1 DESCRIPTION STEEL FOR CARBUNZING CARBURIZED STEEL COMPONENT, AND METHOD OF PRODUCING THE SAME Technical Field [OOO 11 The present invention relates to a steel for carburizing, a carburized steel 10 component, and a method of producing the same, which have small deformation resistance and large critical working ratio at a cold forging, and which have, after a carburizing heat treatment, a hardened layer and hardness of steel portion which are equivalent to a conventional steel. Priority is claimed on Japanese Patent Application No. 201 1-027278, filed 15 February 10,201 1, the content of which is incorporated herein by reference. Background Art [0002] In general, Mn, Cr, Mo, Ni, and the like are added in combination to a steel used 20 for mechanical and structural components. A steel for carburizing which has the chemical composition and is produced by casting, forging, rolling, and the like is subjected to shaping such as forging and machining which is cutting and the like and subjected to heat treatments such as carburizing and the like, and then the steel for carburizing becomes a carburized steel component with a carburized layer which is a 25 hardened layer in a surface layer and a steel portion which is a base metal that is not 6 2 influenced by the carburizing treatment. [0003] In producing cost of the carburized steel component, cost for the cutting is particularly high. The cutting is disadvantageous to a yield, because tools for the 5 cutting are not only expensive, but also the cutting forms a large amount of chips. Thus, replacing the cutting with the forging is attempted. The forging method is divided roughly into a hot forging, a warm forging, and a cold forging. The warm forging has a feature in which scale formation is not much and dimensional accuracy is improved as compared with the hot forging. The cold forging has a feature in which the scale 10 formation is little and the dimensional accuracy is close to the cutting. Thus, it is tried that the cold forging is performed as a finishing after the hot forging is performed as a rough shaping, that the cutting is slightly performed as the finishing after the warm forging is performed, or that the cold forging is only performed for the shaping. However, since mold life decreases with increase in contact pressure to the mold in a 15 case that deformation resistance of the steel for carburizing is large when replacing the cutting with the warm forging or the cold forging, advantage of the cost against the cutting becomes small. Or problems such that cracks are initiated and propagated at an area where large deformation is applied and the like occur when forming into complex shape. For the reason, various techniques have been investigated in order to soften the 20 steel for carburizing and to improve critical working ratio. [0004] For example, Patent Documents 1 and 2 suggest the steel for carburizing which is softened by decreasing Si and Mn content in order to improve cold forgeability. The steels for carburizing have sufficient hardness of steel portion and effective case depth 25 (depth where Vickers hardness is HV550 or more) after the carburizing and have * 5 properties satisfied as the carburized steel component. However, it is insufficient to decrease drastically the deformation resistance at the forging. In contrast, Patent Document 3 suggests the steel for carburizing in which the deformation resistance at the hot forging, the warm forging, and the cold forging is drastically decreased by decreasing 5 considerably C content to 0.001% to 0.07% or less as compared with the conventional steel for carburizing and in which effective hardened layer after the carburizing that is reduced due to the decrease in C content is improved by controlling the amount of additive elements except C. However, the hardness of the steel for carburizing decreases by excessively low C content as the steel, and the hardness of steel portion of 10 the carburized steel component which is not influenced by the carburizing is insufficient. Therefore, a problem such that versatility has restriction occurs. Patent Document 4 suggests the steel for carburizing which is excellent in ductility and is able to be utilized for the cold forging with large working ratio by improving metallographic structure of the surface layer of the steel for carburizing whose shape is a bar and wire rod by 15 spheroidizing annealing. The critical working ratio of the steel for carburizing is improved, and the cracks which are initiated and propagated at the cold forging can be prevented. Moreover, the steel for carburizing has satisfiable properties as the carburized steel component in regard to the hardness of steel portion and the effective case depth after the carburizing. However, the steel for carburizing is ineffective in 20 decreasing in the deformation resistance at the forging, and an improvement such as a decrease in forging load, a prolongation of the mold life, and the like should be performed. [0005] As mentioned above, it is fact that the technique satisfling all properties such as 25 the drastic decrease in the deformation resistance at the forging, the improvement of the r) 4 critical working ratio, the securement of the properties as the carburized steel component, and especially the securement of the effective case depth and the hardness of steel portion is not found. 5 Related Art Document Patent Documents [0006] [Patent Document 11 Japanese Unexamined Patent Application, First Publication No. H11-335777 10 [Patent Document 21 Japanese Unexamined Patent Application, First Publication No. 200 1 - 303 172 [Patent Document 31 Japanese Unexamined Patent Application, First Publication No. 2009-1 08398 [Patent Document 41 Japanese Unexamined Patent Application, First 15 Publication No. 200 1-24094 1 Summary of Invention Technical Problem [0007] 20 In view of the above-mentioned problems, an object of an aspect of the invention is to provide a steel for carburizing, a carburized steel component, and a method of producing the same, which have, in the state of the steel for carburizing, small deformation resistance and large critical working ratio at a cold forging as compared with the conventional steel for carburizing, and which have, after a carburizing heat treatment, 25 a hardened layer and hardness of steel portion which are equivalent to a conventional steel. 5 [OOOS] Hereafter, "forging" only indicates "cold forging." unless otherwise mentioned. Solution to Problem 5 [0009] In order to solve the problems, the inventor has investigated and then found the following results. In order to decrease the hardness of the steel for carburizing and to improve the critical working ratio, C content needs to be decreased as much as possible. On the other hand, in order to obtain the hardness of steel portion required at least as the 10 carburized steel component, C content has a lower limit and needs to be controlled in the target range. In order to satisfl both securing hardenability to obtain the hardness of steel portion required as the carburized steel component and aiming at the decrease in the hardness as the steel for carburizing on condition that C content in chemical composition is less than that of the conventional steel, it is necessary to utilize an improvement effect 15 of the hardenability obtained by B addition and to be the chemical composition in which a hardenability parameter and a hardness parameter which are derived by the inventor are simultaneously satisfied. In addition, in order to stably obtain the improvement effect of the hardenability by B addition, and further in order to prevent the grain coarsening at the carburizing, a Tic precipitation parameter which is derived by the inventor needs to 20 be satisfied. [OO lo] An aspect of the present invention employs the following. [OOll] (1) A steel for a carburizing according to an aspect of the invention includes as 25 a chemical composition, by mass %, Si: 0.0001% to 0.50%, Mn: 0.0001% to 0.80%, S: 0.0001% to 0.100%, Cr: more than 1.30% to 5.00%, B: 0.0005% to 0.0100%, Al: 0.000 1 % to 1.0%, Ti: 0.010% to 0.10%, N: limited to 0.0080% or less, P: limited to 0.050% or less, 0: limited to 0.0030% or less, and a balance consisting of iron and unavoidable impurities, wherein amounts expressed in mass% of each element in the chemical composition satisfy simultaneously a following Equation 1 as a hardness parameter, a 15 following Equation 2 as a hardenability parameter, and a following Equation 3 as a Tic precipitation parameter. 0.10 < C + 0.194 x Si + 0.065 x Mn + 0.012 x Cr + 0.078 x A1 < 0.235 ...( Equation 1) 7.5 <(0.7 x Si+ 1) x (5.1 x Mn+ 1) x (2.16 x Cr+ 1)<44 ...( Equation2) 0.004 < Ti - N x (48 1 14) < 0.030 ...( Equation 3) (2) The steel for the carburizing according to (1) may further includes as the chemical composition, by mass %, at least one of Nb: 0.002% to 0.100%, V. 0.002% to 0.20%, Mo: 0.005% to 0.50%, Ni: 0.005% to 1.00%, Cu: 0.005% to 0.50%, Ca: 0.0002% to 0.0030%, Mg: 0.0002% to 0.0030%, Te: 0.0002% to 0.0030%, Zr: 0.0002% to 25 0.0050%, Rare Earth Metal: 0.0002% to 0.0050%, and Sb: 0.002% to 0.050%, wherein * 7 the hardness parameter is defined as a following Equation 4 on behalf of the Equation 1 and the hardenability parameter is defined as a following Equation 5 on behalf of the Equation 2. 0.10 < C + 0.194 x Si + 0.065 x Mn + 0.012 x Cr + 0.033 x Mo + 0.067 x Ni + 5 0.097 x Cu + 0.078 x A1 < 0.235 ...( Equation 4) 7.5 < (0.7 x Si + 1) x (5.1 x Mn + 1) x (2.16 x Cr + 1) x (3 x Mo + 1) x (0.3633 x Ni + 1) < 44 ...( Equation 5) (3) In the steel for the carburizing according to (I) or (2), a metallographic structure may include, by area%, a ferrite and a pearlite of 85% to 100% in total. 10 (4) In the steel for the carburizing according to (3), the metallographic structure may include, by area%, the ferrite and spheroidal cementites of 85% to 100% in total. (5) In the steel for the carburizing according to (1) or (2), a shape may be a bar or a wire rod in which a cross section perpendicular to a longitudinal direction is round, 15 and when a distance from a periphery to a center of the cross section is defined as r in unit of rnm, in a metallographic structure of a surface layer which is a portion fiom the periphery to r x 0.01, a ferrite and a pearlite may be limited, by area%, to 10% or less in total, and a balance may include at least one of martensite, bainite, tempered martensite, tempered bainite, and cementites. 20 (6) In the steel for the carburizing according to (5), in the cementites included in the metallographic structure of the surface layer, the cementites of 90% to 100% may be cementites whose aspect ratio is 3 or less. (7) A method of producing the steel for the carburizing according to any one of (1) to (3) may include: a casting process to obtain a bloom; a hot working process of 25 hot-working the bloom to obtain a hot worked steel material; and a slow cooling process 8 slow-cooling by a cooling rate of more than 0 "CIS to 1 "CIS in a temperature range where a surface temperature of the hot worked steel material is 800°C to 500°C after the hot working process. (8) The method of producing the steel for the carburizing according to any one 5 of (1) to (4) and (7) may further include a spheroidizing annealing process of spheroidizing-annealing the hot-worked steel material after the slow cooling process. (9) The method of producing the steel for the carburizing according to any one of (I), (2), and (5) may include: a casting process to obtain a bloom; a hot controlled rolling process of hot-rolling the bloom by controlling conditions so that a surface 10 temperature at an exit side of a final finish rolling becomes 700°C to 1000°C to obtain a hot-controlled-rolled steel material; a rapid cooling process of rapid-cooling so that the surface temperature of the hot-controlled-rolled steel material is more than 0°C to 500°C after the hot controlled rolling process; and a self-reheating process of self-reheating the hot-controlled-rolled steel material after the rapid cooling process at least one time or 15 more. (10) The method of producing the steel for the carburizing according to any one of (1), (2), (5), (6), and (9) may further include a spheroidizing annealing process of spheroidizing-annealing the hot-controlled-rolled steel material after the self-reheating process. 20 (1 1) . A carburized steel component according to an aspect of the invention includes a steel portion and a carburized layer with a thickness of more than 0.4 mm to less than 2 mm which is formed on an outside of the steel portion: wherein, in the carburized layer, a Vickers hardness at a position of 50 pm in depth from a surface is HV 650 to HV 1000, a Vickers hardness at a position of 0.4 mm in depth from the surface is 25 HV 550 to HV 900, and a metallographic structure at the position of 0.4 mm in depth * from 9 the surface includes by area% martensite of 90% to 100%; and wherein, in the steel portion at a position of 2 rnm in depth from the surface, a chemical composition consists of the chemical composition according to (1) or (2), and a Vickers hardness is HV 250 to HV 500. 5 (12) A method of producing the carburized steel component according to (1 1) may include: a cold working process of cold-working the steel for the carburizing to give a shape; a carburizing process of carburizing or carbonitriding the steel for the carburizing after the cold working process; and a finish heat treatment process of quenching or quenching and tempering after the carburizing process. (1 3) The method of producing the carburized steel component according to (1 1) or (12) may further include, a cutting process of cutting to give a shape after cold working process and before the carburizing process. Advantageous Effects of Invention [OO 1 21 According to the above aspects of the present invention in regard to the steel for the carburizing, the carburized steel component, and the method of producing the same, it is possible to provide a steel for carburizing, a carburized steel component, and a method of producing the same, which have, in the state of the steel for carburizing, small 20 deformation resistance and large critical working ratio at a cold forging as compared with the conventional steel for carburizing, and which have, after a carburizing heat treatment, a hardened layer and hardness of steel portion which are equivalent to a conventional steel. As a result, the carburized steel component, which has a shape of a gear and the like and which is conventionally produced by processes such as a hot forging, a 25 normalizing, a cutting, a carburizing and the like, can be produced by processes of a cold forging 10 and the carburizing. Thereby, it is possible to reduce the cost for the cutting, to improve the yield, and to produce the carburized steel component by the cold forging with a shape which cannot be conventionally produced by the cutting. Moreover, for the carburized steel component which is conventionally produced by the processes of the 5 cold forging and the carburizing also, forgeability is greatly improved. Thereby, it is possible to improve mold life and to form the carburized steel component into more complex shapes. Description of Embodiments [00 1 31 Hereinafter, a preferable embodiment of the present invention will be described in detail. [00 1 41 Through thorough research in order to obtain simultaneously both properties of 15 a steel for carburizing before a forging, such as a decrease in deformation resistance (decrease in hardness) and an improvement of critical working ratio, and properties of a carburized steel component after a carburizing heat treatment (such as an improvement of effective case depth and hardness of steel portion), the inventor has acquired the following knowledge (a) to (g). [00 1 51 (a) The steel for carburizing before the forging can be softened with a decrease in C content. However, in chemical composition with ultra low C content, it is impossible to bring the properties of the carburized steel component after the carburizing heat treatment (for example, the effective case depth and the hardness of the steel 25 portion) close to that of conventional steel for carburizing with C content of d approximately 11 0.20% (for example, JIS-SCR420). In order to obtain the hardness of the steel portion required at least as the carburized steel component, a lower limit of C content exists. [00 161 5 (b) In order to obtain the effective case depth and the hardness of the steel portion as much as possible with C content as low as possible, it is necessary to increase the fraction of martensite in metallographic structure at the steel portion of the carburized steel component. [00 1 71 10 (c) In order to increase the fraction of the martensite in the metallographic structure at the steel portion of the carburized steel component, it is necessary to increase amount of alloying elements such as Mn, Cr, Mo, Ni, and the like which improve hardenability of the steel so as to satisfy an equation of a hardenability parameter as described below. 15 [00 1 81 (d) On the other hand, the increase in the amount of the alloying elements leads to adverse effect such that the hardness of the steel for carburizing increases by effect of solute strengthening of ferrite derived from the alloying elements. Thus, it is necessary to utilize addition effect of B which improves the hardenability by ultra low 20 addition but hardly increases the hardness of the ferrite and necessary to control the amount of C and the alloying elements so as to satisfl an equation of a hardness parameter which is derived by the inventor as described below. [00 191 (e) In order to obtain stably the improvement effect of the hardenability of B, 25 it is necessary to prevent B from precipitating as BN and to dissolve B in the steel as * 12 solid-solution by fixing most of N contained in the steel as TiN during the carburizing heat treatment. Thus it is necessary to add stoichiometrically excessive Ti as compared with N content. Moreover, in order to prevent abnormal grain growth of austenite grain during the carburizing heat treatment, it is necessary to precipitate dispersedly Tic in the 5 metallographic structure as much and fine as possible. As described above, in order to secure the solid-soluted B and to precipitate dispersedly Tic voluminously and finely, it is necessary to control the amount of Ti and N so as to satisfy an equation of a Tic precipitation parameter which is derived by the inventor as described below. [0020] 10 (f) B addition is very effective in improving the hardenability of the steel portion of the carburized steel component as above-mentioned. However, when gas carburizing is conducted by converted gas method, it is not expected to obtain the improvement effect of the hardenability by B addition in a carburized layer which is a surface layer of the carburized steel component. The reasons are that N penetrates from 15 atmosphere into the surface layer of the carburized steel component during the carburizing treatment, the solid-soluted B precipitates as BN, and the amount of the solid-soluted B which contributes to the improvement of the hardenability becomes insufficient. Thus, in order to secure the hardenability in the carburized layer which is the surface layer of the carburized steel component, it is necessary to satisfy the equation 20 of the hardenability parameter as described above (c). [002 11 (g) In order to soften further the steel for carburizing, it is preferable to perform slow cooling on conditions as described below after hot rolling or hot forging at producing the steel for carburizing. Thereby it is possible to control the metallographic 25 structure of the steel for carburizing and to soften further the steel for carburizing. 4 Otherwise, 13 rapid cooling may be performed on conditions as described below after the hot rolling at producing the steel for carburizing, and then spheroidizing annealing may be performed. Thereby it is possible to enhance ductility by improving the metallographic structure of the surface layer of the steel for carburizing and to obtain the 5 steel for carburizing with large critical working ratio. [0022] Hereinafter, limitation range and reasons for the limitation of base elements of the steel for carburizing and the steel portion of the carburized steel component according to the embodiment will be described. In addition, % as described below is mass%. 10 [0023] C: 0.07% to 0.13% C (Carbon) is added to secure the hardness of the steel portion in the carburized steel component which includes the carburized layer and the steel portion. As described above, C content of the conventional steel for carburizing is approximately 0.2%. In the 15 steel for carburizing and the steel portion of the carburized steel component according to the embodiment, C content is limited to 0.13% or less which is less than the conventional value. The reasons are that, when C content is more than 0.13%, the fraction of cementites and pearlite in the metallographic structure of the steel for carburizing increases, the hardness of the steel for carburizing before the forging increases notably, 20 and the critical working ratio also decreases. On the other hand, when C content is less than 0.07%, it is impossible to bring the hardness of the steel portion of the carburized steel component to that of the conventional steel for carburizing even if the hardness is increased as much as possible by adding a large amount of the alloying elements as described below which improve the hardenability. Therefore, C content needs to be 25 controlled to the range of 0.07% to 0.13%. Preferable range is 0.08% to 0.12%. More e 14 preferable range is 0.08% to 0.1 1%. COO241 Si: 0.0001% to 0.50% Si (Silicon) is an element which improves tooth surface fatigue strength by 5 increasing considerably resistance to temper softening of low-temperature-tempered martensite steel such as the carburized steel component. To obtain the effect, Si content needs to be 0.0001% or more. On the other hand, when Si content is more than 0.50%, the hardness of the steel for carburizing before the forging increases, the deformation resistance increases, and the critical working ratio decreases. Therefore, Si content 10 needs to be controlled to the range of 0.0001% to 0.50%. Within the range, Si is added intentionally in case that the tooth surface fatigue strength of the carburized steel component is regarded as important, and Si is decreased intentionally in case that a decrease in the deformation resistance and an improvement of the critical working ratio are regarded as important. In the former case, preferable range is 0.10% to 0.50%. In 15 the latter case, preferable range is 0.0001% to 0.20%. [0025] Mn: 0.0001% to 0.80% Mn (Manganese) is an element which enhances the hardenability of the steel. In order to increase the fraction of the martensite after the carburizing heat treatment by 20 the effect, Mn content needs to be 0.0001% or more. On the other hand, when Mn content is more than 0.80%, the hardness of the steel for carburizing before the forging increases, the deformation resistance increases, and the critical working ratio decreases. Therefore, Mn content needs to be controlled to the range of 0.0001% to 0.80%. Preferable range is 0.25% to 0.60%. 2 5 [0026] S (Sulk) is an element which forms MnS by bonding to Mn and improves machinability. To obtain the effect, S content needs to be 0.0001% or more. On the other hand, when S content is more than 0.100%, cracks may be initiated at MnS as 5 fracture origin during the forging, and the critical working ratio may decrease. Therefore, S content needs to be controlled to the range of 0.000 1 % to 0.100%. Preferable range is 0.003% to 0.020%. [0027] Cr: more than 1.30% to 5.00% 10 Cr (Chromium) is an element which enhances the hardenability of the steel. In order to increase the fraction of the martensite after the carburizing heat treatment by the effect, Cr content needs to be more than 1.30%. On the other hand, when Cr content is more than 5.00%, the hardness of the steel for carburizing before the forging increases, the deformation resistance increases, and the critical working ratio decreases. Therefore, 15 Cr content needs to be controlled to the range of more than 1.30% to 5.00%. Moreover, Cr has little influence which increases the hardness of the steel for carburizing as compared with other elements such as Mn, Mo, and Ni which have the same effect, and Cr is relatively effective in improving the hardenability. Therefore, in the steel for carburizing and the steel portion of the carburized steel component according to the 20 embodiment, the large amount of Cr is added as compared with the conventional steel for carburizing. Preferable range is 1.35% to 2.50%. More preferable range is more than 1.50% to 2.20%. [0028] B: 0.0005% to 0.0100% 25 B (Boron) is an element which enhances the hardenability of the steel by low * addition 16 in case of solid-soluting in the austenite. The fraction of the martensite after the carburizing heat treatment can increase by the effect. Moreover, since it is not necessary to add a large amount of B to obtain the effect, the hardness of the ferrite hardly increases. Namely, since there is the feature in which the hardness of the steel 5 for carburizing before the forging hardly increases, B is intentionally utilized in the steel for carburizing and the steel portion of the carburized steel component according to the embodiment. When B content is leis than 0.0005%, the improvement effect of the hardenability is not obtained. On the other hand, when B content is more than 0.0100%, the effect is saturated. Therefore, B content needs to be controlled to the range of 10 0.0005% to 0.0100%. Preferable range is 0.0010% to 0.0025%. In addition, when N of a certain amount or more exists in the steel, B forms BN by bonding to N, and the amount of the solid-soluted B decreases. As a result, the effect of improving the hardenability may not be obtained. Thus, in case of adding B, it is necessary to add simultaneously a suitable amount of Ti for fixing N. 15 [0029] Al: 0.0001 % to 1 .O% A1 (Aluminum) is an element which forms A1N in case that solid-soluted N exists in the steel. However, since N in the steel is fixed as TiN by Ti addition in the steel for carburizing and the steel portion of the carburized steel component according to 20 the embodiment, the solid-soluted N hardly exists in the steel. Thereby, A1 does not form AlN and exists as solid-soluted A1 in the steel. The solid-soluted A1 is effective in improving the machinability. In case that finish cutting and the like is conducted at producing the carburized steel component, it is preferable that A1 content is 0.0001% or more. On the other hand, when A1 content is more than 1 .ON, the hardness of the steel 25 for carburizing before the forging increases, the deformation resistance increases, and the critical working ratio decreases. Therefore, A1 content needs to be controlled to the range of 0.0001% to 1.0%. Preferable range is 0.010% to 0.20%. [0030] Ti: 0.010% to 0.10% 5 Ti (Titanium) is an element which has the effect of fixing N in the steel as TiN. By Ti addition, the formation of BN is prevented, and the solid-soluted B which contributes to the hardenability is secured. Moreover, stoichiometrically excessive Ti as compared with N content forms Tic. Tic has pinning effect of preventing grains from coarsening during the carburizing. When Ti content is less than 0.01 0%, the 10 improvement effect of the hardenability by B addition is not obtained, and the grain coarsening cannot be prevented during the carburizing. On the other hand, when Ti content is more than 0.10%, a precipitation amount of Tic increases excessively, the hardness of the steel for carburizing before the forging increases, the deformation resistance increases, and the critical working ratio decreases. Therefore, Ti content 15 needs to be controlled to the range of 0.010% to 0.10%. Preferable range is 0.025% to 0.050%. [003 11 In addition to the above mentioned base elements, the steel for carburizing and the steel portion of the carburized steel component according to the embodiment include 20 unavoidable impurities. Herein, the unavoidable impurities indicate elements such as N, P, 0, Pb, Sn, Cd, Co, Zn, and the like which contaminate unavoidably from auxiliary materials such as scrap and the like and from producing processes. In the elements, N, P, and 0 needs to be limited to the following in order to obtain satisfactory the effect of an aspect of the present invention. In addition, % as described below is mass%. 25 Moreover, although a limited range of the unavoidable impurities includes 0%, it is * industrially difficult to be stably 0%. N: 0.0080% or less N (Nitrogen) is the impurity contained unavoidably and an element which 5 decreases the amount of the solid-soluted B by forming BN. When N content is more than 0.0080%, even if Ti is added, it is difficult to fix N in the steel as TiN and to secure the solid-soluted B which contributes to the hardenability. Moreover, when N content is more than 0.0080%, coarse TiN which acts as the fracture origin of the cracks during the forging is formed, the critical working ratio of the steel for carburizing before the forging 10 decreases. Therefore, N content needs to be limited to 0.0080% or less. Preferably, it is 0.0050% or less. Since it is preferable that N content is as small as possible, the limited range includes 0%. However, it is not technically easy to control N content to be 0%, and also production cost of the steel increases in order to be stably less than 0.0030%. Thus, preferable limited range of N content is 0.0030% to 0.0080%. More 15 preferable limited range of N content is 0.0030% to 0.0055%. Generally, in ordinary producing condition, N of approximately 0.0060% is contained unavoidably. [0033] P: 0.050% or less P (Phosphorus) is the impurity contained unavoidably and an element which is 20 segregated at austenite grain boundary, embrittles prior austenite grain boundary, and results in intergranular cracking. When P content is more than 0.050%, the influence becomes excessive. Therefore, P content needs to be limited to 0.050% or less. Preferably, it is 0.020% or less. Since it is preferable that P content is as small as possible, the limited range includes 0%. However, it is not technically easy to control P 25 content to be 0%, and also the production cost of the steel increases in order to be stably 5, less 19 than 0.0030%. Thus, preferable limited range of P content is 0.003% to 0.050%. More preferable limited range of P content is 0.003% to 0.015%. Generally, in ordinary producing condition, P of approximately 0.025% is contained unavoidably. 0: 0.0030% or less 0 (Oxygen) is the impurity contained unavoidably and an element which forms oxide inclusions. When 0 content is more than 0.0030%, coarse inclusions which act as the fracture origin of fatigue cracking increase, which results in a decrease in fatigue properties. Therefore, 0 content needs to be limited to 0.0030% or less. Preferably, it 10 is 0.0015% or less. Since it is preferable that 0 content is as small as possible, the limited range includes 0%. However, it is not technically easy to control 0 content to be 0%, and also the production cost of the steel increases in order to be stably less than 0.0007%. Thus, preferable limited range of 0 content is 0.0007% to 0.0030%. More preferable limited range of 0 content is 0.0007% to 0.001 5%. Generally, in ordinary 15 producing condition, 0 of approximately 0.0020% is contained unavoidably. [003 51 In addition to the above mentioned base elements and impurities, the steel for carburizing and the steel portion of the carburized steel component according to the embodiment may further include, as selective elements, at least one of Nb, V, Mo, Ni, Cu, 20 Ca, Mg, Te, Zr, REM, and Sb. Hereinafter, limitation range and reasons for the limitation of the selective elements will be described. In addition, % as described below is mass%. [0036] In the selective elements, Nb and V are effective in preventing the grain 25 coarsening. Nb: 0.002% to 0.100% Nb (Niobium) is an element which forms Nb(C,N) by bonding to N and C in the steel. Nb(C,N) suppresses the grain growth by pinning the austenite grain boundary, 5 and thereby prevents microstructure from coarsening. When Nb content is less than 0.002%, the effect is not obtained. When Nb content is more than 0. loo%, the effect is saturated. Therefore, it is preferable that Nb content is 0.002% to 0.100%. More preferably, it is 0.010% to 0.050%. [003 81 10 V: 0.002% to 0.20% V (Vanadium) is an element which forms V(C,N) by bonding to N and C in the steel. V(C,N) suppresses the grain growth by pinning the austenite grain boundary, and thereby prevents the microstructure from coarsening. When V content is less than 0.002%, the effect is not obtained. When V content is more than 0.20%, the effect is 15 saturated. Therefore, it is preferable that V content is 0.002% to 0.20%. More preferably, it is 0.05% to 0.10%. [003 91 In the selective elements, Mo, Ni, and Cu are effective in increasing the fraction of the martensite at the carburizing heat treatment. 20 [0040] Mo: 0.005% to 0.50% Mo (Molybdenum) is an element which enhances the hardenability of the steel. In order to increase the fraction of the martensite after the carburizing heat treatment by the effect, it is preferable that Mo content is more than 0.005%. Moreover, Mo is the 25 element which does not form oxides and hardly forms nitrides under gas atmosphere of * 2 1 the gas carburizing. By Mo addition, an oxide layer, a nitride layer, or an abnormal carburized layer due to the oxide layer or the nitride layer are hardly formed on the surface of the carburized layer. However, addition cost of Mo is expensive. In addition, when Mo content is more than 0. 50%, the hardness of the steel for carburizing 5 before the forging increases, the deformation resistance increases, and the critical working ratio decreases. Therefore, it is preferable that Mo content is 0.005% to 0.50%. More preferably, it is 0.05% to 0.20%. [0041] Ni: 0.005% to 1.00% Ni (Nickel) is an element which enhances the hardenability of the steel. In order to increase the fiaction of the martensite after the carburizing heat treatment by the effect, it is preferable that Ni content is more than 0.005%. Moreover, Ni is the element which does not form oxides and nitrides under the gas atmosphere of the gas carburizing. By Ni addition, the oxide layer, the nitride layer, or the abnormal carburized layer due to 15 the oxide layer or the nitride layer are hardly formed on the surface of the carburized layer. However, addition cost of Ni is expensive. In addition, when Ni content is more than 1.00%, the hardness of the steel for carburizing before the forging increases, the deformation resistance increases, and the critical working ratio decreases. Therefore, it is preferable that Ni content is 0.005% to 1.00%. More preferably, it is 0.05% to 0.50%. [0042] Cu: 0.005% to 0.50% Cu (Copper) is an element which enhances the hardenability of the steel. In order to increase the fiaction of the martensite after the carburizing heat treatment by the effect, it is preferable that Cu content is more than 0.005%. Moreover, Cu is the 25 element which does not form oxides and nitrides under the gas atmosphere of the gas %r carburizing. By Cu addition, the oxide layer, the nitride layer, or the abnormal carburized layer due to the oxide layer or the nitride layer are hardly formed on the surface of the carburized layer. However, when Cu content is more than 0.50%, the ductility in a high temperature region of 1000°C or higher decreases, which causes a 5 decrease in yield of continuous casting and rolling. In addition, when Cu content is more than 0.50%, the hardness of the steel for carburizing before the forging increases, the deformation resistance increases, and the critical working ratio decreases. Therefore, it is preferable that Cu content is 0.005% to 0.50%. More preferably, it is 0.05% to 0.30%. In addition, in case of adding Cu, it is preferable that Ni content is more than 10 half of Cu content by mass% in order to improve the ductility in the high temperature region. [0043] In the selective elements, Ca, Mg, Te, Zr, REM, and Sb are effective in improving the machinability. 15 [0044] Ca: 0.0002% to 0.0030% Ca (Calcium) is an element which has an effect of morphology control such that the shape of MnS which is formed by S added for the machinability improvement is controlled to be spheroidal without extending. By Ca addition, anisotropy of the shape 20 of MnS is improved, and mechanical properties are not impaired. Moreover, Ca is element which improves the machinability by forming a protective film for a surface of a cutting tool during the cutting. To obtain the effects, it is preferable that Ca content is more than 0.0002%. When Ca content is more than 0.0030%, coarse oxides and sulfides may be formed, and the fatigue strength of the carburized steel component may 25 be negatively influenced. Therefore, it is preferable that Ca content is 0.0002% to 0.0030%. More preferably, it is 0.0008% to 0.0020%. [0045] Mg: 0.0002% to 0.0030% Mg (Magnesium) is an element which controls the morphology of MnS and 5 improves the machinability by forming the protective film for the surface of the cutting tool during the cutting. To obtain the effects, it is preferable that Mg content is more than 0.0002%. When Mg content is more than 0.0030%, coarse oxides may be formed, and the fatigue strength of the carburized steel component may be negatively influenced. Therefore, it is preferable that Mg content is 0.0002% to 0.0030%. More preferably, it 10 is 0.0008% to 0.0020%. [0046] Te: 0.0002% to 0.0030% Te (tellurium) is an element which controls the morphology of MnS. To obtain the effect, it is preferable that Te content is more than 0.0002%. When Te content is 15 more than 0.0030%, the steel excessively embrittles at high temperature. Therefore, it is preferable that Te content is 0.0002% to 0.0030%. More preferably, it is 0.0008% to 0.0020%. [0047] Zr: 0.0002% to 0.0050% 20 Zr (Zirconium) is an element which controls the morphology of MnS. To obtain the effect, it is preferable that Zr content is more than 0.0002%. When Zr content is more than 0.0050%, coarse oxides may be formed, and the fatigue strength of the carburized steel component may be negatively influenced. Therefore, it is preferable that Zr content is 0.0002% to 0.0050%. More preferably, it is 0.0008% to 25 0.0030%. 24 [0048] Rare Earth Metal: 0.0002% to 0.0050% REM (Rare Earth Metal) are elements which controls the morphology of MnS. To obtain the effect, it is preferable that REM content is more than 0.0002%. When 5 REM content is more than 0.0050%, coarse oxides may be formed, and the fatigue strength of the carbwized steel component may be negatively influenced. Therefore, it is preferable that REM content is 0.0002% to 0.0050%. More preferably, it is 0.0008% to 0.0030%. Herein, REM indicate a generic name of a total of 17 elements in which 10 scandium of the atomic number 2 1 and yttrium of the atomic number 39 are added to 15 elements from lanthanum of the atomic number 57 to lutetium of the atomic number 71. In general, misch metal which is a mixture of the elements is supplied and added to the steel. [0049] 15 Sb: 0.002% to 0.050% Sb (antimony) is an element which prevents decarburization and carburization during the producing processes (the hot rolling, the hot forging, the annealing, and the ike) of the steel for carburizing. To obtain the effect, it is preferable that Sb content is more than 0.002%. When Sb content is more than 0.050%, carburizing during the 20 carburizing treatment may deteriorate. Therefore, it is preferable that Sb content is 0.002% to 0.050%. More preferably, it is 0.005% to 0.030%. [0050] Next, the hardness parameter, the hardenability parameter, and the Tic precipitation parameter which needs to be satisfied simultaneously as the steel for 25 carburizing and the steel portion of the carbwized steel component according to the C 2 5 embodiment will be described. [005 11 Hardness parameter The amounts expressed in mass% of each element in the chemical composition 5 needs to satisfy a following Equation A as the hardness parameter. Moreover, when Mo, Ni, and Cu which are selective elements are contained, the hardness parameter is redefined as a following Equation B on behalf of the Equation A. 0.10 70 71 70 69 69 69 7 1 69 69 69 70 6 9 70 69 6 9 68 59 65 65 71 71 68 65 72 6 7 67 69 69 Microstructure Total Fraction Ferrite and Pearlite after Slow Cool~ng Process (%) 1 00 100 100 92 100 none none none none none none - occur none occur occur Hardness after Slow Cooling Process (HV) 104 1 52 11 9 ' 123 . 123 Total Fraction Ferrite and Spheroida Cementites after SA Process (Oh) 100 1 00 100 91 100 after SA Process (HV) 98 96 105 108 106 102 94 106 104 106 105 106 104 106 106 110 133 129 11 1 95 99 103 113 76 102 121 102 102 100 ' 100 100 1 00 100 1 00 100 95 100 1 00 100 81 64 100 92 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 89 100 100 100 100 100 96 100 100 100 100 100 110 94 117 117 120 116 119 113 120 124 123 199 151 134 97 102 110 134 78 110 133 113 112 Table 3 Steel for Carburizina Carburized Steel Component -- Production Result Evaluation Resul6 .. Evaluation Result z 6 Finish Attained Microstructure^of Hardness Critical Working Ratio Carburized Layer Steel Portion Z .- Temperature Surface SurFace Layer after after after after Hardness Hardness Martensite Hardness Chemical at Temperature Total Fraction Cementites Slow Cooling SA Process Slow Cooling SA Process at at Fraction at Composition at Ferrite and with Process Process 50D m 0.4mm at 2mm at Industrial Applicability [0136] According to the above aspects of the present invention in regard to the steel for the carburizing, the carburized steel component, and the method of producing the same, it 15 is possible to provide a steel for carburizing, a carburized steel component, and a method of producing the same, which have, in the state of the steel for carburizing, small deformation resistance and large critical working ratio at a cold forging as compared with the conventional steel for carburizing, and which have, after a carburizing heat treatment, a hardened layer and hardness of steel portion which are equivalent to a conventional 20 steel. Accordingly, the present invention has significant industrial applicability. CLAIMS 1. A steel for a carburizing comprising as a chemical composition, by mass %, C: 0.07% to 0.13%, Si: 0.0001% to 0.50%, Mn: 0.0001% to 0.80%, S: 0.0001% to 0.1 00%, Cr: more than 1.30% to 5.00%, B: 0.0005% to 0.0100%, Al: 0.0001% to 1.0%, Ti: 0.010% to 0.10%, N: limited to 0.0080% or less, P: limited to 0.050% or less, 0: limited to 0.0030% or less, and a balance consisting of iron and unavoidable impurities, wherein amounts expressed in mass% of each element in the chemical composition satisfy simultaneously a following Equation 1 as a hardness parameter, a following Equation 2 as a hardenability parameter, and a following Equation 3 as a Tic precipitation parameter. 0.10 < C + 0.194 x Si + 0.065 x Mn + 0.012 x Cr + 0.078 x A1 < 0.235 ...( Equation 1) 7.5 <(0.7 x Si+ 1) x (5.1 x Mn+ 1) x (2.16 xCr+ 1)<44 ...( Equation2) 0.004