High Cycle Fatigue: A Mechanics of Materials Perspective part 60 pps

576 Appendix G Figure G.22. Level 2 front surface. Figure G.23. Simulated FOD using light gas gun impact. several velocities created the impact sites. The microstructural changes, aside from the scale of damage, were consistent for all specimens. The primary microstructural features due to impact damage were a compressed microstructural zone and the formation of adiabatic shear bands. The presence of adiabatic shear bands is an important indication that ballistic FOD simulation accurately represents the high rate deformation process seen during actual FOD. Adiabatic shear bands form only during high rate deforma- tion by effectively melting and re-solidifying the metal, resulting in a different grain structure. The presence of shear bands around the impact of a spherical projectile has been noted by some studies [7, 8]. Roder et al. [8] examined the damage caused by the impact of hardened steel spheres fired at 309 m/s at a flat plate and mapped the distribution of shear Appendix G 577 Original surface level Pile up Plastic zone Shear band pattern Figure G.24. Shear band pattern beneath impact crater [8]. bands. As can be seen from Figure G.24, their orientation is such that they could increase the susceptibility to fatigue crack growth. Figure G.25 is a back-scattered electron image showing an area of the edge of a V-notch produced by firing a cube projectile at Ti-6AL-4V plate. The damage strongly resembles that seen on RB199 fan blades displaying shear bands with evidence of Figure G.25. Edge of ballistic damage on plate. 578 Appendix G void opening. The microstructure is similar to the schematic representation shown on Figure G.24. The final type of simulation is engine debris ingestion. This method is mentioned here only for the sake of completeness. Engine debris ingestion is prohibitively expensive and of little scientific value. However, it is the only method that accurately simulates the effect of FOD on an entire engine. Specimen design Once the appropriate impact procedure is selected, the next step is to determine which specimen geometry will be used. In the process of specimen design, it is necessary to determine what level of refinement is necessary in order to best capture the behavior of interest. For example, in the case of High Cycle Fatigue (HCF) design, it may only be of interest to know whether or not a crack will initiate from the FOD damage site. This is based on the philosophy that cycles accumulate so quickly under HCF loading conditions that cycle counting is impractical. In this case, the specimen must be designed so that stresses at the specimen notch tip are similar to those on the leading edge area of interest. As mentioned previously, these stresses are dominated by centripetal forces and can therefore be adequately simulated by standard uniaxial testing with any number of specimen geometries. In order to capture experimentally the effect of FOD on a specific airfoil design, it is necessary to damage and test that particular configuration. Airfoil-based FOD evaluation involves shaker table or siren tests with simulated FOD. Shaker tables involve attaching a simulated blade specimen using to a high frequency actuator (∼400 to 2000 Hz) in a cantilever arrangement. Siren tests rigidly fix the base of the blade and a “siren” blasts air over the free end. This allows the blade to resonate at many of its natural frequencies, which can enable testing up to 20kHz. However, these tests are limited to fully reversed loadings (R =−1) and require full-scale blades in order to capture the effect of blade stress distributions. Additionally, these tables are unable to simulate the centrifugal force present in rotating turbo machinery. The obvious benefit of this type of test is the inherent applicability to the geometry that is being tested. Unfortunately, this type of testing is typically very costly, requires specialized equipment, and may not be applicable to arbitrary geometries. Recent work sponsored by the USAF has developed improved test methods to investigate the behavior and life of FOD’d fan blades. These test methods are intended to supplement the siren tests and provide a more rigorous evaluation of FOD effects. In addition, these test methods will enable the designer to evaluate FOD effects over the full range of loading and leading edge geometries without fabricating full-scale blades. A cornerstone of this effort is the ability to accurately simulate blade stresses and FOD damage in the laboratory. The typical fan blade in a large gas turbine engine is a complex airfoil with variable camber and twist as shown in Figure G.26. Appendix G 579 Tip Outer panel Inner panel Shroud Root region Dovetail Leading edge Figure G.26. Typical fan blade. In many cases, larger blades contain mid-span shrouds, as shown in Figure G.26, to enhance the stability of the blade. The stresses at the leading edge during engine operation are the result of complex loads and moments that vary along the length of the blade due to inertial forces, pressure loads and geometry variations. The dominant LCF loads that control the mean stresses are those derived from the centrifugal and gas loads on the blade. The dominant HCF loading is typically caused by the vibration mode near or in the engine running range. As we move along the length of the blade from the root region to the tip region, the ratio of the LCF loadings and HCF loadings varies. In the root and mid-section regions, the leading edges are subject to relatively large mean stresses that significantly decrease towards the tip regions. Therefore, stress-ratio (R) effects ranging from R = 08 (tension–tension) to R =−1 (fully reversed tension – compression) need to be considered. The leading edge regions also see stress gradients due to the camber of the blade, and these gradients may be critical to accurately simulating blade stresses in a test specimen. Figure G.27 presents a normalized stress distribution from a vibratory analysis of a typical fan blade. Due to the change in camber along the length of this blade, the critical stresses are located in the mid-section or lower panel of the blade. Figure G.28 contains a detailed contour plot of the stresses through the highest intensity cross section. Notice the relatively large stress gradient within the first 6.4 mm (0.25 in.) of the leading edge. In recent years, a test specimen that can simulate leading edge stresses has been designed under a USAF contract and is shown in Figure G.29. The specimen and its use are discussed in detail in Chapter 7. The artificial leading edges are far from the neutral axis so the leading edges will be highly stressed. This geometry was selected because (a) it could be easily cut from flat forgings, (b) it could have variable leading edge geometries, (c) it could be rather easily loaded to various stress ratios or with LCF–HCF mission cycles, and (d) the stress gradient in the leading edge could be adjusted by varying the overall height of the specimen. The 580 Appendix G JAN 1 30 1998 14:53:29 xv = 1 DIST – 5.962 XF = –.235987 YF – 13.505 ZF = .016863 Z – BUFFER –.619413 –.439407 –.2594 –.079393 .100614 .28062 .460627 .640634 .820641 1.001 ANSYS A A AIRFOIL VIB RUN – 1ST FLEX MODE Y Z K Figure G.27. Normalized stress distribution across typical fan blade. *DIST = 1.839 ANSYS 5.4 JAN 30 1998 14:56:04 YV – 1 *XF – .260981 *YF = 12.6 *ZF = .027775 SECTION –.619413 –.439407 –.2594 –.079393 .100614 .28062 .460627 .640634 .820641 1.001 AIRFOIL VIB RUN – 1ST FLEX MODE YX Z 1 Figure G.28. Stress distribution across Section A-A. specimen is loaded in four-point bending which enables uniform bending stresses in the loading span section. An elastic stress analysis of this specimen was performed to compare the leading edge stresses of the blade to the specimen. Figure G.30 contains contour plots comparing these Appendix G 581 5.1 mm (0.2 in.) 0.25 mm (0.01 in.) 6.35 mm (0.25 in.) 152 mm (6.0 in.) Tip details 1.02 mm (0.040 in.) 0.25 mm (0.010 in.) See tip details 15.2 mm (0.6 in.) Figure G.29. Diagram of simulated leading edge specimen. Blade stresses Specimen Stresses B B A A σ A σ B ≈ 2 σ A σ B ≈ 1.7 Figure G.30. Comparison of calculated blade and specimen stresses. stresses. Notice the stress gradients from points A to B are very similar. If desired, the gradients could have matched exactly by reducing the overall 5.1mm (0.2 in.) height of the specimen. Due to the geometry of the specimen, the location of the neutral axis is shifted toward the bottom of specimen that contains the simulated leading edge. As a result, the highest magnitude stress actually occurs on the top of the specimen since it is farther from the neutral axis; however, the stresses on the top of the specimen are compressive which are not as damaging in fatigue as tension. Peak tensile stresses are located at the simulated 582 Appendix G 4.37 (111) 1.50 (38) Gage section 1.00 (25) A A 1.00 R. (25.0) 0.68 (17.3) 0.200 (5.1) 1.00 R. (25.0) Figure G.31. Overview of diamond cross-section tension (DCT) specimen. leading edge and the stress concentration associated with the FOD damage should ensure failures in the FOD location. Having gone down in complexity from full airfoils to laboratory specimens in four point bending, the last specimen type to discuss is a simple uniaxial specimen. This category of specimens is inclusive of all geometries where the application of a load along the major axis does not result in bending or equivalent stress gradients. For applicability to airfoil geometries, FOD testing has been performed on specimens with a diamond cross section as shown in Figure G.31. The use of this geometry is discussed in Chapter 7. NUMERICAL FOD SIMULATION This section describes the basic methodology that is required in order to develop a method for predicting the damage to a blade or vane from the impact of a foreign object. The examples used are based on work that has been carried out by the USAF. While the basic methodology for numerical simulation should remain the same, new tools and methods will inevitably be developed, as better technology, such as improved material models, becomes available. The flaws inherent in the selected examples are to be viewed by the reader as pitfalls that should be avoided and not as unchanging shortcomings of the analysis method. Researchers worldwide have studied numerous variables related to FOD impact dam- age and residual stress distribution [2, 6–10]. In order to model damage accurately, it Appendix G 583 is necessary to use an explicit finite element code or a particle-in-cell code that can capture the peculiarities of dynamic material behavior and response. All of the examples used in this appendix were computed using the explicit finite element (hydrocode) code MSC/DYTRAN [11], though there are several other codes that will also model dynamic impact behavior. Characteristic materials, airfoil leading edge geometries and impact conditions repre- senting gas turbine compressor blades were selected for this study. Titanium (Ti-6Al-4V) specimens with representative leading edge radii were impacted with steel balls at angles and velocities seen by typical compressor airfoils. A parametric analysis with varying impactor size, speed, angle, and specimen leading edge radii was conducted. Finite element models were generated using an eight-noded reduced integration-explicit Lagrangian brick element throughout the mesh for both the specimen and impacting ball. Tetrahedral and Penta elements were avoided in the mesh by utilization of an interface in the transition region that acts as a contact surface and is used to transfer loads across surfaces with dissimilar meshes. Because the reduced integration element has only one integration point at the centroid of the element, hourglass controls were used to eliminate zero energy modes or “hourglassing.” The density of the mesh was weighted towards the impact site to better catch the contact between the ball and the specimen and to better predict the stress field. Figure G.32 shows a representative finite element mesh for a sharp-edged specimen being impacted at 30  with a 0.079 in. (2 mm) diameter ball. Different specimen model meshes were utilized near the impact site for each diameter ball to keep the number of elements across the length in the impact region identical for each diameter ball. Ballistic events introduce high strain rates and titanium has been shown to be highly rate sensitive. Therefore, a strain-rate–dependent constitutive material model must be used for accurate analysis. Selected models should allow for the modeling of nonlinear material behavior with appropriate allowances for plasticity, material flow, and hardening. For ballistic impact simulation, appropriate strain rates can vary from 10 −4 sec −1 to 10 6 sec −1 . This creates attendant problems such as how can material properties at these strain rates be measured accurately. One shortcoming of most explicit finite element model is their material failure criteria. For example, DYTRAN allows material failure, but the failure routines are not sophis- ticated and cannot accurately model crack propagation or the generation of new free surfaces. The lack of surface creation features in this package means that caveats must be placed on predictions of failure. For the example in this document, a basic material failure model based on the von Mises yield function was selected for evaluation. This chosen material model allows for failure of the element by definition of an effective plastic strain at failure. Once the failure limit is reached, the element loses all its strength. The single effective plastic strain variable utilized does not distinguish between different modes, and once the limit is reached regardless if it is tension, compression, shear, or 584 Appendix G RCONN Interface Figure G.32. Representative mesh for sharp-edged specimen impact. mixed, it fails. The failure criterion does not have sufficient accuracy to model material dependent critical failure modes. The steel balls were modeled as linear elastic with a modulus of 29.6 Msi (204GPa) and a density of 0283 lb/in 3 7832 kg/m 3 . As with all finite element analyses, whether they are explicit or implicit, the density of the mesh plays a role in the stress predictions and a mesh refinement study was conducted. However, explicit codes are much more sensitive to this refinement. In implicit codes, it is necessary to converge the mesh based on the area the analyst is interested in. In explicit codes, it is necessary to have a totally converged mesh so that all areas of stress and displacement are modeled correctly. This is necessary due to the fact that stress waves pass through nearly every point on the component during an impact event and that problems with mesh refinement away from the point of interest may affect the traveling wave speed and magnitude. The specimen mesh refinement study was conducted with Appendix G 585 Out-of-plane view Out-of-plane view Out-of-plane view C C B A A Section A-A coarse Section B-B medium Section C-C fine Figure G.33. Mesh geometries used in mesh refinement study. the ball mesh density kept constant. Figure G.33 shows three successively finer meshes used in this analysis to determine the relative effect and efficiency of mesh refinement. In typical mesh refinement studies, the output of the finite element model, such as stress, is compared to the previous iteration of element size. When the output changes by a very small value, the mesh is deemed to be refined. Unfortunately, the prediction of damage size did not reach an asymptote with the mesh options shown in Figure G.33. Instead, the size of predicted damage grew, and then decreased, so that the medium mesh predicted the largest damage. The results of the refinement were then compared to actual damage. This is shown in Figure G.34. As can be seen from the analytical predictions, the medium mesh predicts the experi- mental results with the most accuracy. Both the coarse and fine meshes underpredict the depth and height for the test condition. Although the failure model is not very sophisti- cated, it predicts the general shape of failure remarkably well. The failure routine is based on a full element failure and partial element failure is not allowed; therefore, the mesh density (element size) will affect the failure predictions. A comparison of the smoothness of the predicted shapes with the abruptness of the corners seen in the experiment indicates that the deformation/failure model is not predicting the shearing deformation sufficiently accurately and that the deformation in the predicted shapes is not sufficiently local. It should be noted that penetration depth is relatively easy to predict, regardless of the material model used. It is suggested that predicted shape would be a better indicator of accuracy. . presence of adiabatic shear bands is an important indication that ballistic FOD simulation accurately represents the high rate deformation process seen during actual FOD. Adiabatic shear bands form. the scale of damage, were consistent for all specimens. The primary microstructural features due to impact damage were a compressed microstructural zone and the formation of adiabatic shear bands ball. Tetrahedral and Penta elements were avoided in the mesh by utilization of an interface in the transition region that acts as a contact surface and is used to transfer loads across surfaces with