[0001] The present invention relates to a steel sheet and a production method for the same. Piiority is claimed on Japanese Patent Application No. 2019-075691, filed in Japan on April 11, 2019, the content of which is incorporated herein by reference. [Background Art] 10 [0002] Recently, for automobiles, in order not only to reduce the weights of vehicLe bodies to incre.ase gas mileage and reduce the amount of carbon dioxide exhausted but also to absorb impact energy in the event of impact to secure the protection and safety of people on board, a number of high-strength steel sheets have been in use. However, 15 generally, an increase in the strength of a steeL sheet deteriorates defonnability (ductility, bendability, and the like) and is likely to c.ause breaking in large-strain regions that are locally generated during impact deformation. Since this fact acts as an obstacle to weight reduction with an increase in strength, a variety of measures have been proposed. 20 [0003] For example, Patent Document 1 discloses a high-strength steel sheet having a tensile strength of 900 ::MPa or higher capable of satisfying both a high strength and excellent formability. In Patent Document 1, the steel structure contains, in terms of the area ratios, 5% or more and 80% or less of ferrite and 15% or more of auto- 25 tempered martensite, 10% or less of bainite, 5% or less of retained austenite, and 40% - 1 - 5 or less of martensite as quenched, the average hardness of the auto-tempered martensite is HV S 700, and the average number of iron-based carbide precipitated in autotempered martensite per square millimeter of 5 nm or larger and 0.5 ~tm or smaller is set to 5 x 104 particles or more. In addition, Patent Document 2 discloses a thin steel sheet having a tensile strength of 900 MPa or higher and favorable weldability and also having favorable elongation. The thin steel sheet of Patent Document 2 is disclosed to have a steel structure in which the area ratio of ferrite is 25% or more and 65% or less, the area ratio of mrutensite containing iron-based carbide precipitated in mrutensite grains is 35% or 10 more and 75% or less, the total ru·ea ratio of crystal structures other than the ferrite and the martensite as residual stmctures is 20% or less (which may become 0%), the average grain diameters of the ferrite and the martensite are each 5 ~m or Less, and the total atomic concentration of Si and Mn on the interface between the fenite and the mrutensite is 5% or more. 15 In addition, Patent Document 3 discloses a cold-rolled steel sheet having a steel structure in which a total of 60 area% or more of ferrite and bainite are contained, 3 area% or more and 20 area% or less of retained austenite is contained, the average grain diameter of the ferrite and the bainite is 0.5 ~m or more and 6.0 pm or less, and the C concentration in the retained austenite is 0.5 mass% or more ru1d 1.2 mass% or Less, 20 having an element concentration distribution in which the average spacing in a direction o1thogonal to a rolling direction between a Mn-concentrating pmtion and a Siconcentrating portion elongated in the rolling direction at a position 50 ~m deep from the surface of the steel sheet is 1000 ~tm or Less, having surface properties in which the maximum depth of cracks on the surface of the steel sheet is 4.5 ~m or less and the 25 number density of cracks that are 6 ~tm or less wide and 2 ~un or Less deep is 10 - 2 - cracks/50 J.tm or less, and having mechanical properties in which the tensile strength (TS) is 800 MPa or higher and 1200 MPa or lower, the work hardening index (n3-s) in a region with plastic strain of 3% or more and 8% or less is 0.10 or more, and the bendability satisfies Expression (1) separately. 5 [Citation List] [Patent Document] 10 [0004] [Patent Document 1] PCT International Publication No. WO 2009/096596 [Patent Document 2] PCT International Publication No. WO 2018/030503 [Patent Document 3] Japanese Patent No. 5659929 [Summary of the Invention] [Problems to Be Solved by the Invention] [0005] In consideration of the fact that, for high-strength steel sheets, there is a 15 demand not only for improvement in the formability-strength balance but also for improvement in impact resistance as described above, the objective of the present invention is to provide a high-strength steel sheet (including a zinc-plated steeL sheet, a zinc alloy-plated steel sheet, a galvannealed steel sheet, and an alloyed zinc alloy-plated steel sheet) that is excellent in terms of formability, strength, and impact resistance and 20 a production method for the same. A high strength in the present invention refers to the fact that, as the strength of a steeL sheet, the maximwn tensile strength (TS), which is thought to be necessary to absorb a sufficient amount of energy in the event of impact deformation, is 900 MPa or higher. [Means for Solving the Problem] 25 [0006] - 3 - The present inventors cru.Tied out intensive studies regru.·ding a method for solving the above-described problem. As a result, it was found that (i) localization of impact deformation can be suppressed by forming, in steel sheets, a heterogeneous structure in which millimeter-level homogeneity (hereinafter, macro homogeneity) is 5 increased but micrometer-level homogeneity (hereinafter, micro homogeneity) is decreased by forming a structure including a soft structure and a hard structw-e mainly containing martensite as a microstructure and, furthermore, (ii) when such a hard structure contains cementite and a transition carbide, plastic deformation easily begins in the event of impact and the occwTence of fracture is suppressed. 10 The present invention has been made based on the above-desc1ibed finding, and the gist of the present invention is as described below. [0007] [1] A steel sheet according to an aspect of the present invention, in which a chemical composition contains, by mass%, C: 0.050% to 0.180%, Si: 0.01% to 1.20%, 15 Mn: 0.80% to 3.00%, Al: 0.005% to 0.600%, Ti: 0.005% to 0.120%, P: 0.050% or less, S: 0.0080% or less, N: 0.0125% or less, 0: 0.0040% or less, Nb: 0% to 0.075%, V: 0% to 1.000%, Cr: 0% to 1.50%, Ni: 0% to 1.50%, Cu: 0% to 1.50%, Mo: 0% to 1.00%, W: 0% to 1.000%, B: 0% to 0.0060%, Sn: 0% to 1.000%, Sb: 0% to 0.200%, and one or more of Ca, Ce, Mg, Zr, La, and REM in total: 0% to 0.0100% with a remainder of Fe 20 and impurities, a microstructure within a range from a position of 1/8 of a sheet thickness from a sw-face in a sheet thickness direction to a position of 3/8 of the sheet thickness from the surface in the sheet thickness direction contains, in terms of a volume fraction, ferrite: 10% to 75%, matiensite: 20% to 90%, retained austenite: 0% to 5%, bainite and bainitic ferrite in total: 0% to 50%, and pearlite: 0% to 5%, a prop01tion 25 ofunrecrystallized ferrite in the ferrite is 0% to 25%, cementite that is contained in the - 4 - mrutensite satisfies Expression (1), a density of transition carbide included in the mrutensite is 1.0 x 1013 pieces/m3 or more, a density of coarse inclusion having an equivalent circle diameter of 10 Jllll or more is 0.50 pieces/mm2 or less, in a surface parallel to the surface at a position of 1/4 of the she.et thickness from the surface in the 5 sheet thickness direction, a ratio of a maximum value Hvmax of Vickers hardness to a minimum value Hvmin of the Vickers hardness is 1.40 or less, and in a distribution map of the Vickers hardness, an average value of minimum distances between peaks ofthe Vickers hardness is 1.00 mm or less. 10 [Math. 1] 1.00 ~ Lf.1 dio.ao · ai 1'30 S 10.00 ... Expression (1) in the Expression (1), di represents a particle diameter of a cementite particle having an ith Largest equivalent circle diameter in unit Jlrn, and ai indicates an aspect ratio of the cementite particle having the ith largest equivalent circle diameter. [2] The steel sheet according to [1], in which the chemical composition may 15 contain, by mass%, one or more selected from the group consisting ofNb: 0.005% to 0.075%, V: 0.010% to 1.000%, Cr: 0.05% to 1.50%, Ni: 0.05% to 1.50%, Cu: 0.05% to 1.50%, Mo: 0.03% to 1.00%, W: 0.030% to 1.000%, B: 0.0005% to 0.0060%, Sn: 0.010% to 1.000%, Sb: 0.005% to 0.200%, and one or more ofCa, Ce, Mg, Zr, La, and REM in total: 0.0001% to 0.0100%. 20 [3] The steel sheet according to [1] or [2], in which, in the microstructure, an average grain diameter of prior austenite may be 5.0 f.!ID or Less, and an average aspect ratio of the prior austenite may be 2.50 or Less. [4] The steel sheet according to any one of [1] to [3], in which the mrutensite that is contained in the microstructure may have 1.0 x 1013 /m2 or more of dislocations. - 5 - 5 [5] The steel sheet according to any one of [1] to [4], in which a zinc plated layer may be formed on the surface. [6] The steel sheet according to any one of [1] to [4], in which a zinc alloy plated layer may be formed on the surface. [7] The steel sheet according to [5] or [6], in which an Fe content in the zinc plated layer or the zinc alLoy plated layer may be, by mass%, 7.0% or more and 13.0% or less. [8] A production method for a steel sheet according to another aspect of the present invention is a production method for the steel sheet according to [1] to [4], the 10 method having a casting process of casting molten steel having the chemical composition according to [1] such that the average cooling rate within a surface temperature range of 700°C to 5500C is 10 °C/hour to 75 °C/hour to obtain a cast piece having a thickness of 100 mm to 500 mm or less, a hot rolling process of heating the cast piece to 1200°C to 1350°C and hot rolling the heated cast piece to obtain a hot- 15 rolled steel sheet, a cooling process of cooling the hot-rolled steel sheet to 1000C or lower, a cold rolling process of cold-rolling the hot-rolled steel sheet such that a total rolling reduction is 30% to 90% and a cold rolling completion temperature is 2500C or lower to obtain a cold-rolled steel sheet, and an annealing process of heating the coldrolled steel sheet at an annealing temperature of 760°C or higher and Ac3 + 200C or 20 lower and cooling the cold-rolled steel sheet to 80°C or lower, in which, in the hot rolling process, during rolling that is carried out at 10500C or higher, Expression (2) is satisfied, and a total rolling reduction is set to 60% or more, rolling that is carried out at lower than 1050°C is carried out under a condition that satisfies Expression (3), in the cooling process, an average cooling rate from a completion temperature of the hot 25 rolling to 630°C is set to 20 °C/second or faster, within a temperature range of 630°C to - 6 - 5000C, Expression (4) is satisfied, in the anneahng process, in a heating step to the annealing temperature, an average heating rate within a temperature range of 40(l'C to 5500C is 3.0 °C/second or faster, within a temperature range of 550°C to Acl °C, Expression (5) is satisfied, an average heating rate within a temperature range of Acl oc 5 to (Acl + 20)°C is 1.0 °C/second or faster, in a cooling step from the annealing temperature, an average cooling rate within a temperatu re range of 720"'C to 550°C is 10 °C/second or faster, within a temperature range of 550°C to (Ms - 80)°C, Expression (6) is satisfied, an average cooling rate within a temperature range ofMs°C to (Ms - 25tC is 10 °C/second or faster, and within a temperat1ue range ofMs°C to 800C, Expression 10 (7) is satisfied, [Math. 2] n 1 1 1 - l I Al . c + 12.1(Nb] + 1 + 4.8 . ([Ti]- 3.0[N]) + 1 + 93.3 [B]) t=l 1 h· 1- h· . (T( · - 1050)6 . I- 1 I h 1.5 i-1 ( Az A3 ) . t io.s . exp Ti + 273- T' I+ 273 > 1.00 ... Expression (2) [Math. 3] 15 Rm+n < 10.00 ... Expression (3) [Math. 4] ... Expression (4) [Math. 5] - 7 - 10 2 100 - 1o.oo > LA1s ·{tn(100 _r)r i=1 ( A19 ) · exp -823 + (0.1i- 0.05) · (Ac1 - 550) Azo · £43 ( 1 )z~1s . 1 + 13[Nb] + 7[Ti]- 21[N] . ti > l.OO ... Expression (5) [Math. 6] ... Expression (6) 5 [Math. 7] 10 0.00 ~ L { 1-exp (-E6 - ~5 )} i=l { ( ~6 • [ Ms - I;,min] J} . l - exp - 1 +0.5[Mn]+0.2[ Cr ]+0.4[Ni] ·{A · exp(- Azs J-A 27 T, + 273 29 · exp( ;1,0 • [ T,- A,, - J/,2 • ln ([ Si] + 0.3[ Al]) ]) · ( 1-exp[ £ 6 - A,,])...,'} . dt0 " 5 < 3.00 ... Expression (7) In the Expression (2), [Nb], [Ti], and [B] indicate amounts ofNb, Ti, and B, respectively, A1, Az, and A3 are constant terms, Ti is a temperature at which ith rolling is 10 carried out in unit °C, T'i is an average temperature of the temperature Ti at which the ith - 8 - rolling is carried out and a temperature T i+l at which (i+ 1 )th rolling is carried out in unit °C, and hi represents a thickness of a steel sheet that is obtained by carrying out the ith rolling in unit rom. In the Expression (3), Rm+n is an index that indicates a refinement behavior of a 5 stmcture via the hot rolling within a temperature range of lower than l05Cf'C when the hot rolling at 1 05Cf'C Of higher is CaiTied OUt in a total Of n timeS and hot rolling at lower than 1 050°C is carried out in a total of m times. 10 In the Expression (4), Pn is an index that indicates a pmgress degree of precipitation within a temperature range from 630°C to 500°C, in the Expression (5), A1s, A19, and A2o are all constants, (1\Tb], [Ti], and [N] indicate amounts of resp ective elements in unit mass%, ti indicates a staying time within an i'b temperature range counted from 55CfC as a stat in unit seconds, and & is a value that is obtained from the Expression (4}, and in the Expression (6), C is an index that indicates a progress degree of bainitic 15 transformation within an iili time range from beginning of calculation, and Di is an index that indicates easiness of generation of cementite in association with bainitic transfonnation within the ith time range from the beginning of calculation. In the Expression (7), & is a value of a middle portion of the Expression (6), A2s, A 26, A 21, A 28, A 29, A 3o, A31, andA32 are constant terms, Ms is a martensitic 20 transformation start temperature, and Ti is an average temperature within the ph time range. Ti, min is a minimum value of Ti up lo ith time ranges after a temperature reaches Ms, and. in addition, [element sign] indicates an amount of each element in unit mass%, and dt indicates a time that is divided an elapsed time which is from a temperature reaches the martensitic transformation start temperature to the temperature reaches 25 80°C, into ten equal parts in unit seconds. - 9 - [9] The production method for the steel sheet according to [8], in which, in the annealing process, a retention time at the annealing temperature may be 3.0 seconds or longer and 200 seconds or shmter. [1 0] The production method for the steel sheet according to [8] or [9], the 5 method may include a temper rolling process of can-ying out temper rolling so that an elongation ratio is 3.00% or less. 10 [ll] The production method for the steel sheet according to any one of [8] to [10], in which, in a cooling step of the annealing process, a hot-dip galvanizing treatment may be carried out on the cold-rolled steel sheet. [12] The production method for the steel sheet according to any one of [8] to [10], in which, in the cooling step of the annealing process, a hot-dip zinc alloy plating treatment may be carried out on the cold-rolled steel sheet. [13] The production method for the steel sheet according to [11] or [12], in which, in the cooling step of the annealing process, an alloying treatment may be carried 15 out after the hot-dip plating treatment or after the hot-dip zinc alloy plating treatment. [Effects of the Invention] [0008] According to the above-described aspects of the present invention, it is possible to provide a steel sheet that is excellent in terms of formability, strength, and impact 20 resistance and a production method for the same. Such a steel sheet is effective for the weight reduction of automobile vehicle bodies with an increase in strength. 25 [Brief Description of the Drawings] [0009] Fig. 1 is a view showing the shape of a test pie.ce for a notched tension test. Fig. 2 is a schetTh 25 In order to produce the steel sheet according to the present embodiment, first, a - 35 - cast piece having the same composition as the above-described chemical composition (component composition) of the steel sheet according to the present embodiment is produced. The cast piece that is subjected to hot rolling is preferably produced by continuous casting from the viewpoint of production cost, but may also be produced by 5 a different casting method (for example, an ingot-making method). The thickness of the cast piece is set to 100 mm or more and 500 mm or less and is preferably set to 150 mm or more and 350 mm or less in order to impatt an appropliate strain amount in a hot rolling process. When the thickness of the cast piece is less than 100 mm, a steel sheet that has been imparted with an approptiate strain amount becomes too thin, and it is 10 difficult to obtain a flat shape. On the other hand, when the thickness of the cast piece exceeds 500 mm, there is a risk that the cast piece may crack dming the cooling of the cast piece. In the casting process, in a cooling step of the cast piece, the average cooling rate from the smface temperature is 7000C to 550°C is set to 10 °C/hour to 75 °C/hom. 15 \Vithin the corresponding temperature range, since the localization of eLements progress in association with phase transformation in the cast piece, when the average cooling rate is slower than 10 °C/hour, segregation progresses excessively, which increases the ratio between the maximum hardness and the minimum hardness in a steel sheet that is finally obtained and degrades the impact resistance. From this viewpoint, the average 20 cooling rate within the corresponding temperature range is preferably set to 10 °C/hour or faster and more preferably set to 13 °C/hour or faster. On the other hand, when the average cooling rate while the surface temperatme reaches 7000C and then reaches 5500C is faster than 75 °C/hour, segregation does not sufficiently progress, the influence of a concentration fluctuation that occurs over a long 25 period of Length on a strength fluctuation of a steel sheet becomes significant, the - 36 - 5 10 average distance between hardness peaks in the steel sheet that is finally obtained becomes large, and the impact resistance deteriorates. From this viewpoint, the average cooling rate is preferably set to 75 °C/hour or slower, more preferably set to 65 °C/hour or slower, and still more preferably set to 30 °Cihour or slower. The cast piece may be once cooled to room temperature by additional cooling or may be directly subjected to hot rolling while rerna.ining at a high temperature since it is possible to reduce energy necessary for heating. [0061] Subsequently, hot rolling is carried out on the cast piece. First, the cast piece is heated up to a temperature of 1200°C or higher. When the heating temperature of the cast piece is low, an element-concentrating portion attributed to a coarse carbonitlide in the cast piece is locally generated, and the ratio between the maximum hardness and the rn.inimum hardness in the steel sheet that is finally obtained becomes 15 large. In addition, in order to carry out subsequent hot rolling at higher temperatw·es and enhance the macro homogeneity of the steel she.et, the heating temperature of the cast piece is preferably set to 1220°C or higher. On the other hand, when the heating temperature of the cast piece exceeds 1350°C, the structure becomes coarse, and an effect of the subsequent hot rolling that homogenizes the inside of the steel sheet is 20 impaired. Therefore, the heating temperature of the cast piece is set to 1350°C or lower and preferably set to 132CfC or lower. [0062] After the heating, hot rolling is carried out on the cast piece. As the hot rolling, first, rolling is cruTied out within a temperatme range from the highest heating 25 temperature to 1050°C (temperature range of 1050°C or higher) such that the total - 37 - rolling reduction (cumulative rolling reduction) reaches 60% or more. When the total rolling reduction within this temperature range is less than 60%, the effect of the hot rolling that homogenizes the inside of the steel sheet is not sufficiently exhibited. The total rolling reduction is preferably set to 70% or more. The upper limit of the total 5 rolling reduction within the temperature range of 1050°C or higher is not patticularly set, but the total rolling reduction is preferably set to 95% or less since excessive rolling impairs the shape of the steel sheet. In addition, since the hot rolling within the temperature range from the highest heating temperature to 1 050°C sufficient! y promotes the homogenization of the inside of 1 0 the steel sheet, there is a need to satisfy Expression (2). [0063] [Math. 9] n 1 1 1 -l I Al . (1 + 12.1[Nb] + 1 + 4.8. ([Ti]- 3.0[N]) + 1 + 93.3[B]) I=l 1 h· 1- ht · (T' · - 1050)6 · 1 1 --h---~1~.5- i-1 ~ ( Az A3 ) . t( o.-~ . exp Ti + 273 - T' i + 273 > l.OO .. . Expression (2) 15 [0064] Expression (2) includes expressions that represent the accumulation degree of strain by rolling and the degree of recrystallization of austenite. As the value of the left side of Expression (2) increases, austen ite grain boundaries migrate inside ofthe steel sheet, and the homogenization of the inside of the steel sheet progresses . 20 Between two terms in the exponent function term, the former (term including the - 38 - constant A2) is derived from an expression that represents the accumulation degree of strain, the latter (term including the constant As) is derived from an expression that represents the degree of recrystallization of austenite, and the other terms are obtained by rearranging the coefficient of the two expressions. 5 The reference signs in Expression (2) will be desctibed. n is the number of times of rolling that is carried out while the temperature of the steel sheet reaches 1 050°C from the highest heating temperature. For each of first rolling to n t.h rolling, the expressions following the A1 term are calculated, and the sum thereof becomes the value of the left side of Expression (2). A1, Az, and A3 are constant terms and are 1.53 10 x 102, 1.60 x 104 , and 2.31 x 104 , respectively. [Element signs] ([Nb], [Ti], [N], and [B]) represent the amounts [mass%] of the respective elements. Ti is the temperature [ 0C] at which i111 rolling is carried out. T' i is the average temperature [0C] of the temperature Ti at which the ith rolling is cartied out and the temperature T i+l at which the (i+ 1 )th rolling is carried out. Here, T' n is defined as the average temperature of the 15 temperatme TIJ at which the nth rolling is carried out and 1050°C. hi represents the thickness [mm] of a steel sheet that is obtained by carrying out the ith rolling. ho is defined as the thickness of the heated cast piece. ti is defined as the elapsed time [se.conds] while the ith rolling is carded out and then the (i+ 1 Yh rolling is carried out. tn is detined as the elapsed time while the nth rolling is carried out and then the 20 temperatw·e of the steel sheet reaches 10500C. [0065] As the value of the Left side of Expression (2) increases, homogenization via the hot rolling progresses. The hot rolling is carried out under a condition under which the value of the left side of Expression (2) reaches 1.00 or more within a temperature 25 range of 1 050°C or higher. In order to increase the homogenization degree of the - 39 - inside of the steel sheet and improve the impact resistance, the hot rolling is preferably carried out under a condition under which the value of the left side of Expression (2) reaches 1.20 or more and more preferably carried out under a condition under which the value reaches 1.40 or more. In the middle of the hot rolling, heating or cooling rna y be 5 appropriately carried out such that Expression (2) is satisfied. The upper limjt of the value of the left side of Expression (2) is not particularly set; however, when the value of the left side of Expression (2) becomes excessively large, the structure of the steel sheet becomes coarse, and it becomes difficult to refine the structure via hot rolling that is carried out after the Lemperature reaches 1 050°C, and thus the value of the left side of 10 Expression (2) is preferabty limited to 6.00 or less. In order to increase the value of the Left side of Expression (2), since a device such as a heating apparatus becomes necessary, the value of the left side of Expression (2) is preferably set to 4.00 or less from the viewpoint of production cost. [0066] 15 The hot rolling conditions while the temperature reaches 1 050°C and then reaches a roiling completion temperature (temperature range of lower than 10500C) are made to satisfy Expression (3). [0067] [Math. 10] 20 Rm+n S 10.00 ... Expression (3) [0068] [Math. 11] - 40 - [0069] ( 1 1 1 ) . 1 + 19.2[Nb] + 1 + 7.5 · ([Ti]- 3[N]) + 1 + 115.0[8] + 2.7[Mo] ( As ) l . exp - r' n+j + 273 . tn+jz [0070] 5 Expression (3) is an index that represents the refinement behavior of the structure via the hot rolling within the temperature range of lower than 1050°C, is delived from a tem1 relating to the generation of a recrystallization nucleus in association with the hot rolling and a term relating to grain growth after the rolling, and is obtained by rearranging coefficients. 10 The reference signs in Expression (3) will be desc1ibed. n is the total number of times of hot rolling at 1 0500C or higher. m is the total number of times of hot rolling at Lower than 10500C. j indicates the order of specific rolling among rollings that are c After the completion of the hot rolling, the steel sheet is cooled to l00°C or lower (for example, room temperature) at an average cooling rate of 20 °C/second or faster within a temperature range of the completion temperature of the hot rolling to 6300C and is cooled within a temperature range of 630°C to 500°C such that Expression 10 (4) is satisfied. When the average cooling rate from the completion temperature of the hot rolling to 630°C is slower than 20 °C/second, in assoc.iation with phase transformation after the hot rolling, carbon is localized and coarse cementite is formed, and a desired structure cannot be obtained in the steel sheel that is finally obtained. In addition, the 15 macro homogeneity of the steel sheet is also impaired by phase transformation within this temperature range. Therefore, in the case of further enhancing the impact resistance, the average cooling rate from the completion temperature of the hot rolling to 630°C is preferably 30 °C/second or faster. The upper limit of the average cooling rate is not pmticularly set, but a special cooling medium is required to achieve a cooling 20 rate faster than 200 °C/second, and thus the average cooling rate is preferably set to 200 °C/second or slower from the viewpoint of production cost. In the present embodiment, the average cooling rate and the average heating rate are each a value obtained by dividing the temperature difference between the starting point and the ending point of a setting range by the elapsed time from the start 25 point to the end point. - 43 - [0072] After that, the temperature history from 630°C to 50 1.00 x 10-s ... Expression (4) [0074] 10 [Math. 14] · [225 - 240[C]- :i S[Mn] -1 S[Si ] - 1 S[Cr]- 21 [Ni] + :n(A£]]4·5 · E3 - o.s · exp (- :~~) · [A 11 + 34[Nb] + 56[8]05 + 7[Mo]]) ( A ) 0.5} · A12 · exp - 17~6 · t1 + A13 · (25 - 200(C]- 27[Mn]- 14[Cr] - 12[Ni] + l8[Al])2 • (1 + [CJ) . [ 1 - exp h~~) n ( ( A15 ) 05 (Ti)-3(N] . AH. exp -1796 . t1 .. fTil- 3fNl + 5.2[Nbl · (1 + 0.32[Ti]0·5 + 0.43 [Ti])-1 + A16 • exp ( - 1~~6) · t1 o.s 5.2[Nb] 0 5 -t] . LTil - 3lNJ + 5.2LNbJ . (1 + 0.87(Nh] . + 1.19(Nb]) [0075] - 44 - In the present embodiment, the temperatme range from 6300C to 500°C is divided every 10°C into 13 sections, and phase transformation and the precipitation degree are calculated in each of the first to 13th temperature ranges. Pt is an index that evaluates the progress degree of precipitation within a temperatme range from 6300C to 5 6200C and is made up of a term X 1 that evaluates the progress degree of phase transformation and a term Yi that evaluates the precipitation degree in a transformed region. As X1 increases, phase transformation further progresses, and as Y 1 increases, the precipitation of a carbide of Nb and Ti (alloy carbide) in the transformed region fmther progresses. 10 Reference signs in the expression wiLl be described. A9, Ato, Au, A12, A13, At4, A1s, At6, and A17 are constants and are 3.70 x 1012 , 3.93 x 104 , 1.93 x 10°, 1.00 x 107, 9.09 X 10·2, 2.80 X 10·3, 2.54 X 104, 4.12 X 10·2, and 3.03 X 104, respectively. [Element signs] ([C], [Mn], [Si], [Cr], [Ni], [Al], [Nb], [B], [Mo], [Ti], and [N]) represent the an1ounts [mass%] of the respective elements. Es is the value of the left 15 side of Expression (3). In a c.ase where the term (25 - 200[C] -27[Mn] - 14[Cr] - 12[Ni] + 18[Al]) becomes negative, the term is regarded as zero in calculation. Subsequently, an evaluation index Pi of the progress degree of precipitation in the region within a temperature range from 630°C to (630 - 10 x i)°C is calculated. 20 After calculation with i = l , calculation is carried out in order using the result for the case of i = 2 and the case of i = 3. The index Pi in a case where i is 2 or more is defined as described below. [0076] [Math. 15] - 45 - X1(i > 1) = [{1- exp( -A, [0077] · [215 + 10i - 240[C]- 35[Mn]- 15(Si)- 15[Cr]- 21 [Ni] + 32[Al]]4·5 · £3 -o.s · exp ( - 90:~0 lOt) ·IA11 + 34(Nb] + 56[B]0 · 5 + 7[MoJl) { . A12 2 . exp ( -908A -to1 0i ) . ti + (- Jn(l- Xi-1)) · {A9 · r215 + 10i - 240(C]- 3S[Mn] - 15[Si] -15[Cr] - 21 [Ni] + 32[Al]l45 · E3 -o.s · exp (- 908A~'toJ · [A11 + 31{Nb] + 56[8]0 ·5 + 7[MoJI(f'l +A, · (1- X1) • (15 + lOi - 200[C] - 27[Mn]- 14[Cr] - l2 (Ni) + 18[Al])2 11 2 · ( 1 + (C]) · [1 - exp ( - [;i])] ] Here, in a case where the term (15 + lOi- 200[C] - 27[Mn)- 14[Cr] - 12[Ni] + 18[Al]) becomes negative, the term is rega1·ded as zero. 5 [0078] [Math. 16] t'1-1 (i > 1) = Pi-1 2 · xi-1 2 · xi -z ( 2 ( A15 ) [Ti] - 3[N] 2 . A14 . exp -908 - 10i . [Ti]- 3[N] + 5.2 [Nb] + A16 · exp (- 908A~7 10i) 5.2[Nh] -l . [Ti]- 3(N) + 5.2[Nb]) [0079] - 46 - (Math. 17] Y; (i > 1) == [A14 · exp (- 181:~ 20J · (ti + t'i-1)0·5 [Ti]- 3[N] [TiJ- 3[N] + S.2[Nb] · (1 + 0.32[Ti] 0·5 + 0.43(Ti])-1 + A16 . ( A 17 ) ( I ) 0.5 exp - 1816- 20i . t i + t i-1 5.2[Nb] [Ti]- 3[N] + S.2[Nb] · (1 + 0.87[Nb] 0·5 + 1.19(Nb])- 1] [0080] [Math. 18] 5 [0081] 'When P13 in Expression ( 4) is less than 1.00 x 1 o·8• a part of Ti and Nb remains as a solid solution, recrystaUization after the cold rolling is suppressed, and unrecrystaLJized ferrite remains. In a case where the fonnabiLity is improved by 10 progressing recrystallization, P13 is set to 1.00 x lo-s or more. In order to enhance the formability, P 13 is preferably set to 2.00 X 10'8 or more. Meanwhile. when P13 is excessively increased, cementite coarsens, and there is a concern that cementite may not dissolve but remain even after a heat treatment is carried out after the cold rolling. Therefore, Pn is limited to 1.00 x 10'7 or less. In - 47 - order to avoid unnecessary coarsening of cementite, P13 is preferably set to 7.50 x 10·8 or less and more preferably set to 6.00 x 1 o-s or less. Before the cold rolling is carried out, the steel sheet may be reheated up to 500°C or higher again after the temperature of the steel sheet drops below 5000C. 5 [0082] Subsequently, a pickling treatment is carried out on the steel sheet that has been cooled to room temperature, and subsequently, cold rolLing is carded out thereon. The total rolling reduction in the cold rolling is set to 30% or more and 90% or less. When 10 the total rolling reduction in the cold rolling is less than 30%, the progress of recrystallization in the following heat treatment becomes insufficient, and unrecrystallize.d ferrite remains. In addition, from the viewpoint of improving the strength-formability-impact resistance balance by refining the structure, the total rolling reduction is preferably 40% or more and mom preferably 50% or more. 15 On the other hand, when the total rolling reduction in the cold rolling exceeds 90%, the anisotropy of the steel sheet increases, and the formability dete1iorates. From the viewpoint of enhancing the fonnability, the total rolling reduction is preferably 80% or less and more preferably 70% or Less in order to reduce the anisotropy of the steel sheet. 20 In the cold rolling, the temperature of the steel sheet increases via processing heating. When the temperature of the steel sheet increases excessively, the accumulation of processing strain does not sufficiently progress, and there is a case where the progress of recrystallization is impaired. Therefore, the rolling reduction and the interpass time are controlled such that the temperature of the steel sheet at a 25 point in time of the completion of the cold rolling (cold rolling completion temperature) - 48 - 5 reaches 2500C or lower. From the viewpoint of formability, the completion temperature of the cold rolling is preferably 2000C or lower in order for recrystallization to efficiently progress. [0083] [Heating step] Subsequently, a heat treatment (annealing) is carried out on the steel sheet after the cold rolling (cold-rolled steel sheet). First, the steel sheet is heated up to the highest heating temperature (annealing temperature); however, in this step, the heating 10 rate is controlled for recrystallization to progress. When the average heating rate from 4000C to 550°C is slower than 3.0 °C/second, since the recovery of dislocations in the steel sheet progresses excessively, and recrystallization is suppressed, the average heating rate within a temperature range of 400°C to 5500C is set to 3.0 °C/second or faster. The upper limit of the average heating rate is not particularly set, but is 15 preferably set to 200 °C/second or slower from the viewpoint of production cost. Subsequently, the steel sheet is heated from 550°C to Acl (°C) such that the temperature history satisfies Expression (5). WE CLAIMS l. A steel sheet, wherein a chemical composition contains, by mass%, C: 0.050% to 0.180%, Si: 0.01% to 1.20%, Mn: 0.80% to 3.00%, AL: 0.005% to 0.600%, Ti: 0.005% to 0.120%, P: 0.050% or Less, S: 0.0080% or less, N: 0.0125% orless, 0 : 0.0040% or Less, Nb: 0% to 0.075%. V: 0% to 1.000%, Cr: 0% to 1.50%, Ni: 0% to 1.50%, Cu: 0% to 1.50%, Mo: 0% to 1.00%, W: 0% to 1.000%, B: 0% to 0.0060%, Sn: 0% to 1.000%, Sb: 0% to 0.200%, and one or more of Ca, Ce, Mg, Zr, La, and REM in total: 0% to 0.0100%, with a remainder of Fe and impurities, - 106 - 5 10 a microstructure within a range from a position of 1/8 of a sheet thickness from a sutface in a sheet thickness direction to a position of 3/8 of the sheet thickness from the smface in the sheet thickness direction contains, in terms of a volume fraction, ferrite: 10% to 75%, or more, martensite: 20% to 90%, retained austenite: 0% to 5%, bainite and bainitic ferrite in total: 0% to 50%, and pearlite: 0% to 5%, a proportion of unrecrystallized fenite in the ferrite is 0% to 25%, cementite that is contained in the martensite satisfies Expression (1), a density of transition carbide included in the martensite is 1.0 x 1013 pieces/m3 a density of coarse inclusion having an equivalent circle diameter of 10 11m or more is 0.50 pieces/mm2 or less, 15 in a surface parallel to the surface at a position of 1/4 of the sheet thickness from the surface in the sheet thickness direction, a ratio of a maximum value Hvmax of Vickers hardness to a minimum value H Vmin of the Vickers hardness is 1.40 or less, and in a distribution map of the Vickers hardness, an average value of 20 minimum distances between peaks of the Vickers hardness is 1.00 mm or less, [Math. 1] 1.00 < Lf=1 di o.ao · a1 1'30 < 10.00 ... Expression (1) in the Expression (1), di represents a particle diameter of a cementite particle having an ith largest equivalent circle diameter in unit J..tm, and ai indicates an aspect - 107 - ratio of the cementite particle having the ith largest equivalent circle diameter. 2. The steel sheet according to claim 1, wherein the chemical composition contains, by mass%, one or more selected 5 from the group consisting of 10 15 Nb: 0.005% to 0.075%, V: 0.010% to 1.000%. Cr: 0.05% to 1.50%, Ni: 0.05% to 1.50%, Cu: 0.05% to 1.50%, Mo: 0.03% to 1.00%, W: 0.030% to 1.000%, B: 0.0005% to 0.0060%, Sn: 0.010% to 1.000%, Sb: 0.005% to 0.200%, and one or more of Ca, Ce, Mg, Zr, La, and REM in total: 0.0001% to 0.0100%. 3. The steel sheet according to claim 1 or 2 , wherein, in the microst:mctw-e, an average grain diameter of prior austenite is 20 5.0 ~tm or less, and an average aspect ratio of the prior austenite is 2.50 or less. 25 4. The steel sheet according to any one of claims 1 to 3, wherein the martensite that is contained in the microstructure has 1.0 X 1013 1m2 or more of dislocations. - 108 - 5. The steel sheet according to any one of daims 1 to 4, wherein a zinc plated layer is fom1ed on the surface. 6. The steel she.et according to any one of daims 1 to 4, 5 wherein a zinc alloy plated layer is formed on the swface. 10 7. The steel sheet according to claim 5 or 6, wherein an Fe content in the zinc plated layer or the zinc alloy plated layer is, by mass%, 7.0% or more and 13.0% or less. 8. A production method for the steel sheet according to any one of claims 1 to 4, the method comprising: a casting process of casting molten steel having the chemical composition according to claim 1 such that the average cooling rate within a surface temperature 15 range of 70(J'C to 550°C is 10 °C/hour to 75 °C/hour to obtain a cast piece having a thickness of 100 mm to 500 mm or less; 20 a hot rolling process of heating the cast piece to 1200°C to 13500C and hot rolling the heated cast piece to obtain a hot-rolled steel sheet; a cooling process of cooling the hot-rolled steel sheet to 1 00°C or lower; a cold rolling process of cold-rolling the hot-rolled steel sheet such that a total rolling reduction is 30% to 90% and a cold rolling completion temperature is 25(J'C or lower to obtain a cold-rolled steel sheet; and an annealing process of heating the cold-rolled steel sheet at an annealing temperature of 760°C or higher and Ac3 + 20°C or lower and cooling the cold-rolled 25 steel sheet to 80°C or lower, - 109 - wherein, in the hot rolLing process, during rolling that is carried out at 1050°C or higher, Expression (2) is satisfied, and a total rolling reduction is set to 60% or more, rolling that is carried out at lower than 10500C is c l.OO 5 ... Expression (2) [Math. 3] Rm+n < 10.00 ... Expression (3) [Math. 4] ... Expression (4) 10 [Math. 5] 10 2 100 3 10.00 > L A18 • {ln (100 _ r)} i=1 ( A19 ) 'exp -823 + (0.1i- 0.05) · (Acl- 550) ... Expression (5) - 111 - [Math. 6] ... Expression (6) [Math. 7] 10 0.00 < :L {I-exp( -E6 - A25 )} i=l { l, A26 · [ Ms-J;,min] J} . I-exp -1+0.5[Mn]+0.2[Cr]+0.4[Ni] . { ~' . exp ( - T, ~73)-~' · exp( A30 • [ T,- A31 - A32 ·In ([ Sij + 0.3( AI])])· ( 1-exp ( £6 - A,,])..o'} . dt0 ' 5 < 3.00 5 ... Expression (7) in the Expression (2), [Nb], [Ti], and [B] indicate amounts ofNb, Ti, and B, respectively, A1, Az, and A3 are constant terms, Ti is a temperature at which ith rolling is carried out in unit °C, T' i is an average temperatme of the temperatw·e Ti at which the iili rolling is carried out and a temperature T i+l at which (i+l)'h rolling is carried out in unit 10 °C, and hi represents a thickness of a steel sheet that is obtained by ccuTying out the iih rolling in unit mm, in the Expression (3), Rm+n is an index that indicates a refinement behavior of a structure via the hot rolling within a temperature range of lower than 10500C when the hot rolling at 10500C or higher is carried out in a total of n times and hot rolling at lower 15 than l050°C is carlied out in a total of m times, in the Expression (4), P13 is an index that indicates a progress degree of - 112 - precipitation within a temperature range from 630°C to 500°C, in the Expression (5), Ats, A19, and A2o are all constants, [Nb], [Ti], and [N] indicate amounts of respective elements in unit mass%, ti indicates a staying time within an ith temperature range counted from 550°C as a stat in unit seconds, and E4 is a value 5 that is obtained from the Expression (4), 10 in the Expression (6), Ci is an index that indicates a progress degree of bainitic transformation within an ith time range from beginning of calculation, and Di is an index that indicates easiness of generation of cementite in association with bainitic transfonnation within the ith time range from the beginning of calculation, and in the Expression (7), E6 is a value of a middle portion of the Expression (6), A25, A26, A21, A28, A29, A3o, A 31, andA32 are constant terms, Ms is a maLtensitic transformation start temperature, and Ti is an average temperature within the i111 time range, Ti, min is a minimum value of Ti up to ith time ranges after a temperature reaches Ms, and, in addition, [element sign] indicates an amount of each element in unit mass%, 15 and dt indicates a time that is divided an elapsed time from a temperature reaches the martensitic transformation start temperature to the temperature reaches 80°C elongation ratio in unit seconds. 9. The production method for the steel sheet according to claim 8, 20 wherein, in the annealing process, a retention time at the annealing temperature 25 is 3.0 seconds or longer and 200 seconds or shorter. 10. The production method for the steel sheet according to claim 8 or 9, the method further complising, after the annealing process: a temper rolling process of carrying out temper rolling so that an elongation - 113 - Dated this 08th day of September, 2021 [MAHUA RAY] IN/PA-867 OF REMFRY AND SAGAR ATTORNEY FOR THE APPLICANT(S) ratio is 3.00% or less. 11. The production method for the steel sheet according to any one of claims 8 to 10, wherein, in a cooling step of the annealing process, a hot-dip galvanizing 5 treatment is carried out on the cold-rolled steel sheet. 10 15 12. The production method for the steel sheet according to any one of claims 8 to 10, wherein, in the cooling step of the annealing process, a hot-dip zinc alloy plating treatment is carried out on the cold-rolled steel sheet. 13. The production method for the steel sheet according to claim 11 or 12, wherein, in the cooling step of the anne.aling process, an alloying treatment is carlied out after the hot-dip plating treatment or after the hot-dip zinc alloy plating treatment.