Nonlinear transient thermal stress investigation of 2D-FG porosity long cylinder sector

We present a nonlinear numerical study of the two-dimensional functionally graded porosity (2D-FGP) transient thermo-elastic problem for the infinite cylinder sector with temperature-dependent material properties. The paper employs a higher-order graded finite element method (graded-FEM) to develop the problem and determines the effective values of the 2D material properties using the Kerner micromechanical model. The sequentially coupled nonlinear thermo-elastic problem is solved by an implicit time-marching technique, and the validity of graded FEM using the cell-vertex finite volume method (CV-FVM) is assessed. Then the effects of material and porosity distributions on the temperature, displacement, stresses, and strength of the 2D-FGP plane strain cylinder sector are thoroughly investigated. The findings show that porosity has a smaller impact on normalized effective stresses (NES) than material distribution, as evidenced by higher NES values in the cylinder sector without porosity and the ZrO2 rich cylinder has the lowest NES value. Despite a temperature difference of only $8^{\circ }K$, the cylinder with no porosity distribution has 56%, 48%, 68%, and 60% higher radial, hoop, axial, and von Mises stresses than the cylinder with a quadratic porosity distribution. At the specific point, higher porosity at $n_r=n_{\theta }=1$ compared to $n_r=n_{\theta }=2$ resulted in a $5^{\circ }K$ temperature decrease and correspondingly lower stresses, indicating that the structure's porosity reduced the effective stress. Because thermal stress is highly sensitive to constituents and porosity distributions, optimizing the parameters is critical to having the most effective stress reductions.