 
ArticlesEmpirical Guidelines for FitnessforService Assessment of Wicket GatesAs seen in the September 2016 issue of Hydro Review (Volume 35, Issue 7). Download the PDF version.
INTRODUCTION A cascading wicket gate failure at one of its 1940sera plants prompted the Tennessee Valley Authority to develop fitnessforservice evaluation criteria, using as a basis technical studies at its 124MW Hiwassee facility. The Tennessee Valley Authority operates numerous hydroelectric facilities that utilize 1940sera wicket gates. Cascading wicket gate failures in Unit 1 of the 140.4MW Guntersville power station, which was constructed in 1935, and concerns raised after inspections of similar gates prompted TVA engineers to pursue comprehensive evaluations of similarvintage wicket gates. TVA chose to develop a risk ranking criteria for 1940sera wicket gates, based on the calculated stresses due to gate stem torque during shearpin activation versus the yield strength of gate material. These findings were compared to linear elastic finite element analyses (FEA) to help confirm ranking philosophy. Based on wicket gates evaluated throughout corresponding TVA facilities, Unit 2 at the 124MW Hiwassee facility was identified as posing the highest risk. Hiwassee, constructed in 1940, is located in Murphy, North Carolina, USA. The original Hiwassee powerhouse design consisted of a single conventional Francis turbine, with space in the powerhouse for an additional unit. In 1956, TVA installed Unit 2, a reversible Francis pumpturbine, which at the time was the world’s largest pumpturbine. It was also the first reversible pumpturbine in the country to use wicket gate control for both output and pumping. TVA worked with Quest Integrity in 2014 to perform destructive material testing on a similarvintage wicket gate, located at the Wilson plant also cast from ASTM  A27 steel. This provided accurate material properties values necessary for comprehensive ASME FitnessforService (FFS) evaluations on the Hiwassee Unit 2 wicket gate. The main objectives of this project were to provide TVA with a comprehensive condition assessment and remaining life estimate of the 1940sera wicket gate types, based on quantitative evidence and supported by a recognized engineering standard. A threedimensional geometry model of the Unit 2 wicket gate at Hiwassee was developed using SOLIDWORKS commercial CAD software and was based on the information found in the engineering and refurbishment drawings provided by TVA. A feature of particular interest was the stemtoleaf boundary region that had been subject to machining during a recent refurbishment. At the request of TVA, and in order to maintain conservatism, the stress relief radius at this location, specified only by a 0.06 inch maximum, was assumed to be zero. The solid geometry was discretized and meshed using Abaqus CAE preprocessing software. Discretizing the geometry into "elements” of finite size allows for numerical approximation of the mathematical model representing the physical response of the structure subjected to various loads and boundary conditions. The stem, stem sleeves, and majority of the leaf and end plates were represented using reduced integration hexahedral elements. The leafcollar and stemcollar boundary regions were modeled using quadratic tetrahedral elements. To accurately capture material response, the average characteristic element length was refined to 0.05 inches along the boundaries of interest. Figure 1 shows the finite element mesh refinement of the wicket gate stemtoleaf intersection. Refinement in this location of stress raisers (e.g. wicket gate stemcollar and leafcollar) is necessary to accurately capture stress and nonrecoverable strain results. Figure 1. Finite Element Mesh and Refinement Material testing was conducted to obtain specific properties (e.g. yield, tensile, fracture toughness, etc.) of the vintage A27 leaf and stem material. To accurately model the physical response of the Hiwassee wicket gate, finite element modeling was conducted using Simulia’s Abaqus FEA software. Multiple stress analyses were performed based on routine gate squeeze and safety element activation (shearpin breakage) conditions. Gate squeeze loading represents the daily operation and a shearpin event represents an upperlimit loading event. The frequency of gate squeeze events  730 events per year in this case  were based on operational records supplied by TVA. TVA requested the frequency of shearpin activation events model a oneinfiveyear occurrence. FITNESSFORSERVICE A FFS assessment is a multidisciplinary engineering approach to determine if a given structure is fit for continued service. The outcome of an FFS assessment supports decisions to operate as is, repair, retire or rerate. The FFS approach also provides a quantitative means for determining when and where to inspect. Comprehensive guidelines for FFS assessments are contained in the ASME FFS1 standard. Global Stability A limit load analysis addresses the failure mode of ductile rupture and detects the onset of gross plastic deformation (i.e., plastic collapse) of the structure. It provides a lower bound limiting load of the structure as the solution to a numerical model. The limit load is the load at which overall structural instability occurs. It is numerically identified as a point in the analysis where for a small increase in load, equilibrium (convergence) is no longer achieved. Stem loading was linearly ramped from gate squeeze loading until the onset of plastic collapse could be distinguished. The load factor is a multiple by which the normal operational loads have been increased in that analysis step. This analysis was conducted for each of the boundary conditions evaluated (i.e., once for the gate squeeze and once for the shearpin activation). Local Failure To ensure the wicket gate is protected against localized failure, elasticplastic analyses were conducted. Equivalent plastic strain (PEEQ) was monitored at peak locations as the stem loading was linearly ramped to the onset of plastic collapse. Values were compared to the limiting strain as outlined in the ASME FFS1 standard. The strain damage was quantified at each load factor as the strain limit damage ratio (SLDR). SLDR compares the local PEEQ to the limiting strain. Locations of peak PEEQ on the wicket gate were considered acceptable for the specified load factor if the SLDR was less than or equal to unity. Cyclic Fatigue – Ratcheting Cyclebycycle accumulation of equivalent plastic strain (ratcheting) is a mode of fatigue where cracklike flaws can initiate in a small number of load cycles. To ensure the wicket gate is protected against ratcheting, computationally intensive cyclebycycle elasticplastic analyses including kinematic material hardening were conducted. In the FEA model, each loading and unloading is represented by an analysis step. Crack Stability and Limiting Flaw Curves One of the first tasks of a damage tolerance analysis is estimating critical flaw sizes. The failure assessment diagram (FAD) method found in the ASME FFS1 standard describes the measure of acceptability of a component that contains a cracklike flaw. The FAD method considers both unstable (brittle) fracture and limit load (plastic overload). In a FFS assessment of a cracklike flaw, the results from stress analyses, stress intensity factor and limit load solutions, material strength, and fracture toughness are combined to compute a nondimensional toughness ratio and load ratio. The computed point, toughness ratio (vertical coordinate) and load ratio (horizontal coordinate), represents the cracklike flaw’s acceptability. If the point falls on or below the FAD curve, the component is considered safe for continued operation; outside of the curve, the component is considered unsafe for continued operation. Alternatively, a technique exists for evaluating a component that has not been identified as having a cracklike flaw. This technique is based on the FAD method and evaluates a number of potential cracklike flaw depthtolength aspect ratios. One way to represent this critical crack information is by plotting a limiting flaw curve based on methods found in the ASME FFS1. Combinations of flaw length and depth are determined that pose a risk for sudden failure due to brittle fracture or plastic collapse. Thus, these flaw dimensions represent points that fall exactly on the FAD. If the characteristic flaw dimensions (e.g., length and height) fall under the limiting flaw curve, then the flaw is considered acceptable; outside the limiting flaw curve, the flaw is unacceptable. The limiting flaw curve provides a means to evaluate many combinations of potential flaw sizes. FatigueDriven Crack Growth Once critical flaw sizes are determined, the next task in the damage tolerance approach is to grow a flaw to failure. The outcome of this analysis will provide an estimate of remaining life and govern how inspection intervals may be determined. Extensive empirical data has demonstrated that the rate of fatigue crack growth in metals can be characterized by the following expression: where:  a is a characteristic crack dimension (length or depth), The stress intensity factor, K, is a fracture mechanics parameter that characterizes the stresses near the tip of a crack. The cyclic stress intensity factor is defined as the difference between the maximum and minimum value of K in a given loading cycle. It is related to stress and crack size as follows: where:  Y is a geometry factor
that depends on the crack dimensions as well as the size and shape of the
component, and Life assessment can be performed by integrating Equation 1, and because constant amplitude loading (i.e., △õ does not vary from one cycle to the next) was assumed, the number of loading cycles required to grow the crack from an initial flaw size, a_{o}, to a final size, a_{f}, is given by: It should also be noted that Equation 1 includes a threshold, △K_{th}, below which the crack growth rate is zero. Consequently, some of the load cycles may not contribute to fatigue damage because △K is below the threshold. The threshold cyclic stress is given by: Inspection Interval After the life of the component has been estimated from the crack growth assessment, the final step in the damage tolerance approach is to determine inspection intervals. The fitnessforservice method is interlinked to nondestructive evaluation. The results from a nondestructive evaluation can be used as input for both the crack stability and crack growth analyses, the outcome of which can be used to define inspection intervals. Further, any flaws that might be detected during an inspection can be evaluated directly using the limiting flaw charts for acceptability and inspection intervals can be reevaluated to ensure that the measured flaw size will not grow to failure between inspections. Inspection methods (e.g., wet fluorescence A/C magnetic particle, longitudinal or phased array ultrasonics, etc.) based on industry best practice were recommended depending on location, access to inspection point and type of material to be inspected. RESULTS Stress Analysis Stress results for each load case, gate squeeze and safety element activation were verified against closed form calculations (e.g., shear stress in shaft crosssection due to torsion) to confirm correct application of loads and boundary conditions. The entire wicket gate was evaluated and "key” locations of interest were identified for further FFS evaluation (see Figure 2). Figure 2 indicates key areas of interest along the boundary of the upper journal and the leaf of the wicket gate (psi). Figure 2. Key Wicket Gate Locations of Interest (psi) Global Stability The applied moment and directional loads were increased until numerical convergence of the elasticplastic analysis was no longer achieved (see Figure 3). This figure shows a cutaway view of the wicket gate stemcollar and leafcollar locations and illustrates the wicket gate response during progressive gatesqueeze loading. The leftmost image represents normal operation; the middle image represents shearpin activation loading; and the rightmost image represents plasticcollapse. The color grey in false color stress contour (psi) indicates areas that have exceeded the von Mises yield criterion. Figure 3. Evolution of Plastic Collapse (psi) Local Failure For the current shearpin rating of 160 kips, the maximum expected wicket gate loading produces a SLDR of 0.281. Therefore, the local equivalent plastic strain is less than the limiting strain at every location and the wicket gate satisfies the criteria for protection against local failure. Cyclic Fatigue Six elasticplastic "cyclebycycle” gate squeeze load and unload cycles were modeled, representing about three days of operation. Eight elasticplastic "cyclebycycle” shearpin activation load and unload cycles were modeled, representing 40 years of occurrences. The area of peak plastic accumulation was consistently found to occur at the leafcollar boundary. Because the plastic strain continues to accumulate and does not elastically "shakedown,” in both cases the "no plastic action” criterion cannot be used to ensure protection from plastic ratcheting. These results are useful, however, in identifying the leafcollar region as a possible site of crack initiation. Von Mises stress was extracted over critical regions at the end of the "cyclebycycle” analyses of the gate squeeze and shearpin activation conditions (See Figure 4). The von Mises stress is an invariant stress that can be used as a yield criterion. It provides a means to compare multiaxial stress values found in components subjected to multiaxial loading (e.g. wicket gate) to yield strength values from uniaxial tensile specimens. These results were used to evaluate the amount of yielded to elastic material across the primary load bearing crosssection of the gate. Figure 4. Von Mises Stress (psi) at the end of
CyclebyCycle ratcheting; Figure 5 shows that even under the most extreme and expected condition of shearpin activation, the wicket gate maintains an elastic core across the primaryloadbearing cross section. Demonstration of an elastic core satisfies the protection against ratcheting due to cyclic loading criteria. Figure 5. Elastic Core of the PrimaryLoad Bear Cross Section of the Wicket Gate Crack stability and Limiting Flaw Curves Based on the stress analysis, the most likely scenario for the formation and propagation of a cracklike flaw would occur along the stemtocollar and leaftocollar boundaries. Upper bound primary through thickness stress profiles that occurred at the maximum stress location in both the stemtocollar and leaftocollar boundaries were used in the FFS assessment. The limiting flaw curves were calculated with the material parameters gathered from the material tests using Quest Integrity’s Signal™ FitnessforService software (see Figure 6). Figure 6. Limiting Flaw Curve for the StemCollar Region Crack dimensions that fall below the curves are considered subcritical, whereas those that fall outside of the curves are critical. Thus, these curves represent combinations of crack lengths and depths that could pose a significant risk of sudden failure. These curves were used to determine future inspection requirements and to evaluate the stability of any measured cracklike indications. Fatigue Driven Crack Growth One of the final steps in the damage tolerance approach is to estimate the remaining life of the component by growing a flaw to failure. A "growtofailure” analysis consists of growing an initial flaw size using the material properties determined from the material tests and constant amplitude cyclic stress until the flaw becomes unstable. The point of instability, or failure, is where the final crack dimensions are on or outside limiting flaw curve. Based on the results from the stress, crack stability and fatigue driven crack growth sensitivity analyses conducted, it was determined that horizontal cracklike flaws along the stem to collar boundary would represent the "limiting” case for the remaining life assessment (see Figure 7). Figure 7. Fatigue Driven Crack Growth for the Limiting Case CONCLUSION Based on the analyses, the following conclusions were established:
Based on these findings, TVA can likely meet the desired 30year interval between major disassembly before a required inspection of the wicket gates.
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