Constrained Sintering of a Glass Ceramic Composite: I. Asymmetric Laminate

Abstract

The camber of asymmetric laminates has been experimentally measured and predicted. Two cases are distinguished: (i) sintering of a viscous layer on a viscous substrate and (ii) sintering of a viscous layer on an elastic substrate. In the first case, particular attention is paid to the microstructure of the shrinking layer: a gradient in porosity as well as in pore size has been found along the thickness. Microstructural observations have been rationalized through an asymmetric stress state in the shrinking layer. In the second case, substrate cracking is predicted as function of Young's modulus and thickness ratio of the elastic substrate.V. Jayaram-contributing editor

Partial Constrained Sintering of Ceramic Layers on Metallic Substrates: A Comparison Between Modeling and Experiments

“…3, the experimentally measured and the modeled camber rates _ k are plotted as function of the isothermal time. It appears that the camber is reduced when increasing the thickness, which might be surprising at first sight but was already shown in Ollagnier et al 21 A more precise analysis of this point requires the knowledge of the stress distribution in the bi-layer, as detailed hereafter. Please observe the very large camber rates, initially at the highest and decreasing continuously and rapidly during the first 60 s of isothermal time to asymptotically approach zero after 1 h. The predictions follow qualitatively the experimental curve and are of the same order of magnitude, which is quite positive when compared with other modeling results, especially when the layers are perfectly constrained on a rigid substrate.…”

“…The integration procedure is the same as in Kanters et al 20 and Ollagnier et al 21 for viscous and elastic materials. Integration domain M corresponds to the substrate and N to the sintering layer.…”

“…The stress state in the film is a biaxial tensile stress and is constant along the film thickness. 21 The mechanical behavior of the substrate is linear viscous, which means that the strain rate is directly proportional to the stress developed in the substrate. These viscous parameters, which depend on material, grain size, density, and temperature, are usually measured on bulk specimens or can be predicted.…”

“…21 In asymmetric geometry, for which camber is allowed, the top-free film surface is expected to be in compression, whereas tensile stress is maximal at the interface with the substrate. This was, for example, the case of an LTCC layer sintered on a porous alumina tape or a silicon substrate.…”

Constrained Sintering of a Glass Ceramic Composite: II. Symmetric Laminate

“…Results are integrated as follows: radial and axial strain rates are calculated. Sintering parameters ( E p , v p ,and ) are then corrected with the new calculated density (please refer to in Part I 28 ).…”