the required properties of a hot work forging die have been well developed from years of experience . such a die must have substantial strength since it is subjected to heavy stresses in the forging operation and substantial hardness to insure against premature wear . it must also have good toughness to withstand the heavy and continuous shock loads to which it is subjected in use . due to the elevated temperatures to which it is exposed in use the die must be resistant to softening and heat checking . abrasion resistance is also a critical factor , since in use the sliding forces exerted on the surface at elevated temperatures are very substantial . and finally , the hardenability of the die must be as high and as uniform as possible within cost , toughness and heat treatment limits . in practice , the cavity initially sunk in the die block from which the die is made eventually wears oversized through use . when the maximum tolerance has been reached the die is removed , the face is cut down to sound metal , and the cavity resunk in the remaining material . this may be repeated several times before the useful life of the die is exhausted . the cost of the dies , including initial cost , hammer and press down time for removal , machining and installation requires that maximum production be obtained after each re - sinking . now , if the die has sufficient strength and toughness to remain in service without fracture , the most important use requirement is that the die be of substantially uniform hardness throughout so the production that can be expected from the last sinking is as great as can be expected from the initial sinking . a hot work forging implement was prepared in accordance with the invention as follows . on the basis of experience , it was determined that a c content of very close to 0 . 55 was best suited for this application . c , of course , provides strength and hardness to the die block . by long usage , a broad range of 0 . 50 - 0 . 60 c has been employed , and , on occasion , an intermediate range of 0 . 53 - 0 . 57 c . si was specified at 0 . 22 , again based on long experience which indicates that this amount of si contributes to cleanliness and deoxidation in the steel making process . the usual si range for this die block usage is 0 . 15 - 0 . 35 . a minimum of 0 . 50 ni is required to impart toughness to the steel , again based on experience . a minimum of 0 . 50 cr is required , based on experience , because of the beneficial effect cr exerts on deep hardening , wear resistance , tempering resistance , and the elevation of the lower critical temperature . a minimum of 0 . 20 mo is required , again based on experience , due to its ability to resist softening in use , for wear resistance , and hardenability . and finally , mn should be present because of its very effective depth hardening ability . if present in quantities very significantly above about 2 %, deleterious effects may be encountered , but up to this limit nearly any amount of manganese will exert a beneficial effect on hardenability and control sulfide hot shortness . now , it has long been known that hardenability can be measured and expressed mathematically , ( i . e . : by the formula log d i = log f c + log f si + log f ni + log f cr + log f mo + log f x , wherein the expression d i represents the ideal critical diameter , and the expressions f c , f si , f ni , f cr , f mo , and f x are factors which represent the hardenability contribution of each of the elements identified by the chemical symbol in the subscript and , with respect to f x , all other elements which may be present and which contribute to hardenability , all as exemplified by the example on page 78 of republic alloy steels , 1961 , republic steel corporation , cleveland , ohio ,) and related to the ability of a die steel to give satisfactory performance . for example , the ideal critical diameter , hereafter referred to by its conventional abbreviation d i , is often used as a measure of hardenability . long experience in die steel usage has disclosed that a minimum d i of 9 is desirable for satisfactory die steel performance . for a more detailed discussion of hardenability and d i , see republic alloy steels , 1961 , republic steel corporation , cleveland , ohio , pages 75 - 102 , wherein it will be noted that the ideal critical diameter can be defined as the diameter of a round which , if quenched in a perfect quench , will harden to 50 % martinsite at the center . for purposes of this invention , however , the mathematical determination of the d i as derived from calculations based on chemical composition is of basic importance , rather than any specific measurement of diameter . after determination of ( a ) the alloy element or elements which must be present to make possible the attainment of the required use properties -- here c , si , ni , cr , mo and mn , and ( b ) the minimum amounts of the most expensive of those elements , in addition to carbon , which must be provided to attain the required end use properties , -- here ni , cr and mo , and ( c ) the d i required , the method of obtaining the required d i is as follows : the d i factor attributable to each of c and the essential elements is determined . this is done by reference to a table giving the hardenability factor attributable to each alloy and level , adding the hardenability factor for the required c content and the hardenability factors for the aim , or required minimums , of the essential alloys ( here si , ni , cr and mo ), determining the hardenability factor for the required d i ( here 9 ), determining the difference , if any , between ( a ) the hardenability factor of the required d i and ( b ) the sum of the hardenability factors for carbon and the essential alloys , and , if ( b ) is less than ( a ), determining the amount of the least expensive alloy capable of exerting a beneficial effect on hardenability , here manganese , corresponding to the aforesaid difference . in the event a maximum practical upper limit of the first hardenability make - up element is reached for any reason , such as refractory attack in the case of manganese , before the required d i is achieved , the hardenability make - up element selection process may be repeated with successively more expensive elements as often as needed to reach the required d i . in the die steel of the present invention the order of addition of hardenability make - up elements on a lowest to highest cost basis would be manganese , chromium , nickel and molybdenum . to further illustrate , and referring to a conventional hardenability characteristics of alloys table and a conventional hardenability characteristics / d i conversion table , such as is found on pages 78 and 79 of the aforesaid reference , and a standard log / anti - log table if required , the sum of the hardenability factors corresponding to a d i of 9 is determined , which determination is derived from the sum of 1 + log 10 d i , namely 1 . 954 . thereafter the hardenability factors for 0 . 55 c , 0 . 22 si , 0 . 5 ni , 0 . 5 cr , and 0 . 2 mo , are determined from the table as follows : hardenabilityelement amount , % factors______________________________________c . 55 . 400si . 22 . 062ni . 5 . 073cr . 5 . 318mo . 2 . 204 sum 1 . 057______________________________________ their sum , 1 . 057 , is subtracted from 1 . 954 to determine the difference of 0 . 897 . since the hardenability factor for mn of 0 . 897 corresponds to 1 . 76 % mn , the steelmaker has determined that 1 . 76 % mn must be present to achieve a desired d i of 9 . if the foregoing calculation indicates that more manganese must be present than would be desirable , such as , for example , a process limitation based on excessive refractory attack due to a high manganese content , then only that quantity of manganese would be added which would avoid refractory attack , and the next least expensive hardenability make - up element , here chromium , would be added to achieve the required d i . first , the hardenability characteristics for c varies slightly with grain size . for calculation purposes a grain size of astm no . 7 is assumed . however , at least in the medium carbon range the variation in the hardenability factor due to grain size is not sufficiently great to significantly deleteriously affect the final result . hence grain size , as a factor , may be disregarded . secondly , since a carbon aim of 0 . 55 is desired , the calculations may be simplified by eliminating c and its hardenability factor ( here 0 . 400 ) from the equation , that is , by reducing the hardenability factor aim of 1 . 954 ( for a d i of 9 ) to 1 . 554 , and then ignoring carbon in subsequent calculations . this results in requiring calculations only for the less controllable elements such as si , cr , ni , mo and v . if the steelmaker is unable to achieve ideal control over other elements , such as si , the factor for such additional element or elements may be eliminated by an aim . as a further example , the following explanation is given of how to carry out the method of this invention . a heat of about 65 tons of steel was melted in an electric furnace with the following aim chemistry specification : c . 55 aim mn 2 max . p . 035 max . s . 035 max . si . 22 aim ni . 50 min . cr . 50 min . mo . 20 min . v residual al . 02 the charge consisted substantially of scrap principally containing the above elements . just prior to tap the heat was analysed to determine if the ladle composition would include ni - 0 . 50 min ., cr - 0 . 50 min ., and mo - 0 . 20 min . thereafter , upon determination that one or more of the three aforesaid elements would not reach ladle specifications as mentioned in the preceding paragraph , additions were made to bring the ladle composition to the desired minimums . thereafter a final analysis for ni , cr , mo and v ( in short , all elements which contribute to d i except p and s , which roughly cancel one another ) was made to ensure the ladle composition would satisfy the minimum requirements and determine the hardenability contributions of other elements in addition to ni , cr , mo and v which are present . thereafter the expected alloy hops were added . as those skilled in the art will appreciate , alloy hops are the difference in composition between the measured element at final in furnace and at the ladle sample which occur without deliberate addition , particularly in vacuum degassed steels as a result of the reduction of alloys in the slag into the bath due to the degassing process . thereafter , the hardenability factors for ni , cr , mo and v were determined from a hardenability characteristic table and added . thereafter the sum was subtracted from 1 . 492 which represents a d i of 9 less the hardenability factors for 0 . 55 c and 0 . 22 si . a mn content corresponding to the difference determined in the preceding step was then determined , and the difference between this quantity of mn and the measured mn was added to the furnace just prior to tap . normal post - tap procedures were followed to reach 0 . 55 c aim and 0 . 22 si aim , and the steel was vacuum degassed . following is a table of heats of steel which were melted according to the foregoing procedure . table i__________________________________________________________________________heat no . c mn p s si ni cr mo v al di__________________________________________________________________________118 , 125 . 56 . 88 . 019 . 030 . 28 . 92 . 81 . 33 . 023 . 036 11 . 22118 , 115 . 53 . 53 . 018 . 033 . 31 . 92 . 97 . 34 . 040 . 005 9 . 68118 , 101 . 55 . 86 . 024 . 024 . 29 . 65 . 85 . 28 . 027 . 032 10 . 09228 , 028 . 53 . 84 . 024 . 032 . 28 . 87 . 78 . 33 . 045 . 004 11 . 04128 , 251 . 50 . 79 . 024 . 035 . 24 . 79 . 90 . 34 . 040 . 026 10 . 84227 , 985 . 55 . 93 . 021 . 031 . 30 . 81 . 90 . 29 . 027 . 024 11 . 85217 , 968 . 57 1 . 04 . 025 . 035 . 30 . 72 . 80 . 31 . 020 . 016 11 . 51118 , 158 . 57 . 79 . 024 . 025 . 31 . 80 . 93 . 33 . 028 . 020 11 . 75128 , 407 . 54 . 56 . 019 . 030 . 33 . 65 1 . 02 . 36 . 030 . 026 9 . 91228 , 123 . 53 . 72 . 023 . 030 . 30 . 80 . 97 . 35 . 034 . 012 11 . 48228 , 117 . 50 . 85 . 024 . 033 . 23 . 84 . 90 . 33 . 025 . 008 10 . 62128 , 339 . 55 . 69 . 022 . 027 . 32 . 92 . 96 . 33 . 026 . 012 10 . 96128 , 289 . 50 1 . 02 . 017 . 035 . 29 . 59 . 80 . 32 . 035 . 018 11 . 35__________________________________________________________________________ in another test a heat was prepared in accordance with the foregoing procedure to the following final chemistry ( heat no . 117 , 905 ). heat treatment to an aim of bhn 352 was employed . ______________________________________ c . 55 mn 1 . 20 p . 024 s . 029 si . 28 ni 1 . 01 cr . 77 mo . 27 v . 033 al . 013______________________________________ the steel was vacuum degassed in the ladle using a purging gas by a process generally illustrated and described in u . s . pat . no . 3 , 236 , 635 , although this procedure is not considered mandatory . the after - vacuum temperature was 2855 ° f . by reference to the hardenability characteristic table , a d i of 13 . 7 was calculated which indicated the required use property could be achieved . a 11 / 4 × 16 × 16 inch thick center slice was taken from the long dimension of an 16 × 16 × 18 inch block . one diagonal and one face to shank hardness traverses were taken , and 3 longitudinal tensile tests were cored and 3 transverse tensile tests were sawed from specimens from the block . the following results were obtained . table ii______________________________________hardness traverse______________________________________along centerline 11 / 2 33 / 4 61 / 2 81 / 4 101 / 4 133 / 4 ( in . from side ) brinnel dia . 3 . 25 3 . 20 3 . 30 3 . 30 3 . 30 3 . 25along diagonal 2 51 / 2 9 111 / 8 131 / 2 17 201 / 4 ( in . from corner ) brinnel dia . 3 . 20 3 . 30 3 . 30 3 . 30 3 . 30 3 . 25 3 . 30______________________________________ it will be noted that from table ii that for a surface hardness of 3 . 25 bd 352 bhn this 16 × 16 × 18 inch block showed a maximum difference of 0 . 10 mm from surface to center . table iii______________________________________tensile tests of 16 &# 34 ; × 16 &# 34 ; × 18 &# 34 ; die block strength - psi per cent in 2 &# 34 ; yield red . oflocation direction tensile yield ratio elong . area______________________________________surface longitudinal 157 141 0 . 89 15 . 0 42 . 8quarter &# 34 ; 162 146 0 . 90 13 . 0 27 . 8diagonalcenter &# 34 ; 158 135 0 . 86 14 . 5 32 . 8surface transverse 165 148 0 . 89 12 . 5 27 . 2quarter &# 34 ; 154 138 0 . 90 4 . 5 9 . 2 * thicknesscenter &# 34 ; 152 129 0 . 85 6 . 5 12 . 6 * ______________________________________ * irregular fractures . the small variation in tensile strength supports uniformity of hardness observed . the center yield ratio of 0 . 85 in a 16 × 16 inch section which is about 5 % higher than the results obtained from a similar center section from a standard proprietary steel of the following nominal composition : c - 0 . 55 , mn - 0 . 75 , si - 0 . 27 , ni - 0 . 75 , cr - 0 . 90 , mo - 0 . 38 , v - 0 . 05 . charpy tests produced a general parabolic curve between a lower reading of 8 ft . lb . at 75 ° f and an average upper reading ( two tests ) of 22 . 5 ft .- lb . at 500 ° f . the steel had a transition temperature of between 100 and 200 ° f . a preliminary field test using a set of die blocks made from heat no . 117 , 905 was used to forge diesel cranks . for the initial sinking about a 15 % increase in die life was experienced over another competitive inexpensive die steel . in summary , the invention makes maximum use of alloys in scrap , makes possible controlled hardenability through a computer program or simple arithmetic . the system lends itself to a computer program due to the empirical nature of the steel composition make - up process , and makes possible the addition of alloys which yield maximum hardenability per dollar expended . although several embodiments of the invention have been illustrated and described , it will at once be apparent to those skilled in the art that the invention is not limited to the precise compositions and procedures hereinabove set forth , since in many instances the illustrative examples are based on an arbitrarily selected d i of 9 , and this factor may be different for different end uses . accordingly , the scope of the invention should not be limited to the specific examples above set forth , but , rather , should be limited solely by the scope of the hereinafter appended claims when interpreted in light of the pertinent prior art .