Electro-thermo-mechanical modeling of Field Assisted Sintering Technology using high-order finite elements validated by experiments

• Applicants: Professor Dr.-Ing. Alexander Düster; Professor Dr.-Ing. Stefan Hartmann; Professor Dr. Ernst Rank
• Co-Applicant: Professor Zohar Yosibash, Ph.D.
• Subject Area: Mechanics
• Term: from 2010 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 165958631

• Final Report Year: 2015

Final Report Abstract

The project was a very interesting and fruitful collaborative research project between five groups; two groups in Israel and three groups in Germany. The main goals were to model field assisted sintering processes, where a powder is compacted under mechanical loads during the sintering process which is induced by an electrical current. This is a very challenging aspect because there are two materials involved in the process: the graphite tools and the powder material itself. Thus, a large number of different and specific experiments had to be performed in view of the electrical, thermal and mechanical properties so that constitutive models could be developed. On the basis of some experience with copper powder, we started to develop a concept to determine which kind of experiments are required for the model development as well as for the entire coupled system. We treated the evolution of the tensile strength evolution of the powder material for various pre-compacted states and the classical evolution of the compaction process under different thermal states. The thermo-mechanical consistent constitutive model of thermo-viscoplasticity for the large strain case was implemented into several finite element programs. Several important aspects could not be treated. First, field assisted sintering was mainly developed for ceramic materials. Thus, the part on the material behavior of ceramics and the modeling aspect of graphite were annulled. Second, the cut of the funding did not allow to combine the novel hp-formulation for the finite element method developed by the TUM-research group with the improved coupling algorithms developed by the TUHH group. The final coupling of all three fields as well as validation based on experimental results had to remain unfinished. However, after the end of the project we were able to simulate the entire three-field problems in the experiment, leading us to two open problems: first, the contact conditions between both powder and graphite as well as graphite and graphite must be investigated under electrical, thermal and mechanical conditions. Second, the influence of radiation (reflection) in the chamber and the chamber’s wall convection must be studied in more detail. The main results are: 1. novel experimental results for graphite tool material and for copper powder under thermal and mechanical agencies, 2. a thermo-mechanically consistent, finite strain constitutive model of thermo-viscoplasticity, 3. fully coupled, monolithic finite element simulations of FAST-processes incorporating a large strain constitutive model and reasonable contact conditions, 4. a theoretical background of monolithic and partitioned multi-field problems, 5. accelerated partitioned approaches in multi-field finite element simulations for volumetric and surface coupling (electrical, thermal and mechanical fields combined with radiation), 6. a derivation of a novel hierarchical hp-finite element formulation, suitable for simulating the physical processes in the moving powder-punch-die system within one discretization, 7. basic investigations of thermo-mechanical coupled problems in view of uncertainty quantification.

Publications

• Accelerated staggered coupling schemes for problems of thermoelasticity at finite strains. Computers & Mathematics with Applications 64(8), 2408-2430, 2012
  Erbts , P., Düster , A.
  
• The Finite Cell Method for Linear Thermoelasticity. Computers & Mathematics with Applications 64(11), 3527-3541, 2012
  Zander , N., Kollmannsberger , S., Ruess , M., Yosibash , Z., Rank , E.
  
• 2013. Electro-thermo-elastic simulation of graphite tools used in SPS processes, in: Altenbach, H., Forest, S. and Krivtsov, A. (eds.), Generalized Continua as Models of Materials, Advanced Structured Materials 22, Springer, 143-161
  Hartmann , S., Rothe , S., Frage , N.
  
• A rigorous application of the method of vertical lines to coupled systems in finite element analysis, in: Ansorge, R., Bijl, H., Meister, A. and Sonar, T. (eds.), Numerics of Nonlinear Hyperbolic Conservation Laws, Notes on Numerical Fluid Mechanics and Multidisciplinary Design 120, 161 – 175, Springer, 2013
  Hartmann , S. and Rothe , S.
  
• Automatic Differentiation for stress and consistent tangent computation, 2013. Archive of Applied Mechanics
  Rothe , S., Hartmann , S.
  
• High-order FEMs for thermo-hyperelasticity at finite strains, Computers & Mathematics with Applications, 67(3), 2014, 477-496
  Yosibash , Z., Weiss , D., Hartmann , S.
  
• A partitioned solution approach for electro-thermo-mechanical problems. Archive of Applied Mechanics. August 2015, Volume 85, Issue 8, pp 1075-1101
  Erbts , P., Hartmann , S., Düster , A.
  
• Homogeneous stress-strain states computed by 3D-stress algorithms of FE-codes. Application to material parameter identification, Engineering with Computers, 31(1), 2015, 141-159
  Krämer , S., Rothe , S., Hartmann , S.
  
• Multi-level hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes. Computational Mechanics 55(3), 499–517, 2015
  Zander , N., Bog , T., Kollmannsberger , S., Schillinger , D., Rank , E.