Simeon H. K. Fitch

A Probabilistically-Based Damage Tolerance Analysis Computer Program for Hard Alpha Anomalies in Titanium Rotors

A probabilistically-based damage tolerance analysis computer program for engine rotors has been developed under Federal Aviation Administration (FAA) funding to augment the traditional safe-life approach. The computer program, in its current form, is designed to quantify the risk of rotor failure due to fatigue cracks initiated at hard alpha anomalies in titanium. The software, DARWIN (Design Assessment of Reliability With Inspection), integrates a graphical user interface, finite element stress analysis results, fracture-mechanics-based life assessment for low-cycle fatigue, material anomaly data, probability of anomaly detection, and inspection schedules to determine the probability-of-fracture of a rotor disk as a function of operating cycles with and without inspections. The program also indicates the relative likelihood of failure of the disk regions. Work is underway to enhance the software to handle anomalies in cast/wrought and powder nickel disks, and manufacturing and maintenance-induced surface anomalies in all disk materials. *Funded under FAA Grant 95-G-04

Efficient Fracture Design for Complex Turbine Engine Components

Many high-energy turbine engine components are fracture critical. However, the complex three-dimensional (3D) geometries and stress fields associated with these components can make accurate fracture analysis impractical. This paper describes a new computational approach to efficient fracture design for complex turbine engine components. The approach employs a powerful 3D graphical user interface (GUI) for manipulation of geometry models and calculated component stresses to formulate simpler 2D fracture models. New weight function stress intensity factor solutions are derived to address stress gradients that vary in all directions on the fracture plane.

Probabilistic Surface Damage Tolerance Assessment of Aircraft Turbine Rotors

This paper describes some of the new surface damage capabilities in DARWIN™, a probabilistic fracture mechanics software code developed to evaluate the risk of fracture associated with aircraft jet engine titanium rotors/disks. An initial framework is presented in which a graphical user interface (GUI) is used to explicitly define the stresses and temperatures at the crack location for several crack geometries. A summary of the approach used to develop new stress intensity factor solutions for these geometries is also presented, including selected validation results.Copyright

A Microstructure-Based Time-Dependent Crack Growth Model for Life and Reliability Prediction of Turbopropulsion Systems

The objective of this investigation was to develop an innovative methodology for life and reliability prediction of hot-section components in advanced turbopropulsion systems. A set of generic microstructure-based time-dependent crack growth (TDCG) models was developed and used to assess the sources of material variability due to microstructure and material parameters such as grain size, activation energy, and crack growth threshold for TDCG. A comparison of model predictions and experimental data obtained in air and in vacuum suggests that oxidation is responsible for higher crack growth rates at high temperatures, low frequencies, and long dwell times, but oxidation can also induce higher crack growth thresholds (ΔKth or Kth) under certain conditions. Using the enhanced risk analysis tool and material constants calibrated to IN 718 data, the effect of TDCG on the risk of fracture in turboengine components was demonstrated for a generic rotor design and a realistic mission profile using the DARWIN® probabilistic life-prediction code. The results of this investigation confirmed that TDCG and cycle-dependent crack growth in IN 718 can be treated by a simple summation of the crack increments over a mission. For the temperatures considered, TDCG in IN 718 can be considered as a K-controlled or a diffusion-controlled oxidation-induced degradation process. This methodology provides a pathway for evaluating microstructural effects on multiple damage modes in hot-section components.

Integration of Manufacturing Process Simulation with Probabilistic Damage Tolerance Analysis of Aircraft Engine Components

Interfaces between manufacturing process simulation software (DEFORM) and probabilistic damage tolerance analysis software (DARWIN) have been developed for bulk residual stresses and average grain size. These interfaces permit full-field results from manufacturing process simulations to be incorporated in predictions of fracture life and reliability. Approaches were presented for modeling the effects of location-specific bulk residual stress and average grain size on crack growth behavior. The interface and the proposed approaches were implemented in prototype software and used to perform demonstration examples for an idealized engine disk. The exercise demonstrates the practical potential for Integrated Computational Materials Engineering (ICME) that directly addresses component integrity.

A Probabilistic Treatment of Expert Knowledge and Epistemic Uncertainty in NESSUS

The risk assessment in many engineering applications is hampered by a lack of hard data. Under these conditions the selection of probability density function (PDF) seems arbitrary. Quite often the data are not only sparse but also vague expert knowledge or conflicting. Several non-probabilistic methods have been proposed in the literature to perform a risk assessment under these conditions. We propose to use probabilistic techniques using uncertain PDFs. The uncertainty on the PDF is characterized by treating the parameters in the PDF as random variables. We expand the classical Bayesian updating scheme to make use of vague or imprecise interval data. Each expert is considered to be a sample from a parent distribution of experts. Consequently, a conflict between experts is accounted for through the likelihood function. The uncertain PDFs can be used in both simulation-based and MPP-based reliability methods. Because of the uncertainty on the PDF of the random variables, the risk or reliability index itself will be a random variable. Design decisions are made on the basis of the risk assessment and an incorrect risk assessment increases the total cost of the design. Since a cost can be associated with either an over or underestimation of the risk, an optimal reliability index can be determined, which minimizes this cost. The probabilistic framework we present in this paper establishes a direct link between the amount and quality of the available data and the optimal reliability estimate. This link allows the decision maker to weigh expected value of additional data collection efforts against the expected optimal reliability index improvement.

Methodology for Application of 3-D Stresses to Surface Damage-Based Risk Assessment

A methodology is presented for application of stress results from three dimensional finite element models for use in fracture mechanics computations. It is based on the assumption that a fatigue crack propagates in a plane normal to the maximum principal stress in a region that can be idealized as a rectangular plate. The methodology, recently implemented in the DARWIN ® probabilistic fracture mechanics program, is demonstrated for (1) a finite width plate with a centrally located hole and (2) an aircraft gas turbine engine rotor disk. Computational error associated with the methodology is less than 1% compared to analytical and finite element solutions. The results can be applied to the probabilistic life prediction of components subjected to surface damage.

A Tool for Probabilistic Damage Tolerance of Hole Features in Turbine Engine Rotors

Over the past two decades, the Federal Aviation Administration (FAA) and the aircraft engine industry (organized through the Rotor Integrity Sub-Committee (RISC) of the Aerospace Industries Association) have been developing enhanced life management methods to address the rare but significant threats posed by undetected material or manufacturing anomalies in high-energy rotating components of gas turbine engines. This collaborative effort has led to the release of several FAA advisory circulars providing guidance for the use of probabilistic damage tolerance methods as a supplement to traditional safe-life methods. The most recent such document is Advisory Circular (AC) 33.70-2 on “Damage Tolerance of Hole Features in High-Energy Turbine Rotors.” In parallel with this effort, the FAA has also been funding research and development activities to develop the technology and tools necessary to implement the new methods, including a series of grants led by Southwest Research Institute® (SwRI®). The most significant outcome of these grants is a probabilistic damage tolerance computer code called DARWIN® (Design Assessment of Reliability With INspection). DARWIN integrates finite element models and stress analysis results, fracture mechanics models, material anomaly data, probability of crack detection, and uncertain inspection schedules with a user-friendly graphical user interface (GUI) to determine the probability of fracture of a rotor disk as a function of operating cycles with and without inspection. This paper provides an overview of new DARWIN models and features that directly support implementation of the new AC on hole features. The paper also simultaneously provides an overview of the AC methodology itself. Component geometry and stresses are addressed through an interface with commercial three-dimensional finite element (FE) models, including management of multiple load steps and multiple missions. Calculations of fatigue crack growth (FCG) life employ a unique interface with the FE models, sophisticated new stress intensity factor solutions for typical crack geometries at holes, shakedown modules, a menu of common FCG equations, and algorithms to address the effects of varying temperatures on crack growth rates. The primary random variables are based on the default anomaly distributions and probability-of-detection (POD) curves provided directly in the AC. Fracture risk is computed on a per-feature basis using one of several available computational methods including importance sampling, response surface, and Monte Carlo simulation. The approach is illustrated for risk prediction of a representative gas turbine engine disk. The results can be used to gain a better understanding of the AC and how the problem is solved using the probabilistic damage tolerance framework provided in DARWIN.Copyright

Uncertainty Modeling to Relate Component Assembly Uncertainties to Physics-Based Model Parameters

Using physics-based models to predict the performance of engineered systems is becoming routine and is increasingly relied upon as a means to predict reliability when testing is prohibitive. To predict reliability, uncertainties in the system parameters must be modeled and propagated through the performance model using an appropriate probabilistic method. Uncertainties in engineered systems exist in loadings, environment, material strength, geometry, and manufacturing/assembly conditions. In many cases, these uncertainties are not direct physics-based model parameters. For example, the variations in the torque of a nut during assembly may be modeled as an initial penetration between two parts of the finite element model. Therefore, intermediate relationships between the physical uncertainties to the physics-based model are required. To account for these variations in the finite element model then requires a change to multiple nodal coordinates. Because of the significant time required to make these changes, a practical approach is required to model the geometry changes in complex finite element models. New capabilities in the NESSUS probabilistic analysis software for creating and applying shape vectors to geometry changes have been developed and implemented and are described in the paper. The probability density functions used to model the uncertainties in these parameters are ideally developed using experimental data or expert judgment. This paper describes several uncertainty modeling approaches for an actual probabilistic analysis using a non-linear transient finite element model in excess of 1 million elements. Examples of combining computational models, analytical equations, and experimental results are presented to relate computational model inputs in terms of measurable random variables.