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One dimensional transient thermoelastic and associated fracture analysis of long porous ceramic plate

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Abstract

Asymmetric thermal shock resistance of porous ceramic materials has been studied. The plate, initially at uniform temperature, is exposed to a sudden temperature on its one surface whilst thermal insulation are considered for the opposing face. The temperature field and transient thermal stress field in the porous ceramic plate uncracking are calculated. Then, the weight function method is used to obtain thermal stress intensity factor at crack tip. The effects of relative density and thermal shock temperature on the crack propagation of the porous ceramic plate are analyzed. Finally, the thermal shock resistance of the porous ceramic materials is acquired based on stress criterion and fracture toughness criterion.

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Acknowledgements

This research was supported by Science and Technology Project of Hebei Education Department (Grant No. QN2020140), the Natural Science Foundation of Hebei Province of China (Grant No. A2021408004), and the doctoral program of Langfang normal university (Grant No. LSLB201601).

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Author notes

  1. Baolin Wang, Chunli Zhang, Yi Yang and Songlin Guo are contributed equally to this work.

Authors and Affiliations

  1. School of Architecture and Engineering, Langfang Normal University, Langfang, 065000, People’s Republic of China

    Yunxia Zhang, Chunli Zhang & Yi Yang

  2. School of Engineering, Design and Built Environment, Western Sydney University, Penrith, NSW, 2751, Australia

    Baolin Wang

  3. School of Civil Engineering, Qingdao University of Technology, Qingdao, 266525, People’s Republic of China

    Songlin Guo

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  1. Yunxia Zhang
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Correspondence to Yunxia Zhang.

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Appendix

Appendix

The dimensionless function \(G\left( {\frac{2H - z}{a},\;\frac{a}{2H}} \right)\) appearing in Eq. (13) is

$$ \begin{aligned} G\left( {\frac{2H - z}{a},\;\frac{a}{2H}} \right) = & f_{1} \left( \frac{a}{2H} \right) + f_{2} \left( \frac{a}{2H} \right)\left( {\frac{2H - z}{a}} \right) \\ & + f_{3} \left( \frac{a}{2H} \right)\left( {\frac{2H - z}{a}} \right)^{2} + f_{4} \left( \frac{a}{2H} \right)\left( {\frac{2H - z}{a}} \right)^{3} \\ \end{aligned} $$
(A1)

where

$$ f_{1} \left( \frac{a}{2H} \right) = 0.46 + 3.06\left( \frac{a}{2H} \right) + 0.84\left( {1 - \frac{a}{2H}} \right)^{5} + 0.66\left( \frac{a}{2H} \right)^{2} \left( {1 - \frac{a}{2H}} \right)^{2} $$
$$ f_{2} \left( \frac{a}{2H} \right) = - 3.52\left( \frac{a}{2H} \right)^{2} $$
$$ \begin{aligned} f_{3} \left( \frac{a}{2H} \right) = & 6.17 - 28.22\left( \frac{a}{2H} \right) + 34.54\left( \frac{a}{2H} \right)^{2} - 14.39\left( \frac{a}{2H} \right)^{3} \\ & { - }\left( {1 - \frac{a}{2H}} \right)^{1.5} - 5.88\left( {1 - \frac{a}{2H}} \right)^{5} - 2.64\left( \frac{a}{2H} \right)^{2} \left( {1 - \frac{a}{2H}} \right)^{2} \\ \end{aligned} $$
$$ \begin{aligned} f_{4} \left( \frac{a}{2H} \right) = & - 6.63 + 25.16\left( \frac{a}{2H} \right) - 31.04\left( \frac{a}{2H} \right)^{2} + 14.41\left( \frac{a}{2H} \right)^{3} + 2\left( {1 - \frac{a}{2H}} \right)^{1.5} \\ & + 5.04\left( {1 - \frac{a}{2H}} \right)^{5} + 1.98\left( \frac{a}{2H} \right)^{2} \left( {1 - \frac{a}{2H}} \right)^{2} \\ \end{aligned} $$

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Zhang, Y., Wang, B., Zhang, C. et al. One dimensional transient thermoelastic and associated fracture analysis of long porous ceramic plate. Arch Appl Mech 93, 2681–2692 (2023). https://doi.org/10.1007/s00419-023-02426-z

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