ASM Handbook, Volume 22B, Metals Process Simulation Copyright # 2010, ASM International® D.U. Furrer and S.L. Semiatin, editors All rights reserved. www.asminternational.org Modeling and Simulation of Press and Sinter Powder Metallurgy Suk Hwan Chung, Hyundai Steel Company Young-Sam Kwon, CetaTech, Inc. Seong Jin Park, Pohang University of Science and Technology Randall M. German, San Diego State University EFFECTIVE COMPUTER SIMULATIONS feasible to repeat this testing for each 20 ton sinter routes work best in the setup mode. of metal powder compaction and sintering are lot of powder. Even so, a great benefit comes The simulations help define the processing at the top of the powder metallurgy industry’s from the fact that the computer simulations window and set initial operating parameters. wish list. There is much anticipated advantage have forced the technical community to orga- Presented here is information relevant to com- to such efforts, yet there are problems that will nize our knowledge and determine where there puter simulation of first-article production, inhibit widespread implementation. Press-sinter are problems. what is best termed setup calculations, realiz- powder metallurgy computer simulations cur- Computer simulations of press-sinter opera- ing that practice relies heavily on adaptive rently focus on the use of minimal input data tions trace to the 1960s (Ref 1 to 20). The process control to keep the product in specifi- to help with process setup. Although the simula- early simulations were generally unstable and cation after the initial setup is accomplished. tions are reasonably accurate, a large data array two-dimensional (for example, the sintering is required to hone in on current industrial prac- of aligned wires). By 1975, a variety of two- tice. For example, final dimensions for automo- dimensional sintering approaches existed. Brief History tive transmission gears are required to be held With the expansion in computer power, the within 10 mm, but the simulations are not capa- implementation of three-dimensional simula- The first major publication on computer sim- ble of such accuracy. Simple factors such as tions arose to provide realistic outputs. In ulation of sintering came out in 1965 (Ref 1). frictional tool heating are missing from the more recent times, the simulations have Early simulations were two-dimensional (sin- simulations. Additionally, powders vary in par- provided valuable three-dimensional treat- tering two wires) with a single diffusion mech- ticle size distribution between production lots, ments to predict the final component size and anism. These simulations were slow, requiring but the simulations assume a nominally uniform shape after sintering. Because the pressed ten times more computer time than the actual powder. Because it is expensive to test each green body is not homogeneous, backward physical sintering time. Most damaging, these powder lot, the logic is to assume a nominal solutions are desired to select the powder, early models were unstable, because they lost set of characteristics. In production, such pro- compaction, and sintering attributes required volume and increased energy. However, within cess and powder variations are handled by con- to deliver the target properties with different 20 years the concept was extended to include stant adaptive control techniques. As an tool designs, compaction presses, and sintering multiple transport mechanisms, multiple sinter- example, when an outside door is opened on furnaces.Inbuildingtowardthisgoal,various ing stages, and even pressure-assisted sintering the press room, it is common that press adjust- simulation types have been evaluated: Monte (Ref 6, 9 to 11). These simulations predicted ments will be required to hold sintered dimen- Carlo, finite difference, discrete element, finite density versus compaction pressure, sintering sions. The press-sinter powder metallurgy element, fluid mechanics, continuum mechan- time, peak temperature, heating rate, green den- simulations have not advanced to such levels ics, neural network, and adaptive learning. sity, and particle size. of sophistication. Instead, the press-sinter pow- Unfortunately, the input data and some of the One of the first realizations was the limita- der metallurgy simulations are used to help set basic relations are not well developed; accu- tions arising from the assumed isothermal up production operations, with heavy reliance rate data are missing for most materials under conditions and simplistic microstructure coars- on experienced operators to make final trial- the relevant conditions. For example, rarely is ening. Dilatometry experiments show that most and-error adjustments. the strength measured for a steel alloy at the sintering occurs on the way to the peak temper- In practice, the variations in powder, press, typical 1120 C sintering temperature. Further, ature, so isothermal models poorly reflect actual tooling, and other process variables are handled constitutive models do not exist for the condi- behavior (Ref 20). Indeed, production powder through skilled technicians, quality charts, and tions relevant to sintering; for example, fric- metallurgy often simply “kisses” the peak tem- adaptive process control that relies on frequent tion in die compaction changes during the perature, a situation far from what is assumed sampling and periodic equipment adjustments. split-second pressure stroke, because lubricant in the simulations. Also, the assumed homoge- The gap between press-sinter practice and mod- (polymer) particles deform and undergo vis- neous and ideal microstructure unrealistically eling may close if more rapid data-generation cous flow to the die wall, effectively changing limits the models. Today (2009), the sintering routes were developed. For example, a study friction constantly during compaction. Thus, body first treated with a compaction or shaping on modeling the press-sinter production of a the simulations are approximations using simulation to predict the green microstructure main bearing cap required 10,000 measures to extrapolated data and simplified relations. For gradients, and subsequent sintering simulations, isolate the behavior. It is not economically this reason, computer simulations of press- use those density gradients, via finite-element 324 / Simulation of Powder Metallurgy Processes analysis, to predict the final size, shape, and includes the initial and boundary conditions. of crack formation, as shown in Fig. 1. The equa- properties (Ref 16 to 19). These must be integrated with microstructure tion for the FSL is expressed as: and property models so that final compact prop- erties can be predicted. Because the constitutive FS ¼ q þ p tan b À d (Eq 1) Theoretical Background and relations for compaction and sintering are Governing Equations completely different, they are described here where q and p are the effective stress and hydro- in two separate sections. static pressure, respectively. Note that d and b The methodologies used to model the press are the offset stress and slope, respectively, for and sinter powder metallurgy include contin- the Drucker-Prager failure surface shown in Constitutive Relation during Fig. 1. Because the models predict green den- uum, micromechanical, multiparticle, and Compaction molecular dynamics approaches. These differ sity versus location, defect sensitivity is possi- ble. For example, elastic relaxation occurs on in length scales. Among the methodologies, Continuum plasticity models are frequently continuum models have the benefit of shortest ejection, and if the stress exceeds the green used to describe the mechanical response of strength, then green cracking occurs. It is in this computing time, with an ability to predict rele- metal powders during compaction. These phe- vant attributes such as the component density, area that the compaction models are most nomenological models, originally developed in effective. grain size, and shape. soil mechanics, are characterized by a yield cri- Mass, volume, and momentum conservation terion, a hardening function, and a flow rule. are evoked in the continuum approach. Representative models include those known as Constitutive Relation during Sintering Although such assumptions may seem obvious, the Cam-Clay (Ref 21), Drucker-Prager-Cap powder metallurgy processes are ill-behaved (Ref 22), and Shima-Oyane (Ref 23) models. Continuum modeling is the most relevant and difficult to properly simulate. For example, Of these, the most successful for metal powders approach to modeling grain growth, densifica- polymers are added to the powder for tool has been the Shima-Oyane model, although for tion, and deformation during sintering. Key con- lubrication, but the polymers are pyrolyzed ceramics, soils, and minerals, other relations are tributions were by Ashby (Ref 6, 9), McMeeking during sintering, resulting in 0.5 to 1.5 wt% generally more successful. and Kuhn (Ref 25), Olevsky et al. (Ref 17, 19), mass loss. Likewise, pore space is not con- The typical initial and boundary conditions Riedel et al. (Ref 13, 26, 27), Bouvard and Meis- served during compaction and sintering, so during compaction are as follows: ter (28), Cocks (29), Kwon et al. (Ref 30, 31), and bulk volume is not conserved. Even so, mass Bordia and Scherer (Ref 32 to 34) based on a sin- conservation equations are invoked to track Initial condition for the powder: Tap density tering mechanism such as surface diffusion, densification, while momentum conservation Boundary conditions: Velocity