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G.E. Totten and G.M. Webster Union Carbide Corporation Tarrytown, NY

C.E. Bates University of Alabama - Birmingham Birmingham, AL

S.W. Han and S.H. Kang Kum Won Industrial Co. Ltd. Ahsan, Korea

ABSTRACT The use of Grossman quench hardenability factors have been traditionally used in almost every text that discusses quenchant selection. In fact, such factors are often used as graphic illustrations for the selection of various quenchants with respect to steel hardenability. However, there a number of problems with this process. The objective of this paper is to analyze the traditional application of Grossman H-factors for quenchant selection. INTRODUCTION Hardness is one of the primary quality and tensile strength indicators in quench and tempered steels. The ability of a quenchant to harden a particular steel under specific quenching conditions traditionally has been experimentally determined by performing cross-sectional hardness surveys on quenched bars. However, quench severity estimation by this method is subject to reproducibility problems due to procedural and lot-to-lot chemistry variations in the steel. Historically, Grossman quench severity, or H-Factors as they are commonly known, have been used to describe quench severity. [1] [2] The Grossmann H-Factor is defined as the ratio of the effective heat transfer co-efficient (h) at the part surface divided by twice the thermal conductivity (k) of the metal: Recently, there has been increasing use of H-Factor characterization of quenchants Variations of Figure 1 [3] have been published to illustrate: oil quench severity equivalency, and quenchant selection with respect to H-Factors [4]. Recently, similar charts have been used to suggest the suitability of particular polymer; poly(alkylene glycol), poly(vinyl pyrrolidone), poly(sodium acrylate) and poly(ethyloxazoline) for quenching particular steel alloys and cross-sections. In view of the apparently increasing interest in the use of this traditional method, it is of interest to review the methods of experimentally determining H-Factors and the limitations of the information inherent in their use. These subjects will be addressed here.

H =

h 2k

Figure1 - Illustration of a typical H-Factor chart suggested for use in polymer quenchant selection.

DISCUSSION 1. Review of Classical Method of H-Factor Calculation

The actual attainable hardness of steel is primarily dependent on carbon content and is independent of the presence of alloying elements. To maximize hardness, it is usually desirable to maximize martensite content. The interrelationship between carbon content, amount of martensite and hardness is illustrated in Figure 2. This data is important in calculating the maximum attainable hardness for any steel grade up to approximately 0.6% carbon. Hardenability refers to the ability of a steel to be hardened by the formation of martensite after quenching. Steels are not considered to have been effectively hardened if they contain less than 50% martensite. Figure 3 - Jominy curves of low, intermediate and high hardenability AISI 4140 steel. Ideal diameter (DI) refers to the diameter of a bar that can be quenched to give 50% martensite in the center with an infinite quench (i.e. salt brine quench). An infinite quench is defined as a sufficiently severe quench so that the heat removal rate is controlled by the thermal diffusivity of the metal and not be the heat transfer rate from the steel to the quenchant. Typically, aqueous salt brine, either caustic or sodium chloride, is used to provide the infinite quench conditions. Typically, DI values may vary from less than one inch for difficult to harden, plain carbon steels such as AISI 1045 to values in excess of 10 inches for high hardenability steels such as AISI 4140. DI values are an excellent means of comparing the relative hardenability of two steels. The use of DI values are a critically important means of determining if it is even possible to harden a particular cross-section size of a particular steel. Ideal diameter is affected by the grain size of a steel as shown in Figure 4. Grain size is defined by a standard ASTM number; the larger the number, the larger the grain size. In general, most steels have a grain size of at least 7-8. DI values can be calculated from the use of alloy factors such as those tabulated in Table 1. For example, to calculate the DI value for the following steel with a grain size of 8: Element C Si Mn Ni Cr Mo Table 1 % 0.30 0.20 0.40 0.15 0.95 0.15

Figure 2 - Correlation of carbon and martensite content with Rockwell hardness. The classical method of illustrating depth of hardening is to perform a Jominy end-quench test. In this test, a standard size cylindrical specimen (1 inch dia. x 4 inch long) is "flood quenched" at the end with a specified spray pressure. Specimen hardness will be greatest at one end where the quenchant spray impinges the specimen and will decrease with increasing distance from the quenched end. After quenching, the hardness of the bar is determined at 1/16 inch intervals (J-values) from the quenched end. This data is used to construct Jominy curves such as those shown in Figure 3. Examples of three Jominy curves representing high, intermediate and low alloy chemistry of AISI 4140 steel are shown in Figure 3. While experimental determination of Jominy curves is the best way of obtaining this data, excellent results can be obtained with various computerized Jominy curve generation programs ("predictors").

Alloy Factors For The Calculation Of Ideal Diameter (A) Base ideal diameter, DIjominy, at the following carbon grain size No. 6 No. 7 No.8 0.0814 0.0750 0.0697 0.1153 -.1065 0.0995 0.1413 0.1315 0.1212 0.1623 0.1509 0.1400 0.1820 0.1678 0.1560 0.1991 0.1849 0.1700 0.2154 0.2000 0.1842 0.2300 0.2130 0.1976 0.2440 0.2259 0.2090 0.2580 0.2380 0.2200 0.2730 0.2510 0.2310 0.284 0.262 0.2410 0.295 0.273 0.2551 0.306 0.283 0.260 0.316 0.293 0.270 0.326 0.303 0.278 0.336 0.312 0.287 0.346 0.321 0.296 ... ... ... ... ... ...

Carbon, % 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

Mn 1.167 1.333 1.500 1.667 1.833 2.000 2.167 2.333 2.500 2.667 2.833 3.000 3.167 3.333 3.500 3.667 3.833 4.000 4.167 4.333

Alloying factor, fX, where element, X is Si Ni Cr 1.035 1.018 1.1080 1.070 1.036 1.2160 1.105 1.055 1.3240 1.140 1.073 1.4320 1.175 1.091 1.5400 1.210 1.109 1.6480 1.245 1.128 1.7560 1.280 1.246 1.8640 1.315 1.164 1.9720 1.350 1.182 2.0800 1.385 1.201 2.1880 1.420 1.219 2.2960 1.455 1.237 2.4040 1.490 1.255 2.5120 1.525 1.273 2.6200 1.560 1.291 2.7280 1.595 1.309 2.8360 1.630 1.321 2.9440 1.665 1.345 3.0520 1.700 1.364 3.1600

Mo 1.15 1.30 1.45 1.60 1.75 1.90 2.05 2.20 2.35 2.50 2.65 2.80 2.95 3.10 3.25 3.40 3.55 3.70 ... ...

(a) The ideal diameter (DI) is calculated from:

DI = D IC · Mn · Si · Ni· Cr · Mo

Where DIC is the basic DI factor for carbon and is the factor for the alloying element The first step is to determine the base DI value which is dependent on the carbon content and grain size. For this steel, the grain size is 8, locate 0.3% under the carbon column in Table 2 and read the base DI value which is 0.1700. The next step is to determine the alloy factors. This is done by locating the elemental percentage in the carbon column and then locating the alloy factor under the appropriate element column. For example, the alloy factor for Si for this steel alloy is 1.14. The remaining alloy factors are calculated similarly:

Figure 4 - Variation of ideal diameter with ASTM grain size and carbon content of steel.

Element Alloy Factor Si 1.14 Mn 2.33 Ni 1.055 Cr 3.052 Mo 1.45 The DI value is calculated by multiplying all of the alloy factors together with the base DI values:

DI = 0.17 x 1.14 x 2.33 x 1.055 x 3.052 x 1.45 DI = 2.10 inches This calculation shows that it is not possible to harden a cross-section larger than 2.1 inches and still obtain at least 50% martensite, no matter what quenchant is used! DI values are dependent on the shape of the specimen being evaluated. For example, round bars, square bars and plates will have their own unique DI values. The DI values for different shapes can be interconverted using Figure 5. These interrelationships are linear since they are dependent on surface to volume ratios. Table 2 shows the cooling rate at each Jominy position when the specimen is quenched in room temperature water. This data shows why section size has such a dramatic effect on as-quenched hardness.

Cooling Rate at Each Jominy Position for Room Temperature Water Distance from water quenched end, 1/16 in. 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 Cooling Rate


C/s 270 170 110 70 43 31 23 18 14 11.9 9.1 6.9 5.6 4.6 3.9


F/s 490 305 195 125 77 56 42 33 26 21.4 16.3 12.4 10.0 8.3 7.0

Figure 5 - Interconversion of ideal bar diameter as a function of shape

As described previously, the Jominy end-quench test is conducted by quenching an austenitized steel bar by spraying one end of the test specimen. However, most commercial quenching processes involve some variation of an immersion quench. When a steel workpiece is quenched in this way, it is important to determine if the bar is adequately through-hardened, or to determine the depth of hardness. Jominy data, obtained by experiment or computer calculation, can also be used to calculate the depth of hardness in standard workpieces that are immersion quenched. This is done by calculating the Jominy equivalent distance as illustrated in Figure 6. This calculation assumes that cooling rates at two positions in the bar will exhibit the same hardness. In this case, the hardness at a subsurface value versus the same hardness at a known J-value on the Jominy bar, are the same. To calculate the equivalent Jominy condition (Jeq), it is first necessary to introduce the Grossman Quench Severity Factor (H). Typical values that have been traditionally used for water, oil, molten salt, brine and air are provided in Table 3. The water quenchant is assumed to be at 80oF. An H-Factor of 5.0 is about as high as is practically achievable and represents an "infinite quench".

Table 2

Table 3

Approximate Grossman Quenching Severity Factor Of Various Media In The Pearlite Temperature Range Circulation or agitation Brine (a) None 2 Mild 2 - 2.2 Moderate ... Good ... Strong ... Violent 5 (a) Ref. 3 (b) Ref. 14 Source: Ref. 15 (c) Water Temperature 580 oF Grossman quench severity factor, H Water (a) (c) Oil (a) & salt 0.9 - 1.0 0.25 - 0.30 1.0 - 1.1 0.30 - 0.35 1.2 - 1.3 0.35 - 0.40 1.4 - 1.5 0.40 - 0.50 1.6 - 2.0 0.50 - 0.80 4 0.80 - 1.10

Air (b) 0.02 ... ... ... ... ...

Table 4 provides a relationship for equivalent bar diameter as a function of Jominy distance for three quenchants; oil, water, and brine. H-Factors for two agitation conditions, still and circulated are also provided. The use of this Table is illustrated by the following example: The Jominy curves shown in Figure 3 indicates that one steel exhibits a Rc hardness of 45 at the J4 (4/16) position. What is the maximum diameter that can be quenched in still water which will produce Rc of 45? The solution is to locate the J4 distance in the end-quench column in Table 4. The equivalent bar diameter is then determined from the still water column that corresponds to the J4 position and is found to be 1.15 inches. An alternative representation of Jominy equivalence is illustrated by Figure 7 where Jominy distance, cooling rate and equivalent bar diameters are shown for a water and an oil quench under "mild agitation" conditions.



Fluid viscosity is 1.0 m/s (1 cSt). Correlation of equivalent cooling rates in the end-quenched hardenability specimen and quenched round bars free from scale. Data for surface hardness are for mild agitation.

Figure 6 - Illustration of interconversion of "Equivalent Jominy Distance" and Bar diameter.

Figure 7 - Equivalent cooling rates at 705oC (1300oF) for round bars quenched in: A. water and B. oil. Table 4

EFFECT OF END-QUENCH DISTANCE & GROSSMANN QUENCH SEVERITY, H, ON THE EQUIVALENT BAR DIAMETER Equivalent bar diameter when quenched (a) Infinite or idealized Still, Circulated, Still, Circulated, Still Brine quench, mm 1/16 in. in. H = 0.25 H = 0.45 H = 1.0 H = 1.5 H = 2.0 H = 1.5 1/16 0.1 0.15 0.3 0.35 0.4 0.7 ... 3 2/16 1/8 0.2 0.3 0.5 0.65 0.75 1.15 3/16 0.35 0.55 0.85 1.0 1.25 1.15 ... ... 6 4/16 1/4 0.5 0.80 1.15 1.3 1.5 1.9 5/16 0.6 0.95 1.4 1.6 1.75 2.2 ... ... 10 6/16 3/8 0.8 1.2 1.6 1.8 2.0 2.4 7/16 1.0 1.4 1.8 2.0 2.3 2.7 ... ... 13 8/16 1/2 1.1 1.5 2.1 2.3 2.5 2.9 9/16 1.3 1.7 2.3 2.5 2.7 3.2 ... ... 16 10/16 5/8 1.4 1.9 2.5 2.7 2.9 3.4 11/16 1.6 2.1 2.8 3.0 3.2 3.6 ... ... 19 12/16 3/4 1.7 2.2 3.0 3.2 3.4 3.8 13/16 1.9 2.4 3.2 3.4 3.5 4.0 ... ... 22 14/16 7/8 2.0 2.5 3.3 3.5 3.7 4.2 15/16 2.1 2.7 3.5 3.7 3.9 4.4 ... ... 25 16/16 1 2.3 2.8 3.7 3.9 4.1 4.6 17/16 2.4 3.0 3.9 4.1 4.2 4.7 ... ... 29 18/16 1 1/8 2.5 3.1 4.0 4.2 4.4 4.9 19/16 2.6 3.3 4.1 4.4 4.5 5.0 ... ... 32 20/16 1 1/4 2.7 3.4 4.3 4.5 4.7 5.1 21/16 2.8 3.5 4.4 4.7 4.8 5.3 ... ... 35 22/16 1 3/8 2.9 3.6 4.5 4.8 4.9 5.4 23/16 3.0 3.7 4.7 5.0 5.1 5.5 ... ... 38 24/16 1 1/2 3.1 3.8 4.8 5.1 5.2 5.6 25/16 3.2 4.0 4.9 5.2 5.3 5.8 ... ... 41 26/16 1 5/8 3.3 4.0 5.0 5.3 5.4 5.9 27/16 3.4 4.1 5.1 5.4 5.5 6.0 ... ... 44 28/16 1 3/4 3.5 4.2 5.2 5.5 5.6 6.1 29/16 3.6 4.3 5.3 5.6 5.6 6.2 ... ... 48 30/16 1 7/8 3.6 4.4 5.4 5.7 5.7 6.2 31/16 3.7 4.5 5.5 5.8 5.8 6.3 ... ... 51 32/16 2 3.8 4.55 5.55 5.8 5.9 6.4 (a) When the end-quench hardness curve of a steel has been found, this table enables the user to estimate the hardnesses that would be obtained at the centers of quenched round bars of different diameters, when that same steel is quenched with various severities of quench. For each successive 1/16 in. position, the hardness obtained in the end-quench test would be found at the center of the bar size. Distance from end in end-quench test Oil Water

The same data that was cited in the previous example for a hardness that would correspond to the J4 position will now be used again. From Figure 3, the J4 position is located and the

centerline equivalent bar diameter is located on the right axis and is found to be approximately 1.25 inches.

Figure 7 can be used to calculate hardnesses at positions other than the at the center of a round bar. For example, what would be the hardness at the 1/2 R position for the same bar? It has already been shown that center of the bar of a maximum of 1.25 inches would be Rc 45 which corresponds to a Jominy position of J4. From the same chart, the 1/2 R position corresponds to J3. From the Jominy curve, the J3 position corresponds to Rc of approximately 48. The Jominy distance conversion chart in Figure 8 can be used to locate either the equivalent diameter or the corresponding Jominy distance for a known H - Factor. For example, if a still water quench is being used, this would correspond to H = 1.0. The equivalent bar diameter in the J4 position would be located by the bar diameter that intersects the J4 position and the H = 1.0 tie line and is seen to be approximately 1.2 from Figure 8. If the H-Factor is known, it is possible to obtain the Jeq distance.



Figure 8 - Calculation of the hardened bar diameter from equivalent Jominy distance. A variation of the Jominy equivalence approach is to use the Lamont transform [2]. This transform allows the interrelationship of any Jominy position and equivalent bar diameter for different amounts of through-hardening if the HFactor for the quenchant is known. Two of the transformation diagrams available are provided in Figure 9. Figure 9 - Croft - Lamont transformation for various H-Factors. NOTE: Other transformation diagrams are available in Reference 2. Although these approaches have served the industry well for many years, there are numerous problems with applying H-Factors, at least as shown, for predictive purposes. One of the difficulties, is the failure to adequately quantify agitation rates. There is no physical meaning to a value denoted as "mild", "violent", etc. Another problem is the way that agitation is applied. For example, with the exception of some induction hardening applications, flood quenching, such as that used for the end-quench test, is not used. Other difficulties have been reviewed by Murthy. [5] 2. Quantitative Experimental Determinations of H-Factors

Monroe and Bates have described the use of a cooling curve technique to estimate H-Factors.[6] In this work, analytical cooling curves were first calculated using a finite difference heat transfer program. Thermal properties of Type 304 stainless steel, the material used to construct the probe used for cooling curve measurement, were input into the program and specific quench severity values were imposed at the probe surface. Cooling curves were calculated for bars with 0.5, 1.0, 1.5 and 2.0 inch diameters and a length of at least four times the diameter which minimized end cooling effects. The calculated time/temperature data were subsequently analyzed to determine the cooling rate at 1300° F (705°C) as a function of imposed quench severity and bar diameter. A temperature of 1300°F (705°C) was selected for cooling rate analysis since much of the metallurgical literature on steel transformations is related to cooling rate at this temperature. The calculation results are presented in Table 5.

H = ( AX C ) exp( BX D )

where: H is the Grossman H-Factor, A is the cooling rate (°F/s) at 1300°F (705°C), A,B,C, and D are statistical model parameters from Table 6. As Figure 10 indicates, this model provides an excellent fit to the modeled data. This approach was used to statistically model the effect of polymer quenchant concentration, agitation and bath temperature on H-factors for a PAG (polyalkylene glycol) [8] and a PVP (polyvinylpyrrolidone) [9] quenchant. The results are summarized in the contour plots shown in Figures 11. These data show that both quenchants are capable of producing a broad range of H-Factors. However, a single HFactor value provides no insight at all into the relative processing latitude of either quenchant.

A statistical model was developed to fit these data:[7] Table 5 Cooling Rate at 1300°F (°F/s) Versus H-Factor Probe Diameter (inches) 0.5 Cooling Rate (oF/s) 15.2 30.0 58.3 85.2 109.8 132.6 159.5 182.7 241.3 286.9 333.7 367.9 427.2 476.2 1.0 Cooling Rate (oF/s) 7.5 14.6 27.5 38.5 47.8 55.8 64.4 71.8 88.7 100.1 111.2 119.0 130.0 140.0 1.5 Cooling Rate (oF/s) 4.9 9.5 17.1 23.1 27.9 31.9 36.0 39.4 46.7 51.5 56.0 58.9 62.7 66.6 2.0 Cooling Rate (oF/s) 3.6 6.9 11.9 15.7 18.6 20.9 23.3 25.1 29.0 31.5 33.8 35.1 37.0 38.5 Approximate H-Factor 0.10 0.20 0.40 0.60 0.80 1.00 1.25 1.50 2.25 3.00 4.00 5.00 7.00 10.00

Table 6 Model Parameters for H-Factor Calculation where: H + AXcebxo H = Grossman H-Factor X = CoolingRate a 1300 oF(1)

A, B, C, D = MODEL PARAMETERS (See below)

Probe Dia. (In.) 0.5 1.0 1.5 2.0

Figure 10 - Grossman hardenability factor versus cooling rate at 1300°F.

A 0.002802 0.002348 0.002309 0.003706

B 0.1857 x 10-7 0.2564 x 10-9 0.5724 x 10 0.3546 x 10

-9 -10

C 1.201 1.508 1.749 1.847

D 2.846 4.448 5.076 6.631

(1) All probes were cylindrical and were constructed from AISI type 304 stainless steel with a Type K thermocouple inserted to the geometric center.



Figure 11 - Grossman H-Factors for a PAG quenchant as a function of bath temperature, agitation rate and concentration for: A. PAG quenchant and B. PVP Quenchant. The Monroe and Bates calculation procedure does permit a good estimate of quenchant H-Factor for the quenching

conditions of interest, however, there are a number of fundamental limitations of with their use to compare various different quenchant media, including different quenchants, that cannot be overcome. These include: 1. Grossman H-Factors only reflect the ability to harden steel. They do not tell anything at all about steel cracking and deformation. For example, there are a number of recent references to the successful use of PAG polymer quenchants to quench 52100 bearing steel [10] and AISI H13 tool steel [11] which would not have been expected to be possible from the various polymer quenchant H-Factor plots such as Figure 1 that are currently available. 2. To estimate cracking propensity and even throughhardening hardness profiles, the total cooling process must be considered. H-Factors tell nothing about potential thermal and transformation stress generation during the quenching process. 3. Grossman H-Factors only refer to quench severity at a single very narrow temperature region (1300°F/705°C) of the steel transformation process. Although they are intended to indicate the ability of a quenchant to harden steel, they do not account for the cooling time required to achieve this process. To properly account for cooling time, a superposition of both the quenching cooling curve and the steel transformation curve must be performed. 3. Quench Factor Analysis An excellent method of using a single number which will reflect this overall hardening process is the application of Quench Factor Analysis to steel hardening. [12] Quench factor analysis is based on the principle that steel hardening can be predicted by segmenting a cooling curve into discrete temperature-time increments and determining the ratio of time required to obtain a specific amount of transformation at that temperature. The sum of the incremental quench factors over the transformation range is equal to the quench factor (Q). Quench factors are calculated from digital timetemperature (cooling curve) data and a CT function describing the TTP (time-temperature-property) curve for the alloy of interest.

critical time values as a function of temperature forms the TTP curve.) K1 = constant which equals the natural logarithm of the fraction untransformed during quenching, i.e., the fraction defined by the TTP curve. K2 = constant related to the reciprocal of the number of nucleation sites. K3 = constant related to the energy required to form a nucleus. K4 = constant related to the solvus temperature. K5 = constant related to the activation energy for diffusion. R = 8.3143 J/K mol. T = temperature, K. The constants K1, K2, K3, K4, and K5 define the shape of the TTP curve shown in Figure 12.

Figure 12 - Illustration of quench factor calculation from a TTP curve. The incremental quench factor (q) for each time step in the cooling curve is calculated from:



K 3 K 42 K5 = - K 1 K 2 exp 2 exp RT RT( K 4 - T )

q =

t CT

CT = critical time to form a constant amount of a new phase or educe the hardness by a specified amount. (The locus of the

where: t is the time step used for cooling curve data acquisition. The incremental quench factor (q) represents the ratio of time that the alloy is at a particular temperature divided by the time required for transformation to begin at that temperature. The incremental quench factors are summed over the entire transformation range to produce the cumulative quench factor (Q) according to:

Pmin = minimum property for the alloy, Pmax = maximum property for the alloy, exp = base of the natural logarithm, K1 = ln(0.995) = -0.00501, Q = quench factor. The solid line in Figure 14 represents the predicted hardness as a function of quench factor and the data points represent measured hardness values at locations in the quenched part where cooling curves were available. These data show a good correlation between predicted and obtained hardness.

q = q = T= M S3 T= Ar

t CT

The cumulative quench factor reflects the heatremoval characteristics of the quenchant as indicated by the cooling curve. It also includes section thickness effects because these influence the cooling curve. Transformation kinetics of the alloy are reflected because the calculation involves the ratio of time the metal was at a particular temperature by the amount of time for transformation to begin at this temperature, i.e., the position of the TTP curve in time as indicated for three hardenability bands of AISO 4130 indicated in Figure 13.

Figure 14 - Illustration of the correlation between predicted and measured hardness of cast 4130 steel as a function of quench factor. The cumulative quench factor under particular quench conditions reflects the heat-extraction characteristics of the quenchant, as modeled by the cooling curve over the transformation range of the alloy, section thickness of the part and transformation kinetics of the alloy. An alloy with a low rate of heat transfer will produce a lower Q-Factor under given cooling conditions compared to an alloy with a high transformation rate. CONCLUSIONS The data presented here show that although the classical approach of using Grossman H-Factors to estimate the quench severity necessary to harden steel, they have a number of deficiencies. Some of these can be overcome by

Figure 13 - TTP curves for cast 4130 steel: a. lowspecification composition, b. a mid-specification composition and c. a high-specification composition. The calculated quench factor can be used to predict the as-quenched hardness in steel using the following equation:

P P = P min + ( P max - P min )exp( K 1 Q)

where: PP = predicted property,

experimental determination from cooling curves. However, a better approach to estimate as-quenched properties such as hardness is the use of Quench Factor Analysis. In general, it is not a recommended practice to select quenchants, especially polymer quenchants, from a graphical representation similar to Figure 1. REFERENCES 1. M.A. Grossman, M. Asimow and S.F. Urban, "Hardenability, Its Relationship to Quenching and Some Qualitative Data", Hardenability of Steel, American Society for Metals, Metals Park, OH, 1939, p. 237-249. 2. J.L. Lamont, "How to Estimate Hardening Depth in Bars:, Iron Age, 1943, October, p. 64-70. 3. A.J. Hick, "Progress in Quenching Technology", Heat Treat. Metals, 1986, 1, p. .1 - 5. 4. G.E. Totten, M.E Dakins and L.M. Jarvis, "How H-Factors Can be Used to Characterize Polymers", Heat Treat., 1989, p. 28-29. 5. N.V.S.N. Murthy, "A Hardenability Test Proposal", Proc. of 2nd International Conference on Quenching and the Control of Distortion, Eds. G.E. Totten, M.A.H. Howes, S.J. Sjöstrom, and K. Funatani, ASM International, Materials Park, OH, 1996, p. 123-131. 6. R.W. Monroe and C.E. Bates, "Evaluating Quenchants and Facilities for Hardening Steel", J. Heat Treat., 1983, December, p. 83-89. 7. M.E. Dakins, C.E. Bates, G.E. Totten, "Estimating Quench Severity with Cooling Curves", Heat Treat., 1992, p. 24-26. 8. G.E. Totten, M.E. Dakins and L.M. Jarvis, "How HFactors Can Be Used to Characterize Polymers", Heat Treat., 1989, December, p. 28-29. 9. G.E. Totten, C.E. Bates and N.A. Clinton, Handbook of Quenchants and Quenching Technology, ASM International, Materials Park, OH, 1993, p. 180.

Quenching and Control of Distortion, Eds. G.E. Totten, M.A.H. Howes, S.J. Sjöstrom and K. Funatani, ASM International, Materials Park, OH, 1996, p. 509-515. 12. C.E. Bates and G.E. Totten, "Quench Severity Effects on the As-Quenched Hardness of Selected Steel Alloys", Heat Treat. of Metals, 1992, 2, p. 45-48.

10. S.G. Yun, S.W. Han, and G.E. Totten, "Continuously Variable Agitation in Quench System Design", Ind. Heat., 1994, January, p. 35-38. 11. G.M. Webster, G.E. Totten, S.H. Kang and S.W. Han, "Successful Use of Polymer Quenchants with Crack-Sensitive Steels", in Proc. 2nd International Conference on


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