Modeling Macroscopic Shape Distortions during Sintering of Multi-layers

Tesfaye Tadesse Molla

Research output: Book/ReportPh.D. thesisResearch

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Ceramic multi-layered composites are being used as components in various technologies ranging from electronics to energy conversion devices. Thus, different architectures of multi-layers involving ceramic materials are often required to be produced by powder processing, followed by sintering (firing). However, unintended features like shape instabilities of samples, cracks or delamination of layers may arise during sintering of multi-layer composites. Among these defects, macroscopic shape distortions in the samples can cause problems in the assembly or performance of the final component, which could result in product rejection. It is generally recognized that macroscopic shape distortion is linked to the sintering kinetics mismatch between the layer materials making the multi-layer during the co-firing process. However, there is still a need for better understanding of the deformational mechanisms with the application of flexible modeling techniques taking into account the various factors during co-firing. In addition, realistic microstructures in time/temperature need to be considered while defining the deformational behaviors of the sintering body in order to improve the predictive capabilities of the existing constitutive models. In this context, a simulation method or framework has been developed, which involves the use of sintering experiments, analytical and numerical methods. In addition to the intrinsic material parameters (shrinkage and viscous behaviors), the effect of extrinsic factors such as gravity, friction and geometry of the sample on the evolution of shape of multi-layers have been investigated. Furthermore, a new type of modeling procedure with a potential to introduce the realistic microstructure of a porous body, while defining the intrinsic material parameters, has been developed. The linear version of the Skorohod Olevsky Viscous Sintering (SOVS) model has been used in the developed simulation models. A combination of free shrinkage rate measurements from optical dilatometry and analytical models has been used to determine the necessary input parameters for simulation of sintering of multi-layer components. Validation of the input parameters has been made indirectly by comparing model predictions for camber evolution during sintering of a bi-layer with measurements thereof. Moreover, a 'master sintering curve'-type model of bi-layer sintering has been derived. This model excels in requiring a single optical dilatometry run to collect all the necessary input parameters for modeling of the sintering of the bi-layers. The determined input parameters have also been used in a finite element model, which is developed based on the continuum theory of sintering, to model the camber development during co-firing. The effect of extrinsic factors (e.g. gravity, thickness ratio and friction) on the shape evolution of bi-layers during co-firing has been studied using the developed model and experiments. Furthermore, a new analytical model describing stresses during sintering of tubular bi-layer structures has been developed by using the direct correspondence between elasticity and linear viscous problems. The finite element model developed in this study and sintering experiments of tubular bi-layer sample have been used to verify and validate the developed analytical model for tubular bi-layered structures. A multi-scale model of shape distortions during co-firing has also been developed by coupling a meso-scale model of sintering based on kinetic Monte Carlo (kMC) methods and a macro-scale continuum model. In this case, computational homogenization theories were used to extract the viscous parameters from a representative volume element (RVE) of the porous body. The RVE was based on the microstructure obtained from the kMC model. Results from the developed analytical as well as numerical models agree well with experimental measurements of densification and camber evolutions during co-firing of bi-layers. Optimizations of the co-firing process by controlling the initial geometry of the sample and structural characteristics are also suggested. Furthermore, the multi-scale model has also shown the expected behavior of shape distortions for different bi-layers systems involving layers with the same and different sinterabilities. Based on the experimental and simulation results, the following conclusions are reached: during sintering of planar multi-layers, understanding of the effect of gravity on the camber evolution can be used in optimizing the co-sintering process so as to help achieve defect free multi-layer components. The initial thickness ratio between the layers making the multi-layer has also significant effect on the extent of camber evolution depending on the material systems. During sintering of tubular bi-layer structures, tangential (hoop) stresses are very large compared to radial stresses. The maximum value of hoop stress, which can generate processing defects such as cracks and coating peel-offs, occurs at the beginning of the sintering cycle. Unlike most of the models defining material properties based on porosity and grain size only, the multi-scale model proposed in this study has no limitation as to the number of internal parameters to define shrinkage kinetics as well as viscous properties. This feature of the model makes it to be a promising approach for extending the continuum theory of sintering.
Original languageEnglish
PublisherDepartment of Energy Conversion and Storage, Technical University of Denmark
Number of pages168
Publication statusPublished - 2014


  • Sintering
  • Constrained sintering
  • Multi-layer ceramic composites
  • Modeling
  • Multi-scale modeling

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