PSI - Issue 72

Nenad Vidanović et al. / Procedia Structural Integrity 72 (2025) 499– 506

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Table 1. Paris’ coefficients for various elevated temperatures with several simulated numbers of cycles for observed crack size a T [°] m C [ MPa√mm ] a [mm] N 360 3.13 5.7915 ∙ 10 −14 550 3.01 1.6405 ∙ 10 −13 0.417 707 650 2.5 2.3610 ∙ 10 −11 RT 3.31-5.19 2.820 ∙ 10 −14 −4.348 ∙ 10 −20 316 3.35-4.46 2.983 ∙ 10 −14 −1.680 ∙ 10 −17 649 2.5-2.95 6.352 ∙ 10 −11 −9.91 ∙ 10 −13 RT 5.1 1.0970 ∙ 10 −19 400 5.6 5.5735 ∙ 10 −21 0.4 3903 550 5.7 4.2276 ∙ 10 −21 550 2.766 1.7959 ∙ 10 −11 0.41 47 1.856 (90s HT) 2.9813 ∙ 10 −9 4.322 (2160s HT) 7.1953 ∙ 10 −15 0.402 10000 650 2.825 7.4429 ∙ 10 −12 6.283 (90s HT) 5.9752 ∙ 10 −20 9.252 (2160s HT) 8.1990 ∙ 10 −28 0.4 1 All the presented numbers were useless when applied to the damaged HPT casing: No combination of C & predicted the crack growth of 0.41 mm after approximately 2 807 cycles under the given loading conditions . There are few reasons why this was the case:  The aged material was being analysed, whilst data in the literature refer to virgin material (also, orientation of the material in the experiment, type of loading…have a great influence on experimental findings),  These coefficients were determined for specimens exposed to constant temperatures, which is rarely the case for aircraft engine components. 2. Proposed f ramework for Paris’ coefficients determination and applied approach The approach, as well as the framework based on numerical simulations, was successfully used to obtain Paris’ coefficients for the aged material based on the limited real operating data which had to be collected. The algorithm of the framework presented in Fig. 2. shows the data flow and the order of activities for C & determination. All numerical methods used in this study were implemented through ANSYS Workbench commercial software. Dimensions of the component are not publicly available, but the problem was overcome by using ultra-precise 3D scanners and then the digital image was converted to a useful 3D CAD file using SpaceClaim module/software. When 3D HPT casing model had been created, FE model was established to meet environmental conditions during the flight. For that purpose, patch-conforming mesh method, using tetrahedral elements (3 616 544 elements or 5 763 797 nodes), was selected (Fig. 3. (a)). First conducted simulation was steady-state thermal analysis, and it was modelled with higher-order 3D 10-node thermal-solid element SOLID 291 with one degree of freedom – temperature – at each node. The purpose was to calculate boundary condition – convective heat transfer – and then to apply it through four different convection film coefficients (Fig. 3. (b)). Next simulation was static-structural analysis, and it was modelled with higher-order 3D 10-node solid element SOLID 187 with three degrees of freedom per node – translations in the nodal X, Y, and Z direction and with applied boundary conditions – temperature distribution obtained in the previous thermal analysis, predefined pressure distribution, three translational and three rotational constrains (Fig. 3. (c)).