Abstract
Finding the geometry and properties of a ceramic tile after its firing using simulations, is relevant because several defects can occur and the tile can be rejected if the conditions of the firing are inadequate for the geometry and materials of the tile. Previous works present limitations because they do not use a model characteristic of ceramics at high temperatures and they oversimplify the simulations. As a response to such shortcomings, this article presents a simulation with a three-dimensional Norton’s model, which is characteristic of ceramics at high temperatures. The results of our simulated experiments show advantages with respect to the identification of the mechanisms that contribute to the final shape of the body. Our work is able to divide the history of temperatures in stages where the evolution of the thermal, elastic, and creep deformations is simplified and meaningful. That is achieved because our work found that curvature is the most descriptive parameter of the simulation. Future work is to be realized in the creation of a model that takes into account that the shrinkage is dependent on the history of temperatures.
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Abbreviations
- \( H(S,p) \) :
-
Mean curvature of a surface S at a point p
- \( H_{\text{upp}} \) :
-
Set of discrete mean curvatures at the nodes of the upper face of the ceramic tile
- \( H_{\text{low}} \) :
-
Set of discrete mean curvatures at the nodes of the lower face of the ceramic tile
- \( \upvarepsilon_{\text{th}} \) :
-
Set of thermal strains in one direction. Von Misses thermal strains are not defined
- \( V\upvarepsilon_{\text{el}} \) :
-
Set of Von Mises elastic strains
- \( V\upvarepsilon_{\text{cr}} \) :
-
Set of Von Mises creep strains
- \( V\upsigma \) :
-
Set of Von Mises stresses
- \( \overline{M} \) :
-
Average of set M. The set can be: \( H_{\text{low}} , H_{\text{upp}} , \upvarepsilon_{\text{th}} , V\upvarepsilon_{\text{cr}} , V\upvarepsilon_{\text{el}} , \) or \( V\upsigma \)
- \( {\text{std}}. {\text{dev}}. M \) :
-
Standard deviation of set M
- \( { \max }\left( M \right) \) :
-
Maximum absolute value of set M
- \( \upsigma_{1} , \upsigma_{2} ,\upsigma_{3} \) :
-
Set of first principal, second principal, and third principal stresses, respectively
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Peris-Fajarnés, G., Defez, B., Serrano, R. et al. Simulation of the Evolution of Floor Covering Ceramic Tiles During the Firing. J. of Materi Eng and Perform 22, 936–942 (2013). https://doi.org/10.1007/s11665-012-0354-5
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DOI: https://doi.org/10.1007/s11665-012-0354-5