AC 33.70-5 A.2.2.5 Figure A-6 illustrates the axisymmetric view of the blade, providing key height and width dimensions in inches and millimeters.
Figure A-6. Test Case Geometry Definition: Axisymmetric View of Blade Showing Height and Width in Inches and (Millimeters) A–7
AC 33.70-5 A.2.2.6 Figure A-7 provides a radially inward view of the blade, illustrating the broach angle and blade thickness in inches and millimeters.
Figure A-7. Test Case Geometry Definition: View of Blade Looking Radially Inward Showing Broach Angle and Blade Thickness in Inches and (Millimeters) A–8
AC 33.70-5 A.2.2.7 Figure A-8 displays the blade attachment profile (View B -B), illustrating the dimensions in both inches and millimeters.
Figure A-8. Test Case Geometry Definition: View B-B Showing Blade Attachment Profile in Inches and (Millimeters) Not to Scale A–9
AC 33.70-5 A.2.3 Mission Profile Definition.
The stresses and corresponding life capability at the disk's slot bottom are primarily driven by the disk's rotational speed but also from the rotor thermal gradient. This test case simulates multiple phases of a typical commercial revenue service operation, capturing changes in disk rotational speed and rotor stress due to thermal contributions through the mission profile. The mission profile is defined by 11 unique time points. A time and disk speed history profile defining these mission points is shown in figure A-9 and table A-1.
Test Case Mission Speed Profile Test Case Mission Temperature Profile 14000 1200 1100 • 600 12000 1000 - 550 900 - 500 Temperature (deg F) 800 - 450 8000 700 Disk Spee 6000 400 4000 300 2000 200 •Disk Slot Bottom 100 *Disk Bore 2000 4000 6000 8000 10000 12000 14000 1600 5000 10000 15000 Mission Time (sec) Mission Time (sec) Figure A-9. Disk Speed and Temperature over Test Case Flight Profile Table A-1. Tabulated Disk Speeds and Temperatures for Test Case Flight Profile Disk Bore Disk Slot Bottom Disk Bore Disk Slot Bottom Rotational Time Temperature Temperature Temperature Temperature Speed Radius = 2.0 in Radius = 8.38 in Radius = 50.8 mm Radius = 212.77 mm sec deg F deg F deg C deg C RPM
42.8 42.8 6.0 6.0 0.0 18 42.8 42.8 6.0 6.0 2708.8 60 64.4 120.2 18.0 49.0 9029.5 608 73.4 208.2 23.0 97.9 9211.1 642 446.0 1,112.0 230.0 600.0 9504.1 1689 975.2 1,050.8 524.0 566.0 12512.6 2008 1,014.8 987.8 546.0 531.0 12182.3 4127 807.8 892.2 431.0 477.9 12158.6 14127 807.8 892.2 431.0 477.9 12046.4 14517 807.8 426.7 431.0 219.3 12042.0 15947 334.4 392.0 168.0 200.0 0.0 A-10
AC 33.70-5 A.2.4 Thermal Gradients and Mission Points.
A unique linear radial thermal gradient is used for each mission point. Temperatures at two different radial points (disk bore and slot bottom) are provided as a reference;
temperatures at all other radial stations vary linearly, proportional to the radius of interest. No axial or circumferential thermal gradients are assumed. An example of this radial temperature gradient is shown in figure A-10 for time point t = 642 seconds.
Temperature 274 ¡Temperature min: 446.
max: 1332.5 min: 230.
Note: 249 max: 722.51 1350.
1250. Contour plot to the left shows 732.22 1150. dimensions in inches and 224 676.67 X2 1050. 621.11
950. temperatures in degrees 565.56
850. Fahrenheit. 510.
750. 454.44
550. 650. Contour plot to the right shows 174.. 398.89 343.33
450. dimensions in millimeters and 287.78 1350. temperatures in degrees Celsius 232.22 149 176.67 (Tz-T1) T(x)= (×-×1) +T1 _124 (×2-×1) 30 Figure A-10. Example of Test Case Linear Thermal Gradient at t-642s A-11
AC 33.70-5 A.2.5 Material and Crack Growth Data.
A.2.5.1 Material Properties Overview.
The stress analysis for this test case requires material properties for the disk and blade.
Both components use the same alloy. Relevant material properties include Young’s modulus of elasticity (E), material density (ρ), coefficient of thermal expansion (α), and Poisson’s ratio (ν). Except for density, all properties vary with temperature. The reference temperature for zero thermal expansion is 68°F (20°C). See table A-2.
Table A-2. Test Case Physical Material Properties A.2.5.2 Material Properties.
The material density is defined as 0.29 lbm/in3 (8027 kg/m3). These material properties are representative of a commonly used alloy, but they have been modified specifically for this test case. These properties should not be used for detailed engineering design or certification.
A.2.5.3 Cyclic Crack Growth Data.
In addition to the physical data, cyclic fatigue crack growth properties necessary for crack growth calculations are provided. The crack growth assessments are based solely on cyclic crack growth without considering time-dependent effects or load interactions. The crack growth rates per cycle, as a function of the change in stress intensity (da/dN vs dK), are given using temperature-dependent constants fitted in the form of the sigmoidal model shown in equation A-1. Applicants may convert the provided model into an equivalent format suitable for their own analysis tools, such as:
• Tabular Input
• Hyperbolic Sine
• Nasgro equation
• Simple Paris law (if cyclic threshold is not considered).
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AC 33.70-5 Equation A-1. Test Case Cyclic Crack Growth Rate 𝑑𝑎 𝑑𝑁 = exp(𝐵) (𝐾𝑒𝑓𝑓𝐾𝑡ℎ ) 𝑃 [ln (𝐾𝑒𝑓𝑓𝐾𝑡ℎ )]𝑄 [ln ( 𝐾𝑐𝑟𝐾𝑒𝑓𝑓)]𝐷 A.2.5.4 Crack Grow th Ra tes.
The crack growth rates described in paragraph A.2.5.3 are displayed in tables A-3 and A-4. For reference:
• The cyclic crack growth threshold is denoted as 𝐾𝐾𝐾𝐾ℎ.
• The material fracture toughness is denoted as 𝐾𝐾𝐾𝐾𝐾𝐾.
A.2.5.5 R Ratio Corrections and Walker Model.
R ratio corrections are applied using the Walker model, where the effective stress intensity Keff, is defined in equation A-2.
𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾 = 𝐾𝐾𝐾𝐾𝑑𝑑𝐾𝐾(1 − 𝑅𝑅)𝑚𝑚 Equation A-2. Walker model Where:
• 𝑅𝑅 is the stre ss intensity ratio, R=Kmin/Kmax
• 𝐾𝐾𝐾𝐾𝑑𝑑𝐾𝐾 𝑑𝑑𝑎𝑎𝑑𝑑 𝐾𝐾𝐾𝐾𝐾𝐾𝑎𝑎 = stress intensities at max and min stress points of the cycle pair.
• 𝐾𝐾 is the Walker exponent.
A.2.5.6 Temperature-Dependent Walker Exponent.
The Walker exponent m varies with temperature, and its values are provided in tables A-3 and A-4. Depending on the computed R ratio:
• Use the m- column if R is negative.
• Use the m+ column if R is positive or zero.
Table A-3. Test Case Cyclic Crack Growth Rate Parameters (deg F) Temperature (deg F) Kth (ksi*sqrt(in)) Kcr (ksi*sqrt(in)) B P
0.517 Q D m+ m-
0.0976 32 5.0025 67.0 -15.062 1.668 -2.523 0.6845 75 5.0025 67.0 -15.062 0.517 1.668 -2.523 0.6845 0.0976 500 7.00 67.0 -14.000 0.900 1.200 -1.800 0.6462 0.1401 700 7.94 67.0 -13.500 1.080 0.980 -1.460 0.6282 0.1601 900 8.88 67.0 -13.000 1.260 0.760 -1.120 0.6102 0.1801 1000 9.35 67.0 -12.750 1.350 0.650 -0.950 0.6012 0.1901 1100 9.82 67.0 -12.501 1.440 0.540 -0.780 0.5922 0.2001 1150 9.82 67.0 -12.501 1.440 0.540 -0.780 0.5922 0.2001 A–13
AC 33.70-5
Table A-4. Test Case Cyclic Crack Growth Rate Parameters (deg C) Temperature (deg C)
0.0 Kth (MPa*sqrt(m))
5.4970 Kcr (MPa*sqrt(m))
73.6 B -18.735 P
0.517 Q
1.668 D -2.523 m+
0.6845 m-
0.0976
23.9 5.4970 73.6 -18.735 0.517 1.668 -2.523 0.6845 0.0976
260.0 7.69 73.6 -17.673 0.900 1.200 -1.800 0.6462 0.1401
371.1 8.72 73.6 -17.173 1.080 0.980 -1.460 0.6282 0.1601
482.2 9.76 73.6 -16.673 1.260 0.760 -1.120 0.6102 0.1801
537.8 10.27 73.6 -16.423 1.350 0.650 -0.950 0.6012 0.1901
593.3 10.79 73.6 -16.174 1.440 0.540 -0.780 0.5922 0.2001
621.1 10.79 73.6 -16.174 1.440 0.540 -0.780 0.5922 0.2001 A.2.5.7 Elastic-Plastic Finite Element Analysis.
For notched locations where local plasticity may occur, it is common to “shake down” elastic stresses before performing crack growth analyses.
Alternatively, a full elastic-plastic finite element analysis can be conducted. If plasticity is considered, the material’s stress-strain properties (listed in tables A-5 and A-6) should be referenced and used along with the Ramberg-Osgood or Ludwick’s model given in equation A-3.
Equation A-3. Ramberg-Osgood Stress Strain Relationship
Table A-5. Test Case Material Constants to be Used for Considerations of Plasticity (deg F) Temperature (deg F) E (ksi) K (ksi) n 32 29,000 205.00 0.0500 68 29,000 205.00 0.0500 500 27,600 202.00 0.0500 700 26,600 200.00 0.0500 900 25,700 195.00 0.0500 950 25,600 200.00 0.0580 1000 25,500 205.00 0.0660 1100 24,400 210.00 0.0750 1150 24,400 210.00 0.0750 A–14
AC 33.70-5
Table A-6. Test Case Material Constants to be Used for Considerations of Plasticity (deg C) Temperature (deg C) E (MPa) K (MPa) n
0.0 199,955 1413.43 0.0500
20.0 199,955 1413.43 0.0500
260.0 190,302 1392.74 0.0500
371.1 183,407 1378.95 0.0500
482.2 177,202 1344.48 0.0500
510.0 176,512 1378.95 0.0580
537.8 175,823 1413.43 0.0660
593.3 168,238 1447.90 0.0750
621.1 168,238 1447.90 0.0750 A.2.6 Anomaly Distribution Curve.
The anomaly distribution, provided in appendix B, defines the probability of occurrence as a function of anomaly depth. No POF benefit is assumed from manufacturing credits for the component in the test case.
A.2.7 Inspection POD.
The POD curve used to determine the effect of an in-service inspection is shown in table D-1. This table is consistent with figure A4-1 of AC 33.70-2. The test case assumes one directed fluorescent penetrant inspection (FPI) at the component's mid-life (1500 flight cycles). The POD relates the probability of detecting an anomaly to flaw length, using the convention shown in figure A-11.
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AC 33.70-5
Figure A-11. Test Case Conventions Used for Test Case Inspection Scenario A.3 Test Case Analysis Guidelines.
Analytical guidelines for probabilistic assessments are provided with the intent to minimize the variations of the manufacturer’s results due to analytical assumptions. The test case presented is based on a typical surface anomaly probabilistic fracturemechanics approach. The blade slot test case considers an anomaly located on the slot surface and on the slot edge (figure A-12). The POF is to be computed for each location. This analytical approach can be broken down into the following steps:
• Stress analysis.
• Slot location definition (maximum p rincipal stress location).
• Crack growth model definition.
• Crack growth calculations.
• Relative risk calculation.
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AC 33.70-5 A.3.1 Stress Analysis.
The applicant should follow their own best practices for performing stress analysis for each time point of the mission profile. This includes:
• Selecting the level of mesh refinement.
• Handling blade attachment (assume frictionless contact).
• Accounting for material and geometric non-linearities.
Acceptable results have been obtained using various mesh refinement levels and blade attachment interface methods.
A.3.2 Slot Location Definition (Max Principal Stress Location).
The risk assessment should focus on locations where maximum principal stress occurs during the mission. These locations include:
• Slot surface.
• Slot edge (figure A-12).
The crack’s center should be placed at the maximum principal stress location.
Figure A-12. Test Case Anomaly Placement within Test Case A–17
AC 33.70-5 A.3.3 Crack Growth Model Definition.
For each location defined in figure A-12, develop a crack growth model using the following assumptions:
• Surface Cracks: Use a 2:1 aspect ratio for a semi-circular crack, with surface length (2c) equal to twice the depth (a).
• Corner Cracks: Use a 1:1 aspect ratio for a quarter-circle crack, with surface length
(c) equal to the depth (a).
• Orientation of the crack plane should be normal to the maximum principal stress.
• Ensure that plate geometry does not extend outside the physical boundaries of the component.
A.3.4 Crack Growth Calculations.
Perform crack growth calculations based on the predicted stresses and crack growth rate data. These calculations determine the residual life (life to failure from an assumed crack size) for each location. Conduct the calculations for a range of initial crack sizes to ensure that the component service life is covered. These are the guidelines for crack growth calculations:
• Assume all anomalies act as sharp propagating cracks, with no incubation/nucleation life.
• The crack plane should be oriented perpendicular to the maximum principal stress at the crack origin. Once defined the plane should remain fixed.
• Consider the impact of stress gradients.
• Use crack growth rate data provided for the test case.
• The effect of beneficial surface residual stresses, such as shot peening, should not be considered in the test case.
• Use a representative stress intensity factor solution for surface and corner cracks.
• A TMF method is prescribed to ensure consistency. The TMF method is used to consider how fast a crack will grow when the temperature and stress profiles are out of phase i.e., the timepoints associated with the peak stress and temperature in the loading cycle are not the same.
Note: The TMF method described in this AC consists of a stress rainflow (based on absolute stress) to determine the mission point’s pairs (peaks & valleys). Then, for each pair, the higher temperature of the pair’s points is used for the crack growth calculation. Figure A-13 shows the normalized (value/maximum) stress and temperature excursions at the slot bottom of the AC test case, where useful mission points were identified using letters A through F. Applying the prescribed TMF method to this mission profile results in the stress pairs and crack growth rate evaluation temperatures given in table A-7.
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