# Engineering of a FGM Interlayer to Reduce the Thermal Stresses Inside the PFCs
## 4 Discussion and Conclusions
Paths are indicated in Figure 5. On the line segment \(\overline{CD}\) a design criterion is not anymore satisfied. the total strain field of the armor and heat sink cannot be paired, at least generally, as was performed in the previous case. In the design study presented in this paper, we hindered the bending of the component by imposing an external kinematic condition. It will then be necessary that a proper fixation system is designed to best achieve this condition in a real component. The design methodology we propose is a direct application of the procedure developed in the analytical cases. However, a number of approximations has been performed to take into account the deviations that the realistic study have from the ideal cases. The interlayer thickness is determined in a way such that the PFM is not enough that its mean thermal strain is equal to the target value of the total strain (that we call \(\varepsilon_{0}\)), while its ideal concentration is computed such that the thermal strain of this sub-component is constant and equal to \(\varepsilon_{0}\). In this study, the target value of the total strain has been obtained as the mean value of the heat sink total strain, computed with a FEM simulation. The ideal concentration function \(C\) of the FGM was then discretized in layers by imposing that the stresses are distributed evenly among the layers. To the best knowledge of the authors, up to now, different trends of \(C\) were either tested in a \"trial-and-error\" fashion, in order to find the one corresponding to the best configuration [10], or found by solving numerically an optimization problem [11; 12; 13]. In this paper we attempted to determine the concentration function of a FGM interlayer analytically, starting from some thermomechanical criteria. From the results of the design study carried out applying the proposed methodology, we derive the following conclusions:  
* The proposed methodology allows for an effective design of a PFC having a rather insulating heat sink material, the AISI 316L (\(\lambda_{\text{steel}}\sim 15\) Wm\({}^{-1}\)K\({}^{-1}\)). * For the FGM concentration function, the traditionally fixed constraints [10; 20]\(C=0\) at the interface with steel and \(C=1\) at the boundary with the PFM are proved to have a negative impact on the thermal stresses, since they lead to a mismatch of \"free-to-deform\" shape of the sub-components. * The number of FGM layers do not impact the stresses in both the armor and the heat sink, due to the design methodology. The discretization depends only on the desired maximum stress in the FGM due to the thermal gradient, which decreases with a higher amount of layers. The case with an ideal FGM represents its minimum limit. * The engineered interlayer proved to reduce significantly the secondary stress in the PFC, compared to a case with the armor directly bonded to the heat sink. The linearized secondary stress \(\overline{\mathcal{Q}}\) is reduced on average by more than 26%. Most importantly, the most loaded section has a reduction of more than 24% in the secondary stresses. The equivalent primary plus secondary membrane stress \(\overline{P_{m}+Q_{m}}\) is reduced on average by more than 40%, with a reduction of 28% on the most critical segment of the heat sink. Conceptualization, S.R. ; Methodology, G.D.; Supervision, F.R. ; Writing--original draft, G.D. and S.R. ; Writing--review & editing, F.R. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest.