Patrick J. Golden

Measurement of the fatigue crack propagation threshold of fretting induced cracks in Ti–6Al–4V

Abstract A unique fatigue specimen was designed from the used fretting pads of Ti–6Al–4V fretting fatigue experiments. Many of these pads contained cracks that initiated and then arrested during the original fretting experiments. Heat tinting was used to mark the crack surface, and stress relief was applied to some specimens to remove load-history effects. The specimens were subjected to high cycle fatigue step testing and the threshold stresses were measured. The measured fretting crack sizes were used to calculate the crack propagation threshold, ΔKth. The results were analyzed for short crack and load history effects. Crack size effects were readily explained with a simple short crack model. No load history effects were noted for these fretting induced cracks.

Probabilistic Fretting Fatigue Assessment of Aircraft Engine Disks

Fretting fatigue is a random process that continues to be a major source of damage associated with the failure of aircraft gas turbine engine components. Fretting fatigue is dominated by the fatigue crack growth phase and is strongly dependent on the magnitude of the stress values in the contact region. These stress values often have the most influence on small cracks where traditional long-crack fracture mechanics may not apply. A number of random variables can be used to model the uncertainty associated with the fatigue crack growth process. However, these variables can often be reduced to a few primary random variables related to the size and location of the initial crack, variability associated with applied stress and crack growth life models, and uncertainty in the quality and frequency of nondeterministic inspections. In this paper, an approach is presented for estimating the risk reduction associated with the nondestructive inspection of aircraft engine components subjected to fretting fatigue. Contact stress values in the blade attachment region are estimated using a fine mesh finite element model coupled with a singular integral equation solver and combined with bulk stress values to obtain the total stress gradient at the edge of contact. This stress gradient is applied to the crack growth life prediction of a mode I fretting fatigue crack. A probabilistic model of the fretting process is formulated and calibrated using failure data from an existing engine fleet. The resulting calibrated model is used to quantify the influence of inspection on the probability of fracture of an actual military engine disk under real life loading conditions. The results can be applied to quantitative risk predictions of gas turbine engine components subjected to fretting fatigue.

Fretting Fatigue-Based Risk Assessment of Gas Turbine Engine Disks

This paper presents a probabilistic assessment to predict risk in terms of probability of failure of a typical gas turbine engine cold section disk subjected to real life loading conditions. This activity involves calculation of the stress field in the disk/blade interface using available contact mechanics models, estimation of fretting fatigue life, and probabilistic risk assessment using the DARWIN ® software. A finite element analysis (FEA) of the disk-blade assembly is carried out to obtain contact forces and moments along the interface. Contact stresses are calculated from the contact forces and moments using the numerical solution of the singular integral equation that characterizes the contact interface via CAPRI (Contact Analysis for Profiles of Random Indentors) software and the Worst Case Fret model. Using contact stresses and available fretting fatigue models, the fatigue life under fretting environments is determined. Initial fracture risk results suggest that scheduled depot inspections have the potential to significantly reduce the probability of fracture associated with fretting fatigue for the range of values considered under this study. Further investigation is required to assess the influences of additional factors such as residual stress values and dynamic load effects.

Probabilistic High-Cycle Fretting Fatigue Assessment of Gas Turbine Engine Components

High-cycle fatigue (HCF) is arguably one of the costliest sources of in-service damage in military aircraft engines. HCF of turbine blades and disks can pose a significant engine risk because fatigue failure can result from resonant vibratory stresses sustained over a relatively short time. A common approach to mitigate HCF risk is to avoid dangerous resonant vibration modes (first bending and torsion modes, etc.) and instabilities (flutter and rotating stall) in the operating range. However, it might be impossible to avoid all the resonance for all flight conditions. In this paper, a methodology is presented to assess the influences of HCF loading on the fracture risk of gas turbine engine components subjected to fretting fatigue. The methodology is based on an integration of a global finite element analysis of the disk-blade assembly, numerical solution of the singular integral equations using the CAPRI (Contact Analysis for Profiles of Random Indenters) and Worst Case Fret methods, and risk assessment using the DARWIN (Design Assessment of Reliability with Inspection) probabilistic fracture mechanics code. The methodology is

Optimal allocation of testing resources for statistical simulations

Statistical estimates from simulation involve uncertainty caused by the variability in the input random variables due to limited data. Allocating resources to obtain more experimental data of the input variables to better characterize their probability distributions can reduce the variance of statistical estimates. The methodology proposed determines the optimal number of additional experiments required to minimize the variance of the output moments given single or multiple constraints. The method uses multivariate t-distribution and Wishart distribution to generate realizations of the population mean and covariance of the input variables, respectively, given an amount of available data. This method handles independent and correlated random variables. A particle swarm method is used for the optimization. The optimal number of additional experiments per variable depends on the number and variance of the initial data, the influence of the variable in the output function and the cost of each additional experiment. The methodology is demonstrated using a fretting fatigue example.

Toward Developing a Probabilistic Methodology for Predicting High-Cycle Fretting Fatigue in Aero-Engines

This paper reports the results of an investigation focused on identifying the necessary steps required to develop a probabilistic fracture mechanics-based methodology for treating high-cycle fretting fatigue in military engine disks. The current methodology based on finite-element method (FEM) modeling, analytical contact stress analysis, and probabilistic fracture mechanics for analyzing low-cycle fretting fatigue is highlighted first. Incorporation of high-frequency vibratory stress cycles into a composite mission profile containing mostly low-cycle stresses requires the use of the Campbell diagram and the need to identify the mode shape, frequency, and forcing function for blade excitation induced by stator wake, flutter or rotating stall. Forced response computation methods for addressing these phenomena in the literature are reviewed to assess their applicability for integration with a contact stress analysis and a probabilistic fracture mechanics life-prediction code. This overview identifies (1) a promising path for combining vibratory stress computation, FEM structural modeling, contact stress analysis, and probabilistic fracture mechanics for treating high-cycle fretting fatigue at the attachment region of engine disks, and (2) a new approach for treating high-cycle fretting fatigue due to vibratory stresses separately from low-cycle fretting fatigue at various positions of a fan-speed profile.Copyright

Understanding Materials Uncertainty for Prognosis of Advanced Turbine Engine Materials

Abstract : Materials damage prognosis offers the opportunity to revolutionize life management of advanced materials and structures through a combination of improved state awareness, physically based predictive models of damage and failure, and autonomic reasoning. Historically, lifetime and reliability limits for advanced fracture-critical turbine engine materials have been based on expected worst-case total life under fatigue. Recent findings in a variety of advanced propulsion alloys indicate that the life-limiting mechanisms are typically dominated by the growth of damage that begins at the scale of key microstructural features. Such behavior provides new avenues for management and reduction of uncertainty in prognosis capability under conditions that depend on damage tolerance. To examine a range of sources of uncertainty in behavior and models of such behavior, this paper explores the following topics: (1) Duality in Fatigue, (2) Relaxation of Surface Residual Stresses in Laboratory Specimens, (3) Relaxation of Bulk Residual Stresses in Components, (4) Nonlinear Acoustic Parameter for the Detection of Precursor Fatigue Damage, (5) Elevated Temperature Fretting Fatigue, (6) Crack Growth under Spin Pit Environments, and (7) Crack Growth Under Variable Amplitude High Cycle Fatigue (HCF) Loading. Based on the findings, we outline avenues for further technology development, maturation, validation, and transition of mechanistically based models that have the potential to reduce predictive uncertainty for current and future materials.

Experimental resource allocation for statistical simulation of fretting fatigue problem

Abstract : Estimation of statistical moments from simulation, i.e., mean and standard deviation of an output, may involve large uncertainty caused by the variability in the input random variables. The allocation of resources to obtain more experimental data can reduce the variance of the output moments (mean and standard deviation). The methodology proposed and executed used an optimization method to determine the optimal number of additional experiments required to minimize the variance of the output moments given a constraint. A method to generate the output moments based on the moments of the input variables was implemented. The method used the multivariate t-distribution and the Wishart distribution to generate realizations of the population mean and population covariance of the input variables, respectively. This method was sufficient to handled independent and correlated variables. A fretting fatigue problem was explored to minimize the variance of cycles-to failure mean and standard deviation.

Temporal Life Prediction Analysis of a Turbine Engine Blade to Disk Attachment

Fretting fatigue is an important problem for the operation of turbine engines, since it is a significant driver of fatigue damage and failure risk of disks. It occurs when the blade and disk are pressed together in contact and experience a small oscillating relative displacement due to variations in engine speed and vibratory loading. Fretting causes a very high local stress near the edge of contact resulting in wear, nucleation of cracks, and their growth, which can result in significant reduction in the life of the material. It is dependent on geometry, loading conditions, residual stresses, and surface roughness, among other factors. These complexities are not just physically based, but also computationally challenging. Fretting fatigue has been investigated by many researchers, mostly considering static loading, which assumes dominant inertia forces and ignores the dynamic effects. A temporal computational hybrid technique was implemented successfully to investigate fretting fatigue of turbine engine blade and disk attachments. The present work extends its application to specifically investigate the effects of surface contact in an actual blade and disk assembly using a representative loading mission. The present effort focuses on modeling fretting fatigue under the dynamic loading using finite element method. The analyses were performed using temporal forcing function to simulate the blade’s aeroelastic loading. An accurate hybrid technique was implemented successfully to investigate fretting fatigue of turbine engine blade and disk attachments. This technique integrates a set of Singular-Integral-Equations and a micro-scale model to compute the dynamic local contact stresses. Finally, the results are compared with available experimental data of a simulated loading mission of a turbine engine to show the accuracy of the temporal approach. The computational stress results show good agreements with experimentally extracted strain gages data.

Probabilistic framework for prediction of material property distributions from small microstructural models

Abstract : A probabilistic framework for prediction of material property distributions from small scale (i.e. 2-grain) models is proposed. Monte Carlo Simulation and kernel density estimation are used to estimate the material property distribution of a grain boundary with a 2-grain model. Extreme value and order statistics are then employed to estimate the distribution of larger microstructure models. An example of the methodology is presented for identifying the applied uniaxial stress at which plastic slip initiates in a titanium alloy with a crystal elastic finite element model. The framework was verified by comparing the predicted plastic slip initiation strength distribution with the obtained distribution from Monte Carlo Simulation of larger scale finite element models (i.e. n-grain models, up to 600 grain RVE). The methodology performs well for larger microstructure models but less so for smaller ones, for a much smaller computational cost.