Proceedings of the 24th ASM Heat Treating Society Conference, September 17-19, 2007 COBO Center, Detroit, Michigan, USA. Copyright© 2007 ASM International®. All rights reserved.
Microstructure and Property Predictions by Using a Heat-Treatment Planning System, CHT-q/t L. Zhang∗, Y.M. Rong, R. Purushothaman Department of Manufacturing & Engineering, Worcester Polytechnic Institute, Worcester, MA, USA J.W. Kang Department of Material Science & Engineering, Tsinghua University, Beijing, P.R.China
Abstract
reheating furnace of billet, bar and slab which are of rectangular or round sections in rolling and steel plants [1-4]. Some works mainly focus on the combustion problems in boilers or combustors, while the heat transfer between heat resource and load is simple [5-8]. However, there are few studies that consider the simulation of the heat treatment processes of castings, forgings or machined workpieces, which are very popular in automotive, machinery and equipment manufacturing industries. These kinds of workpieces are usually of complicated shape and many workpieces are processed in furnace loads. Therefore the heat transfer between furnace and workpieces, among workpieces and inside workpieces is very complicated. In a previous study, a method was provided to calculate the heating time for workpieces with arbitrary shape [9]. However, the study is based on a fixed furnace temperature.
Steel quenching is a heat treatment operation which results in the change of the microstructure and properties. In this paper, this process is modeled and simulated with an self-developed analytical tool, “Computerized Heat Treating and Planning System for Quenching and Tempering”, i.e., CHT-q/t, which is to predict the temperature profile of load in batch as well as continuous furnaces during heating, quenching and tempering of steels, then to provide information about the mechanical properties as quenched. The system can be also used to optimize the heat treatment process design with the aim to save energy and reduce cost. The microstructure/phase transformation is predicted by solving Avrami-Johnson-Mehl equations through comparing cooling curves against materials TTT diagrams. The hardness of the workpiece is estimated as a distribution of the load, by considering the contribution of microstructure and carbon contents. The results are verified through running JOMINY end-quench hardenability tests. The calculation is a combination of numerical simulation and empirical equations. This tool is suitable for commercial and captive heat treaters for quality control and process optimization.
In order to optimize the heat treating process, a computerized tool is desired to simulate the thermal process as well as the microstructure evolution of the steel materials, so that the heat treating process parameters can be optimally determined to ensure the materials property as required; and at the same time the production cycle time can be minimized so that the manufacturing cost and energy consumption can be reduced. In previous years, the thermal analysis models for loaded furnaces, CHT-bf for batch furnaces and CHT-cf for continuous furnaces, have been developed and validated for modeling and simulating the heating up process [10-12]. When the part and part load is given with specified furnace information, the temperature profiles of the load are computed for the parts both on the surface and in the core, as well as in different locations of the furnace. The predicted temperature profiles are compared against the given thermal schedule to evaluate if the soaking time is necessary and sufficient to ensure the quality of the materials property control. With the help of using CHT-bf/cf, the alternative load designs and thermal schedule determination can be evaluated for optimal solutions.
1. Introduction Heat treatment can be defined as a combination of heating and cooling operations applied to a metal or alloy in solid state. It is an important manufacturing process, which controls the mechanical properties of metals, therefore contributes to the product quality. Heat treatment industry is a 15 billion dollars business in the USA. Meanwhile it is also a main energy consumer. Most heat treating processes have the heating process in the furnace as the first step. There the microstructure and mechanical properties undergo changes and most of energy is consumed. However, currently, the heating process is mainly based on experience. Therefore, the heat transfer simulation in heat treatment furnace is of great importance to predict and control the ultimate microstructure and properties of the workpieces and to reduce energy consumption. Studies have been done to simulate the heating process of workpieces in heating furnace, such as
But CHT-bf/cf only has the heating process model. In this paper, in order to expanded CHT-bf and CHT-cf into an entire heat treating process simulation, to estimate the materials property change during and after the heat treating process, a computerized heat treatment planning system for quenching and tempering of steel, CHT-q/t, has been developed. CHT-q/t is developed based on CHT-bf/cf. It includes the simulation
∗
Corresponding author. E-mail address:
[email protected]. (Lei ZHANG). 100
model of quenching and tempering process for predicting the temperature profile of load in batch, as well as a continuous furnace during heating, quenching and tempering of steel. The microstructure evolution during the thermal process is simulated based on the analysis of the cooling rate at different location of the workpiece, and the phase transformation during the cooling process. Finally, the mechanical properties, mainly the hardness distribution, are estimated based on the resultant microstructure. The relationship between hardness and other properties, such as ultimate tensile strength, yield strength, toughness and elongation, are shown based on empirical knowledge found in literature.
(4b)
λg L*
⋅ Nu L*
circulation fan. The calculations of Nu L* are different for natural convection and forced convection [11 12]. Heat transfer coefficient hquent can be determined by experimental approach. In our Lab at WPI, tank quenching experiments are conducted to generate a serial of hquent values as function of temperature, velocity, viscosity, concentration et al., variations of temperature of liquid quenchant under different stages, vapor blanket, boiling, convection are measured, the corresponding h values are then obtained by reverse calculation. 2.3 Conduction model Fourier equation for the conduction in the solid, such as workpiece, furnace walls, fixtures, and trays/ baskets is given as
The radiation between furnace and the outside layer of a workpiece:
ρc
(1)
∂T ∂ 2T ∂ 2T ∂ 2T = λ( 2 + 2 + 2 ) ∂t ∂ x ∂ y ∂ z
The radiation between the outside layer of the workpiece and workpiece:
Qht = KPID · KAH · Qgross Δt
Qrad _ wp _ wp = σ ⋅ ε ⋅ Fv wp1 _ wp 2 ⋅ A ⋅ (Twp1 − Twp 2 ) 4
(13)
2.4 Furnace model The furnace model contains the PID (Proportional, Integral and Derivative) control, available heat for gas-fired furnaces, and heat terms such as heat input by fan, heat loss from furnace door and walls, heat storage in the furnace wall and auxiliaries and heat loss by cooling tubes for some special furnaces. The effective heat input is
where σ is the Stenfan-Boltzmann constant, ε is emissivity, Fvwp_fce is the view factor of workpiece to furnace, A is the exposure surface area of the workpiece, Tfce and Twp are the temperatures of furnace and workpiece respectively.
4
(5)
where L* is the characteristic length, L* = A1/2. Nu L* is the Nusselt number. It is related to the geometrical features of workpiece, load pattern, thermal properties of atmosphere and
2.1 Radiation In the heat treatment processes of workpieces, there are two kinds of radiation heat transfer: from furnace to workpieces and from workpieces to workpieces.
Qrad _ fce _ wp = σ ⋅ ε ⋅ Fv wp _ fce ⋅ A ⋅ (T fce − Twp )
Qconv = hquent ⋅ A ⋅ (Twp − Tquent )
h conv =
In heat treatment processes, the heat transfer processes involve three modes: the radiation, conduction and convection, as well as the furnace model. To simplify, the following assumptions are made: • The furnace temperature is uniform. The furnace serves as a heating resource and heat storage as well. • Atmosphere temperature is uniform and is the same as furnace.
4
(4a)
where hconv is the convection film coefficient, which can be calculated by following equation:
2. Mathematical Model Development
4
Qconv = hconv ⋅ A ⋅ (T fce − Twp )
(2)
(14)
where KPID is the PID control coefficient, KAH is the available heat coefficient, Qgross is the gross heat input, Δt is the time step.
where Fvwp1_wp2 is the view factor of workpiece 1 to workpiece 2, Twp1 and Twp2 are the temperatures of workpiece 1 and workpiece 2 respectively.
The heat storage in the furnace wall can be calculated by i +1 i i Qstorage = Qhti − Qloss − Qload + Q ifan
The view factors of workpieces to furnace and of workpieces to workpieces can be estimated by the load pattern [11 12].
(15)
where Qgross is the heat loss, Qgross is the heat storage in load, and Qgross is the heat input by fan. Then the furnace temperature is calculated as follows:
2.2 Convection and cooling model The convection heat transfer between furnace and the workpiece, and between workpiece and quenchant is denoted as follows: 101
T
i +1 fce
=Q
n fce
i storage
/
∑ w × cp i
i
where wM is the transformed volume fraction of austenite into martensite, Ms is the martensite start temperature, Mf is the martensite finish temperature, and T is the transformation temperature, T ≤ Ms. It can be observed from the above equations, to calculate b, n and w we need only Ts and tf from the TTT diagram, and t from the cooling curve (Fig.1).
(16)
i
where nfce is the total number of furnace wall and auxiliaries, wi and cpi are the weight and specific heat of the furnace auxiliaries. 2.5 Microstructure and properties prediction model In the transformation model the progress of transformation for the diffusion reactions is followed by an Avrami-Johnson-Mehl equation, assuming additivity, while the fraction of martensite formed is modeled as a function of holding temperature below the martensite start temperature. For the diffusion phase transformations of austenite to ferrite and pearlite, the formation of a new phase on cooling is only possible once the temperature is below the equilibrium transformation temperature. This temperature is dependent on the alloy content of the steel. The kinetics of the growth of ferrite and pearlite are described using the Avrami-Johnson-Mehl equation [13]:
(
w = 1 − exp − b.(t − t s )
n
)
(17a)
where w is the volume fraction of austenite transformed, b and n are the coefficient and exponent of the austenite transformation kinetics, t is the time, and ts is the start time.
Figure 1: Schematic chart illustrating relationship of continuous cooling to a typical TTT diagram.
The values of b and n are evaluated from the given TTT diagram except for ferrite for which it is assumed that n = 1. More generally it can be stated that:
n=
[
log ln (1 − ws ) / ln (1 − w f
[
]
log t s (T ) / t f (T )
)]
− ln (1 − ws ) b= t s (T )
2.6 Properties prediction The properties of the steel are determined by their microstructure. Various equations are used to map the properties of steels based on their microstructures.
(17b)
Since hardness is a function of % Martensite as well as % carbon content (Fig.2), thus regression analysis is being used to get the hardness at a specific martensitic percentage.
(17c)
where the subscripts s and f indicate start and finish, respectively. In a TTT diagram, ws is usually chosen to be 1% and w f 99%, but other percentages may also be chosen. The volume fraction of martensite is then modeled using an equation proposed by Koistinen and Marburger [4]. Below the martensite start temperature Ms, it is assumed that the remaining austenite is transformed into martensite according to equation as:
wM = (1 − wF − wP − wB − wC ) *
(1 − exp(− .011.(M s − T )))
Figure 2: Relationship between hardness, carbon content and amount of martensite [14] (18) Hardness=f(C%, Martensite%), i.e. 102
H= ax2+bx+c (19) where x--C%, a, b, c are constants, which can be obtained from the relationship/curves shown in Fig. 2 by numerical regression method.
temperature below the lower critical temperature, and followed by cooling in air or at any desired rate. CHT-q/t utilizes several databases to facilitate the thermal analysis, microstructure evolution analysis, and property estimation. DB1 – Material Database: Along with material name, material type, thermal properties such as density, specific heat, conductivity, emissivity etc., this database contains the materials TTT diagrams in tabular format for all the materials going to be heat-treated. DB2 – Furnace Database: It consists of different kind of furnaces (both batch and continuous) for heating and quenching. It also includes tank used for liquid quenching. DB3 – Atmosphere Database: It contains the atmosphere present inside the furnace. DB4 – Quenchant Database: The quenchant database contains the quenchant types, including the physical properties of the quenchants such as viscosity, boiling point, latent heat of vaporization, density and specific heat capacity. It also consists of the convective heat transfer coefficient “h” vs. blower horse power. DB5 – Tempering Properties Database: It contains the empirical relations needed to predict the phase transformation and properties after tempering.
Ultimate Tensile Strength, Yield Stress, Toughness and Elongation are all related to Hardness, and some of these relationships are available in the literatures. Therefore, an approach is to build a database using the data from handbooks and literature and use some empirical relations to populate the database and is used to properties prediction in CHT-q/t. The JOMINY end-quench hardenability tests is used here to verify the property prediction model. Fig. 3 is the end-quench hardenbility test data for 4140 steel, the hardness value of position A, B, C and D are 55.5, 48, 36, 31RC respectivly. And the corresponding predicted hardness by the above model are 55.79, 48.68, 36.13, and 31.73RC respectivly, which are well consistent with the test data.
4. Case studies - results and discussion The system has been applied to the focus group members of Center for Heat Treating Excellence (CHTE), WPI. Here two case studies are given. 4.1 Case 1 This case study is oil quenching of a huge part, which weighed 2580 lbs (Fig. 5). The part was heated in the Pit furnace for almost 900 minutes and was removed from the pit furnace using an overhead crane and was quenched in an open tank. CHT-q/t 3D model was used to calculate this case. The calculation space step used here was 2 in., which can save calculation time, therefore 2016 elements was obtained by meshing the part. The total calculating time is around 10min. and the results were shown below.
Figure 3: JOMINY end-quench hardenablility test data for 4140 steel[15]
3. Design of Computer-aided Heat Treatment Planning System-CHT-q/t Fig. 4 shows the function flow-chart, which is the schematic representation of the sequence of operations in CHT-q/t. CHT-q/t contains four basic operations. Heating: consists of heating the parts in batch as well as continuous furnace. Cooling: can be done in batch furnace, continuous furnace and in tank. Quenching: is a rapid cooling of metals from an elevated temperature to a low temperature. In CHT-q/t, gas and liquid quenching of the entire load has been considered. Gas quenching can be done in the same furnace used in heating or in a different furnace particularly used for quenching. A tank is used for liquid quenching. Tempering: can be defined as a process, which consists of heating hardened steel to a
Figure 5: Workpiece in the furnace and the thermocouples 103
Initial condition
W orkpiece
D B1 Material & TTT profile D B
Furnace
Load pattern
Thermal schedule
Module 1 W orkpiece classification & enmeshment W orkpiece shape classification Enmeshment by Biot no .
D B2 Furnace D B Module 2 Heating D B3 Atmosphere D B
Output 1 Heat term & temperatures
Module 3 C ooling H eat transfer for gas quenching in same furnace used in heating D B4 Quenchant D B
H eat transfer for gas quenching in different furnace
Output 2 Cooling curve of each workpiece and inside the workpiece
Heat transfer for oil quenching in tank (load w ith fixture , single workpiece w ithout fixture )
D B5 Quenching properties DB
D B6 Tempering properties DB
Module 4 Phase transformation prediction (Austenite to pearlite / bainite / martensite ) C omparing cooling curve w ith TTT diagram to determine microstructure Mapping of microstructure to properties
Output 3 Mechanical Properties after Quenching
Module 5 Tempering H eating below austenizing temperature
Output 4 Heat term & temperatures
Module 6 Property prediction by empirical equations
Output 5 Mechanical Properties after Tempering
Figure 4: Function flow-chart of CHT-q/t The calculating temperature profiles were plotted in Fig. 6 with the measured results. From the start of heating stage, the calculated temperature increased almost as quickly as the measurement shows. They almost get to the high temperature at the same time. The temperature error is within 30 °F, and the relative error is around 3%. Then quenching starts, the inside temperature was measured. It is observed that the prediction
results match very well with the measurements from the quenching start. The temperature profiles plotted in CHT-q/t interface is shown on Fig. 7. And the predicted properties in a part section are displayed in Fig. 8. 104
1800 1600 Channel 1(Surface temp) Channel 2 (Inside temp) Channel 3 (furnace temp) PartFast PartSlowest
Temperature, F
1400 1200 1000 800 600 400 200 0 0
100
200
300
400
500
600
700
800
900
1000
1100
Time, min
Figure 6: Comparison of results between calculated and measured during process
Figure 7: Cooling curves with TTT diagram
Figure 8: HB Hardness distribution on the part surface (front view)
Figure9: Arrangement of workpieces in the basket and the thermocouple locations 105
900
Fast-3D Slowest-3D Measured1 Measured2
800
Temperature, °C
700 600 500 400 300 200 100 0 0
2
4
6
8
10
12
14
Time, min
Figure10: Comparison of results between calculated and measured during the quench process
4.1 Case 2 This is high pressure quenching case using argon with 12 bar Turbo treater. The workpiece is a cylinder with 1.125” diameter by 4” long, weighted 2lbs, and is made of Alloy Steel 4340. Fig. 9 shows the load pattern. The parts were arranged in vertically in the basket as shown in the Fig. 9. And 3 thermocouple were attached to the load 2 were inside the probe and one right next to the workpiece to measure the gas temperature during the process. The load was quenched from 850 °C to the room temperature. In this case totally 3840 elements was obtained, and it ran around 15 min.
Acknowledgement The authors are grateful to the help for case studies from Bodycote Thermal Processing, American Heat Treating, Sousa Corporation.
References 1.
The calculating results are displayed in Fig. 10, it is very clear that all the parts are fast cooled almost at the same rate, and they are also very well when compared with the measured results.
2.
5. Conclusions CHT-q/t is based on CHT-bf/cf, and it includes the simulation model of quenching and tempering process to predict the temperature profile of load in batch as well as continuous furnace during heating, quenching and tempering of steel. It, then provides information about the mechanical properties of the quenched & tempered part based on the cooling rate and phase transformation analysis. Finally, the process is optimized to save energy and reduce cost.
3.
4.
Two case studies are presented, which shows the calculated results are basically in agreement with the measured one and reasonable.
5.
106
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