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shown in Figure 4. The thermophysical properties of the layers were varied and it was found that if the CTE of the materials was varied within 4 ppm/C of Si3N4, the residual stress in the silicon layer did not decrease to levels much lower than 23-25 ksi. In addition to the stress analyses, micromechanical fracture modeling was also conducted to explain the effects of residual stress in the Si layer on flaw creation, propagation and interaction with pre- existing flaws in silicon nitride. optical/electron microscope or a result of a computer simulation, can be used for analysis. Based on this data, a finite element grid with associated material properties is generated on which mechanical and/or thermal loading can be applied. A solution is then obtained for the specified boundary conditions, distortion, and temperature change. The calculations were done assuming plane stress (σ33=0) and free boundary conditions to mimic unconstrained cooling of a thin plate from its sintering temperature. A typical coating microstructure (Figure 5) was imported into the OOF code, digitized for thermal analysis and then subjected to a temperature change of 1000°C (1832°F). The calculated global stresses were similar to that obtained from equaltion 1 [Figure 3]. Typical EBC Figure 3: Calculation of residual stress in Si layer on monolithic Si3N4. The stress in the coating is fairly independent of the coating thickness. Digitized Microstructure Figure 4: Various architectures considered to drive down residual stress in the Si-layer of the coating. OOF, an object oriented finite element analysis code developed at NIST[15], was used to investigate the response of the coated substrate to thermal loads. The program performs thermoelastic calculations in two dimensions (plane strain or plane stress) using 3- node triangular elements. Several “smart” meshing schemes based on energy minimization are available to mesh curved features, such as grain boundaries. A digital image of a microstructure, either from an Figure 5: EBC coating microstructure and digitized image for OOF analysis In addition to the calculation of the residual stresses, the elements in the OOF code are designed to fail under a Griffith-like strain energy based criterion. The elements crack when the required surface energy can be supplied by the stored strain energy per crack extension (∆L), i.e., 1 σ elemε elem A / ∆L ≥ 2γ (2) 2 ij ij elem where γ is the surface energy of the cracked interface. The analysis involves the following steps: 147 Copyright © 2007 by ASME a. b. Thermal and mechanical loads are applied and the microstructure is equilibrated to determine stress/strain distribution. The energy balance is computed and if an element satisfies the energy criterion for cracking, the stiffness of the element is set to zero. A 30 25 20 15 10 5 0 0 200 400 600 Si Thickness (Microns) 1200 1400 800 1000 Stress (ksi) Intermediate Layer Bond Coat 100 μm Top Si Interlayer SiN Top Si SiNPDF Image | ADVANCED MICROTURBINE SYSTEMS Final Report for Tasks 1 Through 4 and Task 6
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