The Estimation of the Quenching Effects After Carburising Using an Empirical Way Based on Jominy Test Results

graphical and analytical solutions to solve the information transfer from the Jominy test samples to real parts are shown. The essay regarding the analytical solutions for the information transfer from the Jominy test samples to real parts includes detailed information and exemplifications concerning the essence and using the Maynier-Carsi and Eckstein methods in order to determine the quenching constituents proportions corresponding to the different carbon concentrations in carburized layers, respectively the hardness profiles of the carburized and quenched layers. In the final of the chapter, taking into account the steel chemical composition, the geometrical characteristics of the carburized product, the quenching media characteristics, the heat and time parameters of the carburising and the correlations between these values and the Jominy test result, an algorithm to develop a software for the estimation of the quenching effects after carburising, based on the information provided by Jominy test, is proposed. are determined by the presence of residual austenite and its presence implication on the hardness in the superficial layer; the obtained algorithm allows the very easily determination of the information regarding the effects of the carburising and quenching process on layer characteristics, starting from information provided by Jominy test. Metallurgical Engineering is the science and technology of producing, processing and giving proper shape to metals and alloys and other Engineering Materials having desired properties through economically viable process. Metallurgical Engineering has played a crucial role in the development of human civilization beginning with bronze-age some 3000 years ago when tools and weapons were mostly produced from the metals and alloys. This science has matured over millennia and still plays crucial role by supplying materials having suitable properties. As the title, "Recent Researches in Metallurgical Engineering, From Extraction to Forming" implies, this text blends new theories with practices covering a broad field that deals with all sorts of metal-related areas including mineral processing, extractive metallurgy, heat treatment and casting. jominy-test-


The particularities of quenching process after carburising
The aim of the quenching process after carburizing is to transform the "austenite" with high and variable carbon content of the carburized layer in quenching "martensite", respectively the core austenite in non martensitic constituents (bainite, quenching troostite, and ferriteperlite mixture). This goal is achieved by transferring the parts from carburizing furnace into a cooling bath containing a liquid cooling (quenching) medium. The transfer can be directly made from the carburizing temperature (direct quenching), or after a previous precooling of parts from the carburizing temperature to a lower quenching temperature (direct quenching with pre-cooling). In both ways, the austenitic grain size is the same (depending on the chosen carburising temperature and time), but the thermal stresses are different, being higher in the case of direct quenching and lower in the case of direct quenching with pre-cooling, due to higher thermal gradient achieved in the first cooling variant. Consequently, the risks of deformation or cracking of the parts are lower in the pre-cooling quenching, this variant being most commonly used in the industrial practice.
On the other hand, the result of quenching is influenced by three factors: one internal, intrinsic hardenability of steel (determined by its chemical composition -carbon content, alloying elements type and percentage) and two external (technological)thickness of the parts, expressed by an equivalent diameter D ech (the actual diameter in the case of cylindrical parts, or the diameter calculated using empirical relations for the parts with non cylindrical shapes) and cooling capacity of quenching media, expressed by relative cooling intensity -H (in rapport with a standard cooling media -still or low agitation industrial water at 20°C). In Fig. 1 an empirical diagram of transformation of non cylindrical sections (prisms, plates) in circular sections with the equivalent diameter D ech is shown; in Table 1, the indicative values of the relative cooling intensity of water and quenching oils -H are given depending on their degree of agitation related to the parts that will be quenched. If the parts have hexagonal section, it shall be considered that the cylindrical equivalent section has the D ech equal to the "key open" of hexagon.  Lately, in the industrial practice, the so-called synthetic quenching media with cooling capacity that can be adjusted in wide limits have also been used, from the values specific to mineral oils to those specific to water, by varying the chemical composition, temperature and degree of agitation.
The degree of agitation of quenching media can be adjusted by the power and /or frequency of propellers or pumps type agitators, mounted in the quenching bath integrated in the carburizing installation (batch furnaces).
The external factors (D ech , H) determine cooling law of the parts, respectively cooling curves of the points from surface or internal section of the parts; the internal factor (steel hardenability) determines quenching result, expressed by structure obtained from transformation of continuously cooled austenite from austenitizing temperature to final cooling temperature of assembly -parts-quenching medium.
To foresee or verify the structural result of quenching, the overlapping of the real cooling curves (determined by external factors D ech and H) over the cooling transformation diagram of austenite of chosen steel at continuous cooling can be made, which is a graphical expression of intrinsic hardenability of steel.
The diagram of austenite transformation at continuous cooling allows steel to achieve both a quantitative assessment of the quenching structure, the estimation sizes being the proportions of martensitic and non martensitic constituents and to estimate the hardness of quenching structure.

Use of Jominy frontal quenching sample for estimation of quenching process results
The estimation of the steel quenching effects represents an extremely complex stage due to large number of variables that influence this operation, respectively: steel chemical composition, austenitizing temperature in view of quenching, the parts thickness and the quenching severity of the quenching media. The problem can be solved in an empirical way using the frontal quenched test sample, designed and standardized by W. E. Jominy and A. L. Boegehold and named Jominy sample (Jominy test). The simple geometry of sample and the way of performing the Jominy test covers a large range of cooling laws, their developing in terms of coordinates T-t being dependent on the distance from the front quenched part to the end of the Jominy sample. Using these curves a series of kinetic parameters of the cooling process can be obtained: cooling time and temporary (instantaneous) cooling speeds or cooling speeds appropriate for different thermal intervals. From its discovery (1938) until present, the Jominy test has been the object of numerous determinations and interpretations, evidenced especially by means of drawing of the cooling curves, of the points placed at certain distances from the frontal quenched end. The European norm, ISO/TC17/SC7N334E, Annex B1, specify the aspect of the Jominy samples cooling curves in the surface points placed at the distances dj=2.5; 5; 10; 15; 25; 50 and 80 mm from the frontal quenched end (Fig.2 [1]). This representation has the advantage that can be applied to each steel and for each austenitizing temperature T A in terms of quenching, in the common limits T A =830~900°C, because has on the ordinate axis the relative temperature θ=T/T A , respectively the ratio between the current temperature T (in a point placed at the Analyzing the cooling curves from Fig. 2, a difference between those taken from the ISO standard and those from G. Murry work, is observed. To clarify these discrepancies and to adopt an unique and argued assessment of the way of setting out of the cooling curves in the case of Jominy samples, we can start to analyze the modality in which the heat transfers from Jominy sample to the ambient, during cooling of the sample from the austenitizing temperature T A to the ambient temperature T amb took place. In principle, the heat flow in a point P of the Jominy sample, placed at distance x from the frontal quenched end and at the distance r from the axis of the sample, at time t after the start of cooling is given by the differential equation: this can be solved in the following univocity conditions: a. initial condition: T (x,0) =T A ; b. boundary conditions of first order: T (0,t) =T water jet (on the water cooled surface) T (x,t) =T amb (along the cylinder generator) c. boundary conditions of second order defined by the specific heat flux through the frontal cooled surface and through the external cylindrical surface cooled in air, which are proportional with the negative temperature gradients: The heat loss during sample cooling takes place by means of three mechanisms: conduction -at the contact interface between cooling water and direct cooled surface, the heat loss value being a function of time: convection -of the ambient air, the heat loss value being a function of the T (x,t) -T amb difference where  is the convection heat transfer coefficient: radiation -from the cylindrical surface: where  is the radiation constant,    ;  is the emissivity coefficient of the sample surface; 8 24 J 5.67. 10 ms K The solving of the differential equation (1) lead to a solution representing the general form of the cooling curves equations of points placed at the distance x from the frontal quenched end: where the parameter c has speed dimensions (m/s), and the rapport c/x is a constant on which the temporary (instantaneous) cooling speed has a linear dependency: To simplify the analysis, without introducing further errors, can be admitted that T amb~0 and noting T (x,t) =T S (the current surface temperature) and T S /T A =θ (the relative surface temperature), the final solution can be written as: The solution (6) makes the direct connection between the relative temperature θ and time t, values that represent the coordinates in which are drawn the cooling curves of the points (planes) placed at the distance x from the frontal quench end of the Jominy sample.
In the work [2] the using of the relation (4) is exemplified in the case of Jominy samples austenitized at T A =1050 o C, for which the cooling curves of the points placed at the distances x=1, 10, 20 and 40 mm from the frontal quench end (Fig.4) were drawn and on which the ordinate referring to the relative temperature θ=T/1050 and also the ISO and Murry cooling curves for distances x = 1.5 mm (Murry), 9mm (Murry),10 mm (Murry), 20 mm (ISO and Murry) and 40 mm (Murry) were also drawn.
Using data taken from continuous curves presented in Fig.4 and replacing the notation x which represents the distance from the frontal quenched end of Jominy sample with E, the value of parameter c (from eq. 6) has found as c = 0.28, so that eq.(6) of cooling curves will get a particular form (7) and the inverse function, t = f (θ) will have the expression (eq.8) On the other hand, from Fig. 4 it can be seen that between the aspect of the actual cooling curves experimentally determined by Murry and ISO and that obtained by calculation, using the relations (7) and (8), there are differences which are substantially and simultaneously amplifying with the decreasing of the relative temperature θ. In conclusion, we can say that the theoretical analysis presented above is incomplete in that it fails to consider some effects of interaction between the types of heat loss during cooling of the Jominy samples.
Taking into account the higher matching of the Murry curves to theoretical curves, were mathematically processed the data provided by Murry curves and was noted that these are best described also by an exponential function, having the general form t=aE b , and the particular form as: where the parameter a depends on θ also by means of an exponential relation: In conclusion, the relations describing the dependencies tf E (,)   -eq.(8) and ftE (, )   eq. (7), will have the following particularly forms: Once the Jominy sample kinetic parameters are known for a sample made from a certain charge of steel, they can be attributed to a specific part (with an equivalent diameter, D ech known) made from the same charge of steel, taking into account that both the part and also the Jominy test sample to be processed in the same technological conditions (same austenitizing temperature T A and time t A ) and same quenching media (with the same relative cooling intensity, H). This condition will be accomplished in the case where the Jominy sample is "embedded" in the heat treatment charge, composed of identical parts and follows the same processing sequence, in the same heating and cooling equipment. The correlation between the Jominy test sample and real part with the equivalent diameter of D ech is usually graphically provided: a first chart was built by Jatczak [3] (for parts with equivalent discrete diameters of 12.5 mm, 19 mm, 25 mm, 38 mm, 50 mm and 100 mm). Jatczak diagram provides a graphical solution for the function dj = f (Dech, H, r), 0 ≤ r ≤ where R is the coordinate position of the point on the part cylindrical section, that has the same cooling law (curve) with that of points situated in the plane placed at the distance dj from the frontal quenched end of the Jominy sample.
For parts subject to carburizing, the correlation diagram -cylindrical part -Jominy sample will become the curve from the Jatczak diagram, referring to part surface S (as the layer thickness δ is very small compared to the equivalent radius of the part). In this case, the correlation function has the form dj = f (D, H) or D = f (dj, H), where D is the diameter of www.intechopen.com cylindrical part with length L ≥ 3D (or equivalent diameter of the parts with other forms of the section) and dj is the distance from the frontal quenched end of Jominy sample.
In Fig.6,the correlation diagram-Jominy sample -superficial layer of cylindrical parts drawn by U.Wyss [4] based on the method of Grossmann and numerous literature data is reproduced.
-For a cooling intensity of H=0.45, corresponding to intensive agitated oil: -For a cooling intensity of H=0.60, corresponding to strong agitated oil: -For a cooling intensity of H=1.00 , corresponding to low agitated water: The values of cooling intensity, H, shown above, are suitable for quenching oil used at normal temperatures (50 ~ 80 °C) and with different degrees of agitation (of oil and/or parts) in a relatively wide range, starting from absence of agitation (H=0.25) to strong agitation (H=0.6), or a shower or pressure jet oil (H = 1.00), this last situation being equivalent for low agitated cooling water at 20 ° C, .
With these observations, the graphical relation between the carburized layer of part with diameter D and points from the Jominy sample, carburized in the same conditions, in accordance with the scheme shown in Fig.7 is achieved, where both the superficial layer of part and also the Jominy sample are represented at very high magnification in rapport with actual size (the dimension of the carburized layer δ~0.5~2mm and the equivalent distance in the Jominy sample E ~ 2 ~ 20mm).

The graphical solving of correlation between real parts -Jominy sample
From the graphical representation shown in the Fig. 7 results that the A', B' and C' points of the carburized layer of the Jominy test sample, equivalent to A,B and C points of the part carburized layer, are located on the intersections of the horizontal plane placed at the E distance from the frontal cooling plane of the Jominy test piece with the vertical planes placed at the O, δ ef and δ tot from the Jominy test sample generator, characterized through the C s , C ef and C m constant carbon contents.
Based on the above considerations, a graphical solution of the issue regarding the correlation between the Jominy test sample and a part with D diameter, both carburized in identical conditions (same carbon profile and same hardness profile in the carburized layer) has developed by U. Wyss. Using of Wyss graphics solution requires the knowledge of the equivalent diameter of the part (D), the cooling intensity of quenching media (H), the carbon profile of carburized layer and the hardenability curves, respectively the hardness = f (%C) curves at various depths 0 ≤ δ ≤ δ tot in the case hardened layer of the Jominy test sample.
www.intechopen.com The information sources used by Wyss in developing of the scheme shown in Fig. 8 were the following: the D=f(dj) dependence for H=0.35, has been taken from Fig. 6; -the carbon profile curve has been experimentally plotting by means of sequential corrections of the case hardened layer of a part with dimensions of Φ35 x105 mm; Fig. 8. Deduction of the hardness profile in the carburizing layer for parts(d) and for the Jominy test sample from Jominy hardenability curves (c) for a given carbon profile of carburizing layer (b), after carburising at C s = 0.8% C of parts made of a case hardening steel with composition (0.16% C, 1% Mn, 1% Cr) and diameter D = 35 mm and subsequent quenching in oil with cooling intensity H = 0.35 (according to Wyss [4]).
the hardenability curves has been experimentally plotting by means of measuring of the HRC hardness on planes parallel with the Jominy test piece generator, corrected at the depths of the case hardened layer at which the carbon content is that mentioned on curve (0.60%C; 0.52%C; 0.45%C; 0.35%C; 0.29%C and 0.16%C).
The algorithm of using of the graphical solution is shown by arrows in Fig. 8 and involves the following steps: in the diagram (b) the horizontals lines corresponding to the hardenability curves from the diagram(c) will be plotted and the points of intersection with the carbon profile curve will be determined; from these points, vertical lines extending in the space of the diagram (d) are drawn and cross the horizontals plotted in an earlier stage (from the intersection points of the vertical E = 10 mm (diagram (a)) with the hardenability curves drawn for different carbon concentrations in the case hardened layer (diagram (c)); the intersection points belong to the hardness profile curve available for the existing space diagram (d). The point D in the diagram (d) in which the hardness profile curve crosses the horizontal corresponding to HRC ef hardness has the abscise corresponding to the effective depth δ ef (in the example discussed, for HRC ef = 52.5 results δ ef =1.38 mm); -from the crossing point D, the vertical line which will meet the carbon profile curve at point B of which horizontal corresponds to the actual carbon content, C ef (for example the analysis made for δef = 1.38 mm results C ef = 0.4% C).

Essay regarding the analytical solving of the real parts-Jominy sample correlation
The above graphical solution can be transformed into an analytical solution if the equations of the following curves are available: a for 0.6≤H≤1,00; 2≤E≤12(mm) and10≤D≤100 (mm): The parts that will be case hardened by instillation and pyrolysis of organic liquids are usually thin pieces with D ech ≤ 50mm, which are cooled in mineral oil with cooling intensity of H ~ 0.25 ~ 0.60. To this category of products it can be applied the above mentioned relations no. (18-19) thus achieving results very close to those achieved using Wyss relations (Fig.9).
where C δ represents the carbon content measured at the δ depth in rapport with the surface at the case hardening end; C m represents the carbon content of the non -case hardened core and C s is the surface carbon content at the end of case hardening.
where t k represents the carburising time, h=K/D, represents the relative coefficient of mass transfer, K-is the global coefficient of mass transfer in the case hardening medium; D -the diffusion coefficient of carbon in austenite.
c. For the Jominy hardenability curbes (c) have been deduced by E. Just [6] several regression equations having the general form:  (25-26).The three relations produce results significantly closer each to another and also very close to those provided by the graphical dependencies for a series of German steels presented in the work [7]. Therefore, it was adopted for explaining of the hardenability curve the relation no. (27)   In this purpose, the data from the Table 2 were used and exponential, logharitmic and logistic functions were explored, their graphics having the ordinate at origin different from zero and positive (is known the fact that the technical iron can be quenched to a structure of "massive" acicular ferrite, close to the martensite with low carbon and which, according to relation ( and their principle graphics being shown in Fig. 10. The formulas no. (34) and (35) give results very close each to another and also close to the experimental data referring to steels with carbon content in the limits 0.1~0.8%.
Furthermore the Johnson function can be used with satisfactory results also for the calculation of the hardness of the quenched layers in which the martensite proportion decreases to 50%.
The general calculation relation and the auxiliary relations are shown in Fig.11.
Whereas in many literature works the hardness is expressed in Vickers units, is necessary also a Rockwell-Vickers equivalence relation. In this purpose, mathematical tables and graphics equivalence HRC-HV -were processed and the following relation have been obtained, depending on the load used to determine the Vickers hardness: for loads F≤1Kgf (9,8N) a. Concerning the data provided by the graphical dependencies and relations from Fig.11 it must be specified that these are referring to the "ideal case" in which cooling of the austenite subject to quenching is achieved below M f temperature, who, like the M s temperature decreases with the increasing of steel carbon content (austenite) and becomes negative at higher carbon concentrations than 0.6%. In this case, if the austenite is cooled to room temperature or even above, in structure will remain a significant proportion of residual austenite, which decreases the hardness below the level indicated by the curves in Fig.11.
Typically, the proportion of residual austenite is calculated by Koistinen-Marburger relation:   Returning to the analytical solution of the correlation between Jominy sample and real parts, which should finally allow to draw the hardness curve of the carburized and quenched www.intechopen.com layer, is noted that this solution is materialized in a mathematical model of post carburising quenching, whose solving algorithm is based on knowing of the initial data referring to the following independent variables: a. chemical composition of steel, respectively the alloying factor; . the geometry of parts subject to carburising, respectively the equivalent diameter D ech ; c. the cooling intensity of the quenching medium, respectively the Grossmann (H) relative cooling intensity; d. the requested effective hardness (HRC ef ); e. the requested effective case depth(δ ef ).
Starting from this initial data, the algorithm for determining of the hardness curve of carburized and quenched layer will require the following sequence of steps: Step I taking into account the geometry of parts subject to processing, the equivalent diameter D ech is calculated with one of the equivalence relations mentioned in Fig.1.
Step II taking into account D ech and h, is calculated the equivalent distance E from the frontal quenched end of the Jominy sample by means of the relation (19)  for several German case hardening steels (Fig.12) with the average chemical composition (according to DIN-tab.3), without mentioning of the calculation formula or the effective values of the alloying factors S. Fig. 12. Correlation between the effective carbon content and the Jominy equivalent distance for different German steels with the average standard chemical composition [4].
In addition, U. Wyss suggested the using of a linear relation to calculate the actual carbon content as it follows: In which the slope f c is a hardenability factor of steel, having the values written on the corresponding lines, drawn in Fig.12.
In connection with this approach of the problem, it is observed that the use of relation (46) is possible only for certain intervals corresponding to equivalent distance E, intervals on which the value obtained for C ef52.5 is not lower than 0.33% and is not different more than ±0.03% in rapport with curve (parable) replaced by the line corresponding to a given steel. These limits for E are mentioned also in the table placed on the right of Fig. 12.
In the work has been calculated the effective carbon content with formula (45), both for the German steels and also for the Romanian steels having an average chemical composition according to DIN and STAS (Table 3), using for the calculation of the alloying factor the relation S=21Mn+22Cr+7Ni+33Mo. The variation of the effective carbon content with the Jominy equivalent distance for the specified steels is shown in Fig. 13.
The analysis of the curves from Fig.13 led to following conclusions: a. for the steels with close values of the alloying factor, S, the curves are close positioned or even overlapped (case of 20MoNi35, 16MnCr5, 18MnCr10 and 21TiMnCr12 steels, having S=44.3 ~45.25 and of the steels 15CrNi6 şi 21MoMnCr12, having S~55.55); b. the ordinates at origin and the rate of curves are strongly decreasing with the increasing of the value of the alloying factor, S. As a result, the curves can be replaced with straight lines with different slope, but also with ordinates having different origins, both being dependent of alloying factor S. Putting the condition that the replacing lines do not lead to deviations higher than ±0,03%C, the generalized equation of these lines was:  Table 4. The values of parameters ef C 0 , c f and the intervals for E in which is applied the linearizing relation (47) for the German and Romanian steels with medium standardized chemical composition.
In fact, the effective carbon content can has lower values than those ensuring a certain minimum proportion of quenching martensite. If in Fig.11 will be drawn the horizontal corresponding to the effective hardness of 52.5 HRC can be found that this value is assured by the following combinations of effective carbon contents and respectively martensite percentages in the hardening structure: On the interval 80≤M≤100%, the effective carbon content has a lineraly variation with the martensite proportion, according to relation: Setting the condition that for the effective case depth the actual proportion of martensite to be within the required range (to provide appropriate mechanical characteristics of the carburized and quenched layer), can be noted that the maximum amount of the effective carbon content should not exceed 0, 56% (value which is close to the carbon surface content of about 0.8%, with a drastic reduction of the carburizing depth, particularly in steels with low hardenability, respectively with an alloying factor S ≤ 30).On the other hand, the value of the C ef52,5 will not decrease more below 0.34%C because even the quenching structure for the effective depth is fully martensitic, its hardness decreases significantly below the set value (52.5HRC). This is the reason for why U.Wyss adopted for the 17CrNiMo6 steel the www.intechopen.com amount C ef =0.33%, although in the carburized layer of steel, the information offered by relation (45) and Fig.13 shown that the hardness of 52.5HRC can be obtained even for the content of 0.17%C of core (at E=13 mm). In a subsequent paper [7], Weissohn and Roempler suggest as minimum value for the carbon content with the concentration of 0.28% (for which HRC 100M~4 9.4, according to Fig.11). Adopting a value below that of the 0.34% could be justified for alloyed steel intended for carburising, due to the fact that alloyed martensite has a hardness higher with 1~2HRC than that of unalloyed steels.
In conclusion, for the calculation of the effective carbon content ( ef HRC C ,52.5 ) can be used the linearizing relations (47-49),with supplementary restrictions: ≤0.56% (respectively 100≥M≥80%) Step IV Using C ef and δ ef , can be calculated the carburising time (t k ) at isothermal carburising with a single cycle or the active carburising time (t k ) ,respectively the diffusion time (t D ), at carburising in two steps. The performing of this calculation supposes the knowing of thermal regime (t k, t D ), the chemical regime(C potK, C pot D ), the corresponding evaluation of the global mass transfer in the carburising medium (K); and the diffusion coefficient of carbon in austenite (D).
Step V is based on knowing of the carbon profile and of the cooling law (curve) of the layer and has as final purpose the drawing of the layer hardness profile. The carbon profile can be determined after the step IV, and the cooling curve of layer can be drawn using the relation (11).
The most direct method for determining and drawing of the hardness profile consist in overlapping of the cooling curve of the case hardened layer on the transformation diagrams of continuous cooling of austenite (CCT diagrams) "of different steels" from the layer, steels with carbon content that decreases from surface to core. The method is illustrated in Fig.14, for the case where the diagrams for the austenite transformation, corresponding for three steels with different carbon content that will be carburized, are known: a. with carbon content of core, C m ; b. with effective carbon content, C ef ; c. with carbon content of surface, Cs Because the temperatures corresponding to Ms point and the transformation ranges for the three diagrams are placed differently in the plane T-t (at a lower position and to the right, as the carbon content increases), the intersections of these with the cooling curve led to different structures (decreasing of the proportions of bainite and increasing of the proportions of martensite), respectively with different hardnesses (HRC m < HRC ef < HRC 100M For an accurate drawing of the hardness profile, is necessary to know a minimum number of 5-6 austenite transformation diagrams, corresponding to different carbon contents for a steel having in its chemical composition, all the other elements that are permanently accompanying and alloying elements with the same contents. But, this kind of technical "archive" is not currently available, even in the richest databases for the usual casehardening steels. To overcome these difficulties can be used a hardness calculation method based on knowledge of chemical composition and of a kinetic parameter characteristic to cooling law of the case hardened layer. This parameter can be the cooling time at passing through a certain temperature enclosed between the austenitizing temperature (T A ) and ambient temperature (T amb ). Most of the kinetic parameters of this type are the times of passing through temperatures of 700°C, 500°C and 300°C respectively t 700 ,t 500 şi t 300 , highlighted also on CCT diagrams in Fig. 14 ). The advantage of using of these kinetic parameters is that can be built structural diagrams in coordinates T-lgt or T-lgv, in which the cooling curves are replaced by verticals lgt or lgv and on basis of these, also structural diagrams in coordinates % structural constituents -lgt (lgv).

Method Maynier-Carsi
In the works [8] and [9] is used a calculation method derived from the analysis of 251 diagrams of transformation of austenite at continuous cooling, method in where the kinetic factor taken in consideration is the instantaneous cooling speed at passing of the cooling curve through the temperature of 700°C,respectively: In the calculation, the authors have introduced also the austenitizing parameter:  parameter (of the austenitic grain size), and Ei represent the proportion of carbon, adding elements and alloying elements.
The particular forms of the regression relations are given in The two relations offer results in accordance with data of Fig. 15, for 1.5≤E≤30mm.
Admitting that the austenitizing temperature, for the data shown in Fig.15 is T A =850°C (which is not specified in the work [9], but is usually used in other works in the field), the absolute instantaneous cooling speed v 700 can be replaced with the relative speed v 0,825TA , which will be calculated with the relation: , value which is very close to that given by the relation(54), this is confirming also the validity of the relations (11) and (12).
Taking into account the critical speeds (calculated with the relations from Table 5) and the carbon profile curve of the carburized layer allow the overlapping of the structural diagrams at different carbon concentrations and taking into account the speed v 700 (v 0,825TA ) of layer, allow the positioning of the vertical of this speed in the space of the structural diagram and the deriving of the proportions of the quenching constituents for each carbon content (respectively for each depth) of carburized layer.

The Eckstein method
In paper [10], another drawing method of the hardness profile curve is provided, which is considered to be described as a complex exponential function as it follows: where S H is the surface hardness, respectively the martensite hardness which has the superficial carbon content C s , E is the equivalent Jominy distance in the depth of the case hardened layer, and b and c are the coefficients dependent on the steel chemical composition.
For the calculation of the Jominy equivalent distance, the author provides the formula:  Due to fact that in both relations, the independent variable is the cooling time A T t 0.59 , become necessary to find a modality for calculation of this time depending on part diameter , D, on cooling intensity of the quenching medium, H and on the carburising depth δ. In this purpose, were used the data provided by the graphical dependencies from work [10], referring to the experimental determination of the time A t /5 in accordance with the carburising depth δ, which are combined with the data provided by Fig. 16 and 6   In order to properly use the relation (58), the b and c coefficients also have to be known; for these coefficients no information is available in the technical literature, including the work [10].
In conclusion, the effects of post carburising quenching process can be quantified by the calculation algorithm required by Maynier-Carsi, but corrections have to be applied; these corrections are determined by the presence of residual austenite and its presence implication on the hardness in the superficial layer; the obtained algorithm allows the very easily determination of the information regarding the effects of the carburising and quenching process on layer characteristics, starting from information provided by Jominy test.