### Design of Spark Plasma Sintering Graphite Die Using Topology Optimization

#### Abstract

The Spark Plasma Sintering (SPS) is a sintering process which uses a graphite die and punchers in its tool system. This technique has been employed to sinter a large number of materials, especially Functionally Graded Material (FGM), in which the material gradation, in some cases, requires a temperature gradient in the sample region during the manufacturing process to ensure uniform sintering. An optimized die design that generates a temperature gradient can be developed by changing the die wall thickness. However, this design presents some difﬁculties because it deals with bidimensional problems subject to convection and radiation heat transfer boundary conditions, and with conductive and/or non-conductive FGM sample. Thus, in this work, the Topology Optimization Method (TOM) is applied to design a graphite die to achieve a predeﬁned temperature gradient. The TOM is able to provide an optimum topology for the die by seeking a material distribution inside a given domain that extremizes a cost function and satisﬁes the constraints of the optimization problem. In order to simulate the SPS process, a electrical-thermal coupled steady state problem is modeled using ﬁnite element formulation based on the governing equations. In the developed model, the convective heat transfer is neglected once the process takes place in vacuum, the radiation process is linearized to reduce the modeling complexity, and the properties of the graphite and sample are assumed not to depend on temperature. In the topology optimization problem the temperature gradient is established through a cost function that minimizes the difference between the prescribed gradient and the calculated temperature subjected to a material volume constraint. Results of optimized graphite dies are presented.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**