# Mechanical Integrity Analysis of a Printed Circuit Heat exchanger with Channel Misalignment
## 3 Results and Discussion
### Stress at Stress Classification Line (SCL)  
The main standard for the design of nuclear equipment is American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel (BPVC) section III. ASME code section III has specific requirements on how to assess the result from the stress analysis to make the necessary verifications to avoid failure. In this work, PCHE is classified as \"safety-related\" components associated with metallic components used in the construction of high-temperature reactor systems. For this problem, ASME Section III, Division 5, Subsection HB, Subpart B, which covers elevated temperature service components, is considered as the construction code. In this study, finite element analysis is utilized to analyze and obtain the stress intensities. In order to comply with design codes stated in ASME section III, the stress linearization method is needed. Stress linearization is a technique used to decompose actual stress distribution across thickness into membrane and bending stress. This technique is stated in ASME Section VIII, Division 2 [26]. The stress linearization method is done by following the statement given by ASME VIII below. The membrane stress tensor is the tensor comprised of the average of each stress component along the stress classification line, or:  
\[\sigma_{(ij,m)}=\frac{1}{t}\int_{0}^{t}\sigma_{ij}\,dx \tag{1}\]  
Figure 4: Huber–von Mises stress (**a**) and total displacement (**b**) distribution due to pressure load (at misalignment of 0.85 mm). Figure 5: Maximum stress intensity for each misalignment condition. The bending stress tensor is the tensor comprised of the linear varying portion of each stress component along  
\[\sigma_{(ij,p)}=\frac{6}{t^{2}}\int_{0}^{t}\sigma_{ij}\left(\frac{t}{2}-x\right)dx \tag{2}\]  
The equivalent stress can be calculated by  
\[\sigma_{e}=\left[\sigma_{x}^{2}+\sigma_{y}^{2}+\sigma_{x}\sigma_{y}+3\tau_{xy}^ {2}\right]^{1/2} \tag{3}\]  
To obtain the linearization result, stress classification lines (SCLs) are necessarily needed. Stress classification lines should represent the areas of interest of the proposed geometry, such as the sodium-to-sodium area, steam-to-steam area, and sodium-to-steam area. For this purpose, 10 SCLs have been taken throughout the geometry as shown in Figure 6 below. Numerical simulation using COMSOL Multiphysics 5.3 resulted in 10 linearized stress values as shown in Figure 6. Linearized stress values between sodium channels are represented by SCL 1, SCL 2, and SCL 3. The interest areas between steam channel stress values are represented by SCL 4, SCL 5, and SCL 6. SCL 7-10 represent areas between steam and sodium channels. The linearization results are shown in Figure 7.  
The linearization results are compared with the ASME Section III stress value requirements for design load conditions. For design load conditions, a variable named \(S_{o}\) is needed. \(S_{o}\) is the maximum allowable value of the general primary membrane stress intensity for use as a reference for stress calculation under design loading. For the load-controlled stress limit under the design limit, two equations are used for compliance  
\[P_{m}\leq S_{o} \tag{4}\]  
\[P_{L}+P_{b}\leq 1.5S_{o} \tag{5}\]  
where Pm is the general primary membrane stress intensity resulted by linearization along the SCLs and PL + Pb is the combined primary membrane stress intensity and bending stress intensity. Therefore, values decrease with the increase of working temperature, as shown in Figure 8. The proposed system aims to be used in sodium fast-cooled reactor wherethe maximum working temperature of a steam generator heat exchanger is 550 \({}^{\circ}\)C. Therefore, for this purpose the maximum allowable stress (So) should be set at 88 MPa. Hence, the 1.5 So will be 132 MPa. The maximum resulting value using the linearization method is 27.5 MPa for the primary membrane stress intensity and 32.8 MPa for the combined primary membrane and bending stress intensity. These values are obtained from linearization along SCL 6.