effect of porosity on the hardenability of p/m steels
TRANSCRIPT
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EFFECT OF POROSITYON THE HARDENABILITY OF P/M STEELS
Suleyman Saritas*, Roger D. Doherty and Alan LawleyDepartment of Materials Engineering, Drexel University, Philadelphia, PA 19104, USA
* Gazi University, Department of Mechanical Engineering, Maltepe/Ankara, 06570, TURKEY
ABSTRACT
Pores in sintered P/M steels influence their thermal response and thus hardenability. Porosity decreasesthermal conductivity and attendant cooling rates, and it reduces the mass of the steel from which heat isremoved during quenching. The latter effect is quantified by a factor (1-�), where ε is the fraction ofporosity; in contrast, the influence of ε on thermal conductivity is more complex. In the present study, thehardenability of three sintered steels (Fl-4405, FLC2-4405 and FLN2-4405) with levels of porosity in therange 7v/o-16v/o has been determined experimentally using an instrumented Jominy test in whichthermocouples gave direct readings of cooling rate as a function of distance from the water-quenched endof the bar. The cooling of the Jominy bars was also simulated by means of a three – dimensional modelusing the finite difference method. Cooling curves are given for the three steels as a function of the levelof porosity at distances in the range 5 mm to 65 mm from the water-quenched end of the Jominy bars; thecorresponding hardness traces define the 50% martensite distance. The model predicts a decrease incooling rate with an increase in porosity, hence hardenability should decrease whereas the experimentaldata show clearly that the P/M steels with a level of porosity > 12v/o cool faster than a baseline pore-freewrought steel. This is attributed to penetration of the water via the interconnected pores in the sinteredsteels.
INTRODUCTION
Hardenability is the ability of a steel to harden by the formation of martensite on quenching. It is thedepth to which steel hardens when quenched from its austenitizing temperature. Grossman [1,2] defineshardenability in terms of the ideal diameter (DI) of a cylinder in which 50% martensite is obtained at itscenter by quenching in a medium with an infinite cooling rate (H = �). Quenching in a medium withlimited cooling rate, for example still water (H = 1), requires the definition of a new diameter, the criticaldiameter (DO), where 50% martensite is obtained at the center of the cylinder by quenching in thatmedium. While DO is dependent on the quenching medium, DI is a material property and can becalculated from the composition of the steel and from its austenitic grain size. The first hardenability test
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representative of industrial heat treating conditions developed by Grossman has several practicaldrawbacks. In particular it requires many cylinders with a length more than twice the diameter andjudgment is required in determining the amount of the constituents present in the quenched cylinders. Thetest most commonly used now was developed by Jominy [3] and it has been standardized by ASTM [4].
The hardenability of a steel is dictated by metallurgical factors (primarily alloy composition, austeniticgrain size, homogeneity of alloying elements) and the cooling rate. The cooling rate is a function ofcomposition and porosity. There is an extensive database on the hardenability of wrought steels [1,2, 5-8].The open literature on the hardenability of P/M steels is limited and of a more recent vintage [9-32].
The main difference in behavior between P/M steels and wrought steels is the presence of porosity in theformer. It is known that porosity exerts a strong and deleterious effect on the mechanical properties ofP/M steels [20, 33-35]. There is experimental evidence to show that porosity also affects the thermalbehavior of P/M steels [20, 36-40]. Grootenhuis et al [36] measured the thermal conductivity of P/Mbronze with levels of porosity up to 45v/o at temperatures in the range 20-200 ºC (68-392 ºF) andproposed that a straight-line relationship exits between thermal conductivity and porosity, given by:
ε1.21−=oK
K(1)
where K is the thermal conductivity of the porous material, Ko is the thermal conductivity of the pore-freematerial and � is the fractional porosity. Eq.1 fits their experimental data. Based on Eq.1, for mono-sizedspheres, the thermal conductivity is zero at � = 48v/o, i.e., (1- �/6). This is the maximum level ofporosity that can be attained with mono-sized spheres. In the case of parallel cylindrical pores of infinitelength, Eq.1 is represented by:
ε−= 1oK
K(2)
Figure 1. Comparison of experimental data and proposed equations forthermal conductivity of porous materials [37]
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Koh and Fortini [37] made thermal conductivity measurements on P/M copper and stainless steel with upto 35v/o porosity at temperatures in the range 100-1000 ºC (212-1832 ºF). They question the validity ofEqs. 1 and 2 and suggest that an equation proposed by Aivazov and Domashnev [41] gives an improvedfit to the experimental data:
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1
χεε
+−
=oK
K (3)
where � is the sensitivity of thermal conductivity to pores (for stainless steel � = 11). It is seen fromFigure 1 that Eqs. 1 and 2 constitute upper and the lower boundaries of the thermal conductivity. Inpressed and sintered P/M materials, the pores are not cylindrical or mono-sized spheres. For P/Mapplications the level of porosity is generally lower than 30v/o; in this range, Eq.1 represents thedependence of thermal conductivity on porosity satisfactorily (Figure 1). Eq. 3 represents the dependenceof experimentally determined values of thermal conductivity at all porosity levels (Figure 1).
The amount of heat stored in a porous material is directly proportional to (1-�). Thus, a reduction inthermal conductivity by a factor > (1-�) due to the presence of porosity will decrease the cooling rate ofthe porous material. In this paper, a combined experimental and modeling (finite difference) investigationof the cooling rates and hardenabilities of P/M steel Jominy bars at various levels of porosity is reported.
EXPERIMENTAL PROCEDURE
Materials
In this study, three high performance P/M steels based on Hoeganaes Ancorsteel 85HP were examined.The compositions and the coding of the alloys (based on MPIF 35) were:
FL-4405 : Ancorsteel 85HP + 0.6w/o graphite,FLC2-4405 : Ancorsteel 85HP + 2w/o Cu + 0.6w/o graphite,FLN2-4405 : Ancorsteel 85HP + 2w/o Ni + 0.6w/o graphite.
No lubricant was added during mixing of the elemental powders. The admixed powders were compactedby cold isostatic pressing (CIP) at pressures ranging from 246 MPa (35 ksi) to 422 MPa (60 ksi) toprovide cylindrical bars with a diameter 35 mm and length 125 mm. The green bars were sintered at1120 ºC (2050 ºF) in a 75v/o H2 and 25v/o N2 atmosphere for 30 min in a Hayes furnace. Sintereddensities and the corresponding porosity levels were in the range 6.50 g/cm3 (16.7v/o) to 7.22 g/cm3
(7.4v/o). ASTM Jominy specimens [4] were machined from the sintered bars (Figure 2). This figure alsoshows the positions of 4 thermocouples mounted in the specimen. To mount the thermocouples, 4 holeseach 0.84 mm diameter were drilled into the specimens at distances of 5, 25, 45 and 65 mm from thewater-quenched end. The tips of the holes were located along the axis of the specimen.
Wrought pore-free SAE 4150 was also included in the study as a baseline comparison purposes.Although the composition of SAE 4150 is not identical to that of the P/M steels examined, it provided anunderstanding of the cooling response in the absence of pores during cooling from the austenitizingtemperature.
Continious cooling transformation (CCT) diagrams of FL-4405 and SAE 4150 are given in Figure 3. CCTdiagrams for the two other P/M steels are not available, but CCT diagrams of sintered steels with similarcompositions were used in interpreting the transformations taking place during cooling from theaustinitizing temperature.
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Figure 2. Geometry of Jominy hardenability specimen and positions of thermocouples
Thermocouples and Datalogger
For recording the cooling rates of the bars in the Jominy tests, four K-type thermocouples 3 m in lengthand 0.813 mm sheath diameter were utilized (Omega Engineering). The thermocouple wires wereinsulated in ceramic fiber and placed inside an Inconel sheath. Since the sheath diameter is very fine, thethermocouples are flexible and can be bent without damage. Data acquisition from the thermocoupoleswas achieved by means of a 6-temperature channel datalogger (OM 3000/Omega Engineering). Thedatalogger has a capacity of 100,000 measurements and is capable of receiving data in 100 ms intervals.
Jominy Test
The furnace was heated to the austenitizing temperature 850 ºC (1562 ºF), and the instrumented Jominybar placed in the furnace on a graphite block. The specimen was kept in the furnace until the thermo-couple in the center of the bar reached 840 ºC (1544 ºF). Total time in the furnace was about 30 min.After opening the furnace, the datalogger was set to the recording mode and the bar transferred rapidly tothe Jominy jig. Because of the constraints imposed by the thermocouples, transfer and location of thespecimen to the fixture took about 10 s. The thermocouples recorded a temperature of about 820 ºC(1508 ºF) when the water jet hit the end of the Jominy bar. Cooling was continued for 20 min, at whichtime all the thermocouples recorded temperatures < 50 ºC (122 ºF), then the test was terminated.Representative time-temperature recordings made during the Jominy test are plotted in Figure 4.
Hardness measurements (HRA) were made on diametrically opposite ground flats as a function ofdistance from the water-quenched end of the Jominy bars. The 50% martensite “Jominy distance”criterion was determined metallographically from one of the two flats on the bar.
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(a)
(b)
Figure 3. CCT diagrams: (a) SAE 4150 and (b) FL-4405
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TC5
TC25
TC45
TC65
Figure 4. Cooling curves of FL-4405 with 14.4v/o porosity.TC � Thermocouple; numbers refer to distance (mm) from the water-quenched end.
EXPERIMENTAL RESULTS
Cooling curves of the alloys at each sintered density level are shown in Figures 5-8. The associatedJominy hardenability traces are given in Figure 9. Table I summarizes the sintered densities and Jominydistances (50% martensite) of the P/M steels as a function of sintered density. As a second criterion, the“Jominy distance” was defined at an apparent hardness level of 65 HRA [28].
Table I. Materials, Densities and Jominy Distances
Jominy Distance (mm)Bar#
Alloy SinteredDensity(g/cm3)
Porosity(v/o) 65 HRA 50%
Martensite1 4150 (wrought) 7.80 0 * *2 7.13 8.6 8 83 7.01 10.1 4.75 6.54 6.80 12.8 - 105
FL-4405(85 HP + 0.60w/o
graphite)6.60 14.4 - 13
6 7.22 7.4 10 137 7.00 10.3 8 9.58 6.84 12.3 5 139
FLN2-4405(85 HP + 2w/oNi +0.60w/o graphite)
6.50 16.7 - 1310 7.11 8.8 12 1211 6.98 10.5 8 812 6.73 13.7 - 1113
FLC2-4405(85 HP + 2w/oCu +0.60w/o graphite)
6.55 16.0 - 13* For wrought 4150, hardness is 81 HRA (60HRC) at the water-quenched end. At a distanceof 76 mm from the water-quenched end, the hardness is 67 HRA (33 HRC).
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8.8v/o
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13.7v/o
16.0v/o
Figure 5. Cooling curves of P/M steels as a function of porosity at a distance of 5 mmfrom water-quenched end: (a) FL-4405, (b) FLN2-4405, (c) FLC2-4405
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FLC2-4405 (16.0v/o)
Figure 6. Cooling curves of P/M steels as a function of porosity at a distance of 25 mmfrom water-quenched end: (a) FL-4405, (b) FLN2-4405, (c) FLC2-4405
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FLC2-4405 (16.0v/o)
Figure 7. Cooling curves of P/M steels as a function of porosity at a distance of 45 mmfrom water-quenched end: (a) FL-4405, (b) FLN2-4405, (c) FLC2-4405
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Figure 8. Cooling curves of P/M steels as a function of porosity at a distance of 65 mmfrom water-quenched end: (a) FL-4405, (b) FLN2-4405, (c) FLC2-4405
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Figure 9. Hardenability curves of P/M and wrought steels as a function of porosity:(a) FL-4405, (b) FLN2-4405, (c) FLC2-4405
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SIMULATION ANALYSIS
Cooling of the Jominy bars was simulated by means of a three-dimensional (3D) finite difference (FD)method using an array of points 20 x 10 x 10 (Figure 10) with the points spaced 2.5 mm apart in the threedirections I, J and L. The sample was set at 923 °C (1694 °F) and the surface at 123 °C (254 °F). Porositylevels of 2.5v/o, 5v/o, 10v/o, 15v/o and 20v/o were simulated by introducing randomly selected pointstreated as cubic pores. For simplicity in computation, the quenched surface (0, J, L) was allowed tocontain pores but the other surfaces (I, 0, L) and (I, J, 0) did not contain pores. A further restrictionimposed in the model was that if a pore was present at (I, J, L) then the six adjacent positions {(I-1, J, L),(I+1, J, L), (I, J-1, L), (I, J+1, L), (I, J, L-1), (I, J, L+1)} were pore-free (Figure 10(b)). Also, the poreswere not allowed to donate or accept heat from any of their six adjacent points.
Figure 10. Finite difference model: (a) 3D representation of cubic volumes, (b) 2D section through 3D array of cubic volumes
The standard equation used in 3D/FD models is:
NK(I,J,L) = K(I,J,L) + (DT.A /DX*DX) ( K(IN,J,L) + K(I1,J,L) + K(IJKN,L) + K(I,J1,L) + K(I,J,LN) + K(I,J,L1) - 6* K(I,J,L) ) (4)
I,J+1,L
I+1,J,LI-1,J,L I,J,L
I,J-1,L
(b)
10
1 I 20
J
Waterquenchedend Heat
flow
1
(a)
10
L
1
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where, I1 = I +1, IN = I-1, etc (5)When one of the points adjacent to (I, J, L), for example (I, JN, L) was a pore, then K(I, JN, L) was setequal to K(I, J, L) to prevent heat transfer to (I, J, L) before evaluation of the temperature change fromK(I, J, L) to N K(I, J, L). The effect of this was that the temperature remained higher behind a porewhereas in front of the pore the temperature fell more than it would in the absence of a pore.
Other aspects of the model were conventional; the sides of the box were given periodic boundary condi-tions, that is (I, 10, L) was identical to (I, 0, L), and the back surface ( 20, J,L) was a neutral surface fromwhich no heat was lost. This condition was achieved by setting K(20, J, L) = K(19, J, L). The back layerdid not contain any pores.
With no pores (P= 0), the program always showed the same time for the temperature to fall by 100 °C(212 °F) called the “100 °C cooling time” at layer 19, determined by the average of all the temperaturesK(19, J, L). This, coupled with P = 0, required a time of 301.25 s using an arbitrary thermal diffusivity of0.000001 m2/s. With no pores present, this time was the same as that obtained previously using one-dimensional (1D) and two-dimensional (2D) models. With no pores present, all temperatures at the sameI value were identical and these temperatures were the same as those in the 1D and 2D models at the samedistance from the water quenched surface.
When the material contained pores, the cooling rate was significantly lower. There was also a variation inthe time to cool 100 °C (212 °F) from run to run, depending on where the pores were located. If, forstatistical reasons, there were more pores near the water-quenched surface, cooling took longer than ifmore of the pores were further from the water-quenched end of the bar. The set of averaged temperatureswas similar for all levels of porosity, including P = 0, when measured at the end of the run when the meantemperature was 827 °C (1521 °F) at a depth I = 19. Regions with a statistically higher density of poresshowed a higher local temperature gradient, as expected.
Table II lists the average time at a finite porosity P to cool by 100 °C (212 °F) at the end of the bar. Sincethe product of the thermal diffusivity � and the time t is a constant:
)0(
)(
)(
)0(
==
==
Pt
Pt
P
PR
αα
(6)
where R is defined as the decrease in α
Table II. Results of 3-D Finite Difference Analysis
Porosity, P, (v/o) Average Time, <t> (s) R0 301.25 1
2.5 309 ± 0.6 1.026 ± 0.0025 317 ± 1.5 1.052 ± 0.00510 332.17 ± 1.5 1.103 ± 0.00715 355.6 ± 2 1.18 ± 0.00820 382.5 ± 2.5 1.27 ± 0.01
The second set of simulations was a 1D model of the cooling of a 100 mm rod along its axis. The initialtemperature was 800 °C (1472 °F) and the surface was set at 25 °C (77 °F). It was run for 1200 s with thetemperatures recorded at 10s intervals at distances of 5, 25, 45 and 65mm from the water-quenched end. The correct value of the thermal diffusivity (0.000006 m2/s,) was used for P = 0. For the increase inporosity, the thermal diffusivity was decreased by a factor 1/R (from Table II).
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Figure caption is on page 15
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Figure 11. Cooling curves for P/M steels with 0 to 20v/o porosity, predicted by finite difference analysis:(a) 5 mm, (b) 25 mm, (c) 45 mm and (d) 65 mm from water-quenched end.
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The results shown in Figure 11 are similar to those obtained by Kaviany [42]. At small values of thermaldiffusivity and small P (P< 0.1 falls as 1/1+P), but at higher P the fall is higher. If this is translated backto thermal conductivities, the drop in k would be larger than that for thermal diffusivity:
� = k / (C �) (7)
where C is the specific heat (J/kg/K) and � is the density (Kg/m 3). C. � (J/m 3/K) is the specific heat forunit volume will decrease as (1/(1+P). Thus, k will decrease at least as 1/(1+P)2 initially, but morerapidly after P>0.1.
DISCUSSION
The FD analysis has showed that the thermal diffusivity, and thus the thermal conductivity, of P/M steelsare dependent on the inherent porosity level. Cooling curves predicted by FD analysis are similar in shapeto those recorded by thermocouples in the Jominy test. There are, however, significant differencesbetween the two sets of curves. Unfortunately, the current FD analysis does not to be account of the heatgenerated as a result of any transformation reactions, cooling from the surfaces of the cylinder byconvection, and cooling by conduction trough the metallic support in the Jominy test rig.
The positions of thermocouples were selected such that the one nearest to the water-quenched end willalways be in the martensitic region (in terms of Jominy distance). The second thermocouple was expectedto be in the mixed martensite/bainite region, the third thermocouple in the bainitic region, and the fourththermocouple in the mixed bainite/ferrite+pearlite region.
Examination of the cooling curves at a distance of 5 mm from the water-quenched end (Figure 5) showsthat all the alloys over the porosity range examined are martensitic. The attendant cooling rate for all thealloys was > 30 ºC/s. The recordings also show that the wrought SAE 4150 exhibited the slowest coolingrate at this distance. Faster cooling rates were associated with the alloys of higher porosity. This showsclearly that water from the jet penetrated the pores in the sintered bar and increased the cooling rate. Asseen in Table I, at porosity levels > 12v/o the apparent hardness was < 65 HRA, but the 50% martensitedistance was > 10 mm for all the alloys. The only explanation for this result appears to be the penetrationof water into the sintered alloys via interconnected pores.
The cooling rate at a distance of 25 mm from the water-quenched end is between 3-10 ºC/s and thiscorresponds to a cooling rate that results in the formation of mixed martensite and bainite (Figure 3(b)).Values of the 50% martensite distance given in Table I are all < 25 mm. The cooling curves show thatthere are no significant differences in the cooling rates of the P/M steels and SAE 4150. Some of the highporosity alloys cooled faster than wrought SAE 4150, which is attributed penetration of the water into thepores of the sintered bars.
Cooling rates at distances of 45 and 65 mm from the water-quenched end were between 1-2 ºC/s. Thecorresponding CCT diagrams predict that the bainite transformation should take place in these regions.These cooling rates are faster than those required for the formation of ferrite + pearlite. The coolingcurves exhibit flat regions over these distances. The flat region of the wrought SAE 4150 occurs at about450 ºC (842 ºF) and that of P/M steels at about 550 ºC (1022 ºF). Both temperatures correspond to theupper bainite transformation.
The Jominy curves given in Figure 9 show a dependence of hardness on the level of porosity. As porositydecreases the curves are displaced upward (to higher hardness levels) and almost parallel to each other.Could this be attributed to an increase in hardenability? The answer to this question lies in definition ofhardenability. If hardenability is a material property dependent on chemistry and grain size, then the
17
answer is no. But, if hardenability is defined as depth to a certain hardness (for example 65 HRA or 75HRA) [27-28], which is of utility for practical purposes, then the answer is yes.
CONCLUSIONS
1. The finite difference method predicts that the thermal diffusivity and thermal conductivi-ty of P/M steels are dependent on their inherent porosity levels. Thus increasing the levelof porosity decreases the cooling rate and should affect hardenability.
2. Instrumented Jominy tests have been conducted to monitor accurately the cooling ratespresent in the alloys at specific distances away from the water-quenched end. Thesemeasurements provide an improved understanding of the transformations taking place inthe P/M steels.
3. Measurements taken at a distance of 5 mm from the water-quenched end show that theP/M steels with a level of porosity > 12v/o cool faster than fully dense wrought steels.This is attributed to the penetration of water into the interconnected pores and whichincreases the cooling rate of the sintered alloys.
ACKNOWLEDGEMENT
Professor Saritas is indebted to the Hoeganaes Corporation for financial support during a sabbatical leave(2000/2001) at Drexel University. The company also provided the powders and sintering facilities.
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