PSI - Issue 7

Dalila Dimaggio et al. / Procedia Structural Integrity 7 (2017) 198–205 D. Dimaggio et al. / Structural Integrity Procedia 00 (2017) 000–000

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In a linear damage accumulation according to Palmgren-Miner all blocks of the load spectrum are evaluated with the S-N line by using a modified k’ slope after the knee-point. For the test load spectrum with 2 blocks the characteristic damage sum D ch can be calculated by equation (6):

N n

(6)

1 N D n = + b ch

2

b

1

2

b

b

n b1 : number of cycles in block 1 of the near- service spectrum with amplitude σ a,b1 n b2 : number of cycles in block 2 of the near- service spectrum with amplitude σ a,b2,trans N b1 , N b2 : endurable number of cycles from modified S-N lines The best fit of the test results are achieved with the modified S-N line parameters:

• k’=2k-1 below the knee-point of the S-N line ( σ k > σ a >0.6∙σ k ) • with the slope k* below the second knee-point σ k1 ,N k1 (σ a <0.6∙σ k ) * k −

  

0.6    ⋅ σ k

k σ

and

1 k N N =

k

• the characteristic damage sum D ch =1 For the application to the turbine blade it is assumed, that these parameters are also valid for the real load spectrum with 10 7 vibration cycles at real occurring stress ratios R real during one turbine operation cycle. 5. The software In order to apply the numerical model to a real case study an ad-hoc MATLAB® software has been developed for the calculation of HSV 90% on FEA results extracted from ANSYS® elastic analysis. The necessary inputs, i.e. the stress tensor and the nodes spatial coordinates, can be easily obtained from ANSYS® and used in MATLAB®. Once HSV 90% is calculated for the component, the life evaluation can be performed following the steps of the numerical approach described in chapter 4. The software evaluates the HSV 90% by selecting the FEA nodes having a VonMises stress σ VM in the range of 0.9σ max,VM ≤ σ VM ≤ σ max,VM and calculating the corresponding volume through the alpha-shape Edelsbrunners’s algorithm [10] with an α -radius optimized on mesh size dimensions. For doing so, a sufficiently refined mesh is necessary in order to collect a three-dimensional cloud of points. 6. Application to component The developed approach has been applied on a real case study, i.e. the dovetail of a steam turbine last stage blade which is a critical area due to high stresses reached at some points of the dovetail. The spectrum of local stress at the critical location for one typical run-up/down operation cycle of the turbine consists of one block of stresses caused by centrifugal force (Block1: stress amplitude σ a,b1 , stress ratio R=0, number of cycles=1 ) and one block of stress due to vibrations (Block2: stress amplitude σ a,b2 , stress ratio R=0.95, number of cycles=10 7 ). T he stress amplitude of Block2 with R=0.95 must be transformed into an equivalent σ a,b2,transf (R=0) stress by means of equation (6) obtained from the local Haigh diagram (Figure 4). Life estimation has been performed based on a FEA sub-model with refined mesh. Figure 6 shows the calculated HSV 90% , the maximum Von Mises node is highlighted together with all the nodes of the highly stressed region. It must be noticed that a refined sub-model is essential to perform a life evaluation through HSV 90% , a rough mesh would not even let the selection of a 3D cloud of nodes for volume calculation. The software calculates an HSV 90% =11.71mm 3 and the corresponding support factor n HSV =1.048 (eq.3).