ASM Handbook Volume 22 Modeling and Simulation: Processing of Metallic Materials

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ASM Handbook Volume 22 Modeling and Simulation: Processing of Metallic Materials 9. Simulation of PM Processes 9.A. Press and Sinter Powder Metallurgy Suk Hwan Chung 1, Young-Sam Kwon 2, Seong Jin Park
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ASM Handbook Volume 22 Modeling and Simulation: Processing of Metallic Materials 9. Simulation of PM Processes 9.A. Press and Sinter Powder Metallurgy Suk Hwan Chung 1, Young-Sam Kwon 2, Seong Jin Park 3, and Randall M. German 4 1 Hyundai Steel Co., , Kodae-Ri, Songak-Myeon, Dangjin-Gun, Chungnam, Korea 2 CetaTech, Inc., TIC 296-3, Seonjin-Ri, Sacheon-Si, Kyongnam, Korea 3 Center for Advanced Vehicular Systems, Mississippi State University, 200 Research Blvd., Starkville, MS 39759, USA 4 College of Engineering, San Diego State University, 5500 Campanile Drive, San Diego, CA Introduction Effective computer simulations of metal powder compaction and sintering are at the top of the powder metallurgy industry s wish list. There is much anticipated advantage to such efforts, yet there are problems that will inhibit widespread implementation. Press-sinter powder metallurgy computer simulations currently focus on the use of minimal input data to help with process set-up. Although the simulations are reasonably accurate, a large data array is required to hone in on current industrial practice. For example, final dimensions for automotive transmission gears are required to be held within 10 µm, but the simulations are not capable of such accuracy. Simple factors such as frictional tool heating are missing from the simulations. Additionally, powders vary in particle size distribution between production lots, but the simulations assume a nominally uniform powder. Since it is expensive to test each powder lot, the logic is to assume a nominal set of characteristics. In production, such process and powder variations are handled by constant adaptive control techniques. As an example, when an outside door is opened on press room it is common that press adjustments will be required to hold sintered dimensions. The press-sinter powder metallurgy simulations have not advanced to such levels of sophistication. Instead, the press-sinter powder metallurgy simulations are used to help set-up production operations with heavy reliance on experienced operators to make final trial and error adjustments. 1 In practice, the variations in powder, press, tooling, and other process variables are handled using skilled technicians, quality charts, and adaptive process control that relies on frequent sampling and periodic equipment adjustments. The gap between press-sinter practice and modeling might close if more rapid data generation routes were developed. For example, a study on modeling the press-sinter production of a main bearing cap required 10,000 measures to isolate the behavior. It is not economically feasible to repeat this testing for each 20 ton lot of powder. Even so, a great benefit comes from the fact that the computer simulations have forced the technical community to organize our knowledge and determine where there are problems. Computer simulations of press-sinter operations trace to the 1960s [1-20]. The early simulations were generally unstable and two-dimensional (for example the sintering of aligned wires). By 1975, a variety of two-dimensional sintering approaches existed. With the expansion in computer power, the implementation of three-dimensional simulations arose to provide realistic outputs. In more recent times, the simulations have provided valuable threedimensional treatments to predict the final component size and shape after sintering. Since the pressed green body is not homogeneous, backward solutions are desired to select the powder, compaction, and sintering attributes required to deliver the target properties with different tool designs, compaction presses, and sintering furnaces. In building toward this goal, various simulation types have been evaluated: Monte Carlo, Finite Difference, Discrete Element, Finite Element, Fluid Mechanics, Continuum Mechanics, Neural Network, and Adaptive Learning. Unfortunately, the input data and some of the basic relations are not well developed; accurate data are missing for most materials under the relevant conditions. For example, rarely is the strength measured for a steel alloy at the typical 1120 C sintering temperature. Further, constitutive models do not exist for the conditions relevant to sintering; for example, friction in die compaction changes during the split-second pressure stroke since lubricant (polymer) particles deform and undergo viscous flow to the die wall, effectively changing friction constantly during compaction. Thus, the simulations are approximations using extrapolated data and simplified relations. For this reason, computer simulations of press-sinter routes work best in the set-up mode. The simulations help define the processing window and set initial operating parameters. Presented here is information relevant to computer simulation of first article production, what is best termed set-up calculations, realizing that practice relies heavily on adaptive process control to keep the product in specification after the initial set-up is accomplished. Brief History 2 The first major publication on computer simulation of sintering came out in 1965 [1]. Early simulations were two-dimensional (sintering two wires) with a single diffusion mechanism. These simulations were slow, requiring ten times more computer time than the actual physical sintering time. Most damaging, these early models were unstable since they lost volume and increased energy. However, within 20 years the concept was extended to include multiple transport mechanisms, multiple sintering stages, and even pressure-assisted sintering [6,9-11]. These simulations predicted density versus compaction pressure, sintering time, peak temperature, heating rate, green density, and particle size. One of the first realizations was the limitations arising from the assumed isothermal conditions and simplistic microstructure coarsening. Dilatometry experiments show most sintering occurs on the way to the peak temperature, so isothermal models poorly reflect actual behavior [20]. Indeed, production powder metallurgy often simply kisses the peak temperature, a situation far from what is assumed in the simulations. And the assumed homogeneous and ideal microstructure unrealistically limits the models. Today the sintering body first treated with a compaction or shaping simulation to predict the green microstructure gradients, and subsequent sintering simulations use those density gradients, via finite element analysis, to predict the final size, shape, and properties [16-19]. Theoretical Background and Governing Equations The methodologies used to model the press and sinter powder metallurgy include continuum, micromechanical, multi-particle, and molecular dynamics approaches. These differ in length scales. Among the methodologies, continuum models have the benefit of shortest computing time, with an ability to predict relevant attributes such as the component density, grain size, and shape. Mass, volume, and momentum conservation are evoked in the continuum approach. Although, such assumptions might seem obvious, still powder metallurgy processes are ill-behaved and difficult to properly simulate. For example, polymer are added to the powder for tool lubrication, but the polymers are pyrolyzed during sintering, resulting in 0.5 to 1.5 wt. % mass loss. Likewise, pore space is not conserved during compaction and sintering, so bulk volume is not conserved. Even so, mass conservation equations are invoked to track densification, while momentum conservation is used to follow force equilibrium, including the distortion effect from gravity. Energy conservation is also essential in the continuum approach. However, it is typical to assume temperature is uniform in the compact; set to room temperature during compaction and following an idealized thermal cycle (often isothermal) during sintering. Both are incorrect, since tool heating occurs with repeated compaction 3 strokes and compact position in the sintering furnace gives a lagging thermal history that depends on location. Indeed, since dimensional precision is the key to powder metallurgy, statistical audits have repeatedly found that subtle factors such as position in the furnace are root causes of dimensional scatter. For example, fluid flow and heat transport calculations show considerable temperature differences associated with atmosphere flow and component shadowing within a furnace. Since such details are not embraced by the models, the typical assumption is to ignore temperature distribution within the component, yet such factors are known to cause part distortion during production. Additionally, constitutive relations are required to describe the response of the compact to mechanical force during compaction and sintering. Many powder metallurgy materials are formed by mixing powders that melt, react, diffuse, and alloy during sintering. This requires sophistication in the models to add phase transformations, alloying, and other factors, many of which depend on particle size and other variations [15]. From conservation laws and constitutive relations, a system of partial differential equations is created that includes the initial and boundary conditions. These need to be integrated with microstructure and property models so that final compact properties can be predicted. Since the constitutive relations for compaction and sintering are completely different, they are described here in two separate sections. Constitutive Relation during Compaction Continuum plasticity models are frequently used to describe the mechanical response of metal powders during compaction. These phenomenological models, originally developed in soil mechanics, are characterized by a yield criterion, a hardening function, and a flow rule. Representative models include those known as the Cam-Clay [21], Drucker-Prager-cap [22], and Shima-Oyane [23] models. Of these, the most successful for metal powders has been the Shima-Oyane model, although for ceramics, soils, and minerals other relations are generally more successful. The typical initial and boundary conditions during compaction are as follows: Initial condition for the powder: tap density Boundary conditions: velocity prescribed in upper and bottom punches and friction condition in the tooling side wall; usually assumed the same for all tool surfaces independent of wear and independent of lubricant flow during the compaction stroke. During compaction and ejection, a damage model, such as the Drucker-Prager failure surface [22] and failure separation length (FSL) idea [111] is required. To predict crack formation, 4 the FSL assumes there is an accumulated separation length from the Drucker-Prager failure surface, which provides the possibility of crack formation, as shown in Figure 1. The equation for the FSL is expressed as follows: F S = q + p tan β d. (1) where q and p are the effective stress and hydrostatic pressure. Note that d and β are the offset stress and slope for Drucker-Prager failure surface shown in Figure 1. Since the models predict green density versus location, then defect sensitivity is possible. For example, elastic relaxation occurs on ejection and if the stress exceeds the green strength, then green cracking occurs. It is in this area the compaction models are most effective. Constitutive Relation during Sintering Continuum modeling is the most relevant approach to modeling grain growth, densification, and deformation during sintering. Key contributions were by Ashby [6,9], McMeeking and Kuhn [25], Olevsky et al. [17,19], Riedel et al. [13,26,27], Bouvard and Meister [28], Cocks [29], Kwon et al. [30,31], and Bordia and Scherer [32-34] based on sintering mechanism such as surface diffusion, grain boundary diffusion, volume diffusion, viscous flow (for amorphous materials), plastic flow (for crystalline materials), evaporation-condensation, and rearrangement. For industrial application, the phenomenological models are used for sintering simulations with following key physical parameters: Sintering stress [20] is a driving force of sintering due to interfacial energy of pores and grain boundaries. Sintering stress depends on the material s surface energy, density, and geometric parameters such as grain size when all pores are closed in the final stage. Effective bulk viscosity is a resistance to densification during sintering and is a function of the material, porosity, grain size, and temperature. The model of the effective bulk viscosity has various forms according to the assumed dominant sintering mechanism. Effective shear viscosity is a resistance to deformation during sintering and is also a function of the material, porosity, grain size, and temperature. Several rheological models for the effective bulk viscosity are available. The above parameters are function of grain size. Therefore, a grain growth model is needed for accurate prediction of densification and deformation during sintering. Typical initial and boundary conditions for the sintering simulations include the following: 5 Initial condition: mean particle size and grain size of the green compact for grain growth and initial green density distribution for densification obtained from compaction simulations. Boundary conditions: surface energy condition imposed on the free surface and friction condition of the component depending it is size, shape, and contact with the support substrate. The initial green density distribution within the pressed body raises the necessity to start the sintering simulation with the output from an accurate compaction simulation, since die compaction induces green density gradients that depend on the material, pressure, rate of pressurization, tool motions, and lubrication. The initial and boundary conditions help determine the shape distortion during sintering from gravity, nonuniform heating, and from the green body density gradients. Numerical Simulation Even though many numerical methods have been developed, the finite element method (FEM) is most popular for continuum models of the press and sinter process. The FEM approach is a numerical computational method for solving a system of differential equations through approximation functions applied to each element, called domain-wise approximation. This method is very powerful for the typical complex geometries encountered in powder metallurgy. This is one of the earliest techniques applied to materials modeling, and is used throughout industry today. Many powerful commercial software packages are available for calculating two-dimensional (2D) and three- dimensional (3D) thermo-mechanical processes such as found in press and sinter powder metallurgy. To increase the accuracy and convergence speed for the press and sinter simulations, developers of the simulation tools have selected explicit and implicit algorithms for time advancement, as well as numerical contact algorithms for problems such as surface separation, and remeshing algorithms as required for large deformations such as seen in some sintered materials, where up to 25 % dimensional contraction is possible. Figure 2 shows the typical procedure for computer simulation for the press-sinter process, which consists of five components; simulation tool, pre- and post processors, optimization algorithm, and experimental capability. Pre- and post- processors are important to use the simulation tools efficiently. Pre-processor is a software tool to prepare input data for the simulation tool including computational domain preparation such as geometry modeling and mesh generator. Figure 3 is an example of the component, compaction, and sintering models, in this case for an oxygen sensor housing. To execute this model requires considerable input, 6 including material property database (including strain effects during compaction and temperature effects during sintering) and processing condition database (loading schedule of punches and dies for compaction simulation and heating cycle for sintering simulation). Postprocessor is a software tool to visualize and analyze the simulation results, which enhances the usefulness of the simulations. From the standpoint of process set-up calculations, the optimization algorithm is essential to maximize computer simulation capability providing optimum part, die, and process condition design. Experimental capability is very important in computer simulation providing a means to evaluate changes in materials, powders, compaction schedules, heating cycles, and generally to provide verification of the simulation results. Experimental Determination of Material Properties and Simulation Verification Material Properties and Verification for Compaction One of the first needs is to measure the powder density as a function of applied pressure to generate the material parameters in the constitutive model for compaction, including the Coulomb friction coefficient between the powder and die. Note these factors vary with the powder lot, lubricant, tool material, and even tool temperature. The procedure to obtain the material properties based on the generalized Shima-Oyane model is as follows [24]: Measure the pycnometer and tap densities of the powder. Conduct a series of uniaxial compression tests with die wall lubrication to minimize the die wall friction effect. The tap density is considered the starting point (after particle rearrangement) corresponding to zero compaction pressure. By curve fitting, six material parameters (α, γ, m, a, b, and n) are determined for the yield surface Φ as follows q Φ = σ m 2 + α p σ m γ m ( 1 D) D. (2) where q and p are the effective stress and hydrostatic stress or pressure, D is the relative or fractional density, and σ m is the flow stress of matrix material which is expressed as m n m σ = a + bε. (3) where ε m is the effective strain of matrix material. Series of uniaxial compression tests are performed without wall lubricant then the Coulomb frictional coefficient is obtained by FEM simulation. 7 Figure 4 is an illustration of the compaction curve for an iron-based powder (Distaloy AE, Höganäs) in a simple cylindrical geometry. Uniaxial compression tests are provided for two samples, the smaller sample of 2 g in a 12 mm diameter die with die wall lubrication and the larger sample of 8 g without wall lubrication. By curve fitting, the six material parameters are as follows [24]: α = 6.20, γ = 1.03, m = 7.40, a = 184 MPa, b = 200 MPa, and n = By FEM simulation, the Coulomb frictional coefficient was obtained as 0.1. Table 1 shows the example of complete set of material properties of iron-based powder as input data for the compaction simulation. Verification of the predicted density gradients in the green compact has been approached by many techniques. The most reliable, direct, and most sensitive comes from taking hardness or microhardness traces on a polished cross-section. Thus, to verify the compaction simulation results, the relation between hardness and green density is conducted according to the following procedure: Use the same samples as used for obtaining the material parameters Pre-sinter the compacts at a temperature sufficient to bond the particles but below the temperature range where dimensional change or chemical reactions occurs. Carefully prepare a metallographic cross-section of the pre-sintered samples and treat with a vacuum annealing cycle to minimize any hardness change induced by the cutting process. Measure hardness of each sample with a known green density and from that develop a correlation between density and hardness. Apply the same procedure and hardness traces to real components and from precise measures of hardness and location develop contour plot of the green density distribution for comparison with the computer simulation. As an example, Figure 5 is a plot of the correlation between green density and hardness for WC-Co system. For this plot, pre-sintering cycle of WC-Co system was at 790 o C for 30 min, and the annealing cy
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