PSI - Issue 28

L.V. Stepanova et al. / Procedia Structural Integrity 28 (2020) 2277–2282 Author name / Structural Integrity Procedia 00 (2019) 000–000

2281

5

Fig. 3. Stress tensor components r  and   : comparison of the approximate solution and numerical solution (FEM) for 5 n 

3. Steady state creep of a rotating disc The problem of estimating the radial extension of a spinning circular disc is one of the classical problems in creep (Boyle and Spence (1983)). Boyle and Spence (1983) presented the approximate solution of the problem by the quasilinearization method. We would like to give the solution for rather large values of the creep exponent. The equations are similar to the equations of the previous problem. However, when we consider a circular disc of constant thickness with outer radius b containing a hole of radius a and the disc is spinning with velocity, the rotational body force has to be taken into account. Hence, the problem can be reduced to the system of the equations               / 1 / / 1 / . (1 / ) / (1 / ) / 1 / / r r r r r rr r r r Qr a rb r b rb rb d r a a b rb r b b b b r b rb dr                                                          (8) The figs. 4 and 5 show the variation of the stress and strain tensor components for 9 n  .

σ θ

σ r

1

0.12

n=9

n=9

1

0.9

0.1

1

2

2

0.8

converged solution

3

0.08

3

4

0.7

4

5

6

5

0.06

6

converged solution

0.6

0.04

0.5

0.02

0.4

r

r

Fig. 4. Convergence of radial stress r  (left) and circumferential stress   (right) using quasilinearisation for 9 n  0 1 1.2 1.4 2 1.8 1.6 1 1.2 1.4 1.6 1.8

2