PSI - Issue 14

Manish Kumar et al. / Procedia Structural Integrity 14 (2019) 839–848 Manish Kumar et. al/ Structural Integrity Procedia 00 (2018) 000–000

845

7

Integration point Node

(a)

(b)

Fig. 3: Data transfer procedure: (a) data transferring from old integration points to nodal points, (b) data transferring from nodal points to new integration points The equilibrium is disturbed due to the transfer of data from old configuration to new configuration. Consequently, to restore the equilibrium, Newton-Raphson iterative procedure (Khoei, 2015) is followed with a null step (no change in external loading). A dummy force vector is assembled based on the induced internal stresses after the data transfer. The force on both natural and essential boundaries is kept zero in dummy force vector. The elasto plastic analysis is performed assuming dummy force (in reverse manner) as an applied force. The converged solution of elasto-plastic analysis takes the continuum to a state in which continuum has an equilibrium between induced internal stresses and external force with increased crack length and complete history of the applied load. 3. Results and Discussion The mixed mode creep crack growth in turbine disc of an aero-engine subjected to a radial load at 650 °C is predicted using the XFEM based numerical scheme. The disc is made of Inconel 718 whose mechanical properties are provided in Table 1 (Structural Metals Handbook, 1995). The disc has four holes in the web portion as shown in Fig. 4a. The thickness of the rim, hub and web are 20 mm, 20 and 10 mm respectively. At the periphery of each hole, a crack of 0.7 mm at 51° is assumed. Due to symmetry, a quarter model of the disc is taken for the analysis as shown in Fig. 4b along with loading and boundary conditions. A uniformly distributed load of 100 MPa is applied at the outer surface of the rim. A non-uniform mesh of 6832 elements is taken such that the element size near the crack tip is 0.14 mm. Power law and ( ) C t -integral are used as the creep law and creep crack characterization parameter respectively. The creep related data of Inconel 718 at 650 °C is given in Table 1 (Kim et al ., 2008). The crack growth direction is estimated by the maximum principal stress criterion as mentioned in Section 2. The evaluated crack growth path is presented in Fig. 5. The hub and rim portions are shown by red colour whereas initial crack and crack growth are shown by black and red colours respectively. The computed creep crack growth vs time result is shown in Fig. 6. The crack growth rate increases rapidly with the increase in crack length which is as per the theoretical expectation. The contour plots of von-Mises stress near the crack tip region are shown in Fig. 7after 241.5, 1118.5 and 1990.3 hours.

Table 1. Material properties for Inconel at 650°C. Parameter

Value of parameter

Yield strength at 650 °C

992 MPa

Poisson ratio

0.28

Young’s modulus at 650 °C Power Law constant, A Power Law exponent, b Constant of da/dt (mm/h), γ

205 GPa

4.6774 × 10 -92

29.89

3.209 × 10 -3

da/dt exponent, 

0.1421