Modeling and Simulation for Material Selection and Mechanical Design Part 6 pot

The heat transfer coefficients h during quenching were calculated as a function of temperature by the methods mentioned below and were used for the simulation as the surface boundary con

2 Models of Simulation

The simulation model in carburizing–quenching process is a steel cylinder of

20 mm diameter, 60 mm length and 0.45% carbon It is assumed that the model is located in a uniform coolant Then, the finite element model belongs to an axisymmetrical problem As an initial step of the heat treat-ment process, calculations for the heating and carburizing process were used

to simulate thermal stress field, thermal distortion as well as carbon distri-bution in the model The quenching process of the model was started from the initial temperature 8508C and the model was cooled to 308C with oil The heat transfer coefficients h during quenching were calculated as a function of temperature by the methods mentioned below and were used for the simulation as the surface boundary condition in Eq (4)

3 Identification of Heat Transfer Coefficients

It is important to determine the heat transfer coefficients in the quenching process of metal parts for numerical simulation However, it is rather diffi-cult to evaluate heat transfer coefficients during quenching of actual steel Figure 2 The specimen and sheathed thermocouples

Figure 3 The carburizing–quenching process

parts which depend on not only the quenchant but also the shape, size, surface condition, and thermal properties of parts, etc It is, therefore, very difficult to evaluate the heat transfer coefficients in quenching of steel parts Some approximate methods are estimating the coefficients from the cooling curve data of standard probes which are used for evaluation of the cooling power of liquid quenchants

We have already reported the availability of the lumped-heat-capacity method for the estimation of the heat transfer coefficient from the cooling curve data of the JIS silver probe (pure silver solid cylinder of 10 mm dia-meter by 30 mm length, Japanese industrial standard K 2242 [72]) which has a high thermal conductivity A computer program ‘‘LUMPPROB’’ based on the lumped-heat-capacity method was developed [73] On the other hand, it was confirmed that the inverse method is more suitable for estima-ting the heat transfer coefficients from quenching data of the ISO probe (Inconel 600 alloy solid cylinder of 12.5 mm diameter by 60 mm length, International standard ISO 9950 [74]), because of its low thermal conductiv-ity We developed a computer program ‘‘InvProbe-2D’’ [75], which uses both a lumped-heat-capacity method and a two-dimensional inverse method with the least residual method In this section, we used these programs for the estimation of the heat transfer coefficients during quenching Furthermore, more precise heat transfer coefficients were estimated by a trial-and-error method, in which the calculation of cooling curves and mod-ification of the surface boundary condition were repeated until the simu-lated cooling curves gave good agreement with the measured cooling curves of the steel specimen

4 Carbon Diffusion and Distribution

Fig 4(a)shows the changes of carbon content with time in different posi-tions during the carburizing process The carbon content in the surface of the steel cylinder increases from 0.45% to 0.9% in 250 min Fig 4(b)and (c) compares the difference of carbon content of the steel cylinder before and after the carburizing process The carbon content decreases being reserved in heating furnace for 35 min after carburization, which shows the effect of diffusion on carbon content distribution

5 Heat Transfer Coefficients and Cooling Curves

The heat transfer coefficients used for the simulation are shown in Fig 5 The coefficients are estimated by using the inverse method program

‘‘InvProbe-2D’’ and the cooling curve data of the ISO Inconel 600 alloy probe The cooling curves that were calculated with these heat transfer

content On the other hand, depending on measured hardness as shown in Fig 8,distribution of martensite after carburized–quenching also is verified

7 Distortion During Quenching

Figure 9shows the distortion of the calculated and the measured diameter of the steel cylinder after carburizing–quenching Except for the influence of surface boundary condition, the calculated distortion of the center part

of the cylinder is in good agreement with the measured value as shown in Fig 9 However, because identification of the heat transfer coefficient on the corner of the cylinder is difficult, prediction of the distortion on the corner remains to be solved

Figure 6 Calculated and measured cooling curves in different position

Figure 7 Distribution of (a) martensite and (b) equivalent stress

B Residual Stress and Distortion in

Carburizing–Quenching of Gear

Based on the series of governing equations above, a finite element program called ‘‘HEARTS’’ was developed to predict the temperature field, carbon diffusion, phase transformation and distortion during carburizing–quench-ing process

The simulation model in carburizing–quenching process is a JIS-SCM420 steel gear with edge circle diameter of 36 mm, teeth number 16 and module 2 mm as seen in Fig 12 Figure 13 shows the variation of TTT-curves of the material when carbon content is changed to 0.8% by using

Figure 10 The calculated and experimental residual stress on the surface

Figure 11 Comparison of residual stresses with and without consideration of transformation plasticity

was cooled to 308C with oil The heat transfer coefficients h during the quenching were calculated as a function of temperature by the methods men-tioned below and used for simulation as the surface boundary condition

1 Carbon Diffusion and Distribution

Fig 17 shows the changes of carbon content in different positions with time during the carburizing process The carbon content in the surface of the steel gear increases from 0.45% to 0.9% in 250 min Fig 18(a) and (b) Figure 14 Process conditions of carburizing–quenching

Figure 15 Heat transfer coefficient depending on temperature

4 Distortion after Quenching

Figure 21shows the distortion of the calculated and the measured diameter

of the steel gear after carburizing–quenching And except for the influence

of surface boundary condition, the calculated distortions of the center part

of the gear are in good agreement with the measured value as shown in Fig 22.However, because identification of the heat transfer coefficient on the corner of the gear is difficult, prediction of the distortion on the corner remains to be solved

Figure 20 Equivalent stress

Figure 21 Deformation of gear

stress formation during casting A unified inelastic constitutive relationship capable of describing both elastic–viscoplastic solids and viscous fluids to apply simulation of the casting process was proposed and verified by experi-mental and numerical results On the other hand, a proposal based on the finite element method to couple temperature, stress fields as well as defor-mation during solidification was presented Depending on the simulations

of the continuous or semi-continuous casting, the mechanism of the residual stress formation during these casting processes can be represented The thermo-mechanical modeling was also verified by a comparison with the experimental data, such as the measured residual stress and variation tem-perature in casting Vertical semi-continuous direct chill casting process is one of most efficient methods to produce ingots of aluminum alloys and other metals It is beneficial for optimizing the operating conditions to simu-late thermo-mechanical field in the solidifying ingot So many reports have been published concerning such analyses of the temperature distribution incorporating solidification by finite element method, but a few papers treat the induced stress=strain field Simulations of thermal stress in continuous casting slab were made by using elastic–plastic constitutive models [79,80], and viscoplastic stresses [81–84] were simulated based on the solidification analysis by Williams et al [31] However, in their studies, the influence of casting speed was neglected, so that the numerical simulation along with the variation of casting conditions could not be realized In order to solve this problem, Ju and Inoue [62] proposed a numerical simulation method

by the Eulerian coordinate, and application to the continuous casting pro-cess of steel slab was performed

A Residual Stress Formation During

Semi-continuous Casting

The aim of this section is to apply the coupled method of temperature and stresses incorporating solidification developed for semi-continuous direct chill casting of aluminum alloys When the bottom block plate is located

at the upper position and the length of the growing ingot is small, the tem-perature, liquid–solid interface, and stresses in the ingot vary with time, both in the sense of space and of material However, when the ingot becomes long enough, the physical field in the upper part is regarded to

be time-independent or steady in the spatial coordinate fixed to the system

In the first part of this section, a steady heat conduction equation with heat generation due to solidification is formulated in a spatial coordinate system when considering the material flow A numerical calculation for the temperature in the solidifying ingot as well as the simulation of the location

of liquid–solid interface is carried out by a finite element technique

Most metallic materials at low temperature may be treated as an elastic–plastic solid However, if they are heated beyond the melting point, the materials can be regarded as a viscous fluid, and they behave in a time-dependent inelastic manner at high temperature close to the melting tem-perature Therefore, a unified constitutive model needs to be established

to describe the elasto-plastic and viscoplastic behavior of the solidified part

of the ingot as well as the viscous property of the liquid state Taking into account the effects of such phenomena, a modification of Perzyna’s consti-tutive model similar to the one in other sections is presented in the second part of this section, and some experimental results of the viscosity appearing

in the model are presented for a Al–Zn type alloy By using the model, elastic–viscoplastic stresses are calculated for the ingot to establish the residual stress distribution, and are verified by the measured data from a hole-drilling strain-gauge technique

Finally, results of a numerical simulation are presented on the influ-ence of operating conditions on temperature and stresses, such as ingot size, casting speed, and initial temperature, to provide fundamental data for opti-mizing the operating condition

1 Finite Element Model and Casting Conditions

The theory and the procedure developed above are now applied to the simu-lation of the vertical semi-continuous direct chill casting process shown schematically in Fig 23 The material treated is a Al–Zn type alloy with 5.6% zinc and 2.5% magnesium A quadrilateral finite element mesh pat-tern of 600 elements with 1941 nodes illustrated inFig 24is employed for both analyses of temperature and stress fields

The boundary condition for heat conduction is assumed in such a way that the temperature of the meniscus of molten metal is prescribed to be w0, and that heat is insulated along the central line and the bottom of ingot as well as the surface contacted with the refractory The cylinder facing the mold is regarded as the boundary Sqon which heat flux is given The other part of the surface Shis given by a heat transfer boundary due to the cooling

of water.Figure 25depicts the measured heat flux q absorbed by the mold, and heat transfer coefficient h depending on flow rate of water TWis shown

inFig 26

Other data used for temperature calculation incorporated with solidi-fication are shown inTable 1.Characteristic results of calculated tempera-ture and residual stresses for an ingot of 1 m in length with the diameter of

240 mm are compared with experimental data to verify the method Simula-tions in other cases of different operating condiSimula-tions such as casting velocity, size of the ingot, and cooling rate are also made

Figure 27 View of the calculated temperature profile.

Figure 28 Temperature variation at the center and surface of the ingot

controlling the quality of the strip because of the existence of the deforma-tion of the strip itself, due to thermal expansion or thermal stress There are two key points: firstly, if the solidification is completed before the liquid reaches the minimum clearance point between the rolls, then the strip will occur at a fixed gap Hence, one of the key points is controlling of Figure 29 Volume fraction of solid along the distance from meniscus

Figure 30 View of deformation

Figure 31 View of stress distributions.

solidification Another key point is that the viscoplastic deformation incor-porating material flow must be considered in this thermo-mechanical process

1 Continuous Casting System by Twin-Roll Method

The twin-roll continuous casting system is schematically illustrated in Fig 42(a).In this process, molten metal is between the two rolls rotating

in opposite directions with same angular velocity The level of the molten metal is always kept constant by overflowing the excess molten metal from the nozzle As soon as the molten material is poured into the rolls, solidification takes place on the roll surface, which is cooled by circulating water inside the roll Therefore, the problem then is to find this steady solidification profile and the distribution of temperature and fluid velocities

in both the liquid phase and the solid phase On the other hand, due to the symmetry to the central line, half of the model shown in Fig 42(b) is treated for the analysis

Figure 32 Iso-stress contours

2 Analytical Models and Parameters

The procedure developed above is now applied to the simulation of the thin slab casting process under the same operating conditions The results are summarized as follows Figure 43 represents the finite element descri-tization of the whole region of the strip and roll The surface of roll as well

as the contacted boundary with the roll and strip is assumed to belong to Figure 33 Calculated stresses by (a) elastic–viscoplastic model and (b) elastic– plastic models

heat transfer boundary and the surface of the strip to the heat radiation boundary

In order to verify the numerical analysis method proposed in Section 2, continuous casting of SUS304 steel is taken into consideration

in this section In continuous casting process of SUS304, the thickness

of the slab is 1 mm, and two casting speeds are used Vc¼ 400 and

600 mm=sec

3 Calculated Results

Simulated results of steady temperature field both in the strip and roll is shown inFig 44(a) and (b) for the casting speeds of 400 and 600 mm=sec Figure 34 Stress distribution in several sections of ingot