[Document Type] Specification [Title of the invention] STEEL FOR INDUCTION HARDENING [Tecl~tiicaFl ield of the Invention] [OOOI] The present invention relates to a steel for induction hardening having excellent tnachinability, and particularly to a steel which is appropriately applicable to induction hardening and is used in power transmission components (for example, gears, bea~ings,C VT sheaves, and shatts) for vehicles, construction macliines, agricultoral machines, wvindmills for power generation, industrial machines and the like. Priority is claimed on Japanese Patent Application No. 2014-033352, filed on February 24,2014, the content of wvl~ichi s incorpo~atedh erein by reference. melated At] [0002] Hitherto, power transmission components such as gears have been \widely used after being subjected to a surface hardening treatment. As a surface hardening nlethod, carbarizing, nitriding, induction hardening, and the like are employed. Among the methods, "carbnrizing" is for the porpose of increasing the carbon level of only the surface layer of a material so as to be hardened while maintaining the toughness of the central portion of the material. The carburizing treatment is mainly for the purpose of iniproving fatigue strength and is applied to the materials such as gears and components of CVTs and CVJs for vehicles. However, the carburizing treatment method that has been widely enlployed these days requires batch processing in a gas atmosphere, and the batch processing requires that a component temperatore is held at, for example, about 930°C for several hours or longer. Therefore, high energy and costs are consumed in the carburizing treatment. In addition, in an achlal operation, in addition to problems such as a tendency to\vard environmental destruction due to a treatment of carburizing materials, there is also a problem of a difficulty in achieving an in-line systenl. [0003] In order to solve these problems, there has been research conducted for obtaining desired strength properties only by an induction hardening treatment. This is because the induction hardening treatment requires a shorter time for surface hardening treatment and loxver energy consumptio~ci ompared to the carburizing treatment, and is thus very advantageous in reducing environmental burdens. Hoxvever, in order to obtain a required surface hardness through the induction hardening treatment, there is a problem in that the C content of a steel provided for the induction hardening treatnient (steel for induction hardening) has to be increased. In a case of increasing the C content of the steel, the machinability of the steel before indnction liardening is deteriorated. [0004] As the steel that is used in a case of producing components after being carburized, so-called case hardening steel having a C content of 0.18 mass% to 0.23 mass% such as JIS SCr420 or case hardening steel having a C content of about 0.2% such as JIS SCM420 has been nsed. The biggest reason that the steel having a low C content, snch as case hardening steel, is used as the tilaterial of a conlponent is to ensure ~nachinability. The hardness of the case hardening steel having a low C content is lo\v and thus the machinability of the case hardening steel is high. Therefore, in a case \\here a production method including a carburizing process is applied to case hardening steel, nlachining ol'shapes can be easily perfornled before component having high strength. [0005] I-Iowever, in order to enable a component subjected to induction hardening to obtain an appropriate surface hardness, the C content of the steel itself has to be at least 0.4% or higher. In this case, the hardness of the steel is increased before cutting, resulting in a deterioration in n~achinability. In order to replace carburizing nit11 induction hardening, a steel xvl~ichh as good machinability is required, even xvl~ent he C content is increased and tllus the steel is hardened. That is, in a case where there is an attempt to use induction hardening to produce a conlponent that has been produced using carburizing in the related art, the biggest problem is the machinability of the steel. [0006] The related art regarding a steel for induction hardening is described as follows. Patent Document 1 is the invention regarding a steel for induction hardening and discloses a steel in which the Si content is limited to 0.50% or less, the A1 content is limited to 0.10% or less, and the area fraction of martensite in a structure before induction hardening is controlled to be 70% or higher. In this method, the strengtl~o f the steel after the induction hardening is significantly improved. However, the workability, particularly tnacl~inabilityo f the steel of Patent Document 1 before indnction hardening is low. [0007] Patent Docr~men2t proposes a steel for induction hardening having excellent ~~iachinability. Patent Document 2 discloses a techniqoe in which the average aspect ~atioof feuite grains and the inte~g~anuldairs tance of the ferrite grains are co~~trolled to be within specific ranges by appropriately controlling the area fractions of fe~rite, pea~lite,a nd bainite, and the addition of specific amounts of Al and B is necessary, the~ebyim proving macl~inability. However, the steel of Patent Docun~en2t has a small ferrite area fraction and thus has high internal hardness. Internal hardness does not change before and after induction hardening, and thus the steel having high internal hardness has high hardness during cutting \\fork before induction hardening. Since there is a liigll possibility that steel having high hardness may cause breakage such as chipping of a tool during cutting, it is thought that cutting conditions to which the steel disclosed in Patent Document 2 can be applied are limited and there may be cases where productivity is degraded. [OOOX] Patent Document 3 proposes a technique for i~nprovingth e machinability of a steel for induction hardening by increasing an A1 content. However, in Patent Document 3, a comparison between the inachinability of the steel of the invention and the machinability of case hardening steel is not perfornled. Therefore, it is unclear whether or not good machinability to the same extent as that of case hardening steel can be obtained using the technique disclosed in Patent Document 3. [Prior Art Document] [Patent Document] [0009] [Patent Document 11 Japanese Uuexamined Patent Application, First Publication No. 2007-131871 [Patent Document 21 Japanese Unexamined Patent Application, First Publication No. 2012-219334 [Patent Docurnetit 31 Ja [Non-Patent Document] [OOlO] [Non-Patent Document 11 "Material facto~os n machitiability of free cutting steel", by Hiroshi Yaguchi, heat treatment Vol. 41 No. 4, P193 [Non-Patent Document 21 "The effect of sulfide morphologies 011 tlie machinability of shape-controlled-solfide free ~i~achininstge el" by Hayaislii Masakazu, et al., CAMP-ISIJ, Vol. 15, (2002), P583 [Disclosure of the Invention] [Problems to be Solved by the hivention] [0011] An object of tlie present invention is to provide a steel for induction hardening which solves the defects of tlie inventions of the related art described above and exhibits excellent machinability and high surface hardness after induction hardening. Particularly, an object is to provide a steel for induction hardening which is approp~iate for replacing a carburizing treatment, which is inclr~ded in a production process of components used as power transmission components (for exaniple, gears, bearings, CVT sheaves, and shafts) for vehicles, construction machines, agricultural machities, witidtliills for power generation, and itidustrial machines, wvith an induction hardening treatment, and has excellent macliinability. [Means for Solving the Problem] [0012] The inventors conducted intensive research to solve tlie problems. First, patticularly focusing on A1 and S, wliicli are considered to have significant effects on tnacliinability, tlie research was conducted tliroogli literature reviews atid experiments. [OO 131 Regarding S, tlie follo\ving (a) is described in Non-Patent Docntnents 1 and 2. In addition, regarding Al, the followitig (b) is described in Patent Document 3. [0014] (a) By including S in steel, the machinability of tlie steel is improved. This is because in a case of including S in the steel, voids that are generated at the interfaces behveeti Mtl sulfide-based inclusions (hereinafter, sometimes referred to as MIIS inclusions) and the primly phase cause stress conceritration at cutting sliear regions (regions that utldergo shear deformation due to cutting) and thus at1 effect of reducing cutting energy can be obtained. In tnany cases, the adhesion of MIIS inclusions onto a tool is not observed. Therefore, it is thought that an effect for improving machiaability obtanined by including S is mainly caused by tlie formation of voids. [OOlS] The effect of the size of MIIS inclusions on machinability \\rill be described belo~v. Machinability expressed in VLlOOO as an index typically increases as the average particle size of MnS iticlusiot~si ticreases. It is thought that this is because voids are tnore easily generated at the interface between the MIIS incl~isionsa nd the primary phase in tlie cutting sliear region as the MnS inclusio~~insc rease in size. [0016] (b) In a case ~vliereA 1 is present in steel in a solid solution state, solid soluted Al and oxygen react ~vitlei ach other during cutting and a hard coatit~go f Al oxides is formed on a tool. This coating suppresses tlie wear of the tool. Therefore, Al contained in the steel significantly inlproves the service life of the tool used to cut the steel. [00 171 As described above, it is thought that in order to improve the machinability of the steel, it is effective to pronlote the generation of voids in the cutting shear region by increasing the size of the MnS inclusions in the steel and to suppress the wear of the tool by adding Al to the steel and for~ningth e coating ofAl oxides on the tool. How\lever, the machinability of the steel for induction hardening cannot be sutticientlp improved only by these techniques. In order to obtain sufficient surface hardness after induction hardening, it is required that the C content of the steel for induction hardening is 0.40 mass% or more. In the above-described technique, the machinability of the steel containing 0.40 mass% or Inore of C cannot be st~fficiently improved. The inventors further repeated various experiments and obtained the follo\$ing knowledge. [0018] (A) By including both Al and S, machinability is significantly improved. The combined effect of Al and S is not a simple addition of the effect for improving machinability by the MnS inclusions and the effect for improving machinability by AI. The inventors found that in a case where a coating ofAl oxides is present on a tool, \w~hen a predeter~ni~~aendlo unt of S is fi~rthecr ontained, the adhesion of MnS inclusions onto the tool is promoted. In a case where both Al and S are contained in steel, in addition to an effect of forming the coating ofAl oxides on the tool by Al and stlppressing the wear of the tool, a cotubi~~eedff ect ofAl and S, that is, an effect of promoting the adhesion of the MIIS inclusions onto the tool by the coating ofAl oxides can also be obtained. By the conlbined effect, lnb~icitya t the interface bchvccn the tool and chips can be significantly increased. The inventors discovered the abovedescribed combined effect by minutely inspecting tlie tool after cutting using SEMEDS, AES, TEM-EDS, or tlie like. Fu~tliernioret,h e inventors also found that tlie combined effect cannot be sufficiently obtained even wllen both A1 and S are contained in the steel for tlie follo\ving reason (B). [OOI 91 (B) In the case where both Al and S are contained in tlie steel, in contrast to the typical case described in (a), the niachinability of tlie steel is improved as the average particle size of the MnS inclusions in the steel decreases. This is because the nuniber density of the MnS inclusio~iin creases as the average particle size of the MnS inclusions decreases, and thus the number of contact points of the MnS inclusions and the tool increases, resulting in the enhancement of the lubricity itnprovitlg effect of the MnS inclusions. As described in (A), in tlie steel containing both A1 and S, lubricity applied to the interface between tlie tool and chips, other than the generation of voids in a cutting shear region, is the main cause of a machinability i~nprovingm echanism by the MnS iticlusions. In a case where tlie MnS it~clusio~airse small in size, a stress concentration effect is small. Therefore, the effect for improving niachinability based on the generation of voids is suppressed. On the other band, in tlie case where the size of the MnS inclusions is sniall, the number density of MtiS inclusions per corresponding amount of MnS increases, and thus tlie frequency of contact points behveen the tool and the MnS inclusions increases, thereby iriipmvi~igth e lubricity at the interface beheen the tool and the chips. [0020] As described above, by including both A1 and S and refining MnS, the coating lubricity at the interface between the tool and the steel can be improved, thereby significa~ttlyim proving machinability. These items found by the i~lventorsa re techniqaes that are not present in the related art. [0021] Further~~~othree, i nventors found that the refinemet~ot f MIIS is achieved by controlli~~thge cooling rate during casting and controlli~~thge ratios of Mn and S. roo221 In addition, the inventors found that in a case \\here an AI content is increased in order to improve nlachinability, coarse AIN is likely to be generated in the steel and this coarse AIN reduces the senrice life of a cutting tool and degrades the machinability of the steel. The inve~~tofrosu nd that the number of coarse AIN can be decreased and the machinability of the steel can be improved by setting the product of the Al content and the N content in the steel to be within appropriate ranges and perfomling a solutionizing treatment on tile steel before hot rolling of the steel. [0023] Moreover, the inventors cxa~~~iat n~letdho d to enable the machinability of a steel for iuduction hardening to which this teclmique is applied to be as high as that of case hardening steel. As a result, the inventors found that a steel for inductioa hardening having machit~abilityt o the same or higher extent than that of case hardening steel can be obtained by controlling the chemical co~llpositioo~f ~th e steel to satisfy the followving Expression (3) in addition to employing the above-described 15.5 5 (-1.40 x A1 + 0.0175) x (214 x (C + (117) x Si + (115) x Mn + (119) x where Al, C, Si, Mn, and Cr indicate the contents (mass%) of the corresponding elements in steel. [0024] The present invention has been coolpleted on the basis of the above-described knowledge. That is, the gist of the present invention is as follo\vs. [0025] (1) According to an aspect of the present invention, a steel for induction hardening includes, as a chemical composition, by mass%: C: 0.40% to 0.60%; Si: 0.01% to 1.4%; Mn: 0.2% to less than 1.0%; Cr: 0.01% to less than 0.5%; Al: 0.1 1% to 0.17%; S: more than 0.03% to 0.07%; N: 0.0030% to 0.0075%; P: less than 0.05%; B: 0% to 0.005%; Mo: 0% to 0.2%; Ni: 0% to 1.0%; Co: 0 %to 1.0%; Ca: 0% to 0.005%; Mg: 0% to 0.005%; Zr: 0% to 0.005%; Rem: 0% to 0.005%; Ti: 0% to 0.2%; Nb: 0% to 0.2%; V: 0% to 0.35%; Sb: 0% to 0.015%; Te: 0% to 0.2%; Pb: 0% to 0.5%; Bi: 0% to 0.5%; and a remainder includes Fe and impurities, in ~vl~icthhe chemical co~npositions atisfies Expressions (A) to (C), at a 114 position of a diameter of the steel, an area fraction ofAIN having an equivalent circle diameter of more than 200 nm is 20% or less of an area fraction of all AIN having an equivalent circle diameter of 40 nrn or more, and at the 114 position of the diameter of the steel, a number density of Mn sulfide-based inclusio~lsh aving a maximum diameter of 0.3 pm or more and 10 kun or less is 100 piecesll~imo~r more and 2500 piecesl~nrno~r less. 0.000330 5 Al x N i 0.000825.. .(A) 4.6 SMnIS 5 14.0 ...( B) 15.5 5 (-1.40 x Al + 0.0175) x (214 x (C + (117) x Si + (115) x Mn + (119) x \vIiere the symbols "C", "Si", "Mti", "Cr", "Al", "N", and "S" included in Expression (A), Expression (B), and Expression (C) respectively indicate amonnts of C, Si, Mn, Cr, Al, N, and S by unit mass%. [0026] (2) The steel for induction hardening described in (1) tnay fi~rtherin clude, as the chemical cotnposition, by mass%, one or two or more of B: 0.0003% to 0.005%, Mo: 0.01% to 0.2%,Ni: 0.05% to 1.096, and Cu: 0.05% to 1.0%. [0027] (3) The steel for induction hardening described in (1) or (2) may further include, as the cheti~icalc otnposition, by mass%, one or twvo or niore of Ca: 0.0003% to 0.005%, Mg: 0.0003% to 0.005%, Zr: 0.0003% to 0.005%, and Rem: 0.0003% to 0.005%. [0028] (4) The steel for illductiot~h ardening described in any one of (I) to (3) tnay filrther include, as the cliemical composition, by mass%, one or b ~oor n iore of Ti: 0.005% to 0.2%, Nb: 0.005% to 0.2%, and V: 0.005% to 0.35%. [0029] (5) The steel for induction hardening described in any one of (1) to (4) nlay further include, as the chenlical composition, by mass%, one or two or more of Sb: 0.0003% to 0.015%, Te: 0.0003% to 0.2%, Pb: 0.01% to 0.5%, and Bi: 0.01% to 0.5%. [Effects of the Invention] [0030] According to the present invention, a steel for induction hardening xx41ich has excellent machinability and exhibits excellent surface hardness after induction hardening can be provided. Accordingly, a steel for induction hardening used for producing power transnlissio~cl o~npo~lentthsr ough induction hardening instead of carburizing can be provided. [Brief Description of tlie Draxving] [003 11 FIG. 1 is a diagram sho\ving the relationship between the hardness (HV) of a steel and the cutting distance (m) until the end of the service life of a tool, which represents the machinability of tlie steel, and an effect of the Al content in tlie steel on the relationship. [Enibodiments of tlie hivention] [0032] First, tlie reason for limiting the content of each alloy element in the chemical co~npositiono f a steel for inductio~h~ar dening according to an embodimelit will be described. Hereinafter, tlie sy~nbol"%" indicates "mass%" if not particularly defined in the description of tlie reason for limiting the corlterlts of the alloy elements. [0033] (C: 0.40% to 0.60%) C is an elenlent xvhich is included in the steel to ensure the strength of steel and the surface hardness of the steel after induction hardening. In a case xvliere tlle C content is less than 0.40%, the above-described effects are not obtained. However, in a case \vilere the C content is tilore than 0.60%, the toughness of the steel is deteriorated. Furthennore, in tlie case where the C content is niore than 0.60%, tlie I~ardtiesso f the steel is inc~easeda, nd ~nachinabilitya nd workability during forging and the like are also significantly deteriorated. Therefore, the C content is set to 0.40% to 0.60%. In older to stably obtain the above-described effects, the lower limit of tlie C content is prefetably set to 0.45%, 0.50%, or 0.55%. [0034] (Si: 0.01% to 1.4%) Si is an elenlent \vhich contributes to deoxidizing during steel production and contributes to i~nproviugth e strength of tlie steel. In a case where the Si content is less than 0.01%, the deoxidizing effect and the strength improving effect described above cannot be obtained. On the other hand, in a case where the Si content is inore than 1.4%, the toughness and ductility of the steel are deteriorated. Moreover, in the case where the Si content is nlore than 1.4%, hard inclusions are generated in the steel, resulting in deterioration in the n~achinabilityo f the steel. Therefore, the Si content is set to 0.01% to 1.4%. The lo\ver limit of the Si content is prefe~ably0 .05%, 0.10%, or 0.15%, and the upper linlit of the Si content is preferably 0.7%, 0.4%, or 0.3%. [0035] (Mn: 0.2% to less than 1.0%) MI) has an effect for increasing the hardenability of the steel and is thus an effective element to obtain a martensitic structure during u~ductionh ardening. 111 order to obtain this effect, it is necessary that 0.2% or more of Mn is included in the steel. 111 addition, aportion of tile included Mn fornls MnS and improves the machinability of the steel. In order to obtain this effect, it is necessaly that Mn is included to satisfy the following Expression (2) as described later. 011 the other hand, in a case ~vhere I .O% or more of Mn is included in the steel, the hardness of the steel inc~eases,t he toughness of the steel is deteriorated, and machinability and nlo~kability during forging and the like are significantly deteriorated. Therefore, it is necessary that the Mn content is \vithin a range of 0.2% to less than 1.0%. Tlle lower limit of the Mn content is preferably 0.3%, 0.35%, or 0.4%, and the upper limit of tlie Mn content is plcfcrably 0.9%, 0.7%, or 0.5%. [0036] (CI: 0.01% to less than 0.5%) Cr has an effect of inlproving the hardenability of the steel. Furthermore, Cr inlparts resistance to ten~pers oftening to the steel and accordingly improves the fatigue strength of tlie steel. In a case where the Cr content is less than 0.01%, these effects cannot be obtained. On the other hand, in a case where the Cr content is 0.5% or more, Cr carbides are generated and the steel beconle embrittled. In addition, in the case where the Cr content is 0.5% or more, Cr is concentrated into cementite and the cenleatite is stabilized. Accordingly, fusion of the carbides to austenite during induction hardening is impeded, and the hardness of a hardened layer beconies uneven. Therefore, it is necessary that the amount of Cr is 0.01% to less than 0.5%. The lower limit of the Cr content is preferably 0.05% or O.l%, and the upper limit of the Cr content is preferably 0.4%, 0.3%, or 0.2%. [0037] (Al: O.lI%to 0.17%) A1 is an element effective in deoxidizing the steel. Furthennore, as described above, A1 is an element which significantly itnproves the machinability of the steel by being included si~nnltaneouslyw ith S. In a case \\!here tlie A1 content is less than 0.1 1%, the amount ofAl oxides generated on tile tool during cr~ttingis small, and a sufficient coating ofAl oxides for suppressing the wear of the tool cannot be only the effect for improving machinability is saturated, but also coarse Al-based inclusions are likely to be generated in the steel, resulting in a deterioration in macl~inabilityo r fatigue strength. Therefore, the Al content is set to 0.1 1% to 0.17%. The lower limit of the Al content is preferably 0.12% or 0.13%, and the upper limit of the A1 content is preferably 0.16%, 0.15%, or 0.14%. [0038] (S: more than 0.03% to 0.07%) S binds to Mn to fonn MnS, and has an effect' for improving machinability in proportion to the amount thereof. hl addition, as described above, by sin~ultaneonsly including A1 and S, MIIS is adhered onto the tool and the lubricity of the surface of the tool is improved, thereby significantly improving inachinability. In order to sufficiently obtain these effects, it is necessary that more than 0.03% of S is included in the steel. On the other hand, in a case where more than 0.07% of S is included, an excessive amount of MIIS that is formed acts as a path of propagation of fatigue cracks, resulting in a significant deterioration in tlle fatigue strength, tougl~ness,a nd the like of the steel. Therefore, it is necessary that the S content is witl~ina range of more than 0.03% to 0.07%. The lower limit of the S content is preferably 0.035%, 0.040%, or 0.045%, and the upper limit of the S content is preferably 0.060%, 0.055%, or 0.050%. [0039] (N: 0.0030% to 0.0075%) N binds to Al, V, and the like in the steel to form nitrides andlor carbonitrides. These nitrides andlor carbonitrides have a fimction of suppressing grain growth by enabling pinuing of austeuite grain boundaries and thus preventing coarse~~inogf a structure. In order to obtain these ctfects, it is necessary that 0.0030% or more of N is included in the steel. On the othcr hand, when N is excessively included in the steel in a proportion of more than 0.0075%, the ductility of the steel in a high ten~perature range of 1000°C or higher is deteriorated. The deterioration in ductility causes a reduction in yield during continoous casting and rolling of the steel. In addition, coarse AIN degrades the machinabilitj~o f the steel. Therefore, it is necessary that the N content is set to 0.0030% to 0.0075%. The lo\ver li~niot f theN content is appropriately 0.0035%, 0.0040%, or 0.0045%, and the upper limit of the N content is appropriately 0.0070%, 0.0065%, or 0.0060%. [0040] (P: less than 0.05%) P is contained as an impurity and is segregated at the austenite grain boundaries to cause etnbrittle~nenot f prior austenite grain boundaries, thereby causing boundary cracking. Therefore, it is preferable that the P content is reduced as nluch as possible. Therefore, it is preferable that the anlount of P is set to be within a range of less than 0.05%. Since it is not necessary to include P in order to solve the problems of the steel according to the embodiment, the lo\ver limit of the P content is not particularly limited. However, excessive costs are required to limit the anlount of P to 0.001% or less. Therefore, the lower limit of the P content is appropriately 0.001%, 0.002%, or 0.005%. The upper linlit ofthe P content is appropriately 0.04%, 0.03%, or 0.025%. [0041] The steel according to the e~nbodimente xhibits appropriate effects by including the above-described basic elements it1 the chemical composition thereof. I11 elements in addition to the above-tnentioned basic elements, the properties of the steel are finther improved. [0042] (One or hvo of B: 0% to 0.005%, Mo: 0% to 0.2%, Ni: 0% to 1.0%, and Co: 0% to 1.0%) B lnay not be included in the steel. Therefore, the lower limit of the a~nount thereof is 0%. On the other hand, the steel according to the etnbodiment may contain B as necessary. Solid soluted B in austenite has an effect of significantly in~proving the hardenability of the steel even \\~l~eat lm inute amount of B is included in the steel. Therefore, B is an effective ele~nentto obtain a martensitic stnlcture during induction hardening. III order to stably obtain this effect, the steel according to the e~nbodirnent may contain 0.0003% or more of B. On the other hand, in a case where more than 0.005% of B is included, the above-described effect is saturated. Therefore, in a case of including B, it is preferable that the B content is within a range of 0.0003% to 0.005%. The lo\ver limit of the B conteut is appropriately 0.0005%, 0.0010%, or 0.0015%, aud the upper litnit of the B content is appropriately 0.004%, 0.003%, or 0.0025%. In addition, the amount of solid saluted B is reduced by N having a function of forming BN. On the other hand, Ti fortns TiN to fix N, and accordingly prevents a reduction in the arnount of solid soluted B. In a case of including B, it is preferable that Ti is simultat~eouslyi ncluded in the steel in order to stably ensure the amount of solid soluted B. [0043] - Mo, Ni, and Cu may not be included it1 the steel. 'l'lierefore, the lo\\ler limit of the contents thereof is 0%. On the other hand, all of Mo, Ni, and Co ate elements that itliprove strength. In order to stably obtain this effect, the steel according to the e~nboditiletittn ay contain one or tllore of 0.01% or lnole of Mo, 0.05% or lnore ofNi, atid 0.05% or more of Cu. The lower limit ofthe Mo content is preferably 0.02%, 0.03%, or 0.05%, t11e lower limit of the Ni content is preferably 0.10%, 0.15%, or 0.20%, and tlie lower limit of the Cu cor~tetiti s preferably 0.10%, 0.15%, or 0.20%. [0044] In a case xvllere the Mo content is more than 0.2%, the hardenability of the machinability is increased too significantly, and bainite or martensite-auster~ite constittletits are generated in the steel before induction hardening, resulting in a deterioration in the macl~inabilityo f the steel for iaductioa hardening. Therefore, the Mo content is set to 0.2% or less, and is preferably set to 0.1% or less. In a case where the Ni content is tnore than 1.0% or in a case wliere the Cu content is tnore that1 1.0%, as in a case where the Mo content is excessive, the hardenability of the steel is increased too significaotly, and bainite or niartensite-austenite constihtents are generated in the steel before inductiot~h ardening, resulting in a deterioration in the machinability of tlie steel for induction hardening. Therefore, the upper limit of the Ni content is 1.0%, and preferably 0.9%, OX%, or 0.7%. The upper litnit of the Cu content is 1.0%, atld preferably 0.9%, 0.8%, or 0.7%. [0045] (One or hvo or more of Ca: 0% to 0.005%, Mg: 0% to 0.005%, Zr: 0% to 0.005%, and Rem: 0% to 0.005%) Ca, Mg, Zr, and Re111 (rare earth elements) may not be included in the steel. Therefore, the lonrer linlit of the contents thereof is 0%. On the other liru~d,a ll of Ca, Mg, Zr, and Rein are elements that contribute to improving the tnechanical properties of the steel by controlling the morphology of MnS in the steel. In order to stably obtain these effects, the steel according to the en~bodimenmt ay contain one or nlore of 0.0003% or more of Ca, 0.0003% or more of Mg, 0.0003% or more ofZ~;a nd 0.0003% or more of Retn. 011 the other hand, in a case where one or rnore of the Ca content, the Mg content, the Zr content, and the Retn content in the steel are more than 0.005%, oxides contained in the steel are coarsened, resulting in a deterioration in the fatigue strength of the steel. Therefore, the upper limit of each of the amounts of Ca, Mg, Zr, and Rem is 0.005%, and preferably 0.003%, 0.002%, or 0.001%. In addition, Ren~in dicates rare earth elements and one or more selected from Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tni, Yb, and Lu. The amount of Rem is the total amount of Sc, Y, La, Ce, Pr, Nd, Pni, Stn, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. [0046] (One or two or more of Ti: 0% to 0.2%, Nb: 0% to 0.2'36, and V: 0% to 0.35%) Ti and Nb may not be included in the steel. Therefore, the lower limit of the contents thereof is 0%. On the other hand, Ti and Nb contribute to homogenization of the structure by suppressing abnornial gro\vth of grains. 111 order to stably obtain this effect, tlie steel according to the enlbodinlent nlay contain one or more of 0.005% or more ofTi and 0.005% or more of Nb. The lo\\rer limit of the Ti content is preferably 0.010%, 0.050%, or 0.10%, and the lo\ver limit of the Nb content is preferably 0.010%, 0.050%, or 0.10%. [0047] On the other hand, in a case \\41ere the Ti content andlor tlie Nb content is Inole than 0.2%, hard catbidcs are genelated in the steel, ~esoltingin a deterioration in the machinability of the steel. Therefole, both of the Ti content and the Nb content are 0 2% or less. The upper limit of the Ti content is preferablp 0.18%, 0.15%, or 0.13%, and the upper limit of the Nb content is p~efe~ab0ly.1 8%, 0.15%, or 0.13%. [0048] V forms fine carbides, nitrides, and/or carbonitrides with C and/or N to prevent coarsening of grains and thus contributes to homogenizatio~o~f the structure. In order to obtain this effect, the steel according to the embodiment nmjr contain 0.005% or Illore of V. The lowwrer limit of the V content is preferably 0.01%, 0.05%, or 0.10%. 011 the other hand, in a case where the V content is more than 0.35%, hard . and coarse carbides are generated in the steel, and tl1~1tsh e machinability of the steel is deteriorated. Therefore, the V content is set to 0.35% or less. The V co~ltenits preferably less than 0.20% or equal to or less than 0.1 5%. [0049] (One or two or Inore of Sb: 0% to 0.01 5%, Te: 0% to 0.2%, Pb: 0% to 0.5%, and Bi: 0% to 0.5%) Sb, Te, Pb, and Bi may not be included in the steel. Therefore, the lower limit ofthe contents thereof is 0%. On the other hand, Sb, Te, Pb, and Bi are elenlents that inlprove machiuability. 111 order to stably obtain this effect, the steel according to the embodiment may contain one or more of 0.0003% or more of Sb, 0.0003% or more of Te, 0.01% or nlore of Pb, and 0.01% or more of Bi. The lower limit of the Sb content is preferably 0.0005%, 0.0008%, or 0.001%, the lower limit of the Te content is preferablp 0.0005%, 0.0008%, or 0.001%, the lowver limit of tile Pb content is preferably 0.02%, 0.03%, or 0.05%, and the lowver limit of the Bi content is preferably 0.02%, 0.03%, or 0.05%. [OOSO] On the other hand, in a case where the Sb content is more than 0.015%, in a case where the Te content is more than 0.2%, in a case where the Pb content is more than 0.5%, and/or in a case where the Bi content is more than 0.5%, hot brittleness is exhibited, thus causes fissure or a diffictllty in rolling. Therefore, the Sb content is set to 0.01 5% or less, the Te content is set to 0.2% or less, the Pb content is set to 0.5% or less, and the Bi content is set to 0.5% or less. The upper limit of the Sb content is preferably 0.012%, 0.010%, or 0.008%, the upper limit of the Te content is preferably 0.1%, 0.05%, or 0.02%, the upper limit ofthe Pb content is preferably 0.4%, 0.3%, or 0.2%, and the upper limit of the Bi content is preferably 0.4%, 0.3%, or 0.2%. [005 11 (Remainder: Fe and impurities) The remainder of the chenlical composition of the steel for induction hardening according to the e~nbodi~neinst a nd inlpurities. In addition, there may be cases where impurities are incorporated into the steel depending on the circumstances such as raw materials, materials, and production facilities. However, incorporation of impurities is allowed within a range that does not impede the properties of the steel for induction hardening according to the e~nbodiment. [0052] Next, the reasons for limitation regarding Expression (1) to (3), the reason for linliting the area fraction ofAIN having an equivalent circle diameter of more than 200 nrn to 20% or less of the area fraction of all AIN having an equivalent circle diarneter of 40 nm or more, and tllc reason for linliting the number density of Mn sulfide-based inclusions having a lnasin~und~ia lnetel of 0.3 pm 01 nlole and 10 kum or lcss included in the steel to 100 l~ieces/mno~r2 m ore and 2500 pieces/tn~~or~ l2e ss will.be described. [0053] (Area F~actiono f AIN Having Equivalent Circle Diameter of More Than 200 nnl is 20% or Less of Area Fraction of All AIN I-Iaving Equivalent Circle Diameter of 40 nm or More at Position which is 114 of Diameter) In a case of increasing the Al content in order to improve the machinability, AIN having an equivalent circle diameter of more than 200 nm is likely to be genetated in the steel. Hereinafter, there may be cases \vhere "AIN having an equivalent circle diameter of nlore than 200 nm" is referred to as "coarse AIN". In a case \\here coarse AIN is present in the steel, nlechanical wear of a cutting tool significantly occurs due to the coarse AIN, and the effect for improving machinability by the coating of A1 oxides formed by Al contained in the steel is lost. The inventors found by investigating the relationship behveen the amount of coarse AIN and machinability that in a case where the area fraction of coarseA1N at a 114 position of the diameter of the steel is more than 20% of the area fraction of all A1N having an equivalent circle diameter of 40 nnl or more, tnachinability desired by the steel for induction hardening according to the.embodiment cannot be obtained. In addition, AIN having an equivalent circle diameter of less than 40 nni as low as the detection limit is present only in a slight proportion with respect to the area fraction of all AIN and is thus not considered \\'hen the relationship behveen the amount of coarse AIN and machinability is investigated. Therefore, it is necessaty that at the 114 position of the dian~etero f the steel for induction hardening according to the embodiment, the area fraction ofAlN having an equivalent circle diameter of more than 200 nm is 20% or less of the area fraction of all AIN having a1 eqnivalent circle diameter of 40 IIIII or Inore. The area fraction ofAIN liaving an equivalent circle diameter of more than 200 nm is p~efe~ablp 15% or less, 10% or less, or 5% or less of the area fraction of all AIN liaving an equivalent circle diameter of 40 am or more. [0054] In a case where tlie shape of a transverse section of the steel is srrbstantially circular, the 114 position of the diameter is referred to as the middle portion of the radius in the transverse section of the steel, that is, a 114 portion of the diameter. There may be cases where the configu~ationo f the surface layer portion of the steel and the configuration of the central portion of the steel are slightly different from each other due to the difference in cooling rate or the like. Since the 114 position of the diameter of the steel, is positioned beheen the srtrface layer portion of the steel and the central portion of tlie steel, the configuration at the position which is 114 of the diameter of the steel is close to the average of the entire configuration of the steel. Regarding tlie steel according to the enibodiment, control of the amount of coarse AIN is perforined on the 114 position of the diameter of the steel. In addition, control of the atnoilnt of Mn sulfide-based inclusions, \vl~icwl~il l be described later, is also performed on the 114 position of the diameter of the steel for the above reason. [OOSS] (0.000330