Harry R. Millwater

Advanced probabilistic structural analysis method for implicit performance functions

In probabilistic structural analysis, the performance or response functions usually are implicitly defined and must be solved by numerical analysis methods such as finite-elemen t methods. In such cases, the commonly used probabilistic analysis tool is the mean-based second-moment method, which provides only the first two statistical moments. This paper presents an advanced mean-based method, which is capable of establishing the full probability distributions to provide additional information for reliability design. The method requires slightly more computations than the mean-based second-moment method but is highly efficient relative to the other alternative methods. Several examples are presented to demonstrate the method. In particular, the examples show that the new mean-based method can be used to solve problems involving nonmonotonic functions that result in truncated distributions.

Probabilistic methods for Design Assessment of Reliability with Inspection (DARWIN)

Conventional rotor life prediction methodologies are based on nominal conditions that do not account for material and manufacturing anomalies that can degrade the structural integrity of high energy rotors. In order to account for these anomalies, an industry committee recommended adoption of a probabilistic damage tolerance approach to supplement the current safe life methodology. The DARWIN computer program computes the probability-of-fracture as a function of flight cycles, considering random defect occurrence and location, random inspection schedules, and several other random variables. This study focuses on the probabilistic fatigue analysis methodology developed and implemented in DARWIN Version 3.2. The computational efficiency and accuracy of this computer program is illustrated for several realistic rotor models provided by aircraft engine manufacturers. It is shown that the life approximation function (LAF) and importance sampling (IS) methods significantly reduce computation time (nearly two orders of magnitude) compared to the Monte Carlo method.

Probabilistic Methods for Design Assessment of Reliability with Inspection

Conventional gas turbine rotor life prediction methodologies are based on nominal conditions that do not adequately account for material and manufacturing anomalies that can degrade the structural integrity of high-energy rotors. To account for these anomalies, the Rotor Integrity Subcommittee of the Aerospace Industries Association recommended adoption of a probabilistic damage tolerance approach to supplement the current safe-life methodology. The recommendation led to the development of a computer program called DARWIN that computes the probability of fracture as a function of flight cycles, considering random defect occurrence and location, random inspection schedules, and several other random variables. The probabilistic fatigue analysis methodology developed for DARWIN to address hard alpha material anomalies is presented. The capability of this computer program is demonstrated using several realistic rotor models provided by aircraft engine manufacturers. It is shown that the life approximation function and importance sampling methods significantly reduce computation time (nearly two orders of magnitude) compared to the Monte Carlo method. In addition, an optimal zone sampling strategy is presented that can minimize the total number of samples required to achieve e a a desired sampling accuracy result for a given confidence interval. This probabilistic methodology can be used to focus design efforts on variables that have the most influence on risk reduction.

A New Tool for Design and Certification of Aircraft Turbine Rotors

This paper summarizes recent enhancements to a probabilistic damage tolerance software code, DARWIN that can be used for design certification of aircraft jet engine titanium disks/rotors that may contain melt-related anomalies. Evaluations of DARWIN by engine manufacturers are also discussed, including comparisons with existing codes for accuracy and time efficiency In addition, relevant test results, including various fatigue tests on material containing melt-related anomalies, are summarized.

Probabilistic analysis of preload in the abutment screw of a dental implant complex

STATEMENT OF PROBLEM Screw loosening is a problem for a percentage of implants. A probabilistic analysis to determine the cumulative probability distribution of the preload, the probability of obtaining an optimal preload, and the probabilistic sensitivities identifying important variables is lacking. PURPOSE The purpose of this study was to examine the inherent variability of material properties, surface interactions, and applied torque in an implant system to determine the probability of obtaining desired preload values and to identify the significant variables that affect the preload. MATERIAL AND METHODS Using software programs, an abutment screw was subjected to a tightening torque and the preload was determined from finite element (FE) analysis. The FE model was integrated with probabilistic analysis software. Two probabilistic analysis methods (advanced mean value and Monte Carlo sampling) were applied to determine the cumulative distribution function (CDF) of preload. The coefficient of friction, elastic moduli, Poissons ratios, and applied torque were modeled as random variables and defined by probability distributions. Separate probability distributions were determined for the coefficient of friction in well-lubricated and dry environments. The probabilistic analyses were performed and the cumulative distribution of preload was determined for each environment. RESULTS A distinct difference was seen between the preload probability distributions generated in a dry environment (normal distribution, mean (SD): 347 (61.9) N) compared to a well-lubricated environment (normal distribution, mean (SD): 616 (92.2) N). The probability of obtaining a preload value within the target range was approximately 54% for the well-lubricated environment and only 0.02% for the dry environment. The preload is predominately affected by the applied torque and coefficient of friction between the screw threads and implant bore at lower and middle values of the preload CDF, and by the applied torque and the elastic modulus of the abutment screw at high values of the preload CDF. CONCLUSIONS Lubrication at the threaded surfaces between the abutment screw and implant bore affects the preload developed in the implant complex. For the well-lubricated surfaces, only approximately 50% of implants will have preload values within the generally accepted range. This probability can be improved by applying a higher torque than normally recommended or a more closely controlled torque than typically achieved. It is also suggested that materials with higher elastic moduli be used in the manufacture of the abutment screw to achieve a higher preload.

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

Application of Probabilistic Fracture Mechanics to Prognosis of Aircraft Engine Components

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.

Development of a localized probabilistic sensitivity method to determine random variable regional importance

Abstract There are many methods to identify the important variable out of a set of random variables, i.e., “inter-variable” importance; however, to date there are no comparable methods to identify the “region” of importance within a random variable, i.e., “intra-variable” importance. Knowledge of the critical region of an input random variable (tail, near-tail, and central region) can provide valuable information towards characterizing, understanding, and improving a model through additional modeling or testing. As a result, an intra-variable probabilistic sensitivity method was developed and demonstrated for independent random variables that computes the partial derivative of a probabilistic response with respect to a localized perturbation in the CDF values of each random variable. These sensitivities are then normalized in absolute value with respect to the largest sensitivity within a distribution to indicate the region of importance. The methodology is implemented using the Score Function kernel-based method such that existing samples can be used to compute sensitivities for negligible cost. Numerical examples demonstrate the accuracy of the method through comparisons with finite difference and numerical integration quadrature estimates.

A Software Framework for Probabilistic Fatigue Life Assessment of Gas Turbine Engine Rotors

An enhanced life management process based on probabilistic damage tolerance methods has been developed to address material anomalies in titanium rotating components of gas turbine engines. Related methods are being used as tools to investigate the impact of engine monitoring and usage variability on prognosis for field readiness and life management. This paper begins with an overview of the process of probabilistic damage tolerant design, using the DARWIN® computer program to illustrate the interplay between various random variables and the conventional elements of structural design and life prediction. Special attention is then given to the initial distribution of material anomalies, scatter in fatigue crack growth data, and variability in complex mission histories. The significance of each source of variability for different applications is discussed.

Probabilistic failure analysis of bone using a finite element model of mineral-collagen composites

Microdamage accumulation is a major pathway for energy dissipation during the post-yield deformation of bone. In this study, a two-dimensional probabilistic finite element model of a mineral-collagen composite was developed to investigate the influence of the tissue and ultrastructural properties of bone on the evolution of microdamage from an initial defect in tension. The probabilistic failure analyses indicated that the microdamage progression would be along the plane of the initial defect when the debonding at mineral-collagen interfaces was either absent or limited in the vicinity of the defect. In this case, the formation of a linear microcrack would be facilitated. However, the microdamage progression would be scattered away from the initial defect plane if interfacial debonding takes place at a large scale. This would suggest the possible formation of diffuse damage. In addition to interfacial debonding, the sensitivity analyses indicated that the microdamage progression was also dependent on the other material and ultrastructural properties of bone. The intensity of stress concentration accompanied with microdamage progression was more sensitive to the elastic modulus of the mineral phase and the nonlinearity of the collagen phase, whereas the scattering of failure location was largely dependent on the mineral to collagen ratio and the nonlinearity of the collagen phase. The findings of this study may help understanding the post-yield behavior of bone at the ultrastructural level and shed light on the underlying mechanism of bone fractures.