Discrete Element Modeling of Sintering and Thermal Expansion in Macro Porous Structures

Christoph Ohmstede, M.Sc.


Invers opal structures are photonic crystals with highly ordered periodic macro pores. The pores are mutually dependent with a high porosity. The structure has photonic properties and therefore shows a high reflectivity for thermal radiation. Because of this a planned future application is the usage as thermal barrier coatings (TBC) in aero engines or gas turbines. TBCs act as thermal insulators and protect metal parts from too high temperatures. Improved TBCs would allow higher operation temperatures and will increase the efficiency by this way. Application as TBC requires a stable high temperature behavior without changes in macroscopic mechanical, photonic or structural properties. For increasing the stability at high temperatures sintering effects inside the structure and mechanical stress due to thermal expansion have to be reduced.

Sintering processes at high temperatures lead to densification and shrinkage of parts inside the structure. Thermal expansion effects arise during temperature changes in start-up or shut-down phase. If the mechanical stress is too high, cracks and delamination of the substrate can occur and resulting in decrease of functionality. The mechanical stress inside the structure and structural deformation during sintering process cannot be measured directly for which reason a simulation is required. To solve these issues a model is necessary which can describe the material and structural behavior at high temperatures and enables the possibility of investigation of different possible modified structures by simulation.

Project aim

Aim of this project is development of a model using discrete element method (DEM) to describe the sintering and thermal expansion of macro porous structures at high temperatures including crack formation and delamination. This should be done in cooperation with the Institute of Advanced Ceramics, which delivers experimental data for structures of alumina and mullite. The model will allow prediction of high temperature behavior of the macro porous structures under different conditions. The model should enhance understanding of structural changes and support the optimization of stress distribution inside the TBC and between TBC and substrate. Finally, the model should be able to make proposals for further experiments to improve macro porous structures due to changes in the microstructure.


The DEM model for sintering is based on a pioneering work by R. McMeeking and has been already applied by R. Besler. Thermal expansion will investigated by extending DEM with bonded particle model (BPM). For simulations the in-house developed simulation tool MUSEN will be used. The particulate nature of the material is taken into account by DEM and allows modeling the internal microstructure including defects like cracks and delamination. The investigation of the influence of different parameters can be done by modification of a given structure. Different structural parameters for variation can be e.g. pore size and arrangement or wall thickness.


First results show structure shrinkage in z direction leading to deformation of pore shapes. The densification process proceeds mainly from the struts into the nodes. This effects leads to thinning of the struts and represent a preliminary stage of crack formation, which arise later.

Cooperation partners

Institute of Advanced Ceramics, Hamburg University of Technology (Dr. K. Furlan, Dr. R. Janßen)

Project funding and start date

Project started March 2017

Within SFB 985 M³ - Tailor-Made, Multi-Scale, Materials-Systems