HOTPITS is a set of physics-based software tools for treating the degradation processes in Type II hot corrosion, including the initiation, growth, and coalescence of multiple pits, and the transition of pits to fatigue cracks. The HOTPITS methodology has been implemented in DARWIN (R) to provide a probabilistic capability for assessing the risk of hot corrosion-induced fracture in gas turbine components. To illustrate model capabilities, two benchmark computations were performed to simulate the initiation, growth, and coalescence of multiple pits, and their transition to a dominant Mode I crack and to assess the risk of hot corrosion-induced fracture.

HOTPITS is a set of physics-based modeling tools for treating Type II hot corrosion in Ni-based superalloys. The methodology includes modeling the nucleation, growth, and coalescence of pits and microcracks as a random process, as well as the transition of pits to micrcracks and the propagation of the resulting large crack to failure. In this investigation, critical experiments were performed on coupon and low-cycle fatigue (LCF) specimens in order to validate the hot corrosion and the fatigue models in HOTPITS. The pit nucleation, growth, and coalescence models in HOTPITS including the assumption of a random process are validated by the hot corrosion critical experiments performed at two salt contents. The LCF critical experiments, performed using a marker band protocol, validated the stress concentration factor-based models used to predict the pit-to-crack transition in the HOTPITS tool.

A physics-based hot corrosion life-prediction methodology has been developed to treat pit-induced fatigue crack growth in engine disks. This framework has been developed on the basis that hot corrosion commences with the deposition of alkali sulfates on the metal surfaces. The attack by molten sulfates leads to the dissolution of protective oxide and the formation and growth of hot corrosion pits on the metal surface, followed by fatigue crack nucleation at corrosion pits and the propagation of a fatigue crack to final fracture. This hot corrosion-induced time-dependent fatigue crack growth model has been implemented into a probabilistic life-prediction code called DARWIN (R)*. Application of this life-prediction methodology to treat hot corrosion in a generic engine disk is demonstrated via benchmark calculations.

The fatigue life of fracture-critical metal alloys can be strongly influenced by material anomalies that may appear during the manufacturing process. For materials that have more than one type of anomaly, the probability of fracture is dependent on the size, orientation, and occurrence frequency associated with each anomaly type (among other factors). If the crack formation and growth lives associated with each anomaly type are known, the component probability of fracture can be assessed using established system reliability methods. However, these lives are often difficult to obtain in practice for multiple-anomaly materials. In this paper, a probabilistic approach for estimating the marginal densities of fatigue lives for materials with multiple types of anomalies is presented that is based on the method of Kaplan-Meier combined with a data-smoothing technique recommended by Meeker and Escobar. The approach is illustrated for risk prediction of a nickel-based superalloy containing multiple types of anomalies.

Probabilistic design computer programs are usually tailored to a specific mechanics problem and do not involve general-purpose finite element analysis due to efficiency and simplicity concerns. However, as these design codes become more widespread, the capability to extend the applicability of the design code by considering additional finite element-based random variables become more desirable and important. This research describes a methodology such that additional finite element-based random variables can be considered without modifying the design code software, that is, the methodology is ''non-intrusive'' and existing software can be extended without access to the source code. Probabilistic sensitivity measures have been developed for both the original and additional random variables such that the significance of the random variables can be determined. Efficiency issues are addressed through the construction and subsequent verification using response surface methods. The methodology is general in that it can be applied to any probabilistic design code and any finite element model as long as the original and additional random variables are independent-there can be correlation within a group. The methodology is demonstrated using a probabilistic fatigue application whereby a probabilistic design code is integrated in an automated fashion with a commercial finite element program.

A new methodology has been developed for automated fatigue crack growth (FCG) life analysis of components based on finite element (FE) stress models, weight function stress intensity factor (SIF) solutions, and algorithms to define idealized fracture geometry models. The idealized fracture geometry models are rectangular cross-sections with dimensions and orientation appropriate to an irregularly shaped component cross-section with arbitrary stress gradients on the crack plane. The fracture model geometry algorithms are robust enough to accommodate crack origins on the surface or in the interior of the component, as well as finite component dimensions, arbitrarily curved component surfaces, arbitrary stress gradients, and crack geometry transitions as the crack grows. Stress gradients are automatically extracted from multiple load steps in the FE models for input to the fracture models. The SIF solutions accommodate univariant and bivariant stress gradients and have been optimized for both computational efficiency and accuracy. The resulting calculations can be used to automatically construct FCG life contours for the component and to identify hot spots. Ultimately, the new algorithms will be used to support automated probabilistic assessments that calculate component reliability considering variability in the initial crack size, initial crack location, crack occurrence rate, applied stress magnitudes, material properties, inspection efficacy, and inspection time.

Two contrasting methods are traditionally available to analyze fatigue crack growth (FCG) lifetime in components. On the one hand, engineering software such as NASGRO and AFGROW provides pre-programmed stress intensity factor (SIF) solutions for simplified crack and component geometries, sophisticated crack growth equations including load interaction models, and relatively fast execution times—often only a few seconds. However, the SIF solutions in these codes are often for simple uniform or linear stress distributions, and the user is left with the task of interpreting how best to (manually) transfer dimensions and stresses from component models into the simplified fracture models.

On-board sensors that can detect and size a crack in a structural component are being developed and will be deployed to enhance structural health monitoring and prognosis. This research examines the simulation of recurring automated inspections resulting from simulated on-board 'crack' sensors, and their potential effect on reducing the probability-of-fracture of structural components. The concept of a probability-of-detection (POD) curve is used to characterize the performance of the sensor, as done for traditional inspections. However, we assert that, unlike the simulation of traditional infrequent inspections, recurring inspections for an automated system should be modeled as dependent with respect to the first inspection due to the largely repeatable aspects of the sensor and data collection system. This assertion has a large effect on the computed probability of detecting a crack and alleviates the substantial over prediction of sensor efficacy generated using the assumption of independent inspections for automated systems. Furthermore, it is demonstrated that the fundamental feature that determines the efficacy of a recurring automated on-board sensor is the probability of detecting a crack of critical size, i.e., the size that will cause fracture, and this feature is by and large separate from the shape of the POD curve. This information can be used to determine the required accuracy of an on-board automated inspection to achieve a specified reliability of a structural component. The methodology is demonstrated using fatigue and fracture of a representative titanium compressor disk from a gas turbine aircraft engine but is applicable to any structural system with recurring automated inspections.

The fracture risk of aircraft engine components is sensitive to small changes in the applied stress history. Although standard missions have been developed for design of military aircraft, stress values based on data obtained from flight data recorders can differ significantly from the design values. In this paper, a comprehensive framework is presented for probabilistic treatment of aircraft engine usage that consists of the following four stages: (1) data retrieval, (2) mission identification, (3) stress characterization, and (4) risk prediction. An example is presented that illustrates the approach for a number of actual flight histories. The framework can be applied to quantitative risk predictions of gas turbine engine components for enhanced life management, including potential life extension and associated cost savings.

Fatigue life prediction of aircraft gas turbine engine rotating components requires estimates of the applied stress values throughout the life of the component. These values may vary considerably from flight-to-flight, and are highly dependent upon the mission type. However, engine flight data recorders currently do not have the capability to identify the mission type, so an automated mission identification method would greatly improve remaining life predictions. In this paper, a method is presented for predicting the most likely mission type for a given flight history. It is based on volume integration of the joint probability densities that are common to both the flight history and a standard mission. An analytical framework is presented, including a brief description of the adaptive kernel method used to estimate the probability densities of the flight history and standard mission. The effectiveness of the method is illustrated using rainflow stress data associated with actual flight histories. The results can be used to improve fatigue and fracture risk predictions of military gas turbine engines.

The empirical models commonly used for probabilistic life prediction do not provide adequate treatment of the physical parameters that characterize fatigue damage development. For these models, probabilistic treatment is limited to statistical analysis of strain-life regression fit parameters. In this paper, a model is proposed for life prediction that is based on separate nucleation and growth phases of total fatigue life. The model was calibrated using existing smooth specimen strain-life data, and it has been validated for other geometries. Crack nucleation scatter is estimated based on the variability associated with smooth specimen and fatigue crack growth data, including the influences of correlation among crack nucleation and growth phases. The influences of crack nucleation and growth variability on life and probability of fracture are illustrated for a representative gas turbine engine disk geometry.

On-board sensors that can detect and size a crack in a structural component are being developed and will be deployed to enhance structural health monitoring and prognosis. This research examines the simulation of recurring automated inspections resulting from simulated on-board “crack” sensors, and their potential effect on reducing the probability-of-fracture of structural components. The concept of a probability of detection (POD) curve is used to characterize the performance of the sensor, as done for traditional inspections. However, we assert that recurring inspections for an automated system should be modeled as dependent with respect to the first inspection due to the largely repeatable aspects of the sensor and data collection system. This assertion has a large effect on the computed probability of detecting a crack and alleviates the substantial over prediction of sensor efficacy generated using the assumption of independent inspections for automated systems. Furthermore, it is demonstrated that the fundamental feature that determines the efficacy of a recurring automated on-board sensor is the probability of detecting a crack of critical size, i.e., the size that will cause fracture, and this feature is by and large separate from the shape of the POD curve. This information can be

Simulation-based system reliability prediction may require significant computations, particularly when the expected value of the system failure probability is relatively low. A methodology is presented for variance reduction of sampling-based series system reliability predictions based on optimal allocation of Monte Carlo samples to the individual failure modes. An algorithm is presented for adaptively allocating samples to member failure modes based on initial estimates of the member failure probabilities pi. The methodology is demonstrated for a simple series system and a gas-turbine engine disk modeled using a zone-based series system approach. For the example considered, it is shown that the computational accuracy of the method does not appear to depend on the initial pi estimate. However, the computational efficiency is highly dependent on the initial pi estimate. The results can be applied to improve the efficiency of sampling-based series system reliability predictions.

Titanium gas-turbine engine components may contain anomalies that are not representative of nominal conditions. If undetected, they can lead to uncontained failure of the engine and associated loss of life. A probabilistic framework has been developed to predict the risk of fracture associated with titanium rotors and disks containing rare material anomalies. A recent Federal Aviation Administration Advisory Circular also provides guidance for the design of these components. However, some materials may exhibit relatively higher anomaly occurrence rates compared to those found in titanium alloys. In addition, the crack formation life for these materials may be nonnegligible and must be considered in the risk computation. When these materials are used, a single disk could contain a number of anomalies with unequal crack formation periods, and so the existing probabilistic framework is no longer valid. A methodology is presented for probabilistic life prediction of components with relatively large numbers of material anomalies. It is an extension of the probabilistic framework originally developed for titanium materials with hard alpha anomalies. The methodology is presented and illustrated for an aircraft gas-turbine engine disk. The results can be applied to fracture-mechanics-based probabilistic life prediction of alloys with large numbers of material anomalies..

The risk of fracture associated with high energy rotating components in aircraft gas turbine engines can be sensitive to small changes in applied stress values which are often difficult to measure and predict. Although a parametric approach is often used to characterize random variables, it is difficult to apply to multimodal densities. Nonparametric methods provide a direct fit to the data, and can be used to estimate the multimodal densities often associated with rainflow stress data. In this paper, a comparison of parametric and nonparametric methods is presented for density estimation of rainflow stress profiles associated with military aircraft gas turbine engine usages. A nonparametric adaptive kernel density estimator algorithm is illustrated for standard parametric probability density functions and for rainflow stress pairs associated with F-16/F100 engine usages. The kernel estimates are compared to parametric estimates, including a hybrid approach based on separate treatment of maximum stress pairs. The results provide some insight regarding the strengths and weaknesses of parametric and nonparametric density estimation methods for gas turbine engines, and can be used to develop improved stress estimates for probabilistic life predictions.

It is generally accepted that traditional logistics functions including periodic nondestructive inspections and planned maintenance increase the reliability and readiness of turbine engines. Nevertheless, further significant enhancements in reliability and readiness are believed to be possible through the implementation of a prognosis system based on online monitoring and interpretation of critical engine operating parameters and conditions to diagnose potential problems and forecast readiness. An approach is presented for improving probabilistic life prediction estimates through the application of prognosis methods. Actual F-16/F100 usage data from flight data recorders were interfaced with a probabilistic life prediction code to quantify the influence of usage on the probability of fracture of an idealized titanium compressor disk. For the example cases considered, it is shown that usage variability leads to about 6 × × variability in life and from 10 × × to 100 × variability in the probability of fracture. The results suggest that variability in usage could provide a basis for selectively extending the life of aircraft engines.

This paper summarizes the development of a probabilistic micromechanical code for treating fatigue life variability resulting from material variations. Dubbed MICROFAVA (micromechanical fatigue variability), the code is based on a set of physics-based fatigue models that predict fatigue crack initiation life, fatigue crack growth life, fatigue limit, fatigue crack growth threshold, crack size at initiation, and fracture toughness. Using microstructure information as material input, the code is capable of predicting the average behavior and the confidence limits of the crack initiation and crack growth lives of structural alloys under LCF or HCF loading. This paper presents a summary of the development of the code and highlights applications of the model to predicting the effects of microstructure on the fatigue crack growth response and life variability of the α+β Ti-alloy Ti-6Al-4V.

Material anomalies are occasionally introduced in the commercial grade alloys used in aircraft gas turbine engine rotating components. If undetected during manufacturing or subsequent field inspection, the anomalies can lead to uncontained engine failures. Over the past several years, a probabilistic framework has been developed to predict the risk of fracture associated with rotors and disks in commercial aircraft en- gines. The framework was originally developed for titanium materials, where inherent anomalies may be pre- sent in the form of brittle alpha phase particles that are assumed to form growing cracks during the first cycle of applied load. Since the anomaly occurrence rate associated with titanium is extremely small, component failure probability can be approximated as the sum of the failure probabilities of subregions (zones) of ap- proximately equal risk. In contrast, some gas turbine materials may exhibit a larger number of anomalies that are either introduced during component manufacturing or are inherently associated with material processing. When these materials are used, a single disk could contain a number of anomalies with unequal crack forma- tion periods, so the existing probabilistic framework is no longer valid. In this paper, a probabilistic fracture mechanics methodology is presented for risk assessment of components with relatively large numbers of ma- terial anomalies. It centers on the zone-based probabilistic framework originally developed for titanium mate- rials with hard alpha anomalies, and is extended for application to other alloys. The methodology is presented and illustrated for an aircraft gas turbine engine disk. The results can be applied to fracture-mechanics-based probabilistic life prediction of alloys with large numbers of material anomalies.

Most of the existing crack growth models rely on empirical constants derived from curve fits of data at specific test conditions. Although statistical information can be obtained for many of these constants, multiple experimental tests typically must be performed to represent the wide range of the response. In this paper, an alternative approach is presented that links fatigue crack growth parameters to material and microstructural size parameters via a microstructure-based fatigue crack growth (FCG) model. In addition, variation of initial crack size due to microstructural variation is modeled in terms of a crack-size-based fatigue crack initiation model. Variations of microstructural parameters are described in terms of a probabilistic framework. The probabilistic, microstructure-based, FCG approach is illustrated for a Ni-based superalloy in which the influence of changes in the main descriptors of the individual microstructural parameters on initial crack size, crack growth rate, and fatigue life is shown. Stochastic model results are compared with existing experimental data to illustrate the feasibility of the approach for predicting da/dN variability due to microstructure variations.

The presence of rare metallurgical or manufacturing anomalies in aircraft turbine rotors/disks may contribute to uncontained engine failures. A probabilistic methodology has been developed to quantify the risk of fracture and the influence of periodic inspection on overall risk, supplementing the current safe life approach. This paper summarizes the methodology and computational implementation, including a brief description of a new method for defining surface damage-related crack growth using 3D finite element results. The results can be applied to risk assessment of aerospace structures where uncertainties associated with fatigue crack growth must be quantitatively addressed.