Modeling the Heat Treatment Response of P/M Components

Transcription

1 Modeling the Heat Treatment Response of P/M Components Research Team Makhlouf M. Makhlouf, Professor Richard D. Sisson, Jr., Professor Virendra S. Warke, Ph.D. Student Focus Group Members David Au Quebec Metal Powders, Ltd. Ian Donaldson GKN Sinter Metals Worcester John Fulmer Nichols Portland Bill Jandeska General Motors Chaman Lall Metal Powder Products Co. Jean Lynn DaimlerChrysler Corporation. Stephen Mashl (Chair) Bodycote IMT, Inc. Sim Narasimhan Hoeganaes Corporation Renato Panelli Mahle Metal Leve S.A. Rocco Petrilli Sinterstahl G.m.b.H. Sylvain St-Laurent Quebec Metal Powders, Ltd. S. Ryan Sun Borg Warner, Inc. Objectives PROJECT STATEMENT The main objective of this project is to develop and verify a computer simulation software and strategy that enables the prediction of the effects of heat treatment on powder metallurgy components. The simulation should accurately predict dimensional change and distortion, residual stresses, type and quantity of metallurgical phases in the microstructure, and hardness. Strategy The project is divided into four major tasks as follows: Task-1 of the project is to assess the capability of a commercially available heat treatment tool for predicting the heat treatment response of wrought alloys. This task includes modeling the heat treatment response of wrought 5160 steel and validating the model predictions against measured data. 1

2 Task-2 of the project is to model the heat treatment response of fully dense P/M parts (46XX alloy). In this phase, the input database required for the model will be generated and used to predict the heat treatment response of fully dense P/M parts. The model predictions will be verified against measured data. Task-3 of the project includes modeling the heat treatment response of porous P/M components. Here the input data required for the model will be generated for two different porosity levels. The model will be modified to accommodate the effect of porosity on heat treatment response for the given alloys; again the model predictions will be verified against measured data. Task-4 of the project includes modeling the heat treatment response of a production part with two different levels of porosity and subjected to two different heating methods. The model predictions will be verified against measured data. The deliverable from the project is a tested software tool and strategy for predicting the effect of heat treatment on the characteristics of P/M components. SUMMARY OF ACCOMPLISHMENTS IN THIS QUARTER TASK 1: Assessment of Dante s ability to predict heat treatment response of wrought components. Task1.1: The heat transfer coefficient used earlier was obtained by using the lumped parameter analysis. During this quarter, a more accurate method that employs inverse heat transfer calculations was used and the magnitude of the heat transfer coefficient was adjusted. Task1.2: Two samples of hot rolled 5160 steel with similar dimensions to those used in the model were prepared, and were heat treated and quenched in Houghton-G oil. Hardness measurements were performed on these samples and were compared with the model predictions. Distortion measurements were performed on the samples using a CMM machine and were compared with the model predictions. Residual stresses at specific locations on the part were measured using the X-Ray diffraction technique and the measurements results were compared with the model predictions. Amount of retained austenite after quenching was measured using XRD along the cross section of each sample and compared with the model predictions. 2

3 WORK PLANNED FOR NEXT QUARTER Thoroughly investigating the x-ray diffraction method and the crack compliance method for measuring residual stresses in metallic components, comparing the two techniques, and adopting the one technique that is more reliable and produces repeatable measurements. Fixturing and programming the CMM machine to enable direct comparison of the measured part distortions to the model predicted part distortions. Fine-tuning the model in order to improve its predicting ability. (Finishing Task-1). Producing samples from fully dense, powder-forged 46XX series alloy steel for Task- 2. These include samples for dilatometry and mechanical property measurements (to generate parameters used internally by the software to make the predictions), as well as samples to be used in verifying the model predictions. Perform dilatometric measurements to generate the kinetics parameters as well as transformation plasticity data required by the model. Perform mechanical property measurements to generate the temperature-dependant, phase specific data required by the model. Changes in project statement None. Report organization The body of the report is organized in several Appendices as follows: Appendix A contains details of the procedures used to measure the heat transfer coefficient, the residual stresses, and the type and amount of metallurgical phases present in the part after quenching. This appendix is divided into four main sections as follows: A.1: Measurement of the heat transfer coefficient. A.2: Measurement of residual stresses using the x-ray diffraction method. A.3: Measurement of residual stresses using the crack compliance method. A.4: Measurement of the amount of retained austenite using x-ray diffraction. Appendix B contains details of the progress made in Task-1 of the project during this quarter. 3

4 Appendix: A A.1: Measurement of the heat transfer coefficient Overview One of the challenges in modeling the thermal response of materials is the heat transfer coefficient. Even the most sophisticated software uses fundamental laws of heat flow to numerically model the heat transfer process. As a result, the accuracy of the model predictions invariably depends on the accuracy of the boundary conditions, initial conditions and material property data used in the heat flow equations. While the material property data is relatively easy to determine and the initial conditions are usual known, the boundary conditions between the metal part and the quenching medium, i.e., the heat transfer coefficient, are dependant on many factors including the initial conditions, the geometry of the part, the chemistry of the part and the quenching medium, and the surface condition of the part. Moreover, some of these factors may interact with one another. Because of the critical nature of the heat transfer coefficient in computer modeling, an effort is made to provide a system and procedure for accurately determining this parameter. The method involves quenching a heated cylindrical probe machined from the material under consideration and equipped with a thermocouple connected to a fast data acquisition system into the quenching medium and acquiring the temperaturetime profile. The probe dimensions are so chosen such that the Biot number for the quenching process is <0.1. This insures that significant thermal gradients will not be present in the radial direction in the probe. Accordingly, a simple heat balance analysis (usually referred to as a lumped parameter analysis) can be performed on the system (probe + quenching medium) to yield the heat transfer coefficient. Since the Bi < 0.1, the error associated with the calculation of the heat transfer coefficient is less than 5%. Conversely, an inverse heat transfer analysis may be performed on the temperaturetime data whereby the heat equation is solved in reverse numerically (knowing the temperature time profile and the heat equation, work backwards to obtain the heat transfer coefficient). The inverse heat transfer method can yield more accurate values of the heat transfer coefficient than the lumped parameter analysis method. Experimental setup & measurement procedure A small cylindrical probe 9.5 mm in diameter and 38mm long is manufactured from the steel. A hole is drilled down to the geometrical center of this probe, and a thermocouple is inserted for measuring the time-temperature data. Graphite powder was packed into the hole before the thermocouple was inserted in order to ensure intimate contact between the probe and the thermocouple. The probe was heated to 850 C, and held at that temperature for 20 min after equilibration in order to ensure the completion of transformation. Subsequently, the probe was quenched into Houghton-G oil maintained at room temperature. Figure 5 is a schematic representation of the probe. While quenching, 4

5 the temperature of the probe was acquired as a function of time using a very fast data acquisition system that has a scan rate of 1000 scans/sec. Themocouple Probe Figure 5: Schematic diagram of the probe used to calculate heat transfer coefficients. Calculation of the heat transfer coefficients using the lumped parameter analysis: A heat balance applied to the probe results in Equation 1, which can be used directly to calculate the heat transfer coefficient at the surface of the probe. ρvc h = A s dt ( T T ) dt s p f (1) In Equation 1, h is the heat transfer coefficient at the surface of the probe, _,V, C p, and A s are the density, volume, specific heat, and surface area of the steel probe, respectively. T s is the temperature at the surface of the probe, which, due to the geometry of the probe, is approximately equal to the measured temperature at the center of the probe. T f is the bulk temperature of the quenching medium. The derivative of temperature with respect to time term in Equation 1 is calculated from the measured temperature vs. time data. Calculation of the heat transfer coefficients using the inverse heat transfer method: The main idea behind the inverse calculation is to back calculate the convective boundary fluxes fro the measured temperature-time profile of the part. There are six steps involved in the calculation that are solved in a continuous loop until the criteria in step 5 and step 6 are satisfied, these steps are as follows: (1) Solving the direct heat transfer problem - the normal heat transfer problem is solved for the temperature profile in the probe, where some guessed value for the convective heat transfer coefficient at the surface of the probe is used as a boundary condition. 5

6 Usually, the heat transfer coefficients obtained from the lumped parameter analysis is used as the guess value to obtain faster convergence. (2) Solving inverse problem - the difference in temperature at the center of the part calculated in step (1) is compared with the measured data, and the problem is solved in the reverse direction to calculate h by compensating for this temperature difference. (3) Check for stability - the stability of the solution is checked. (4) Check for convergence - the convergence of the solution is checked against the required degree of accuracy. Figure 6 shows a comparison of the heat transfer coefficients obtained by both methods. Figure 6: Comparison of the heat transfer coefficients obtained from the lumped parameter analysis and the inverse calculations. 6

7 A.2: Measurement of residual stresses using the x-ray diffraction method Overview X-ray diffraction is one of the widely used techniques for measuring residual stresses. When a polycrystalline material is deformed elastically, the lattice plane spacing in the constituent grains changes from a stress free value to some new value corresponding to the magnitude of the residual stress in the part. This micro stain causes a shift in the diffraction lines to a new 2_ value. On the other hand, if the material is deformed plastically, the lattice planes usually become distorted in such a manner that produces broadening of the diffraction lines. Usually both kinds of micro strain are superimposed on one another in the diffraction pattern of a plastically deformed material. There are two methods by which the strain can be obtained using x-ray diffraction, in the first method, x-ray diffraction can be used to measure the residual strains by knowing the strain-free spacing between diffracting planes (d). In the second method, if the strain free (d) spacing is not known, a calibration procedure can be used in which the strain produced by known stresses can be compared with the sample to be tested. The residual stress can be calculated from these strain values by knowing the appropriate elastic constants for the material, e.g., the modulus of elasticity and Poisson s ratio. Experimental setup & measurement procedure In this section, the experimental setup for measuring residual stresses using the x-ray diffraction technique for the quenched 5160 steel samples is discussed. Figure 1 shows a schematic diagram of the sample where 1 indicates the location where residual stresses are measured. Location 1 is chosen for testing because the residual stresses are expected to be highest in magnitude at this location due to the non-uniform heat flow in the sample, which in turn causes non uniform phase transformation and results in high levels of stress in thin sections. Figure 2 is a schematic of the diffractometer used to measure residual stresses in the sample. This arrangement is specific to _- _ diffratometers 1. In these machines the sample is stationary on a platform and the x-ray source and detector move in a circular path as shown by dotted circle in Figure 2. In Figure 2, N s is the normal to the surface of the sample, and N p is the normal to the diffraction planes who s d-spacing is to be measured. 1 Manufactured by PANalytical Inc., Natick, MA. 7

8 1 Figure 1: Sample location (position 1) where the residual stress measurements are performed. N s N p ψψ Sample Figure 2: Schematic diagram of the machine setup for measuring residual stress. In order to measure the residual stress, the position of a particular peak is observed for three or more _ values. The peak position is accurately calculated using a parabolic fitting technique.[1] Once the peak position is known, the d-spacing for each _ can be calculated using Bragg s law as given by Equation 1 8

9 n λ = 2d sin( θ ) (1) The biaxial stresses in the sample can be obtained by rotating the sample around N s (Figure 2) in Φ = 0, 45, and 90 and performing the measurements for at least three values of _. Figure 3 shows the measurements performed at location 1 on the sample for three different orientations (i.e., three different _ s) Φ = 0 ο Φ = 45 ο Φ = 90 ο ) A o d-spacing ( sin 2 (ψ) Figure 3: plot for sin 2 _ vs. d spacing for three different sample orientations. By knowing the strain free d spacing, d 0, modulus of elasticity, E, and Poisson s ratio, _ of the material, the two components of the biaxial principle stresses can be obtained from Equation 2 d d d υ 2 υ = ( ) σ φ sin ψ ( σ 11 + σ 22 ) E E (2) After rearranging the terms in Equation 2, it gives a straight line for the d-spacing vs. sin 2 _ plot. Hence, the slope of the lines in Figure 3 gives, and _ 11, and _ 22 can be obtained from Equation 3 σ φ 2 2 = σ 11 cos φ + σ 22 sin φ (3) 9

10 A.3: Measurement of residual stresses using the crack compliance method Overview Techniques for measuring residual stresses using successive extension of a slot are known in the technical literature by several names including the crack compliance method, the fracture mechanics approach, the successive cracking method, the slotting method, the rectilinear groove method, etc. The term crack compliance method arises from the similarity of this technique to the compliance method for measuring crack length in a fatigue or fracture specimen where a known load is applied to a cracked specimen, and the resulting strain is used to determine the crack length. In the residualstress crack compliance method, the crack length is known and the measured strain is used to calculate the residual stress. The techniques presented here measures the residual stress at an incrementally increasing depth from a slot cut into a part containing residual stress. Depth here refers to the direction of extension of the slot. Some measure of deformation, such as strain or displacement, is taken at each increment of depth. From these measurements, the residual stress profile that originally existed in the part is calculated. Usually, only the stress component normal to the slot face is determined. There are several advantages to this test over nondestructive stress measurements such as XRD. One might spend days to get the complete stress state in a part by XRD, however the crack compliance method can do the analysis in less than a day. In order to get the stresses at various depths using XRD, material has to be removed from the surface by etching or by some other method, which can in itself introduce stresses into the sample. Moreover, it is often difficult to measure stress on curved surfaces using XRD. [2] Experimental setup & measurement procedure The experimental setup for the crack compliance method is fairly simple. As shown in Figure 4, strain gauges are mounted on the sample for which the residual stress has to be measured. A very thin slot is machined incrementally into the sample by electrical discharge machining. The slot releases the residual stress normal to the face of the slot, and the part deforms, the deformation is measured by the strain gauges mounted on the sample as a function of the slot depth. This strain data is then used to solve for the stress as a function of the depth. In order to minimize the effect of heating due to machining on the actual residual stress, the samples are often submerged in de-ionized water during cutting. [3] Figure 5 shows data obtained from a typical crack compliance measurement. In this figure, the measured strain is plotted with the increasing depth of the machined slot. 10

11 Figure 4: Schematic diagram of a sample during measurement of residual stress by means of the crack compliance method Figure 5: Plot of measured strain vs. slot depth on the sample [3]. In order to obtain the stress as a function of depth, complex mathematical manipulation is performed on the strain vs. depth data. Figure 6 is a comparison chart for the various residual stress measurement techniques. 11

12 Figure 6: Comparison of various residual stress measurement methods [3]. 12

13 A.4: Measurement of the amount of retained austenite using x-ray diffraction Overview X-ray diffraction is a very popular technique for quantifying the amount of retained austenite in steel parts after heat treatment. This analysis is based on the fact that the intensity of the diffraction pattern of a particular phase in a mixture of phases depends on the concentration of that phase in the mixture. However, in general, this relationship is not linear because the diffracted intensity depends markedly on the absorption coefficient of the mixture, which itself varies with concentration. There are three different methods for quantitative phase analysis by XRD. These are: (1) The external standard method, where the diffraction intensity of the particular phase in the mixture is compared with the diffracted intensity of the pure substance of that phase. (2) The direct comparison method, where the diffracted intensity of the phase of interest is compared with the intensities of all of the phases present in the mixture, and (3) The internal standard method, where the intensity of the phase of interest is compared with the intensity of that phase in another mixture with known concentration. In this discussion, only the direct comparison method is considered, because it can be directly applied to any polycrystalline multi-phasic material and is therefore commonly used to measure retained austenite in ferrous alloys. Experimental setup & measurement procedure The procedure for measuring retained austenite in steel is fairly simple and involves the following six steps: (1) selection of the proper radiation, (2) running the diffraction experiment on the required location on the samples, (3) selecting the optimum peaks of martensite and austenite for the intensity comparison, (4) measurement of the diffracted intensities after background removal from the pattern, (5) comparison of two or more lines if a texture effect is present, and (6) applying the appropriate equations to calculate the concentration of retained austenite. The samples are cut along line 2-2 as shown in Figure 7, and x-ray patterns are taken along the cross section of the sample. Table 1 shows the measurement angles and peaks chosen. The data in Table 1 is applicable only to chromium K _ radiation, which is commonly used for steels. Once the intensities of the peaks are measured, the amount of retained austenite can be calculated by solving Equations 4 and 5 simultaneously. 13

14 2 2 Figure 7: Section lines showing the sample cut for measuring retained austenite. Table I: Peak information for Cr K _ radiation Peak Range for 2_ Peak width 200A M A I I γ α R R γ α c c γ = (4) α c c = 1 (5) α + γ In Equations 4 and 5, I _ and I _ are the measured intensities of the austenite and martensite peaks respectively, R _ and R _ are constants calculated from knowledge of the lattice parameters, crystal structure, and carbon content of each phase, and c _ and c _ are the respective concentrations of the austenite and martensite in the sample. 14

15 Appendix B Progress made in Task-1 of the project Samples, with the dimensions shown in Table I, were machined from a 5160 steel plate. A hole that is mm in diameter and mm in depth for inserting a thermocouple was drilled into one side of the part. The top 9 mm of the hole was bored and tapped with internal threads to allow screwing the sample to the connecting rod, which holds the part in an upright position during heating and quenching. Graphite powder was packed into the hole before the thermocouple was inserted in order to ensure intimate contact between the sample and the thermocouple. These samples were heated to the 850 C, and held at that temperature for 20 min after equilibration in order to ensure the completion of transformation. Subsequently, the samples were quenched into Houghton- G oil maintained at room temperature. Table-I Dimensions of the part. Dimension Magnitude Length mm Height mm Width mm Diameter of center hole mm Results and discussion Hardness, distortion, residual stresses, and retained austenite measurements were performed on these samples and were compared with the model predictions. Figure 1 shows a comparison between the measured and model-predicted hardness values across the sample s cross-section. There is very good agreement between the computerpredicted and measured hardness values except at the part s edge. This discrepancy at the part s edge is attributed to the loss of carbon at the surface due to decarburization. Sealing the tube of the furnace and passing argon gas through it, so that the samples do not come in direct contact with the air, may solve this problem. Building of the new equipment to address this issue is currently underway. A sealed vertical tube, made from stainless steel, will be placed inside a vertical tube furnace. Hot argon gas will be passed through this stainless steel tube with a gas flow rate high enough to minimize oxidation and decarburization, and to ensure uniform heating of the sample. Figure 2 shows a comparison of measured vs. model-predicted retained austenite for the samples. In this figure, it is important to note that the measured data is quite different from the model predictions. The XRD measurements in this case did not show a significant austenite peak; one of the reasons for this could be that the amount of retained austenite in these steel samples is less than 3 %, which is sometimes difficult to measure. 15

16 There is also a significant difference between the measured and the model-predicted amount of retained austenite. This issue needs to be addressed and corrective actions taken Measured Predicted Hardness (HRC) Distance from one end to the center (mm) Figure 1: Comparison of model-predicted and measured hardness values Measured Predicted Volume frac Distance along the cross section of the part (mm) Figure 2: Comparison of measured vs. predicted concentration of retained austenite after quenching. 16

17 Figure 3 shows a comparison of shows a comparison of measured vs. model-predicted residual stresses at a specified location on the sample. Figure 3 shows that the residual stresses predicted by the model are low compared to the measured residual stresses. The reason for this discrepancy between measured and model predicted residual stresses is due to the over estimation of retained austenite by the model. Samples with more retained austenite exhibit lower residual stresses. Moreover, it has become apparent that it is difficult to obtain repeatable measurements of residual stress by means of the XRD method, accordingly, the crack compliance method described in Appendix A will be explored and compared with the XRD method in the next reporting quarter. It is also possible that inaccurate parametric fitting of the dilatometry data that is used to obtain the transformation kinetics parameters may have resulted in the discrepancies between measured and model-predicted retained austenite and residual stress. 0 Measured Predicted Stress (MPa) σ 11 σ Figure 3: Comparison of predicted vs. measured residual stresses Figure 4 shows a comparison between the measured (Fig. 4(a)) and model-predicted (Fig. 4(b)) dimensions of the central hole in the part before and after quenching. Since machining a hole in a flat part invariably involves some error, the radius of the machined hole does not match perfectly the radius created in the model. Therefore, an accurate quantitative comparison between the measured and predicted part distortion is not possible at this time. Nevertheless, Figure 4 provides a useful qualitative assessment of the ability of the software to simulate dimensional distortion in wrought steel. Moreover, in order to quantify the data, a fixture for the CMM machine capable of holding the sample at exactly the same location before and after quenching has been manufactured. 17

18 Also the CMM machine will be programmed such that the measurements can be started from the same point on the circle. This task is currently underway and distortion will be presented in a more quantitative manner in the next report. 0.5 Before quenching After quenching Radius (mm) (a) Before quenching After quenching Radius (mm) (b) Figure 4: Coordinates of the circular hole before and after quenching. (a) Measured using CMM, and (b) predicted by the model. 18

19 References 1. B.D. Cullity, X-Ray Diffraction, 3 rd Edition, Prentice-Hall Inc., 2003, pp M.B. Prime, Residual Stress Measurement by Successive Extension of Slot: Crack Compliance Method, Applied Mechanics Reviews, vol.52, No.2, 1999, pp Web link, Los Alamos National laboratory, USA. 19