QUENCH FACTOR ANALYSIS: STEP-BY-STEP PROCEDURES FOR EXPERIMENTAL DETERMINATION

ABSTRACT There have been a number of procedures reported for the prediction of physical properties of aluminum based on cooling rate data. One of the most common is the cooling rate calculation procedure described by Fink and Willey in their now-classic work on 7075 characterization. Staley has more recently described the use of "Quench Factor Analysis" (QFA) to better predict various properties of aluminum which is the subject of this paper. A discussion of the principles of the calculation and the experimental procedure used for QFA determination from cooling curve data will be provided here. The generation of the multiparametric CT function from cooling curves will also be discussed. INTRODUCTION Fink and Willey performed an extensive study on the effects of quenching on the strength of 7075-T6 and corrosion behavior 2024-T4.[1] This was done by constructing C-curves which were plots illustrating the times required to precipitate sufficient alloy content to change the strength by a certain amount (7075) or change the corrosion from pitting to intergranular (2024). The "critical temperature range", that temperature range that provided the highest precipitation rates was identified.[2] Figure 1 illustrates Fink and Willey's C-Curve for 7075. Figure 2 is a C-Curve similar to one

reported earlier by Willey illustrating the critical temperature range for the transition of pitting to intergranular corrosion for 2024.[3] Various studies were conducted after Fink and Willey's work to determine the relative quench rate sensitivity to yield different properties for various alloys. Figure 3 illustrates the effect of cooling rate on tensile strength for different aluminum alloys and tempers.[2]

Figure 1 - C-Curves illustrating the effect of alloy precipitation on tensile strength for 7075-T6 generated by Fink and Willey.(Reference 1)

G.E. Totten and G.M. Webster Union Carbide Corporation

Tarrytown, NY

C.E. Bates University of Alabama at Birmingham

Birmingham, AL

Figure 2 - C-Curve for 2024-T4 illustrating the critical temperature and cooling time transition for pitting to intergranular corrosion.

Figure 3 - Tensile strength as a function average cooling rate. The average cooling rate in Figure 3 is determined by dividing 200oF by the time difference, in seconds, to cool from 750oF to 550oF which will yield an "average" cooling rate in oF/s. An approach such as this can provide only an approximation of the actual cooling process for the quenchant and cross-section size of interest which may, in fact, be non-linear, interrupted or delayed quench. Therefore, it is desirable to utilize a process that integrates a cooling curve for the quenching process and cross-section size being used with a C-curve (Time-Temperature-Property) curve for the specific alloy of interest.

A numerical process that has been developed which fulfills these objectives is the Quench Factor Analysis (QFA) procedure which was developed by Evancho and Staley.[2,4] The principles of the QFA calculation and the experimental procedures used for QFA determination from cooling curve data will be discussed here. The generation of the multiparametric CT function from cooling curves will also be provided. DISCUSSION Calculation of Quench Factors from Precipitation Kinetic Data The properties of aluminum alloys are dependent on the amount of alloy precipitation that occurs during cooling. The rate law for isothermal precipitation kinetics is:[5]

(1)

where: is the fraction of precipitation which has occurred in time (t) and k is a temperature-independent constant. The value of k depends on the degree of supersaturation and the rate of diffusion and is estimated from:[6]

(2) where:

CT = critical time required to precipitate a constant amount (the locus of the critical line is the C- curve). k1 = constant which equals the natural logarithm of the fraction untransformed (1 - fraction defined by the C-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-1.mol-1 T = temperature in oK.

From these relationships, it is possible to redefine the equation for the amount of solute precipitated during the quench () which can be calculated :[2]

(3) Cahn has shown that the transformation kinetics for non-isothermal conditions, such as those that would be present during a typical quenching process, may be described by: [6,7]

(4) where:

CT = critical time from the C-curve, t = time from the cooling curve, t0 = time at the start of the quench, tf = time at the finish of the quench, = measure of the amount transformed (quench factor).

When =1, the fraction transformed equals the fraction represented by

the C-curve.

As illustrated in Figure 4 [5], the quench factor () is obtained by combining the cooling curve for the quenching process with the C-curve and the value for is obtained by:[2]

(5)

Figure 4 - Determination of quench factor () by the combination of a quenchant cooling curve and a C-curve. A graphical representation of a quench factor determined earlier by Kim, Hoff and Gaskell is illustrated in Figure 6.[5] The quench factor shown is the area projected on to the 1/CT - 1 plane.

Figure 5 - Graphical representation

of the quench factor as the area of the "cliff" projected on to the 1/CT-t plane [5]. Experimental Determination of Quench Factors Figure 6 illustrates the superposition of a cooling curve on a C-curve.[8] Experimentally, cooling curves are generated by acquiring time-temperature data over finite time steps (ti) which is determined by the data acquisition rate. The average temperature between each time step interval is then calculated. The CT value is then calculated for each average temperature using the above equation. The ratio of the time step length used for data acquisition, (ti) is divided by the CT value at that temperature to provide an "incremental quench factor" (q).[8]

(6)

Figure 6 - Schematic illustration of the experimental method used for calculating a quench factor. To obtain the overall quench factor, Q (or in the above equation), the incremental quench factor values are summed progressively as the part is cooled through the precipitation range, normally about 800-300oF (425 - 150oC) as shown in Figure 5.[8]

(7) Effect of Time Step (t) Selection In order to determine the effect of the size of the time step on the quench factor calculation, the quench factors for 7075-T73 quenched in 100oF (38oC) water at 50 ft/min (0.25 m/s) was studied. The results of this study are shown in Table 1. These data show that time step changes in the range of 0.1 to 0.4 seconds caused no appreciable change in the calculated quench factor. However, time step variations between 0.5 to 0.8 seconds caused considerable scatter in the calculated quench factor (Q). Excessively long time steps may result in an inadequate number of data points to properly calculate transition in the critical portion (knee) of the C-curve. It is suggested that the time step interval should be selected such that the average temperature drop is not greater than 75oF (25oC) over the critical cooling range for the alloy of interest.

Table 1

Effect of Time Step Magnitude on Quench Factor Calculation

Property Calculation The tensile strength of the alloy after proper aging can be predicted from the quench factor - Q:[2]

(8) where:

y = predicted yield strength, max = yield strength after an infinite quench (and aging cycle), e = base of the natural logarithm,

K1 = ln (0.995) = -0.00501 Q = quench factor

The relationship between quench factor and yield strength for 7075-T73 is shown in Figure 7.[8]

Figure 7 - Yield strength of aluminum 7075-T73 as a function of quench factor of the material. Low values of Q are associated with high quench rates, minimum precipitation during cooling and high yield strengths. Conversely, higher Q-values are obtained with slower quench rates and are associated with lower strength values. An alloy with a low rate of precipitation will produce a lower quench factor (Q) than an alloy with a high precipitation rate at the same cooling rate. Quench factors calculated for different alloys might be different even if similar section sizes are cooled in the same quenchant, because quench factors take into account individual alloy precipitation kinetics by means of the equation describing the C-curve (CT function) for each alloy. Solute elements are precipitated during cooling from the solution treating temperature at "high" Q-values. As a consequence, an improperly quenched alloy may not properly harden during aging, and it may be susceptible to intergranular

corrosion, stress corrosion or exfoliation. Experimental Apparatus The quench factor provided by a particular quenchant can be determined experimentally using parts or probes instrumented with thermocouples and a testing apparatus in which the quenchant concentration, flow rate, and temperature can be controlled. In principle, any quenchant bath could be used, including the commercial bath used in practice. Figure 8 illustrates one system that has performed well in the laboratory.[10] However, it is important to note that different agitation systems will yield different results due to differences in the directionality and turbulence of fluid flow. An illustration of a bar and sheet probe used for laboratory testing is provided in Figures 8 and 9 respectively.[10] A computerized data acquisition system is used to collect and store the time-temperature data from the instrumented probes or parts during quenching.[11]

Figure 8 - Illustration of a laboratory quench bath capable of providing a controlled uniform flow

rate at a reasonable constant temperature.

Figure 9 - The construction of a 25 mm round bar probe.

Figure 10 - Illustration of a sheet probe. The part or probe is solution heat treated at the proper temperature for the alloy and quenched into the bath containing the quenchant being evaluated at the desired concentration and flow rate. The cooling curves are recorded and the quench factors calculated as described above. C-Curve Availability There are a number of problems that have prevented widespread acceptance of quench factor analysis procedures by the general heat treating industry. One of the most often encountered criticisms of the

quench factor calculation is the unavailability of C-curves for performing QFA calculations. Although it is true that there is not extensive data, C-curves for many of the more commonly encountered alloys have been published. Some of the C-curves that have been reported to data are illustrated in Figures 11-15.

Figure 11 - C-Curve for 7075-T6 yield strength. (Reference 3).

Figure 12 - C-curves for 2024-T851, 7075-T6 and 7075-T76 aluminum alloys. (Reference 9)

Figure 13 - C-Curve for 6351-T6. (Reference 7)

Table 2

Coefficients for Calculating Quench Factors at 99.5% of Attainable Yield Strength

Figure 14 - C-Curves for 7075, 2017, 6061 and 6063. (Reference 12).

Figure 15 - C-Curves for 7075-T6 and 7050-T73 (Reference 2) C-curves have been reported for other alloys but are not shown here. These include: 2219-T87, 2024-T851, and 2024-T351.[7] Unfortunately, no C-curves for quench hardenable aluminum casting alloys have been published.

Bates has summarized the CT constants for a limited number of alloys and tempers which can be used

in quench factor calculations.[8,9]. These values are summarized in Table 2. C-Curve Parameterization The equation of the C-curve was shown previously. However most of the constants for these equations are not available which will permit the calculation of the CT function. Instead, the CT function is calculated by fitting the equation shown (Equation 2) to the C-curve using non-linear regression analysis and solving for the k2-k5 values until minimum error is obtained by a self-directing optimization process.[13] In this way, a CT function can be written for any available C-curve. CONCLUSIONS In this paper, the traditional approach to calculating average cooling rates by the Fink and Willey procedure and the deficiencies of this procedure was discussed. An alternative procedure, Quench Factor Analysis, developed by Evancho and Staley, which provides an integration of the time-temperature-property (C-curve) for the desired aluminum alloy and the cooling curve shape in the critical temperature region was provided. Experimental procedures for the necessary cooling curve data acquisition and subsequent calculation procedure was also provided. The more common C-curves that have been published were shown. A description of a multiparametric non-linear regression analysis procedure to calculate the equation of the C-curve, CT function, was briefly

discussed. With this information, it is possible for the reader to perform QFA analysis on the more commonly available wrought aluminum alloys that may be encountered. Unfortunately similar data is not available for cast aluminum alloys, although the approach is equally applicable. QFA procedures have been utilized by numerous workers in the field to solve various problems encompassing a wide variety of both spray and immersion quenching procedures. [15-19] REFERENCES 1. W.L. Fink and L.A. Willey, "Quenching of 75S Aluminum Alloy", Trans. AIME, 1948, Vol. 175, p. 414-427. 2. J.W. Evancho and J.T. Staley, "Kinetics of Precipitation in Aluminum Alloys During Continuous Cooling",Metallurgical Transactions, 1974, Vol. 5, January, p. 43-47. 3. "Quench Factor Analysis" in Aluminum Properties and Physical Metallurgy, Ed. by J.E. Hatch, 1984, ASM International, Materials Park, OH, p. 159-164. 4. J.T. Staley, "Modeling Quenching of Precipitation Strengthened Alloys: Application to an Aluminum-Copper-Lithium Alloy", Ph.D. Thesis, Drexel University, 1989. 5. J-S. Kim, R.C. Hoff and D.R. Gaskell, "A Quench Factor Analysis of the Influence of Water Spray Quenching on the Age-Hardenability of Aluminum Alloys", in Materials Processing in the Computer Age, Ed. by R. Voller, M.S. Stachowicz and B.G. Thomas, 1991, The Minerals, Metals and Materials Society, p. 203-221. 6. J.W. Cahn, "The Kinetics of Grain Boundary Nucleated Reactions", Acta Met., 1956, Vol. 4, p. 449-459. 7. J.T. Staley, "Quench Factor Analysis of Aluminum Alloys", Materials Science and Technology, 1987, Vol. 3, November, p. 923-935. 8. C.E. Bates and G.E. Totten, "Procedure for Quenching Media Selection to Maximize Tensile

Properties and Minimize Distortion in Aluminum-Alloy Parts", Heat Treat. of Metals, 1988, No. 4, p. 89-97. 9. C.E. Bates, "Quench Optimization for Aluminum Alloys", AFS Transactions, 1994, 93-25, p. 1045-1054. 10. G.E. Totten, C.E. Bates and L.M. Jarvis, "Cooling Curve and Quench Factor Characterization of 2024 and 7075 Aluminum Bar Stock Quenched in Type I Polymer Quenchants", in Heat Treating - Proceedings of the 16th Conference, Ed. by J.L. Dossett and R.E. Luetje, 1996, ASM International, Materials Park, OH, p. 221-229. 11. G.M. Webster and G.E. Totten, "Cooling Curve Analysis - Data Acquisition", in Heat Treating - Proceedings of the 16th Conference, Ed. by J.L. Dossett and R.E. Luetje, 1996, ASM International, Materials Park, OH, p. 427-434. 12. T. Sheppard, "Press Quenching of Aluminum Alloys", Materials Science and Technology, 1988, Vol. 4, July, p. 635-643. 13. K.B. Orzak, "The Programs CT and Quench for Calculating CT-Curve Parameters and Quench Factors for Aluminum Alloys, Unpublished Report. For a copy, contact Dr. George E. Totten, Union Carbide Corporation, 777 Old Saw Mill River Road, Tarrytown, NY 10591. 14. P. Archambault, J.C. Chevrier, G. Beck and J. Bauvaist, Heat Treatment '76, Proceed. of 16th International Heat Treatment Conference, 1981, Metals Society (London), p. 105-109. 15. P. Archambault, J.C. Chevrier and G. Beck, "A Contribution to the Optimization of the 7075 Heat Treatment", Materials Science and Engineering, 1980, Vol. 43, p. 1-6. 16. C.E. Bates, T. Landig, and G. Seitanakis, "Quench Factor Analysis: A Powerful Tool Comes of Age", Heat Treating, 1985, December, p. 13-17. 17. P. Archambault, F. Moreaux and G. Beck, "Decomposition of the Solid Solution During the Quench Cooling

of 7075 Alloy. Cooling Rate and C-Curves", in Aluminum Technology, 1986, The Institute of Metals, (London), p. 408-413. 18. S. Tsuchida, H. Yoshida ans S. Hirano, "Heat Treatment of Aluminum Alloys", Sumitomo Light Met. Tech. Rep., 1990, Vol. 31(2), p. 28-45. 19. J.T. Staley, "Using Simple Kinetic Equations in Heat Treating Aluminum", Technical Bulletin, Alcoa Laboratories, Alcoa Technical Center, Alcoa Center, PA.