Appendix 1
c. Specific Guidelines for Fracture-Mechanics Modeling, Zone Definition, and Volume Calculations:
(1) Subsurface Zones.
(a) Surface enhancements must not be modeled for the test case, however, they should be considered when analyzing actual components.
(b) The maximum principal stress in each zone should be used in the crack growth calculations.
(c) The impact of stress gradients should be considered. To reach a converged solution, high stress near surface regions of the part may require additional refinement beyond the 5 ksi bands suggested in the general guidelines (e.g., disk bores and bore sides).
Subdivision of these regions into subsurface "onion skin" layers, like the surface volumes discussed next, will likely capture the rapid change in life from surface to subsurface and reduce conservatism in the prediction. Engineering judgment and experimentation will be required to determine the optimum near surface zone geometry (i.e., width and thickness).
(d) A surface crack growth correction factor should be considered in the stress intensity (K) solution for cracks transitioning to surface cracks.
(e) The crack should be positioned at the life limiting location in each zone.
(f) A circular crack geometry (a = c) should be assumed.
(g)The defect area should be considered equal to the area of the circular crack.
(h) The zone volume should be assumed to be equal to the volume of the finite elements (or fractions of elements) used to construct the zone.
(i) When transitioning to a surface crack, the crack depth (a) should be taken as the diameter of the subsurface crack (2a) just as it touches the surface (see FIGURE A1-2).
A1-5
Appendix 1 FIGURE A1-2
(j) Average air crack growth data should be used.
(2) Surface Zones.
(a) Surface enhancement must not be modeled for the test case, however, it should be considered when analyzing actual components.
(b) The maximum principal stress in each zone should be used in the crack growth calculations.
(c) The impact of stress gradients should be considered.
(d) A surface crack growth correction factor should be considered in the stress intensity (K) solution.
(e) The crack should be positioned at the life limiting location in each zone.
A1-6
Appendix 1
(f) A 2:1 crack aspect ratio should be assumed, with surface length (2c) equal to twice the depth (a).
(g) The defect area should be assumed equal to 1/2 the area of a circle with a radius of crack depth (a).
(h) The volume should be based on the zone surface face length and an onion skin thickness of 0.020 in (0.5 mm).
(i) Average air crack growth data should be used.
(3) Surface Corner Zones.
(a) Surface enhancements must not be modeled for the test case, however, should be considered when analyzing actual components.
(b) The maximum principal stress in each zone should be used in the crack growth calculations.
(c) The impact of stress gradients should be considered.
(d) A surface crack growth correction factor should be considered in the stress intensity (K) solution.
(e) The crack should be positioned at the life limiting location in each zone.
(f) A 1:1 crack aspect ratio should be assumed, with surface length (c) equal to depth (a).
(g) The defect area should be assumed equal to 1/4 the area of a circle with the radius of crack depth (a).
(h) The volume should be based on the zone surface face lengths and an onion skin thickness of 0.020 in (0.5 mm).
(i) Average air crack growth data should be used.
A1-7
Appendix 1
4. Test Case Analysis Example
a. Problem Description. The test case geometry consists of a titanium ring disk under simple cyclic loading for 20,000 cycles. The maximum speed is 6,800 RPM and an external pressure load of 50 MPa (7.25 ksi) is applied on the outer diameter to simulate blade loading.
The disk probability of fracture will be calculated assuming no in-service inspection and with a single in-service inspection at 10,000 cycles.
FIGURE A1-3 FIGURE A1-4
(1) Step 1 - Component Stress Analysis. Component stresses are determined in order to perform crack growth analysis, define zones, and calculate zone volumes. Stress analysis results are shown below as a component stress contour plot for the maximum principal stress in each band. Since crack growth calculations are to be performed, maximum principal (hoop) stresses are used.
(a) Assumption. Disk is at constant temperature. No thermal stresses.
A1-8
Appendix 1 FIGURE A1-5 Component Stress Model Component Principal Stress Contour Plot NOTE: Typically a Kt would be applied to the rim stress due to the dovetail slot. However, it has not been included in the test case.
(2) Step 2 - Stress Volume Calculation. Incremental volumes are used to determine the probability of having an anomaly in a particular region of the part. The disk is partitioned into zones, where within a zone the residual life is nearly constant. Next, the volume of each zone is calculated. The disk shown in FIGURE A1-6 has been partitioned in to 36 zones. Guidelines for defining the volume of each zone are provided in paragraph 3 of this Appendix. Stress volume results are shown in Table A1-1 of this Appendix.
(a) Assumptions:
1. Stress volumes partitioned at 5 ksi (34.5 MPa) increments are good starting points to perform the risk integration.
2. A 0.020 in (0.5-mm) thick onion skin provides adequate definition of the surface volumes.
A1-9
Appendix 1 FIGURE A1-6 Component Stress Model Stress VolumeDefinition
0.020 in (0.5 mm) Onion Skin
• 17 10 - 18 11 4 → 121 122 123 * 20 Further break up of the high stress/low 5 → 13. 13. 13.3 ₩ 21 life zones performed 2 to reach 6→ 14.1 14.2 14.3 * 22 convergence 15 2а 152b
15.20 -15.З * 23
- 24 A1-10
Appendix 1 Table A1-1: Zone Volume Data Zone Number Volume 1 0.69 cm3(0.042 in3) 2 18.8 cm3(1.15 in3) 3 34.9 cm3(2.13 in3) 4 29.2 cm3(1.78 in3) 5 24.2 cm3(1.48 in3) 6 20.1 cm3(1.23 in3) 7 16.1 cm3(0.98 in3) 8 0.49 cm3(0.030 in3) 9 134.37 cm 3(8.20 in3) 10 3675.5 cm 3(224.29 in3) 11 6809.8 cm 3(415.56 in3)
12.1 144.48 cm 3(8.81 in3)
12.2 5403.46 cm 3(329.68 in3)
12.3 144.48 cm 3(8.81 in3)
13.1 119.95 cm 3(7.32 in3)
13.2 4488.2 cm 3(273.84 in3)
13.3 119.95 cm 3(7.32 in3)
14.1 99.58 cm 3(6.08 in3)
14.2 3724.1 cm 3(227.22 in3)
14.3 99.58 cm 3(6.08 in3)
15.1 79.82 cm 3(4.87 in3)
15.2a 1958.8 cm 3(119.51 in3)
15.2b 324.02 cm 3(19.77 in3)
15.2c 459.58 cm 3(28.04 in3)
15.2d 182.75 cm 3(11.15 in3)
15.2e 91.13 cm 3(5.56 in3)
15.3 79.82 cm3(4.87 in3) 16 94.90 cm3(5.79 in3) 17 0.69 cm3(0.042 in3) 18 18.8 cm3(1.15 in3) 19 34.9 cm3(2.13 in3) 20 29.2 cm3(1.78 in3) 21 24.2 cm3(1.48 in3) 22 20.1 cm3(1.23 in3) 23 16.1 cm3(0.98 in3) 24 0.49 cm 3(0.030 in3) A1-11
Appendix 1
(3) Step 3 - Crack Growth Model Definition. Crack growth models are constructed for each of the zones defined in Step 2. Examples for zones 17, 22, and 10 are illustrated below in FIGURE A1-7. Guidelines for crack growth analysis are provided in FIGURE A1-2.
(a) Assumptions:
1. The crack is positioned in the most life limiting location within the zone.
2. Surface anomalies are modeled as semicircular cracks.
3. Surface corner anomalies are modeled as quarter circles.
4. Subsurface anomalies are modeled as circular cracks.
A1-12
Appendix 1 FIGURE A1-7: Zone Crack Location Width = 0. 1 m (3.94 in.)
Zone 17 Thickress - 0.125 m (4.92 im.)
Zone 10 • -Zone 22 Thickness - 0.125 m (4.92 in.)
Thicknes = 0.1 = (3.94 in.) Width = 0.1 = (3.94 in.)
A1-13
Appendix 1
(4) Step 4 - Crack Growth Calculations. Crack growth calculations are performed (FIGURE A1-8) using the predicted stresses and crack growth rate data to determine the residual life associated with each zone. The calculations are conducted for range of initial crack sizes to ensure that the component service life is covered.
(a) Assumptions:
1. All anomalies act as sharp propagating cracks and are orientated normal to the maximum principal stress: hoop stress.
2. The crack growth rate curve is the same for both surface and subsurface calculations.
3. Average air crack growth data.
4. No surface enhancement effects.
A1-14
Appendix 1 FIGURE A1-8 A1-15
Appendix 1
(5) Step 5 - Relative Risk Calculation – No In-Service Inspection. The probability of fracture for each stress volume is calculated integrating the volume, anomaly distribution, and residual life information from the previous steps (FIGURE A1-9). The results for each zone are statistically summed to determine the total component probability of fracture.
The calculated probability of fracture without an in-service inspection is 1.9 E - 09 events/cycle.
A1-16