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

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 850 8C 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. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. 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 Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. 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 9 shows 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. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. 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 carb urizing–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. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. 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. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. 4. Distortion after Quenching Figure 21 shows 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. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. 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. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. 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 in Fig. 24 is 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 w 0 , 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 S q on which heat flux is given. The other part of the surface S h is given by a heat transfer boundary due to the cooling of water. Figure 25 depicts the measured heat flux q absorbed by the mold, and heat transfer coefficient h depending on flow rate of water T W is shown in Fig. 26. Other data used for temperature calculation incorporated with solidi- fication are shown in Table 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 conditions such as casting velocity, size of the ingot, and cooling rate are also made. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. Figure 27 View of the calculated temperature profile. Figure 28 Temperature variation at the center and surface of the ingot. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. 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. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. [...]... 1 mm, and two casting speeds are used Vc ¼ 400 and 60 0 mm=sec 3 Calculated Results Simulated results of steady temperature field both in the strip and roll is shown in Fig 44(a) and (b) for the casting speeds of 400 and 60 0 mm=sec Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 35 Isothermal lines by effect of casting speed sec Temperature distribution along the central line and surface... difference in mechanical and physical properties of the material in each layer To solve the first and second problems, a scheme for numerical analysis by the finite element method has already been proposed by the authors [ 86] This chapter shows the simulation of temperature and stress=strain induced in the layers of the plate with progressive domains based on the metallo-thermo-mechanics, and a finite... is evident V DESIGNING OF THERMAL SPRAY COATING FOR CONTROL OF RESIDUAL STRESS Plasma-spray coating is an important method by which a new functional layer can be produced on material surface [85, 86] In the spray coating process, solidified particles form thin lamellae whose microstructure depends on the particle cooling rate during solidification Indeed, lamination of several kinds of materials deposited... liquidus and solidus temperatures Tl ¼ 1 460 8C and Ts ¼ 13998C is depicted in Fig 46 In the early stage of rapid cooling by the roll, the solidified shell is seen to grow gradually toward the central part The change in casting speed is known to affect the distribution of temperature and shell thickness As the casting speed becomes faster, the position of the liquidus line moves downstream Figs 45 and 46, ... boundary of molten state and a moving interface between liquid and solid phases as well as the evaluation of residual stresses There are three complicated aspects to be considered: The first one is that the spray coating process is nonlinear problem with respect to time and location, and the second is that the solidifying process plays an important role in the simulation of temperature and stresses field... 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... structural components, such as plates, and cylinders, especially in the case when exposed to severe temperature gradient However, the residual stresses at an interface between multilayer after coating play an important role that affects thermo -mechanical properties of the materials, since it is associated with the growing liquid boundary due to the supply of the molten material and also from the moving liquid–solid... distribution depending on effect of ingot diameter and cooling water rate molten metal is introduced in the heat conduction equation coupled with mechanical work and latent heat generation by solidification Simultaneously, a method of stress analysis using an elastic–viscoplastic constitutive relationship capable of describing the mechanical behavior of both solid and liquid is proposed Examples of the numerical... from the moving liquid–solid interface depending on the progress of phase transformation It is also necessary to consider the effect of coupling between Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 38 Stress distribution by effect of casting speed temperature and stress=strain fields and the phase transformation, or solidification in this case Some open problems still remain in the... symmetry to the central line, half of the model shown in Fig 42(b) is treated for the analysis Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 33 Calculated stresses by (a) elastic–viscoplastic model and (b) elastic– plastic models 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 . mm, and two casting speeds are used V c ¼400 and 60 0 mm=sec. 3. Calculated Results Simulated results of steady temperature field both in the strip and roll is shown in Fig. 44(a) and (b) for. 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. alloy with 5 .6% zinc and 2.5% magnesium. A quadrilateral finite element mesh pat- tern of 60 0 elements with 1941 nodes illustrated in Fig. 24 is employed for both analyses of temperature and stress