Conventional probability of detection (POD) curve development is an expensive process that may not adequately capture local parameters that can influence POD outcomes. Non-destructive evaluation (NDE) simulation has the capability to consider these parameters but requires information regarding the anomaly sizes that must be found. Probabilistic damage tolerance (PDT) can be used to quantify anomaly sizes that are associated with failure at specific locations throughout a component. In this paper, a methodology is presented for integrating NDE simulation (via the CIVA software) with PDT analysis of turbine engine components (via the DARWIN (R) software). High risk locations are identified using PDT analysis. Anomaly sizes and orientations that lead to failure are identified for the NDE simulation. The resulting POD curves are applied to PDT assessments to quantify the influence of NDE on fracture risk enabling the analyst to identify the locations in a component that may benefit most from NDE inspection. The methodology is illustrated for a representative gas turbine engine component.

Dans l’approche par tolérance aux dommages utilisée notamment en aéronautique, il est essentiel de démontrer la fiabilité des inspections END pour la détection de potentiels défauts structurels, particulièrement dans le cas de pièces obtenues par fabrication additive car ce procédé introduit d’avantages d’anomalies. Les courbes de Probabilité de Détection (POD), qui relient la probabilité de détecter un défaut à sa taille, constituent un indicateur clé en évaluant une taille maximale de défaut que le procédé END peut manquer à un certain niveau de probabilité et avec un certain taux de confiance. Cette information est utilisée, conjointement à d’autres données telles que la géométrie de la pièce, les propriétés mécaniques, les contraintes ou encore les cinétiques d’évolution des défauts, pour adapter la stratégie de maintenance et de contrôle de la pièce afin d’optimiser la sureté et sa durée de vie en service. La fiabilité d’un END et l’évaluation du risque sont basées sur des indicateurs statistiques qui nécessitent un volume de données important si l’on veut que ces indicateurs soient fiables. Ainsi, il est difficile d’obtenir un bon niveau de confiance sur la base d’une approche purement basée sur des essais expérimentaux compte-tenu du volume de maquettes et des coûts engendrés. Les outils de simulation peuvent atteindre cet objectif s’ils ont la capacité de prendre en compte et piloter précisément les paramètres pertinents et grâce aux capacités de calcul intensif maintenant disponibles. Le travail présenté dans cet article met en oeuvre des cosimulations réalisées entre les logiciels DARWIN®, en modélisation probabiliste de la tolérance au dommage, et CIVA, en modélisation END. DARWIN calcule des niveaux de risque de rupture par zone dans une pièce donnée, quand CIVA permet d’obtenir des courbes de probabilité de détection pour différentes méthodes END. L’application présentée illustre le cas d’une pièce de rotor en titane impliquant un contrôle par ultrasons. Il apparait très pertinent de relier la simulation des END et celle de la mécanique de la rupture, deux disciplines assez compartimentées par ailleurs. En effet, DARWIN permet de connaitre les défauts et les tailles critiques associées qui sont les données d’entrées essentielles pour développer une méthode d’inspection pertinente. CIVA permet d’obtenir des courbes POD permettant ensuite à DARWIN de quantifier le niveau de réduction de risque apporté par cet END. Cela souligne l’importance des END pour la sureté de fonctionnement et permet d’adapter la sensibilité du procédé d’inspection afin de trouver le meilleur compromis entre la performance nécessaire et les coûts

In the context of the damage tolerance approach used to drive aircraft maintenance operations, it is essential to demonstrate the reliability of NDE inspections in detecting structural damage especially for additively manufactured components since this process produces components that may introduce material anomalies at any location within a component. The Probability Of Detection curve (POD) that links the probability to detect a detrimental flaw to its size is generally used as a key indicator for that purpose by giving the maximum flaw size that a NDE process can miss with a given level of probability and confidence. This information can then be used along with other inputs such as component geometries, mechanical properties, constraints, service and residual stresses and damage evolution speed to assess fracture risk and then adapt maintenance scenarios to optimize safety and component service life. NDE reliability and risk assessment are based on statistical indicators that need a large amount of data to provide reliable metrics. It is difficult to obtain such indicators using a purely empirical approach that is based on physical trials and measurements as it may involve many mock-ups and costly processes. Simulation tools can achieve this goal via their ability to include and precisely monitor many parameters as well as high computing capacities that are now available. The work presented in this paper involved cosimulations performed between the DARWIN® probabilistic damage tolerance software and the CIVA NDE simulation software. DARWIN computes fracture risk levels throughout a component, while CIVA can efficiently provide Probability Of Detection curves at different locations in a component and for various NDE methods. The presented application deals with a titanium gas turbine engine impeller disk and involves an Ultrasonic NDE inspection technique. It appears to be a very interesting approach to connect together NDE and Fracture mechanics simulations, two disciplines that generally work on their own. Indeed, DARWIN helps the user to determine detrimental flaw types, locations and sizes which are key inputs to develop an effective NDE inspection method. CIVA can provide location-specific POD curves that enable DARWIN to quantity the effect of dedicated NDE on potential risk reduction. This highlights the importance of NDE simulation for safety and helps to identify potential changes in the physical NDE process and the maintenance cycle that provide the best compromise between detection performance and cost.

The traditional approach to low-cycle fatigue (LCF) life prediction involves statistical characterization of total LCF life based on extensive testing of smooth fatigue specimens under multiple stress and temperature conditions. Total LCF life is modeled as a single random variable with a unimodal probability density function (PDF) from which a minimum (e.g., B0.1) life is derived. Recent studies have shown that LCF lives for some materials consist of a short-life group that initiates cracks near the first cycle of loading and a long-life group that forms cracks later in life. The combined lives of these two groups can be modeled as a bimodal distribution. Minimum LCF lives associated with the bimodal PDF are typically longer than those associated with the traditional unimodal PDF. Minimum LCF lives of the bimodal distribution are dominated by the short-life group, and the lifetimes of this group can be estimated using probabilistic damage tolerance (PDT) concepts. In this paper, a probabilistic framework is presented for prediction of minimum LCF lives of the short-life group. It extends a previously developed minimum LCF life model for smooth fatigue specimens for application to full components. It is based on a probabilistic damage tolerance methodology that was previously developed for rare material anomalies in aircraft gas turbine engine materials. The framework is demonstrated via two illustrative examples including a representative gas turbine engine component. The results promote improved understanding of the PDT approach and its application to LCF life prediction.

This work applies Taylor's theory of critical distance to quantify the effect of defects on fatigue initiation in an additively manufactured metal. We focus on hollow pores that are ideal spherical, prolate, and oblate spheroids isolated in an otherwise homogeneous linear-elastic material. These conditions support the development of exact solutions using the exterior Eshelby tensor for a pore in a remote, arbitrary stress field. For spheres, this solution process admits simple closed-form solutions for principal stresses disturbed by the pore. For prolate and oblate spheroids, we present the solutions as graphical curves showing stress variations under uniaxial tension. This report then extends the analysis to determine the effect of defects on a parametric, power-law stress range vs fatigue life model. By propagating the distributed stress fields through this model, this study demonstrates the effect of pore size, pore shape, stress, and parametric fatigue properties on the life reduction due to porosity. These results suggest several approaches to increasing fatigue lives in porous materials, eg, reducing the pore size, promoting spherical pores, and increasing the microstructural parameter (comparable to the El Haddad parameter). Results presented in this work may be useful to inform trends of fatigue strength and fatigue initiation lives in metallic alloys with limited porosity, eg, additively manufactured materials that have been HIP'ed.

Additive manufacturing processes produce components that may introduce material anomalies at any location within a component. NDE inspection can be used to find and remove anomalies that could grow to failure during the service life, but two key inputs are required for an effective inspection: (1) the critical locations to search for anomalies, and (2) the minimum sizes of the anomalies that must be found. A new methodology is presented for probabilistic damage tolerance assessment of additively manufactured components. It consists of a new link between the DARWIN® probabilistic damage tolerance software and the XRSim X-ray NDE simulation software. DARWIN computes fracture risk and critical initial crack sizes throughout a component, providing the two key inputs that are necessary for effective NDE inspections. XRSim computes location-specific POD curves everywhere in a component, providing the key information needed to assess the influence of inspection on fracture risk reduction. The methodology is illustrated for a representative gas turbine engine component manufactured via the direct metal laser sintering process. The results can be used to optimize the effectiveness of NDE inspection of additively manufactured components.

Recent advances in practical engineering methods for fracture analysis of turbomachinery components are described. A comprehensive set of weight function (WF) stress intensity factor (SIF) solutions for elliptical and straight cracks under univariant and bivariant stress gradients has been developed and verified. Specialized SIF solutions have been derived for curved through cracks, cracks at chamfered and angled corners, and cracks under displacement control. Automated fracture models are available to construct fatigue crack growth (FCG) life contours and critical initial crack size (CICS) contours for all nodal locations in two-dimensional or three-dimensional (2D or 3D) finite element (FE) models.

Materials engineering and damage tolerance assessment have traditionally been performed as disjoint processes involving repeated tests that can ultimately prolong the time required for certification of new materials. Computational advances have been made both in the prediction of material properties and probabilistic damage tolerance analysis, but have been pursued primarily as independent efforts. Integrated computational materials engineering (ICME) has the potential to significantly reduce the time required for development and insertion of new materials in the gas turbine industry. A manufacturing process software tool called DEFORM™ has been linked with a probabilistic damage tolerance analysis (PDTA) software tool called DARWIN® to form a new capability for ICME of gas turbine engine components. DEFORM simulates rotor manufacturing processes including forging, heat treating, and machining to compute residual stress and strain, track anomaly location, and predict microstructure including grain size and orientation. DARWIN integrates finite element stress analysis results, fracture mechanics models, material anomaly data, probability of anomaly detection, and inspection schedules to compute the probability of fracture of a gas turbine engine rotor as a function of operating cycles. Previous papers have focused on probabilistic modeling of residual stresses in DARWIN based on manufacturing process training data from DEFORM. This paper describes recent efforts to extend the probabilistic link between DEFORM and DARWIN to enable modeling of residual strain, average grain size, and ALA (unrecrystalized) grain size as random variables. Gaussian Process modeling is used to estimate the relationship among model responses and material processing parameters. These random variables are applied to microstructure-based fatigue crack nucleation and growth models for use in probabilistic risk assessments. The integrated DARWIN-DEFORM capability is demonstrated for a representative engine disk model which illustrates the influences of manufacturing-induced random variables on component fracture risk. The results provide critical insight regarding the potential benefits of integrating probabilistic computational material processing models with probabilistic damage tolerance-based risk assessment.

High-energy rotating components of gas turbine engines may contain rare material anomalies that can lead to uncontained engine failures. A zone-based risk assessment approach can be used to estimate component fracture risk based on groupings of finite elements (FEs) called zones. Creating zones manually is time consuming and requires human judgment. Algorithms have been developed to automatically create zones based on individual FEs, but the associated computation times increase exponentially with the number of FEs. 3D FE models typically contain millions of finite elements. Computation of component risk using individual FE-based automated zoning algorithms may take days or even weeks to complete. An improved optimal autozoning methodology has been developed that substantially reduces the computation time associated with fracture risk assessments. It combines finite elements with similar properties (i.e., stress, temperature, proximity to the surface) into groups called "pre-zones". An automated zone creation algorithm is applied to pre-zones rather than individual FEs, reducing the overall number of computations. In this paper, the optimal autozoning methodology is presented and illustrated for FE geometries in both 2D and 3D gas turbine engine components. Based on the demonstration problem results, it is shown that the computation speed associated with the optimal autozoning algorithm is expected to be three to four orders of magnitude faster than a previous algorithm that created zones at individual FEs. The pre-zoning-based algorithm also requires less memory than previous algorithms, enabling it to solve much larger models. The resulting algorithm provides a feasible and realistic solution for fracture risk assessment of 2D and 3D component finite element models.

Most current tools and methodologies to predict the life and reliability of fracture critical gas turbine engine components rely on stress intensity factor solutions that assume highly idealized component and crack geometries, and this can lead to highly conservative results in some cases. This paper describes a new integrated methodology to perform these assessments that combines one software tool for creating high fidelity crack growth simulations (FRANC3D) with another software tool for performing probabilistic fatigue crack growth life assessments of turbine engine components (DARWIN). DARWIN employs finite element models of component stresses, while FRANC3D performs automatic adaptive re-meshing of these models to simulate crack growth. Modifications have been performed to both codes to allow them to share and exchange data and to enhance their shared computational capabilities. Most notably, a new methodology was developed to predict the shape evolution and the fatigue lifetime for cracks that are geometrically complex and not easily parameterized by a small number of degrees of freedom. This paper describes the integrated software system and the typical combined work flow, and it shows the results from a number of analyses that demonstrate the significant features of the system.

Honeywell Aerospace's DARPA Open Manufacturing program (DARPA OM) is a combined effort of integrated computational materials engineering (ICME) models and mindset enabling a rapid qualification of components for the aerospace industry. The program focuses on laser beam additive manufacturing of Nickel-based Alloy 718Plus, emphasizing an integrated empirical and modeling effort for prediction of material properties produced by this novel process. As this emerging additive manufacturing technology matures, it has forced tools to model and simulate the intricate process to advance to a new level. The complexity during the additive process, such as the rapid heating rates, cooling rates, and transient phase transformation, brings increased uncertainty to the microstructure and material properties of the components. The post build processing for ATI 718Plus Alloy used in this program includes a Stress Relief (SR) followed by Hot Isostatic Pressure (HIP) cycle, and then Solution Heat Treatment (SHT) followed by a two-step Aging. However, the standard post treatment that has been developed for the traditionally formed material often falls short for the additively processed material. This program focuses on mining empirical data to build the next generation of models, and drive future rapid qualification of aerospace components.This paper will discuss the unique microstructure evolution that results from additive manufacturing, how the DARPA team calibrated and validated ICME models for that evolution and for strength modeling, and how the resulting models assisted the development of a new optimized stress-relief temperature.

Advanced Ni-based gas turbine disks are expected to operate at higher service temperatures in aggressive environments for longer time durations. Exposures of Ni-base alloys to these aggressive environments can lead to cycle-dependent and time-dependent crack growth in superalloy components for advanced turbopropulsion systems. In this article, the effects of tertiary γ′ on the crack-tip stress relaxation process, oxide fracture and time-dependent crack growth kinetics are treated in a micromechanical model which is then incorporated into the DARWIN® probabilistic life-prediction code. Using the enhanced risk analysis tool and material constants calibrated to powder-metallurgy (PM) disk alloy ME3, the effects of grain size and tertiary γ′ size on combined time-dependent and cycle-dependent crack growth in a PM Ni-alloy disk is demonstrated for a generic rotor design and a realistic mission profile using DARWIN. The results of this investigation are utilized to assess the effects of controlling grain size and γ′ size on the risk of disk fracture and to identify possible means for mitigating time-dependent crack growth (TDCG) in hot-section components.

Recently a new methodology was developed for automated fatigue crack growth (FCG) life analysis of components based on finite element stress models, weight function stress intensity factor solutions, and algorithms to define idealized fracture geometry models. This paper describes how the new methodology is being used to integrate FCG analysis into highly automated design assessments of component life and reliability. In one application, the FCG model automation is supporting automated calculation of fracture risk due to inherent material anomalies that can occur anywhere in the volume of the component. Automated schemes were developed to divide the component into a computationally optimum number of sub-volumes with similar life and risk values to determine total component reliability accurately and efficiently. In another application, the FCG model automation is supporting integration of FCG life calculations with manufacturing process simulation to perform integrated computational materials engineering. Calculation of full-field, location-specific residual stresses or microstructure is being linked directly with automated life analysis to determine the impact of manufacturing parameters on component reliability.

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 (ΔK th or K th) 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.

While turbine engine Original Equipment Manufacturers (OEMs) accumulated significant experience in the application of probabilistic methods (PM) and uncertainty quantification (UQ) methods to specific technical disciplines and engine components, experience with system-level PM applications has been limited:.To demonstrate the feasibility and benefits of an integrated PM-based system, a numerical case study has been developed around the Honeywell turbine engine application. The case study uses experimental observations of engine performance such as horsepower and fuel flow from a population of engines. Due to manufacturing variability, there are unit-to-unit and supplier-to-supplier variations in compressor blade geometry. Blade inspection data are available for the characterization of these geometric variations, and CFD analysis can be linked to the engine performance model, so that the effect of blade geometry variation on system-level performance characteristics can be quantified. Other elements of the case study included the use of engine performance and blade geometry data to perform Bayesian updating of the model inputs, such as efficiency adders and turbine tip clearances.A probabilistic engine performance model was developed, system-level sensitivity analysis performed, and the predicted distribution of engine performance metrics was calibrated against the observed distributions. This paper describes the model development approach and key simulation results. The benefits of using PM and UQ methods in the system-level framework are discussed.This case study was developed under Defense Advanced Research Projects Agency (DARPA) funding which is gratefully acknowledged.

High-energy rotating components of gas turbine engines may contain rare material anomalies that can lead to uncontained engine failures. The Federal Aviation Administration and the aircraft engine industry have been developing enhanced life management methods to address the rare but significant threats posed by these anomalies. One of the outcomes of this effort has been a zone-based risk assessment methodology in which component fracture risk is estimated using groupings of elements called zones that are associated with 2D finite element (FE) stress and temperature models. Previous papers have presented processes for creation of zones either manually or via an automatic algorithm in which zones are assigned to each finite element in a component model. These processes may require significant human time and computer time. The focus of this paper is on the optimal allocation of multiple finite elements to zones that minimizes the total number of zones required to compute the fracture risk of a component. An algorithm is described that uses a relatively coarse response surface method to estimate the conditional risk value at each node in a finite element model. Zones are initially defined for each finite element in the model, and the algorithm identifies and merges zones based on minimizing the influence on component risk. The process continues until all of the zones have been merged into a single zone. The zone sequence is applied in reverse order to identify the minimum number of zones that satisfies component target risk or convergence threshold constraints. This solution provides the optimal allocation of finite elements to zones. The algorithm is demonstrated for a representative gas turbine engine component. The approach significantly improves the computational efficiency of the zone-based risk analysis process.

Advanced Ni-based gas turbine disks are expected to operate at higher service temperatures in aggressive environment for longer time durations. Exposures of Ni-based alloys to alkaline-metal salts and sulfur compounds at elevated temperatures can lead to hot corrosion fatigue crack growth in engine disks. Type II hot corrosion involves the formation and growth of corrosion pits in Ni-based alloys at a temperature range of 650°C to 750°C. Once formed, these corrosion pits can serve as stress concentration sites where fatigue cracks can initiate and propagate to failure under subsequent cyclic loading. In this paper, a probabilistic methodology is developed for predicting the corrosion fatigue crack growth life of gas turbine engine disks made from a powder-metallurgy Ni-based superalloy (ME3). Key features of the approach include (1) a pit growth model that describes the depth and width of corrosion pits as a function of exposure time, (2) a cycle-dependent crack growth model for treating fatigue, and (3) a time-dependent crack growth model for treating corrosion. This set of deterministic models is implemented into a probabilistic life-prediction code called DARWIN. Application of this approach is demonstrated for predicting corrosion fatigue crack growth life in a gas turbine disk based on ME3 properties from the literature. The results of this study are used to assess the conditions that control the transition of a corrosion pit to a fatigue crack, and to identify the pertinent material parameters influencing corrosion fatigue life and disk reliability.

A new methodology has been developed for automated fatigue crack growth (FCG) life and reliability analysis of components based on finite element (FE) stress and temperature 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 that satisfactorily approximate an irregularly-shaped component cross section. The fracture model geometry algorithms are robust enough to accommodate crack origins on the surface or in the interior of the component, along with finite component dimensions, curved 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 accept univariant stress gradients and have been optimized for both computational efficiency and accuracy. The resulting calculations are used to automatically construct FCG life contours for the component and to identify hot spots. Finally, the new algorithms are used to support automated probabilistic assessments that calculate component reliability considering the variability in the size, location, and occurrence rate of the initial anomaly; the applied stress magnitudes; material properties; probability of detection; and inspection time. The methods are particularly useful for determining the probability of component fracture due to fatigue cracks forming at material anomalies that can occur anywhere in the volume of the component. The automation significantly improves the efficiency of the analysis process while reducing the dependency of the results on the individual judgments of the analyst. The automation also facilitates linking of the life and reliability management process with a larger integrated computational materials engineering (ICME) context, which offers the potential for improved design optimization.

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 illustrated for an actual military engine disk under real life loading conditions.