# Engineering of a FGM Interlayer to Reduce the Thermal Stresses Inside the PFCs
## 3 Conceptual Design of a Steel-Based PFC with a Engineered W/Steel FGM Interlayer
### Mechanical Results  
The FEM model used for the thermomechanical simulation uses the same thermal boundary conditions described at the beginning of this section. The kinematic constraints applied to the whole PFC, equipped now with both interlayer and armor, coincide with the ones applied for the simulation with just the steel heat sink. Figure 9 shows the mesh and the resulting temperature field in the PFC. The mesh is made of 22904 SOLID186 elements, accounting for more than 100 k nodes. The Young's Modulus of the plasma sprayed W and of all FGMs is assumed to be equal to that of the hot rolled tungsten (available in [6]). Admittedly, this is a conservative hypothesis to test the robustness of the design method we are proposing. Hot-rolled tungsten has in fact an \(E\) which is almost double the Young's modulus of steel. Therefore, being the thermal stresses proportional to the rigidity of the bodies, as one can ascertain from Equation (7), we are consciously overestimating such loads. A first computation is carried out in the case of an ideal FGM. To do so, we impose numerically to the interlayer a thermal strain equal to \(\varepsilon_{0}\). On the heat sink and the armor, the thermal field is imported in order to compute the real \(\varepsilon_{T}(T)\). The linearized stresses computed at the different support line segments are reported in Table 4. Comparing Table 2 to Table 4, one notices that the linearized secondary stresses do not change significantly between the cases, especially on the most loaded section \(\overline{CD}\), meaning that the addition of both the armor and the interlayer has not intesified the thermal stresses. Naturally, the primary stresses experience a substantial decrease due to a thicker resistant section which balances the external forces. For completeness, the contour of the von Mises stress on the whole component is shown in Figure 10. One notices that even in this ideal case, the FGM is not stress free. As explained previously, this is due to both the anisotropy in the total strain of the \"free-to-deform\" heat sink (\(\varepsilon_{x}\
eq\varepsilon_{z}\)) and the manufacturing constraint of having the concentration function only dependent on \(y\), and not on \((x,y)\). Figure 9: (**Left**) Mesh used for the FEM model of the whole PFC, having a FGM interlayer (yellow) and a W armor (dark grey). (**Right**) Temperature field in the whole component. The discretization of the concentration function has been carried out using Equations (25) and (26). Up to four FGM layers have been evaluated. Table 5 reports the results of the discretization process, which are the data represented graphically in Figure 8. For the four cases, the linearized stresses in the steel heat sink are shown in Table 6. One notices that, as expected by the design methodology, the steel heat sink is virtually unaffected by the several discretizations. This is a direct consequence of the engineering of the interlayer, which was designed to have the same total strain due to the temperature field, regardless of the number of layers. Table 6 verifies that keeping the mean thermal strain constant among the different layers, indeed ensures that the stresses in the heat sink are only the ones due to the thermal gradient. One can also compare such results with the ideal FGM case (Table 4), finding again marginal variations. All the design criteria for the structural steel sub-component are therefore satisfied even in these four cases. Furthermore, the stresses inside the armor are virtually independent from the discretization. A substantial difference depending on the amount of layers is instead found in the loads inside the FGM. As mentioned before, the stresses due to the thermal gradient increase with the maximum thermal strain of each single layer. Such parameter is reduced with an increasing discretization of the concentration function, reducing the loads in the FGM. Figure 11 shows the contours of the von Mises stress on the whole PFC, for different amounts of FGM layers.