or less, where ε=Aσ ２ +Bσ+C (4) Here, A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [−].

6. The carbon fiber bundle according to claim 1, wherein the density ρ and the coefficient A calculated from the approximate formula (4) for the nonlinearity of the stress σ-strain ε curve in a resin-impregnated strand tensile test satisfy the relationship of formula (5): ε = Aσ ２ + Bσ + C ... (4) where A, B, and C are coefficients of the quadratic function of stress σ [GPa] and strain ε [-]. 0.00621 ≦ 0.00357ρ + A ≦ 0.00645 ... (5) 7. A carbon fiber bundle consisting of a plurality of carbon fibers, wherein the strand elastic modulus E is 330 GPa or more and 400 GPa or less, the crystallite size Lc of the carbon fibers is 2.40 nm or more and 2.60 nm or less, and the degree of crystal orientation π of the carbon fibers is ００２ is 85% or more and 88% or less, and the density ρ of the carbon fiber is 1.780 g / cm ３ 1.800g / cm or more ３ and further, a coefficient A calculated from an approximate formula (4) for the nonlinearity of a stress σ-strain ε curve in a resin-impregnated strand tensile test is −0.000140 or more and −0.000050 or less. ２ +Bσ+C (4) Here, A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [−].

8. The carbon fiber bundle according to claim 7, wherein the mass composition ratio N / C of nitrogen to carbon in the carbon fibers is 0.0008 or more and 0.0150 or less.

9. A carbon fiber bundle consisting of a plurality of carbon fibers, wherein the strand elastic modulus E is 280 GPa or more and 340 GPa or less, the mass composition ratio N / C of nitrogen to carbon in the carbon fibers is 0.020 or more and 0.050 or less, the crystallite size Lc of the carbon fibers is 1.80 nm or more and 1.95 nm or less, and the density ρ of the carbon fibers is 1.805 g / cm ３ 1.830g / cm or more ３ and further, a coefficient A calculated from an approximate formula (4) for nonlinearity of a stress σ-strain ε curve in a resin-impregnated strand tensile test is −0.000170 or more and −0.000090 or less. ２ +Bσ+C (4) Here, A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [−].

10. The carbon fiber bundle according to claim 9, wherein the strand modulus E is 280 GPa or more and 315 GPa or less, the mass composition ratio N / C of nitrogen to carbon in the carbon fiber is 0.025 or more and 0.045 or less, and further, the coefficient A calculated from the approximate formula (4) for the nonlinearity of the stress σ-strain ε curve in a resin-impregnated strand tensile test is -0.000170 or more and -0.000145 or less, where ε=Aσ ２ +Bσ+C (4) Here, A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [−].

11. The carbon fiber bundle according to claim 9, wherein the carbon fiber has a scatterer length of 14.0 nm or more and 19.2 nm or less as measured by small-angle X-ray scattering.

12. The carbon fiber bundle according to claim 9, wherein the coefficient A calculated from the approximate formula (4) for the nonlinearity of the stress σ-strain ε curve in a resin-impregnated strand tensile test is −0.000166 or more and −0.000095 or less, where ε=Aσ ２ +Bσ+C (4) Here, A, B, and C are coefficients of a quadratic function of stress σ [GPa] and strain ε [−].

13. The density of the carbon fiber is 1.806 g / cm ３ 1.818g / cm or more ３ The carbon fiber bundle according to claim 9, wherein:

14. The carbon fiber bundle according to claim 9, wherein the single fiber fineness of the carbon fiber is 0.41 dtex or more and 0.50 dtex or less.

15. Polyacrylonitrile precursor fiber bundles were analyzed by measuring the peak at 1370 cm in the infrared spectrum. －１ 1453 cm for the peak intensity －１ a first flame-stabilizing step of flame-stabilizing the fiber bundle obtained in the first flame-stabilizing step for 8 to 25 minutes until the ratio of the peak intensities of the －１ 1453 cm for the peak intensity －１ The ratio of the peak intensities of the two compounds is in the range of 0.70 to 0.75, and the peak intensity of the two compounds is 1370 cm in the infrared spectrum. －１ The peak intensity at 1254 cm －１ a second flame-proofing step of flame-proofing the fiber bundle obtained in the second flame-proofing step for 5 to 14 minutes until the ratio of the peak intensities of the fiber bundles to the peak intensities of the fiber bundles falls within a range of 0.50 to 0.65; a pre-carbonization step of heat-treating the flame-proofed fiber bundle obtained in the second flame-proofing step in an inert atmosphere at a maximum temperature of 300°C or more and 800°C or less; and a carbonization step of heat-treating the pre-carbonized fiber bundle obtained in the pre-carbonization step at a maximum temperature Tmax of 1,200°C or more and 2,000°C or less, wherein a maximum temperature rise rate β1 [°C / min] in the temperature rise process from 800°C to 1,000°C and a maximum temperature rise rate β2 [°C / min] in the temperature rise process from 1,000°C to the maximum temperature Tmax [°C] in the carbonization step satisfy the relationships of the following formulas (6) and (7). -200 ≦ β1 - 0.1Tmax ≦ 0 ... (6) -180 ≦ β2 - 0.1Tmax ≦ 0 ... (7) 16. A method for producing a carbon fiber bundle according to claim 15, wherein in the carbonization step, the maximum temperature Tmax is set to 1,700 to 2,000°C, the maximum rate of temperature rise β1 at a temperature of 800 to 1,000°C is 100°C / min or less, and the maximum rate of temperature rise β2 at a temperature from 1,000°C to the maximum temperature Tmax is 150°C / min or less.

17. A method for producing a carbon fiber bundle according to claim 15, wherein in the carbonization step, the maximum temperature Tmax is set to 1,200 to 1,500°C, the maximum rate of temperature rise β1 at a temperature of 800 to 1,000°C is 60°C / min or less, and the maximum rate of temperature rise β2 at a temperature from 1,000°C to the maximum temperature Tmax is 60°C / min or less.

18. A prepreg comprising the carbon fiber bundles according to any one of claims 1 to 14 and a matrix resin.

19. A carbon fiber reinforced composite material comprising the carbon fiber bundles according to any one of claims 1 to 14 and a matrix resin.

Images