NASA/TM—2009-215827

An Overview of Prognosis Health ManagementResearch at Glenn Research Center for Gas TurbineEngine Structures With Special Emphasis onDeformation and Damage Modeling

Steven M. Arnold, Robert K. Goldberg, and Bradley A. LerchGlenn Research Center, Cleveland, Ohio

Atef F. SaleebUniversity of Akron, Akron, Ohio

September 2009

https://ntrs.nasa.gov/search.jsp?R=20090037048 2020-03-24T03:02:28+00:00Z

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NASA/TM—2009-215827

An Overview of Prognosis Health ManagementResearch at Glenn Research Center for Gas TurbineEngine Structures With Special Emphasis onDeformation and Damage Modeling

Steven M. Arnold, Robert K. Goldberg, and Bradley A. LerchGlenn Research Center, Cleveland, Ohio

Atef F. SaleebUniversity of Akron, Akron, Ohio

Prepared for theAnnual Conference of the Prognostics and Health Management Society 2009sponsored by the Prognostics and Health Management SocietySan Diego, California, September 27–October 1, 2009

National Aeronautics andSpace Administration

Glenn Research CenterCleveland, Ohio 44135

September 2009

This report contains preliminary Þ ndings,subject to revision as analysis proceeds.

Level of Review: This material has been technically reviewed by technical management.

Available from

NASA Center for Aerospace Information National Technical Information Service7115 Standard Drive

5285 Port Royal RoadHanover, MD 21076–1320

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Available electronically at http://gltrs.grc.nasa.gov

An Overview of Prognosis Health Management Research atGlenn Research Center for Gas Turbine Engine Structures

With Special Emphasis on Deformation and Damage Modeling

Steven M. Arnold, Robert K. Goldberg, and Bradley A. LerchNational Aeronautics and Space Administration

Glenn Research CenterCleveland, Ohio 44135

Atef F. SaleebUniversity of AkronAkron, Ohio 44325

Abstract

Herein a general, multimechanism, physics-basedviscoelastoplastic model is presented in the context of anintegrated diagnosis and prognosis methodology which isproposed for structural health monitoring, with particularapplicability to gas turbine engine structures. In thismethodology, diagnostics and prognostics will be linkedthrough state awareness variable(s). Key technologies whichcomprise the proposed integrated approach include (1)diagnostic/detection methodology, (2) prognosis/lifingmethodology, (3) diagnostic/prognosis linkage, (4)experimental validation, and (5) material data informationmanagement system. A specific prognosis lifing methodology,experimental characterization and validation and datainformation management are the focal point of currentactivities being pursued within this integrated approach. Theprognostic lifing methodology is based on an advancedmultimechanism viscoelastoplastic model which accounts forboth stiffness and/or strength reduction damage variables.Methods to characterize both the reversible and irreversibleportions of the model are discussed. Once the multiscalemodel is validated the intent is to link it to appropriatediagnostic methods to provide a full-featured structural healthmonitoring system.

1.0 Introduction

The desire for higher performance (e.g., increased thrust toweight ratio) and efficiencies in gas turbine engines, alongwith the availability of advanced technologies, has resulted indesigners pushing the design envelop to the limit in such areasas, for example, increasing the pressure ratio, decreasing tipclearance, and increasing operational temperatures. Theseadvanced designs have in turn caused significant increases inoverall operational and maintainability costs, due to associateduncertainties in component life and reliability. Similarly, astechnology advances, component costs typically increaseproportionately—thus enhancing the desire for betterclarification of useful (safe) remaining life, to decrease directoperating costs. This need explains the heightened desire for

and increased research activity in the area of conditionmonitoring with an eye toward diagnosis and prognosis ofvarious critical components. To date, in commercial gasturbine engines continuous health monitoring is limited togeneric “global” system measurements like shaft vibrationsand EGT (exit gas temperatures) and localized measurementsare only taken at windows of opportunity rather than on acontinuous basis. These local measurements (which involveexpensive tear down) are still limited; in general, tovisual/optical surface inspection techniques (measurements),which themselves fall short in their ability to detect criticaldefects. Conversely, in military engines which experience farmore intense and often unexpected loadings, condition-basedmonitoring has recently been undertaken as the standard;wherein generic engine data (environment, temperature,pressure, vibration) are collected and monitored, andintegrated and correlated with past mission histories.However, prognostic methodologies, as defined herein, stillremain elusive, as clear linkage between damage (criticaldefects, life limiting events) and response signature(s), be theyrefined or crude, have yet to be established.

Further structural life is known to be extremely sensitive topreexistent damage such as manufacturing flaws and/orservice induced damage that can cause immediate fracture orserve as sources for early fatigue cracking. Current propulsionstructural life management approaches rely on a combinationof predictive models and periodic inspections both on-line andoff-line. The approaches primarily in use today are (Grandt,2004) (1) Safe-Life Design—requires that the component beretired before the initiation of cracks and is susceptible to thepresence of unanticipated structural or material damage thatgreatly reduce the crack initiation portion of the fatigueprocess; (2) Damage Tolerant Design—assumes a structurecontains initial cracks (typically assumed equal to the largestundetected defect size), and defines the ability of the structureto resist fracture from cracks of a given size for a specifiedtime period; and (3) Retirement for Cause—utilizes periodicinspection intervals to locate damaged components that arethen either repaired or replaced. The inspection intervals arebased on the time for an undetected crack to grow to fracture.All three approaches demonstrate the interdependence of

NASA/TM—2009-215827

diagnostic (inspection) and prognosis (life prediction) methodsand stress the importance of developing the fundamentalscientific causal relationships of failure to provide the keydiagnostic/prognostic linkage for different material systemsand structures. Large improvements in safety, life extension,and overall life cycle costs can be attained by employing anew philosophy to propulsion health management.

However, in many of the approaches currently used(Adams, 2004, Springer, 2004), the prognosis of future eventsis based on an extrapolation of events which have occurredpreviously. If the future loading is varied significantly fromthe previously applied loading profiles, the classical prognosismethods will not accurately predict the future response, whichexplains why the accuracy of these approaches is limited toonly short time extrapolations. Similarly, many successes havebeen documented (Fatemi and Yang, 1998, Grandt, 2004) inthe realm of prognosis (analytical modeling predictions);given the damage initiation site and subsequent known loadingconditions. However, for truly accurate predictions of futureevents (that vary significantly from prior events), a physics-based prognostic model is required in which, given an initialload/damage condition, an arbitrary set of future loadingprofiles can be applied (in an off-line approach) to determinethe future damage and ultimate life of the structure. Linkagesto diagnostics methods through the use of state-awarenessvariables are still required, however, in order to provideinformation on the current load/damage state at a given pointin time, so that a physics based prognostics model canindependently determine the future response of the structure.

Consequently, the overall objective of the present structuralhealth management program at the NASA Glenn ResearchCenter (GRC) (which is supported by the NASA IVHM(Integrated Vehicle Health Management) Project within theAviation Safety Program, is to develop, implement andexperimentally verify a lifing (prognosis) methodology forhealth monitoring of structural components operating at hightemperatures, which is tightly coupled (through correspondingstate awareness variables) to detection (diagnosis) techniques.In this project, GRC researchers are focusing on thedevelopment/characterization/ and experimental verificationof a fully associative, physics-based, viscoelastoplastic—damage model which can be utilized as a prognostic toolwithin a hot structural life management system, primarilyaimed at the propulsion system environment; wherein, inducedlocalized softening mechanisms (which are stronglyinfluenced by geometry, loading conditions, inherent defectdistributions and material anisotropy) are considered. Asimplied above, in this work, the term prognostics refers to theability to predict remaining life given the current state of thematerial. A key feature of the viscoelastoplastic model whichconstitutes the basis of our prognostics system is theincorporation of advanced features of the response of metallicalloys at elevated temperatures. As engine structures willencounter elevated temperatures, classical analysis methodsand constitutive equations will not be able to accuratelysimulate the material response. The key feature of our

methodology is that the time-dependent aspect of the materialresponse (i.e., viscoelastic and viscoplastic) dominant atelevated temperatures, are accounted for within the modelalong with the appropriate local and global failure criteria.Therefore, the physics-based prognosis methodology proposedwill be established for high temperature structural componentsunder general loading conditions (multiaxial loading with andwithout overloads, cyclic effects, thermomechanical, etc.) andexperimentally validated with the design of a prognosticallychallenging test matrix. This test matrix will consist of bi-axialexperimental demonstration problems at ambient and elevatedtemperatures that will be suitable for use in characterizing,evaluating and ranking prognostic (and detection) methods.While research is being conducted on both metallic andcomposite structures, and the overall methodology describedherein is applicable to a variety of material systems, thespecific results presented in this paper are focused on titaniumengine components made of Ti-6-4. The general framework,once validated for the Ti-6-4 system, will be applied in thefuture using other prototypical alloys used in gas turbineengines, such as powder metallurgy nickel-based disksuperalloys.

The paper begins with an overview of a proposed fully-integrated diagnostic/prognosis life management system, withspecial emphasis on how the developed prognosis(constitutive) models can fit within the proposed framework.The viscoelastoplastic constitutive model which is the basis ofthe prognosis framework is then described in detail. This isthen followed by the efforts to date on the characterization andvalidation of the specific prognostic component of theproposed integrated framework. Specifically, thecharacterization and validation of the reversible timedependent (viscoelastic) behavior of a representative titaniumalloy (i.e., Ti-6-4) is discussed as well as the current progressachieved in understanding the irreversible (viscoplastic)response. While admittedly there is significant amounts ofwork that have yet to be carried out so as to enable one to fullypredict the deformation and damage response of a metallicstructure, even the preliminary results presented herein willdemonstrate the capability of the proposed prognosis model toanalyze key features of the response of metallic alloys thatclassical analysis methods cannot capture (such as the time-and rate-dependence of the low-strain reversible response).

2.0 Fully Integrated Diagnostic/Prognostic Life Management System(FILMS)

The life of a component is dependent not only upon its pasthistory (i.e., the loads imposed on it, its initial and currentphysical condition) but also upon the future imposed loads andoperating environment. Consequently, if one desires tomaximize the life of a given component one must alwaysknow the current state of the component (state awareness,obtained via detection techniques), and how future events will

NASA/TM—2009-215827 2

Incurred History- Past Events Future Events

Deformationand

Detection Life Models

Algorithms

Requires Knowledge OfLIFE

1. Material Behavior2. Physics of Failure

Appropriate Scale 3.Specific GeometryResponse Signature State Awareness 4.Anticipated Loads/

Measurements is Connecting Link Constraints5.State (material or

structure )

Figure 1.—Depicts the distinction between diagnostic andprognostic methodologies and their integration.

affect its life (prognosis or life prediction), given its presentcondition. Given the above considerations, a two-prongapproach is adopted wherein developed prognosis methodswill be fully linked with complementary detection tools,illustrated in Figure 1. As discussed earlier, it is believed thatonly when these two views are consistently integrated (theconnecting link being the current state of thematerial/structure) can a rational and viable healthmanagement system be established. Consequently, for theproposed prognostic model to be viable, a detection scheme(of the direct type) must be established with sufficientresolution to (1) detect the presence of defect(s), (2) locate thedefect(s), and (3) size the extent of damage throughout thehistory of a component. Given this information, establishing astructurally meaningful connection (based on the physics ofthe failure or defect) with a physics-based coupleddeformation and damage model is essential to predictingreliably the available remaining life given multiple futureevent scenarios.

Figure 2 illustrates how the diagnostic and prognostic toolsneed to be linked to form a full structural health monitoringsystem. The diagnostics tools (utilized in the “past history”portion of the chart) are required to provide the damage stateat a current point in time. The prognostics tools are thenutilized in the “future” portion of the chart to predict the futuredamage and life of the structure. As mentioned earlier, withoutthe use of advanced prognostics tools only extrapolations offuture events based on previously occurring trends (the“Future = Past” line in the chart) can be predicted. However,with the use of a full physics-based prognostic tool, thedamage and life resulting from any potential future loadingprofile can be examined. Note that the “critique window”identified in the figure represents the period of time where thedamage progression is examined in the structure in order toeither extrapolate the future material response (in order togenerate the “Future = Past” type curve) or to provide theinitial conditions for a more physics-based type of prognosismethodology.

Consistent with this vision is the concept of scale-specificresolution —that is the understanding that each successive

Microstructurally-based stochasticbehavior –enables confidence levels.

Diagnostic Viewpoint –Enablesknowledge ofcurrent state. i

W F i CritiqueDA Window

/ j I Prognosis Viewpoint –Enableslife management

ATime (cycles)

bymodifad igfuture loading.

Past History Future

Figure 2.—Depiction of an integrated diagnostic andprognosis approach to incrementally updating a lifemanagement system.

level of fidelity on the prognosis side demands acommensurate level on the diagnostic side. Consequently,many researchers have attempted to assign discriminators toallow the use of rank methods. For example, consider the fourlevels of damage identification (LODI) put forth by Rytter(Rytter, 1993):

(1) Level 1: Determination that damage is present in thestructure(2) Level 2: Level 1 plus determination of the geometriclocation of the damage(3) Level 3: Level 2 plus quantification of the severity of thedamage(4) Level 4: Level 3 plus prediction of the remaining service-life of the structure

Note many of the popular global diagnostic techniquesprovide no more than LODI = 1 fidelity, when the ultimatedesire is to reach level 4. Furthermore, understanding thatfailure is a process and not an event empowers adetection/prognosis philosophy, which can be exploited tomanage the event that is developing, not just react to it. In thiscontext, failure being a process means that the ultimate failureof a structure is due to the accumulation of damage to asignificant enough degree that the structural integrity iscompromised. If the initiation and progression of the lowerlevels of damage are not accurately detected and predicted,determination of the ultimate structural life is questionable atbest. Furthermore, the higher up in the failure processhierarchy (i.e., the closer to ultimate failure) that a fault isdetected, the less manageability remains and the less timeexists before functionality is compromised beyond the usablestate. Ideally damage should be detected well before imminentfailure is present, and the prediction of remaining life shouldbe able to take place well within the zone of safe operation,and well before the part should be removed from service. Thishas been referred to as the predictive horizon (Hess, 2002).

This concept is especially significant when developing aviable health monitoring system for complex “real-world”applications. In constructing such a system one must fully

NASA/TM—2009-215827

Figure 3.—Temporal interrogation of a given component.

recognize the cornucopia of available sensor techniques andtheir practical limitations (e.g., inability to operate in elevatedtemperature environments, limited accessibility, fear thatfailure initiates at sensor sites, etc.). Consequently, any on-linemonitoring device is likely to be quite coarse in nature (i.e.,scalar, e.g., pressure or EGT,) and in its spatial distribution(e.g., at very few specific locations in the engine).Alternatively, off-line diagnostic techniques are often rich intheir spatial content, but ideally limited in their temporaldistribution, that is, taken at intermittent windows ofopportunity rather than on a continuous basis, see Figure 3.Thus the ultimate measure of success for any comprehensivehealth monitoring endeavor (for instance like FILMS,proposed herein) will be the ability to discriminate betweenthese two distinct diagnostic scales (that is, a very spatially-crude but temporally-numerous versus spatially-rich buttemporally-rare). Furthermore, the overarching goal must be toprovide diagnostic data in sufficient quantity and quality suchthat the prognostic tool can make reasonable predictions.

With the above ideas in mind there are five overarchingtechnology areas that must be addressed concurrently toestablish such a robust fully-integrated, multiscale,multimechanism diagnostic and prognosis life managementsystem (FILMS). These are: (1) diagnostic/detectionmethodology, (2) prognosis/lifing methodology, (3)diagnostic/prognostic linkage, (4) experimental validation, and(5) reasoning methodology and material data informationmanagement. In this paper, the areas of prognosis/lifingmethodology and experimental validation will be concentratedon as these components will be developed in the greatest detailand most likely provide the most unique contributions to thedevelopment of an integrated diagnostic/prognostic system.The material data information management topic will also becovered in some detail as the proper capturing, analysis,dissemination and maintaining of material data can play asignificant role in facilitating the characterization andutilization of the sophisticated material model which is theheart of the proposed prognostics approach. The areas relatedto diagnostics and diagnostics/prognostics linkage will bedescribed briefly, to give insight as to how the currentprognostic model can be integrated within the context of a fullhealth monitoring system. Furthermore, in the area ofdetection, multiple approaches (some complementary/some

competitive) will be considered as resources allow as part ofthe research program, with an eye toward down selection andthe development of a hierarchy system with varying scalespecific resolution.

2.1 Detection Methodology

Detection techniques may be classified as global or local.Global methods attempt to assess simultaneously the conditionof the whole structure (e.g., vibration measurements using anaccelerometer), whereas local methods provide informationabout a relatively small region of the system by usinglocalized measurements (e.g., strain gages). Real-timeprognosis demands a global inspection approach based on asparse distributed network of small, efficient, environmentallystable sensors. The objective of accurate long-term lifetimeprediction however, requires high levels of spatial resolution.Clearly, the two approaches are complementary to each other,with the choice of method being dependent on the scope of theproblem at hand and the nature of the sensor network.

2.1.1 Local Sensing/Detection Techniques

Numerous local sensing/detection techniques exist and arebeing studied for health monitoring applications. Somepopular examples include fiber optic strain sensors and piezo-electric patches for ultrasonics. With respect to our currentprogram, in choosing the type of detection/sensor method tobe applied it is essential to fully understand the physical natureof the accumulating damage, in order to properly characterizeand validate the prognostics tool. Hence, high fidelitylaboratory tools will be implemented. These methods willinclude using a full-field optical displacement measurementsystem, thermoelastic stress analysis, as well as distributedstrain gages. Field-friendly approaches will include passive(i.e., modal acoustic emissions) and active ultrasonics (e.g.,guided wave, nonlinear, etc.). Although the high fidelity toolsare not intended for field use, they define the upper limits ofmaterial assessments. The resulting database will allow for thebenchmarking and capability assessments of the innovativesensors being studied within the IVHM project.

2.1.2 Global/Wybrid Detection Techniques

There are basically two approaches for mathematicalrepresentation and implementation of global detectiontechniques, i.e., system-identification and direct post-processing of measurement data. The two approaches differmainly in the amount and type of information used. In oneextreme, the system identification approach is typically basedon a complete analytical model that is optimally fitted to themeasured response. Consequently this indirect approach hastraditionally been restricted to numerical simulations of linearsystems. Another disadvantage of this type of approach, inaddition to the intense computational demands, is the need totreat the “inherent nonuniqueness” of measured data.

NASA/TM—2009-215827 4

However, more recently, novel indirect detection techniquesutilizing such indicators as weighted and mixedtransmissibility functions and nonlinear dynamic behavior inboth the healthy and damaged systems have been emerging.Their advantage stems from their insensitivity to boundary-condition and other system nonlinearities (which can typicallymask damage in most diagnostic features or otherwise causefalse-positive alarms), their ability to use distributed sensorarrays to locate damage, and their applicability for “passive”diagnostics when input measurements are unavailable orenvironmental fluctuations are anticipated. Conversely, direct-detection schemes do not require a priori identification of ananalytical model. Instead, the key ingredient is the selection ofan appropriate damage index that is sufficiently sensitive toperturbations in system properties. Given this damage index,the whole implementation reduces to a pattern-recognitionproblem. Processed experimental data yields a signature that iscompared to the base or reference state. Clearly, sharperresolution will be obtained with more distinct differencesbetween two signatures—thus the need for robust NDE (local)techniques; e.g., see further elaborations in Saleeb andPonnaluru (2006), Saleeb and Prabhu (2002).

In light of the above comments, this program willconcentrate on utilizing full-field strain measurements as wellas obtaining a variety of other detection signatures that can beutilized to evaluate both direct and indirect global detectionschemes. Their determination of the material or structuralcondition will then be used in the companion prognosis tool toassess useful remaining life given various future eventscenarios. Furthermore, the information derived from thesedirect and indirect global detection techniques will be used toguide the detailed local inspection techniques discussed aboveto accurately quantify the specific type of damage stateinduced, and to improve the accuracy in subsequent lifeprediction calculations.

2.2 Prognosis Methodology

A prerequisite for meaningful assessment of componentdurability and life, and consequently design of structuralcomponents, is the ability to accurately predict stresses,strains, failure modes and their subsequent interaction andevolution occurring within a loaded structure, composed of agiven material. Furthermore, since constitutive materialmodels provide the required link between stress and strain,this by necessity demands an appropriate constitutive behaviormodel for any material (be it monolithic or composite) beforethat material can be certified for use by a designer Also, it isclear that the ability to identify the proper failure modes lieslargely in the accurate stress-strain predictions resulting fromconstitutive models and their interaction with the evolvingdamage or failure state. Further complicating matters, themechanisms which induce localized softening (i.e., localinelasticity, nucleation and growth of damage (defects, voids,cracks, etc.)) and ultimately lead to end of useful componentlife are strongly influenced by geometry, loading conditions,

inherent defect distributions (e.g., those due to manufacturing)and environmental conditions. Consequently, it is virtuallyimpossible to predict the location of failure without a completeknowledge of the initial distributions of inherent (e.g.,manufacturing) flaws. Hence, people are motivated to turn tonondestructive evaluation techniques to quantify these flawsand to probabilistic approaches to account for uncertainties.Note, however, that in general the level of these uncertaintieswill change in time due to the path-dependent nature ofdeformation, internal stresses and damage evolutionthroughout a component’s useful life; thereby making a purelyprobabilistic approach insufficient for a complete formulationof a prognosis framework. Yet the possibility that informationcan be gleaned from an intermittent diagnostic interrogation ofthe material still exists and thus could provide the vital link tocomplete the ultimate overall prognosis framework. Thesefacts illustrate the major disadvantage of a purely prognosisapproach—that is, the accuracy of life prediction is dependentupon the knowledge of both constitutive behavior of thematerial that comprises the structure and knowledge of theapplied loads and boundary conditions.

With the above facts in mind, we have decided to evaluate aphysics-based, multimechanism viscoelastoplastic deformationmodel coupled with continuum-based stiffness and strengthdegradation damage parameters as a prognosis methodologyunder general loading conditions, which will be described inmuch more detail in Section 3 of this paper. Although thismodel represents the current state-of-the-art in the area ofprognosis, it is still presently not up to the challenging task ofproviding a complete prognosis tool; as a direct and usefulcomplimentary diagnostic technique that links the current“material state” via state-awareness variable(s) (e.g., stiffnessand strength reduction parameters) that implicitly dictate failureis still lacking. However, as the characterization, validation anddemonstration of the constitutive model is a vital first step in thedevelopment of the health monitoring approach, the fulldevelopment of the prognosis methodology is the current focus.The status of this methodology development effort will befurther discussed in Sections 3 to 5.

2.3 Diagnostic/Prognostic Linkage Via StateAwareness

As stated previously, it is virtually impossible to accuratelypredict the location of failure without a complete knowledgeof the spatial (e.g., location, origin, size) and temporaldistributions of inherent and load-induced flaws—thus theneed for robust global and local diagnostic tools. Similarly,component life is known to be dependent upon accurate stress-strain predictions, which in themselves are strongly influencedby the triggering and evolution of softening mechanisms(which, in turn, are heavily influenced by componentgeometry, loading conditions, inherent defect distributions andenvironmental conditions). Consequently, intermittentcommunication of the diagnostic material state is needed toguide and drive the predictive prognosis capability. It is our

NASA/TM—2009-215827

strong belief that this linkage constitutes the most innovative,and yet challenging, aspects of structural health monitoring.Interestingly, this linkage is the most coveted and yet leastmature and therefore has the highest risk associated with itsdevelopment. However, the state awareness approach has beenconsidered previously. The primary challenges for our workwill be to develop state awareness methods which provide thespecific inputs required for the advanced prognosticsconstitutive model described in Section 3 of this report. Twodifferent approaches will be investigated (as resources allow)in the future. Firstly, a “direct” identification of a spatiallyhigher-order state awareness variable(s), representing thesalient features of the changing condition of the material orstructure, needs to be identified to characterize the precisenature of the damage sustained. Secondly, recognizing that(even with the advanced nature of the analysis employed) acomplete and totally reliable characterization of all of thepossible modes of damage is unlikely, thus a probabilisticframework will ultimately need to be developed in the futureto quantify the likelihood a given set of detection systemoutputs correspond to a particular type of damage. The fulldevelopment and verification of the prognostics model to bedescribed in Section 3 of this paper (particularly the damageprediction features), and the planned correspondingexperimental subcomponent demonstration work described inSection 2.4 must be carried out before the efforts describedhere can be fully completed. However, the followingdiscussion indicates how the prognostics tool will be coupledwith appropriate diagnostics tool, and features that will bepaid particular attention in the final development of theconstitutive model.

2.3.1 Direct State-Variable Awareness Approach

The mechanical deformation results and the diagnosticsignatures (both global and local) which will be coming froma series of in-plane biaxial experiments (to be described laterin this paper) will be employed to:

(1) Identify the type of damage (general flaw/defect/degradations) and its structurally significantmanifestation (e.g., loss of stiffness, strength reduction, and/orincreased damping to name a few).

(2) Quantify (mathematically) the associated state-awareness variable, that is, a scalar, vector or tensor typevariable(s). We anticipate the conclusion will be that therequired state variable(s) will be higher-order in character (i.e.,nonscalar) since they must ultimately account for thecollective arrangement of multiple locations of defects thatvary in size and are anisotropically oriented. Key issues willbe:

(a) How do we obtain these values from measuredsignatures?

(b) How are the obtained values associated with one ormore of the included damage variables (i.e., the stiffnessreduction and/or strength reduction variable) within a

continuum based prognosis method so that the prognosiscalculations are impacted by the evolution of damage (e.g.,growth of crack(s)) and/or these state variables?

(c) What LODI is desired?Clearly the outcome is far from straight forward, nor is it

independent of the type of damage being tracked. Selectionwill be made with an eye toward feature extraction andelimination of the inherent deficiencies in the diagnosticmeasurement. For example, frequency measurements maybe sufficient for level 1 (indicating the presence of damage)but will not let one move to LODI levels 2 through 4, due totheir scalar nature.(3) Characterize the damage and state awareness variable

(e.g., crack length) and its evolution; and associate it with thecorresponding failure mechanism (fatigue crack) and itsevolution.

Address the statistical variation in measurements andimpact on the prognosis methodology.

(4) Develop an updating scheme so that intermittent and/orcontinuous diagnostic information (state awareness) can andwill impact the prognosis algorithm.

(a) The scheme must address the level of measurementand analysis fidelity required both spatially and temporallyto achieve the desired LODI.

(b) Perform sensitivity studies to identify the level oferror or uncertainties.

2.4 Experimental Subcomponent Demonstration

A key aspect of any credible life management system is anexperimental demonstration. To properly characterize amaterial, a set of experimental characterization and validationtests need to be conducted, both at coupon and subcomponentlevels. Uniaxial coupon tests are required in order to fullycharacterize the time dependent reversible and irreversibledeformation and damage response of the material. Forexample, to characterize a metallic material using theviscoelastoplastic model described later in this paper, anextensive series of tensile, creep, relaxation, step and cyclictests need to be performed at a variety of loading rates andtemperatures. Examples of the processes used to characterize arepresentative titanium alloy will be described anddemonstrated in detail later in this paper and are alsodiscussed in (Saleeb et al., 2001; Saleeb and Arnold, 2001;Arnold et al., 2001; Saleeb and Arnold, 2004).

However, in order to fully investigate the crack propagationresulting from realistic multiaxial loading conditions, and toallow for the full validation of the prognostic tool, in-planebiaxial plate testing (at both room and elevated temperature)will be the primary focus of the experimental validation effortafter the uniaxial characterization and validation processes arecomplete, so that a variety of high quality diagnosticmeasurements (signatures) including full field displacementand strain measurements can be successfully made. Theavailability of such accurate measurements, both spatially and

NASA/TM—2009-215827 6

TABLE 1.—TEST MATRIX FOR BIAXIAL TEST PROGRAM

BUiuN Bann lJ^, l0% ^`^ ^ ^rPF 2^' lCi' (S . CC4.

x x x li,^;nI]0 IsrPC x x x x x x x x

x x li x x

^= ^0 tiPCI x x x x x x x x

temporally, are essential in providing validation data for theprognostic tool, but also to provide the prerequisiteinformation for defining an appropriate state-awarenessvariable(s) and their associated diagnostic technique(s). Afurther benefit to concentrating on biaxial plate testing is thelarge number of “static” structural applications that will beimpacted because of the resulting enhanced level ofunderstanding; for example, wings, nozzles, inlets, ships,tanks, etc. This list is further extended when one factors in thatboth room temperature and elevated temperature biaxialtesting will be performed; thus allowing the study of materialnonlinearity effects, which are present in many of the targetedapplications, and the simulation thereof is a specific strengthof the constitutive model which comprises the prognostic tool.Although the specific test matrix has not be finalized to date,Table 1 outlines a proposed matrix that illustrates both thespirit and thought process, which will embody the final testmatrix. In keeping with our two-prong philosophy of bothdeveloping prognostics methods and accompanyingdiagnostics techniques, we have chosen to construct an in-plane test program along two lines; variation in imposed loadhistory and inflicted defect configurations. In this way,assessment of both local and global NDE techniques (in thecontext of associated state awareness variable(s)) and theselected prognosis methodology can be readily achieved.

The baseline plate configuration to be examined will be theclassic problem of a plate with a single stress riser (e.g., ahole) loaded uniaxially and biaxially under both monotonicand cyclic histories. This baseline case will be complimentedby two other configurations with multiple stress risers ofvarying character (i.e., holes, slots, cracks, etc.), which mightcorrespond to inherent structural attachment configurationsand/or large scale structural damage.

The variety of crack initiators will be examined with an eyetoward developing a significant database to characterize andvalidate the proposed life management system under relativelyrealistic conditions and to enable assessment of theuncertainties in the underlying failure mechanisms. Figure 4(top) illustrates the baseline (B) configuration which, whencombined with the specified load histories in Table 1, willbecome prognostically challenging (PC) problems. The secondconfiguration, a center hole surrounded by a symmetric pattern

F2

0 F1

Baseline

O O000O O

F2

DiagnosticallyChallenging

i-^-- F1

Diagnostic &PrognosticallyChallenging (DPC)

Figure 4.—Schematic of biaxially loaded plate with variousinflicted defect configurations.

of smaller holes, (see Fig. 4 (middle)) is considered to fall intothe category of diagnostically challenging (DC) due to theinherent nonequal excitation intensities around the inflicteddefects. Additionally, this configuration is anticipated to beprognostically challenging. The third configuration, a centerhole with other multiple damage sites with varying character(location, size, geometry, sharp, smooth, etc.), is considered tobe both diagnostically and prognostically challenging (DPC),irrespective of the applied load history and will thus be usedprimarily for validation/demonstration of the developed lifemanagement system. Furthermore, a number of these tests willactually be performed “blind”, i.e., the inflected damage statewill be kept hidden from the analysts during the verificationprocess in order to fully verify the developed approach.

With respect to imposed load history, a number of biaxialityratios (BR = F1/F2) are anticipated: for example BR = 0(uniaxial), BR = 1 (equal biaxiality —pressure sphere), BR = 2and/or 0.5 (representing that in a cylindrical pressure vesselsuch as a combustor liner) and lastly a varying ratio, BR = V,wherein one component is held fixed while the other is varied.Although monotonic load histories will be imposed, emphasiswill be placed on fatigue induced cracks, with more complexhistories involving thermal cycles, periodic overloads, andstepped histories being conducted for validation at later stagesof the research program. Consequently, initially roomtemperature BR = 0,1,2 monotonic and simple cyclic histories(see light blue cells in Table 1) will be conducted so as toenable state-awareness characterization, diagnostic down-selection and prognosis enhancements. The remainder of the

NASA/TM—2009-215827 7

tests in Table 1 are to be conducted both at room and elevatedtemperature (see yellow and green cells in Table 1).

A key aspect of this experimental program will be theprecise documentation of the order (both temporally andspatially) of flaw insertion (be it operator and/or load historyinduced) thus enabling appropriate interrogation of the data(i.e., diagnostic signature and deformation and life—structuralmanifestation) to assess both sides of the proposed lifemanagement system, i.e., Figure 1. For example consider thefollowing envisioned test procedure:

(1) Obtain material property and uniaxial response curvesrequired by the viscoelastoplastic prognosis model.

(2) Perform flat plate characterization tests: Fully knownconditions with a single stress riser (see Fig. 4 (top)).

(a) Apply all desired diagnostic techniques to “virgin”plate (no hole).

(b) Induce hole of specified diameter, location andcharacter (thus overwhelm any inherent defects/flaws dueto manufacturing)—again apply all down selecteddiagnostic techniques to the plate.

(c) Mechanically load plate and monitor initiation andpropagation of crack(s) by taking a variety of spatial (full-field, and discrete location) measurements (strain-based,vibration and all other selected diagnostic techniques) atvarious time intervals (intermittent and continuous)throughout the mission profile, see Figure 4 (middle).

Steps (a), (b), and (c) for different load histories wouldbe repeated. In the case of validation tests (i.e., whenmultiple stress risers (see Fig. 4 (bottom) are present) theabove steps will be used except for the insertion of thefollowing step (d) in between steps (b) and (c):

(d) Impose predefined defects (with specific character) atspecified locations; obtain all signatures. This will simulatematerial randomness in that multiple initiation sites canoccur at unexpected locations when a mechanical load isapplied, thus challenging both diagnostic and prognosismethodologies.

The results will thus enable the quantification ofdetectibility sensitivities in the state-awareness variable(s) andprognosis methodology characterization. Given the above-generated data, we hope to be able to answer the followingquestions:

(1) Can we detect the presence, location and character (size,geometry, nature) of a defect be it operator or history induced.

(2) Can we detect/predict when and where damage (crack)initiates (criteria specific) and how and at what rate does itpropagate within a plate given a biaxial load history.

Note the presence of a variety of stress risers will providethe required randomness to validate both diagnostic andprognosis aspects, as well as allow linkage/ connectionbetween them to be established.

(3) What are the appropriate state awareness variables forthis type of damage mechanisms?

(4) What is the remaining life of the plate at any given timeand how should one modify the load to maximize remaininglife.

(5) What level (fidelity) and type of detection signatures arerequired to provide a specific confidence level of prognosis(criteria specific)?

2.5 Material Data Information Management

To properly characterize and validate the constitutive modelat the heart of the prognostic tool, the ability to capture thefundamental response data (i.e., the entire uniaxial/multiaxialresponse curve with its full pedigree, chemistry, processing,heat treatment, testing information, etc.) and applicationpotential of a given material system and not just specificpredefined (generally accepted point wise) values is required.Furthermore, as knowledge evolves these and other yetunmined data need to be processed and linked therebybecoming information and ultimately knowledge.Furthermore, although specification of typical test matricesinvolve, either explicitly or implicitly, a priori selection of amodeling approach; to maximize the value of any givenexperimental program (for both present as well as yet to bedeveloped models) one must attempt to capture and documentas much material response information as possible withoutprejudice to any particular model (idealization).

This general data, information, knowledge pyramid is at thecore of the material data life cycle (see Fig. 5(a) proposed bythe Material Data Management Consortium (MDMC)(MDMC, 2006), wherein data is captured and consolidatedfrom external sources, legacy databases as well as internal(possibly proprietary) testing programs. Next, data is analyzedand integrated to create or discover useful information andthen disseminated to the people who need and use it. Thecontinual maintenance of the whole system (the data andinformation generated as well as the relationships, or links,between them) becomes the last yet essential stage of the datalife cycle. Note that the middle ring of Figure 5(a) providesadditional information regarding the type of data utilized andfunctions performed during each phase in the data life cycle;while the outer most ring details the individuals most likelyresponsible for these functions.

To support the various required activities throughout thisdata life cycle requires the (preferably seamless) integration ofa variety of software tools. These range from data input,reduction/analysis, visualization, reporting tools; materialparameter estimation tools; product life management tools(PLM); to structural analysis codes that utilize a centraldatabase. These tools should enable material and structuralengineers to input, manage and utilize information in as anefficient, reliable and user-friendly way as possible. Finally,these tools should also enable enterprise-wide (even world-wide) solution or access.

A possible material database schema at a very high levelillustrating a portion of the information contained and itsassociated linkage within this centralized database is depicted

NASA/TM—2009-215827

Figure 5.—(a). Four aspects of material data lifecycle and (b)schematic illustrating a possible data schema for thematerial information.

in Figure 5(b). Note that within each dotted area a number oflower level data tables would be grouped. For instance withinthe Test Data Management area, one would find data tables foreach category of test data (i.e., tensile, creep, relaxation,cyclic, crack growth, etc.) wherein each individual recordwould contain both generally accepted point values and thecomplete response histories for each individual test along withimages of failure surfaces and microstructures. Within theStatistical Test Data section, one would find the correspondingconsolidated (statistically combined) response of a givenmaterial for each test category of interest. Finally, after furtherconsolidation and characterization of company- specificalgorithms and life modes, the corresponding material designallowables (e.g., stress, strain, elongation, etc.) would bestored for each material of interest. Such information storageand linkage enables full traceability of each and every dataitem.

3.0 Coupled MultimechanismViscoelastoplastic Deformation andDamage Model

As discussed earlier, a key concept in the FILMSmethodology, described previously, is the linkage of anadvanced constitutive model used for prognosis with anaccompanying diagnostic system. Due to its vital role in theoverall structural health management approach thedevelopment, characterization and validation of a unified,coupled deformation and damage constitutive model is thecurrent focus in this research program due to resourcelimitations. The primary tool for carrying out the prognosismethodology is a multiscale framework depicted in Figure 6which includes a set of constitutive equations known as theGVIPS (Generalized Viscoplasticity with Potential Structure)model (Arnold and Saleeb, 1994; Saleeb et al., 2001; Saleeband Arnold, 2001; Saleeb and Arnold, 2004). This model is acomplete (fully associative) potential framework whereinstrain, stress, and the thermodynamic functions (stored energyand dissipation), have been appropriately partitioned to form ageneral viscoelastoplastic, multimechanism, deformation anddamage model. This GVIPS framework attempts to simulatethe underlying physical processes associated with microscopicdefects (e.g., dislocations, grain boundaries, voids, etc. inmetals) and their complicated interactions which span anentire spectrum of length scales (i.e., from the “atomistic(nano)—microscale”, to the “mesoscale” to the final“macroscale”) by introducing the notion of multiplicity ofmechanisms in the mathematical description. Consequently,the complex nonlinear, time-dependent deformation anddamage response of any metallic structure can be analyzedusing this framework.

As the model can be applied in making off-line predictionsof the deformation, damage and life of a structure given anarbitrary loading history, as well as within an on-boardprognostics system where a given set of current damageparameters and load states measured by sensors and lined bystate-awareness methods, could be utilized for predicting thedamage progression and life of a structure accounting for anynumber of possible future loading scenarios. Also, as will beelaborated on shortly, the strength of this particular modelingapproach is its ability to fully account for the time- and rate-dependence and nonlinearity of the material response, andtheir interactions, in both the reversible and irreversibleregimes, in ways that classical plasticity and creep analysismethods cannot.

The mechanisms referred to above, reflecting the vastlydifferent interactions in the material microstructure, give riseto the introduction of an aggregate of individual internal statevariables (i.e., qi;, αi;, 9, and yr, see Figure 7); e.g., many

NASA/TM—2009-215827 9

Figure 6.—Multiscale framework describing the interaction between experimentation, analysis and detectiontechniques to enable accurate deformation and life modeling.

Figure 7.—Analog representation of multimechanism deformation and damage GVIPS framework with key governing equations.

NASAfTM—2009-215827 10

tensors each accounting for interactions at different lengthscales, that is, “short” range (atomistic movements such asclimb and diffusion), and “long” range (dislocation movement,subcells and grains). In addition to the differences in“microstructural” length scales, the time rates of changegoverning their dynamics are also known to be vastlydifferent, hence the notion of multiple (or spectrum of)characteristic relaxation times in the GVIPS formulation, i.e.,Mijkl and rI ijkl , see Figure 7.

Furthermore, with energy measures providing the majorconsideration in dislocation dynamic theories (e.g., in studyingthermal activation, mass and vacancies diffusion, energybarriers such as jog formation energy, rate-dependent andmultispecies (distributions of finite-strength obstacles, etc.))and the intricate interaction of such “unit” processes, withtheir vastly different energy contents and rate-limiting values,the partitioning of the overall supplied work into energystorage (e.g., hardening) and energy dissipation (e.g., recoveryand inelastic flows) components that proceed with varyingdegrees of competition during the deformation of the materialbecame a motivating factor. Hence the emphasis on acomplete-potential “energy” structure which leads to a“hierarchy” of representations, from the Gibb’s ( 0) anddissipation (S2) functions (grandparent), to the kinematicdecomposition of the deformation and microstructure stateequations (parent), to the kinetic and evolution equations(children). This structure then guarantees (1) that the overallresponse is always bounded in terms of the total and/or ratequantities (e.g., transient to steady-state creep, or from a stateof nonlinear hardening to a state of saturation in hardening)and (2) the availability of symmetric tangent stiffness matriceswhich greatly enhance computational robustness. Finally, theuse of multimechanisms (embedding the effects of manytime/length scales) in the GVIPS class of formulation enablesthe specialization of this general model into simpler, and morerestricted in scope, formulations, e.g., purely elastic, linearviscoelastic, classical rate-independent elastoplastic, as well asmore elaborate forms of hereditary descriptions (involvingviscous effects, nonlinear hardening, dynamic recovery,thermal/static recovery, relaxation, ratcheting or shakedownphenomena under load cycles) to name a few. More recently(Saleeb and Wilt, 2005), this formulation has been extended toinclude two types of damage measures, that is, strength andstiffness reduction. In the case of irreversible materialsoftening strength reduction, each of the hardening functionshb are degraded separately by the scalar A

(b), which is the

measure of the amount of strength reduction damage for eachmechanism (b), and varies from 1 to ∞ (1) denoting theundamaged (“virgin”) state and ∞ the fully damaged state).Consequently, a new associated pair of conjugate statevariables Y(b)

and A(b) (stress- and strain-like, respectively)

whose time evolutions are given in terms of the totalhardening stored energy of plasticity (i.e., plastic energyrelease Y (b)) for the corresponding mechanism, b areintroduced. On the contrary, for softening due to materialstiffness degradation, the entire viscoelastic moduli tensors

Eijkl and M(a)

ijkl are degraded simultaneously by the scalardamage parameter T, where Y and T are the new conjugate(stress- and strain-like, respectively) set of stiffness-damagestate variables. Note, the quantity T is the measure of theamount of stiffness damage and varies from 1 to ∞ (1 againdenoting the virgin undamaged state and ∞ being the fullydamaged material). It is important to note that the evolution ofdamage is directly evaluated and does not require any iterativeupdates in the implicit integration scheme for the other stressand internal variables. In the present model, a single stiffnessdamage mechanism (identified by the dotted line in thereversible strain region, i.e., the upper region, of Figure 7).

Although the GVIPS class model inherently representsnumerous distributed defects (dislocations /micro/meso/macrocracks) and their interaction phenomenologically, and has thepotential for tackling the problem of damage evolution fromlocalization to final macro failure, it currently lacks a reliablecriteria for tracking such intricate evolution (i.e., macro-crackinitiation and propagation (branching, kinking, etc.)) ofdamage as expected in realistically loaded structures.Providing these criteria, associating the above damagevariables with appropriate state-awareness variables anddemonstrating the ability to predict life accurately will be thefocus of the next steps in the project, i.e., establishing the stateawareness linkage between the prognosis and diagnosismethods, after the initial characterization and validation of thebase material model is complete. Note, the time dependentaspect of the model (i.e., viscoelastic and viscoplastic) willprimarily dominate at elevated temperature; while roomtemperature typically allows significant simplification to bemade within the model. However, as will be described insomewhat more detail subsequently, the ability of this modelto analyze the key time-dependent aspects of the materialresponse at elevated temperatures represents a significantadvantage of the modeling method over classical approaches.As this general, multimechanism, hereditary deformation anddamage model has been shown to accurately represent a widespectrum of material responses under different loadingconditions for the case of titanium alloys (Arnold et al., 2001;Saleeb et al., 2001; Saleeb and Arnold, 2004). Examplesinclude (1) rate-dependent (effective) material tangentstiffness during initial loading or any subsequent reversedloading, (2) pure transient response (e.g., in creep orrelaxation) within the reversibility region, (3) anelasticbehavior upon stress reversal, irrespective of the load level, aswell as, (4) other response features common to ‘unifiedviscoplastic’ formulations (e.g., rate-sensitivity, creep-plasticity interaction, thermal recovery, etc.).

To describe the GVIPS model in more detail, we begin witha key assumption of the additive decomposition of the totalstrain tensor, εij,

E E E E= + +ve I

or

th

(1)

E7 = Eij

− E Eth

ij ij

NASA/TM—2009-215827 11

into three components; that is a reversible mechanical strain,ε

veij , (i.e., elastic/viscoelastic); an irreversible strain, E' , (i.e.,

inelastic or viscoplastic); and a reversible thermal strain, thε ij

component. Numerous models describing the evolution of theinelastic strain have been proposed in the literature (Dowling,1999; Lemaitre and Chaboche, 1990; Skrzypek and Hetnarski,2000; Odqvist, 1936). Here we will utilize the GVIPS model,including its more recent extension into the coupleddeformation and damage regime (Saleeb and Wilt, 2005),which has been formulated with sufficient generality to permitsystematic introduction of multiple mechanisms.

The following generalized anisotropic, coupled deformationand damage material behavior constitutive model to providefor both viscoelastic (time-dependent reversible) andviscoplastic (time-dependent irreversible) responsecomponents ; where there are 6+ 2M reversible constants (i.e.,Es, M(a), ν, ρ(a), ce , Y0 , μ

e, n

e ) and 3+9N irreversible constants

(i.e., κ, n, μ H(b), R (b), m (b), b , c(i) Y.(i) g(i) n(i) ) where M

KO@), d,

o d d

is the number of viscoelastic and N defines the number ofviscoplastic mechanisms.

I

σij = Eijkl

ε −εkl + q

ij (2)

q(a)

= M( a) E −Z + M

(a) a )−1 (a) Ψ− 1ij ijkl kl kl ijkl nklrs qrs − ( σij (3)( )

I [. f(F)ΓY- ifF ≥ 0,

εij =

0 otherwise,(4)

a (b) _ (b) E

R( b) G ^,,,

π(b) — e( b )

(5)— 1 7,^-

Qijklkl

( )

H( b ) − G( b )

if π(b)

− (σkl − aj, ! 0

where,

Q. ) = H() ( 1− G()b

β, )b

×

Z.

β α

(b )

a(b)

va

2 κb)

G(b

) [1 − {1 −β} G( ]

ij kl

I

Note Zijkl is the “generalized” inverse of Λ ijkl ; see (Saleeb andWilt, 1993); for further elaboration on this.

Next the evolution of stiffness degradation is governed by

W= ceY

Y = 1 [( εy εy )ne − 1

(6)

μe Y

o

when the current magnitude of the total strain ( ε ) is greater

than a cut-off value ( εcut )

below which no damage

accumulates, i.e., Ψ = 0. Similarly, if the current magnitude of

the inelastic strain is above a given cut off value ( V t ) the

evolution of the strength reduction damage variable(s), θ (b),

becomes:

θ( b

) = c Y( b )

d

1

1 ^ 27C nd

]

(7)k

( b) = ( 2e°A °"e

μd Y

o

Note in the above state, flow and evolution equations, thevarious stress components and material functions are definedas follows:

q+i

=M IV

q+i ij ij

a=1 b=1

Γij =Λ ijkl (

σkl − αkl),π(b )

= Λ ijkl α9 (9)

F n 10f (F) = 2μ

( )

g ( G(b

)) = H(b)(

1 − vG()b

)β

m (11)

and

1F =

2κ2(σij −αij) Λ ij/d (σld −αkl ) −1 (12)

G(b) = 1 (a

(b ) Λ . . a(

b))

(13)2 ij ykl kl

b)

Furthermore, all three fourth-order viscoelastic moduli

tensors, Eijkl, Mijkl and Tj kI , are taken to be coaxial, that is,

Eijkl

= Es Nijkl

,MYkI = M( a )

Nijkl ,

and 'r)1 I = ρaMjkl

where,

Nijkl t(1+ ν)(1−2ν)δij

δkl +(1+ν)(δik

δjl

+δilδ

jk

)1

A key feature of the current GVIPS constitutive model, asopposed to more traditional plasticity and viscoplasticity typesof approaches that have been applied to the analysis of metals,is that in the GVIPS formulation, the total strain (εij) ispartitioned into reversible ( ε-Y

ve ) and irreversible ( vpε ) regimes

NASA/TM—2009-215827 12

and the stress is partitioned into equilibrium ((Y s, and σij–αij)

and nonequilibrium components ( q i ) and α^!) ), as shown in

Figure 7.In general, previous models assumed the reversible or

“elastic” regime to be time-independent and the irreversiblestrains were considered to be either time-independent(“plastic”), or more commonly time-dependent(“viscoplastic”). Recent research efforts have determined thatstrains in the reversible regime can be both time-independentand time-dependent (Saleeb and Arnold, 2001; Arnold et al.,2001) depending on the temperature. Therefore concepts fromviscoelasticity, which previously had not been applied tometals, actually need to be applied to the constitutiveequations employed to analyze metals. Furthermore, in theregime of time-dependent strains, due to the wide spectrum ofrate-dependence of the material in both the reversible andirreversible domains, multiple mechanisms (spring-dashpotsets in terms of the mechanical analogues, see Fig. 7) need tobe included. The more mechanisms that are used, the morelikely the characterized model is to appropriately model thebehavior across all strain rates. Obviously, the moremechanisms that are present, the more model parameters andexperiments, which isolate these various mechanisms arerequired, so judgment has to be employed in choosing thenumber of mechanisms.

Recently, the GVIPS model was extended to includedamage to account for the softening due to stiffness and/orstrength-reduction mechanisms present in the material (Saleeband Wilt, 2005). It is this feature of the model, when linkedwith state-awareness capabilities, which will provide therequired ability of the prognostic model to compute thedamage progression and ultimate life in a structure.

4.0 Characterization of GVIPS Model

Now, given fundamental material response histories, themost important, and often times most difficult 1 aspect ofmodeling the behavior of a given material is obtaining therequired material functions (e.g., f(F) and g(G)) and associatedmaterial parameters, see Equations (12) and (13). Thedifficulty associated with this process typically stems from notonly the variety in mathematical forms for the materialfunctions (e.g., power law, exponential, hyperbolic sine, etc.),but also given the material functions, there is often no uniqueset of material parameters for any given load path. Therefore,numerous iterations and difficult compromises are requiredbefore a final set of material parameters (for the assumedmaterial functions) can be obtained.

Traditionally, characterization has been accomplishedthrough basic trial and error procedures (i.e., graphical and/or

1 Depending upon the sophistication of the constitutive modeland environment; e.g., room temperature versus elevated temperatureand loading conditions.

mechanistic) which attempt to fit the predicted response fromthe constitutive model to that response exhibited by theexperimental test data. In the case of idealized elastic, elastic-plastic or steady state creep material behavior; theseapproaches are quite successful; however for more general andsophisticated constitutive models, they are rather limited,difficult, and many times less than fruitful. This is particularlytrue when dealing with models that possess a very largenumber2 of material constants (such as the GVIPS model) that:(1) are often lacking in their direct physical interpretation (thisis not the case in the GVIPS model), (2) may have vastlydifferent magnitudes, and (3) are highly interactive. Furthercomplications arise when a large number of experimental testsof various types (i.e., stress-, strain-, or mixed-control) undertransient and/or steady-state conditions, are expected to besimulated. Thus there is an obvious need for a systematicdevelopment of a general methodology for constitutiveparameter estimation. Recently, software tools have beendeveloped (e.g., COMPARE (Saleeb et al., 2002; Saleeb, et al.,2004) and Z-mat (Z-mat, 2006)) to enable a design engineer toeasily and efficiently bridge the gap between constitutive theoryand experimental test data. Optimum material parameters aredetermined by minimizing the errors between experimental dataand the correlated responses. Within COMPARE the estimationof material parameters is accomplished by casting the problemas a minimum-error, weighted least-squares, multiobjectiveoptimization problem; wherein, this optimization problem issolved using the Sequential Quadratic Programming Technique.Also, COMPARE is sufficiently general to handle acomprehensive set of test data, under arbitrary load-controlvariables, multiaxial stress/strain state, and transient as well assteady-state response measurements. Figure 8 shows aschematic flowchart of the process COMPARE uses to obtainthe required parameters.

It is important to realize from the outset, that the resultingset of material parameters (regardless of the parameterestimation tool used to obtain them) is nonunique (due to thenonlinear nature of the problem), however if a sufficientamount of “data content” is provided then it is generallybelieved that the final obtained parameters should be relativelyindependent of the initial guess and bounds provided. Heredata content is meant to imply not just quantity but alsovariety of experimental data; which will highlight andilluminate various issues such as multiaxiality, time scale,control mode (stress versus strain) and multiple deformationand damage mechanisms, to name a few. For example in thecase of time scales, if one only provided stress-strain tensiledata then one should not expect a model, that possessessufficient breadth, to be able to accurately predict both creepand relaxation response; since the time duration of these typesof tests far exceeds that of a tensile test. Similarly, if oneprovides only creep or relaxation data, one should not expect

2In the specific model presented, the total number of materialparameters required is 9 +9N + 2M where N defines the number ofviscoplastic mechanisms and M the number of viscoelastic.

NASA/TM—2009-215827 13

Figure 8.—Flow chart for COMPARE software.

the model to accurately represent the typically shorter timedomain tensile behavior of a given material (Arnold, 2006).

5.0 Characterization Results

To demonstrate the ability of the GVIPS model to simulatethe full range of the deformation and damage response ofadvanced metallic materials, the viscoelastoplastic behavior ofan advanced titanium alloy, Ti-6Al-4V (commonly referred toas Ti-6-4), is being investigated. The characterization processis only partially complete for the deformation response and iscurrently incomplete for the damage response (which isadmittedly the portion of most significance for thedevelopment of prognostics tools). However, even the effortswhich have been completed to date provide insight into thecomplexity of the material response of this alloy, and how theelevated temperature response of this material hascharacteristics which are not normally accounted for inclassical methods of materials analysis, but which can beaccounted for by using the GVIPS model. Ti-6-4 is an alpha-beta titanium alloy, represents the salient features of a class ofmaterials (titanium) to be used in such targeted applications ascompressor blades, disks, etc., and represents over 50 percentof all titanium to be used in jet engine components. Thereforeits selection enables the appropriate physics-of-failure to bestudied, incorporated and validated within the GVIPSprognosis model. After examining the literature for

deformation and life data, numerous holes in the materialcharacterization database (both with respect to reversible andirreversible behavior) for Ti-6-4 existed, thus necessitating anextensive amount of deformation and damage testing (ofwhich approximately 65 percent is complete) and analysis tobe conducted.

The need for an advanced viscoelastoplastic model toanalyze the deformation response of Ti-6-4 at elevatedtemperatures is demonstrated in Figure 9, where the variationof the moduli and threshold stress (x) (delineates the reversibleand irreversible strain regimes) are plotted as a function oftemperature in Figure 9. The modulus ES represents the“infinitely slow” modulus, i.e., the elastic modulus of thematerial if it was loaded at an infinitely slow strain rate,whereas the modulus ED represents the “dynamic modulus”,which is the modulus of the material, if it is loaded at an“infinitely fast” (i.e., very high, 1×10–3) rate. As can be seen inFigure 9, at elevated temperatures there is a significantdifference between the two modulus values, indicating thateven in the so-called “elastic” range, there is significant time-dependence. Below a temperature of about 300 °C, the twomoduli are approximately equal, indicating the response of theTi-6-4 material is rate-independent yet not necessarily time-independent. Above this temperature, the response is rate-dependent and time-dependent. To appreciate the practicalsignificance of this fact, the operating temperatures typicallyencountered in aircraft engines are also noted below the

NASA/TM—2009-215827 14

Figure 9.—Variation of modulus and threshold stress as a function of temperature for Ti-6-4 material.

horizontal axis in Figure 9, as well as the occasional, higher-temperature regime encountered during over-temp maneuvers.Clearly, even when one is within the typical engine designrange and expecting the material response to be reversible, or“elastic”, the materials behavior (at least in the case of Ti-6-4)would in fact be rate-dependent and would deform anadditional σ∗/Es amount of strain over time, where σ∗ is thecurrent applied stress. Consequently, at stresses below κ, ifclassical elasticity methods were used in the design, then thisrate dependence, i.e., viscoelastic response, would not becaptured. Furthermore, at stresses above κ, the materialresponse is viscoplastic due to the rate-and-time-dependence,and similarly using the classical methods of plasticity inanalysis and design, would also not be accurate.

Figure 9 further indicates that the value of the thresholdstress, κ , decreases significantly as a function of temperature.While not shown here, the important point to note is that atelevated temperatures the threshold stress ( x) is significantlybelow the traditional “proportional limit” or “yield stress” ofthe material. This factor then leads to the conclusion thatirreversible material behavior takes place at stress levels wellbelow those considered using traditional methods for theanalysis of metals. If classical design methods were used, thematerial response below the “proportional limit” would beassumed to be fully reversible, and only the response after theproportional limit would be assumed to be irreversible.However, as is shown in the figure, that assumption could lead

to significant inaccuracies in the predictions of the materialresponse.

The modulus Es can be determined from a creep test and arelaxation test conducted within the reversible regime, asdemonstrated in Figure 10. In this figure, results from twocreep tests (one below κ and one above) and a relaxation testare shown on the same stress-strain plot. Note, the pointswhere the creep and relaxation cease (thus indicating anequilibrium state) are connected and the slope of the resultingline can be considered to be the time independent stiffness, Es.

The value of the threshold stress x can be computed by aprocess known as “viscoelastic subtraction” (Arnold et al.,2001). In this procedure, a creep test is conducted well belowx (estimated for example by taking a stress level 50 percentbelow the proportional limit resulting from a slow-rate tensiletest (e.g., 1 × 10–6 or less)), and after the creep stops, thematerial is unloaded and then held at zero stress or strain untilall of the strain or stress is recovered. If the creep stress is inthe “irreversible” range of the material response, after a periodof time being held at zero stress the strain recovery will cease,leaving an inelastic (irreversible) strain. The value of thethreshold stress can then be computed by using the value ofthis creep stress, the inelastic strain obtained, and the time-independent stiffness Es (see the equation in Figure 10).

N

ED = ES + M

( a ) (14)a = 1

NASA/TM—2009-215827 15

Figure 10.—Determination of threshold stress and time-independent stiffness for GVIPS model.

TABLE 2.—CHARACTERIZED VISCOELASTIC MATERIALCONSTANTS FOR Ti-6-4 MATERIAL

Temperature°C

371 427 482 538

Es (psi) 10,687,600 8,890,370 7,037,810 2,444,950M1 (psi) 110,887 499,594 736,202 1,399,370P1 (1/s): 700 200 38 31M2 (psi) 1,200,000 1,453,840 1,722,430 2,133,740P2 (1/s): 9,580 622 338 250M3 (psi): 931,104 1,299,240 1,586,740 2,064,350P3 (1/s): 55,086 6,085 1,024 882M4 (psi): 580,000 959,668 1,276,920 1,797,670P4 (1/s): 110,000 60,031 6,731 3,000M5 (psi): 291,605 1,345,300P5 (1/s): 20,000 12,643M6 (psi): 1,097,820P6 (1/s): 85,187

Repeating this procedure for each temperature, theviscoelastic behavior of the material (Ti-6-4) can becharacterized across a range of temperatures. In this case,Table 2 shows the resulting characterized material constantsfor Ti-6-4 from 371 to 538 °C. The variation of the parameterswith temperature is shown schematically in Figure 11.

The value of the Maxwell mechanism, spring moduli ( M(i))increases linearly with temperature, indicating that theviscoelastic response and time-dependence increases withincreasing temperature. Conversely, the characteristicrelaxation time (ρa, a = 1 to M) decreased in a parabolicfashion with temperature, indicating that the level of transientresponse increased as the temperature was increased. Asdiscussed earlier, the value of the time-independent stiffness(Es) also decreased parabolically, but unlike with therelaxation time, the rate of decrease was higher at highertemperatures. As can be observed in Table 2, the number ofmechanisms required to characterize the material increased

Parameter

TemperatureFigure 11.—Variation of viscoelastic parameters with

temperature.

with temperature, as well. This result suggests that the amountof reversible time-dependence in the material responseincreased with increasing temperature.

The overall characterization of the viscoelastic materialresponse for Ti-6-4 has thus far been very successful.Figure 12 shows experimental and computed stress-strainresults from a representative creep test and a representativerelaxation test conducted at 538 °C, below κ. For the creeptest, the creep response (including creep shutdown), unload,and strain recovery at zero load were all well correlated. Therelaxation response (including relaxation shutdown) was alsowell correlated. Figure 13 shows a normalized plot of theexperimental and computed stress-time response resultingfrom relaxation tests conducted at several temperatures. Thetemperature dependence of the relaxation response wascaptured, and the overall quantitative correlation between theexperimental and computed results was reasonable. Theseresults all indicate that the GVIPS model can simulate thetime-dependent reversible deformation response of metallicalloys.

NASA/TM—2009-215827 16

0

2500

2000 • Creep-Experiment

Creep-Computed

Relaxation-Experim

Relaxation Com u1500

1000 '"'•

N

500

00.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004

-500

Strain (infin)

Figure 12.—Correlation of viscoelastic creep and relaxation response of Ti-6-4 at 538 °C.

1

0.9 •• N•N•N

0.8

11.11111 N•••N•N•N••••••N••N•••N••N••••••••••N

3 71 C

•••••••••1.11••1••1••1••11.11.111.1••11.11.11.11.11.11••1••1••1••11.1^ 427 C

0.7

9 0.6 n

E nn.

bb 482 C'n...

0.5 • • n.........

nn ...uu....uuou...uuu........uuu.........

0.4

r q •••• • •

••• •••• •• •• •••• • •

0.3 •• • i ••^••••••••

538 C0.2

0.1

0

0 20000 40000 60000 80000 100000

Time, s

Figure 13.—Correlation of viscoelastic relaxation stress-time response at various temperatures for Ti-6-4.

To characterize the viscoplastic (irreversible) portion of the material could be quantified. The expected temperature-

material response, a series of creep and relaxation tests have dependence of the various viscoplastic material parameters is

been initiated. The deformation test program thus far shown schematically in Figure 14.

completed is summarized in Table 3. A series of relaxation Test results obtained to date demonstrate the rate- time- and

tests were conducted at temperatures ranging from room history-dependence of the material response. These results

temperature 20 to 538 °C. The relaxation tests were carried out show that advanced, multimechanism, viscoelastoplastic

at a variety of strain rates. Thus, the interaction of the strain models are required to model the details of the material

rate-dependence, time and temperature-dependence of the response. Traditional modeling methods are incapable of

NASA/TM—2009-215827 17

Parameter

TABLE 3.—TEST MATRIX TO CHARACTERIZETHE IRREVERSIBLE MATERIAL RESPONSE

OF Ti-6-4 MATERIAL

Test type Temperature( C)

Strain rate(1/s)

strain le%el(in/in)

stress le%el(ksi)

relaxation 20 0.0000006 0.018relaxation 20 0.001 0.018relaxation 200 0.0000006 0.018relaxation 200 0.001 0.018relaxation 316 0.0000006 0.018relaxation 316 0.00099 0.018

creep 316 0.00101 75creep 316 0.00101 81creep 316 0.00103 85

relaxation 371 0.0000006 0.018relaxation 371 0.00099 0.018

creep 371 0.001 75relaxation 427 0.0000006 0.006relaxation 427 0.0000006 0.018

step relaxation 427 0.0000006 .006, .012relaxation 427 0.0000008 0.006relaxation 427 0.0000008 0.006relaxation 427 0.0000008 0.018

step relaxation 427 0.0000008 .006, .012, .018step relaxation 427 0.0000008 .012, .018

relaxation 427 0.0000099 0.018relaxation 427 0.00001 0.018relaxation 427 0.000099 0.018relaxation 427 0.0001 0.018

creep 427 0.000977 70relaxation 427 0.001 0.018relaxation 1 427 0.001 0.018

steprelaxation 427 0.001 .006, .012, .018step relaxation 427 0.001 .006, .018step relaxation 427 0.001 .012, .018

creep 427 0.001037 65creep 427 0.001039 55creep 427 0.0024 75

relaxation 482 0.0000006 0.018relaxation 482 0.00099 0.018relaxation 538 0.0000006 0.006relaxation 538 0.0000006 0.018relaxation 538 0.0000006relaxation 538 0.001 0.018

creep 538 0.0011 55creep 538 0.0011 15creep 538 0.0012 35

Modulus %arious %arious ±0.001

Temperature

Figure 14.—Variation of viscoplastic parameters withtemperature.

capturing the complex phenomena observed in thedeformation response of metals at high temperature. Forexample, in Figure 15 the normalized stress-time plots fromrelaxation tests conducted at various temperatures at slow(6×10–7/s)- and fast (0.001/s)-loading strain rates are shown.As can be seen in the figure, there is a noticeable strain ratedependence of the material response, and the rate-dependenceincreases with increasing temperature. These results alsosuggest the need for at least two, if not more, viscoplasticmechanisms since the material response given only a singlemechanism would show identical relaxation response evenwhen loaded at different initial strain rates.

A series of relaxation and step relaxation tests wereconducted at 427 °C which included a pure relaxation test inwhich the material was loaded to 1.8 percent strain andrelaxed for 24 hr; a two-step relaxation test where the materialwas loaded to 1.2 percent strain, relaxed for 24 hr, and thenreloaded to 1.8 percent strain where the material was relaxedagain; a two-step relaxation test where the material was loadedto 0.6 percent strain, relaxed, reloaded to 1.8 percent strainand relaxed; and finally a multistep test where the materialwas loaded to 0.6 percent strain, relaxed, loaded to 1.2 percentstrain and relaxed, and finally loaded to 1.8 percent strain andrelaxed. Stress-strain curves from these tests are shown inFigure 16, and the corresponding stress-time curves (takenfrom the relaxation portion which took place at 1.8 percentstrain) for each of these tests are shown in Figure 17. Thestress-strain curves show that the prior history (i.e., steprelaxation) did not largely affect the overall stress-strainresponse, as upon reloading the material trended towards theoriginal stress-strain curve. However, the stress-time curves,shown in Figure 17, do demonstrate the history-dependence ofthe material, as the relaxation response varied based on theprior stress relaxations.

Standard creep tests were also conducted at severaltemperatures and stress levels. Although not shown in the testmatrix displayed in Table 3, step-creep and creep-overloadtests were also conducted to quantify the history-dependenceof the material, as well as the “creep-plasticity” interaction.Figure 18 shows stress-strain curves from the various types ofcreep tests that were conducted at 427 °C. The step-creep testsserve to demonstrate the history-dependence of the materialresponse. The creep overload test shown in Figure 18, inwhich the material is loaded to a 75 ksi stress level, thenunloaded to 65 ksi stress level and crept as compared to a“virgin” creep curve conducted at 65 ksi level, serves todemonstrate the “creep-plasticity” interaction observed inmetals, and in particular Ti-6-4. Phenomena of this typecannot be simulated using classical time-independentplasticity coupled with time-dependent creep analysismethods.

NASA/TM—2009-215827 18

1

0.9slow

0.8-fast 316 °C

0.7

0.6slow

0.5............ fast 427 °C

0.4

0.3

0.2-slow

0.1 fast

0

.. 538 °C

-20000 0 20000 40000 60000 80000 100000 120000

time (secs)

Figure 15.—Effect of strain rate and temperature on viscoplastic relaxation response for Ti-6-4 material.

90000

80000

70000

60000

a 50000CL

WWA 40000Ca

30000

20000

10000

0 r

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Strain

Figure 16.—Stress-strain results from relaxation and step relaxation tests conducted at 427 °Cto demonstrate history dependence of viscoplastic behavior.

NASAfTM—2009-215827 19

90000

80000

70000

60000

w 50000'stotoE 40000

30000

20000

10000

0

astrain rate = .001 /s

1

prior relaxations at

f

0.6%

1.2%

virginsample

-100000 10000 20000 30000 40000 50000 60000 70000 80000 90000

time (secs)

Figure 17.—Stress-time results for relaxation at 1.8 percent strain from relaxation and step relaxationtests conducted at 427 °C to demonstrate history dependence of viscoplastic behavior.

80000

strain rate = 0.001/sec

75000 test

70000

65000 creep test

Na0 60000dN

55000

50000

45000

40000 ' `

0 0.005 0.01 0.015 0.02 0.025 0.03Strain, in/in

Figure 18.—Stress-strain curves of creep, step creep and creep overload tests at 427 °C.

NASAfTM—2009-215827 20

0.03strain rate = .001/s minimum rate 2.20e-07/sec

0.025

virginsample

C 0.02

c

prior stress1.11e-07/sec

0.015

overloadNQ.G!luU

0.01

1.52e-07/sec

prior stresssteps

10000 20000 30000 40000 50000 60000 70000 80000 90000

time, secs

Figure 19.—Strain versus time results from creep tests conducted at 65 ksi and 427 °C to demonstrate historydependence of viscoplastic material behavior.

0.005

0

Figure 19 shows the corresponding strain-time curves for thestandard creep, step-creep and creep-overload tests generatedfrom creeping at a stress level of 65 ksi. As can be seen in thefigure, the creep response of the material is strongly dependenton the material’s prior history before the creeping (constantload portion of the history) took place. It is precisely thiscreep-plasticity interaction phenomenon that demanded,decades ago, the development of “unified” viscoplastic models(like the current GVIPS formulation) to accurately capture thistype of behavior. The term unified implies that only a singleinelastic strain (which captures both time-dependent and time-independent behavior) is included in the constitutive model.Overall, titanium alloys demonstrate a full range of rate- andtime-dependent material response over a wide stress andtemperature range. The goal of the project will be tocharacterize this full range of material behavior using theGVIPS model. Ongoing work includes the characterization ofthe viscoplastic portion of the GVIPS model as well as themeasurement and characterization of the influence of damagemechanisms on the mechanical response of Ti-6-4. Theseresults will be documented in future publications.

6.0 Conclusions

A novel, integrated prognostic model (with linkages todiagnostics methods) has been proposed for structural healthmonitoring, with particular applicability to hot engine

structures. The key requirements for prognostics methods, anda general discussion of how these methods can be linked withdiagnostics techniques, have been discussed, as well as anexperimental approach for fully exploring and validating theproposed methodology. The necessity of including anadvanced multimechanism viscoelastoplastic model as a keycomponent of the prognosis methodology has beendemonstrated. To provide a prognosis method that is not justan extrapolation of previously observed material behaviors,advanced constitutive models are required which can be linkedto the diagnostic methods through state-awareness techniques.As engine structures will encounter elevated temperatures,classical analysis methods and constitutive equations will notbe able to accurately simulate all of the features of the materialresponse. Therefore, the advanced GVIPS viscoelastoplasticconstitutive model will be of significant use as a trueprognosis tool. To partially demonstrate the ability of theprognostics tool to simulate advanced features of the materialresponse of metallic alloys, results obtained from thecharacterization of the reversible portion of the material modelfor a representative titanium alloy (i.e., Ti-6-4) have beenpresented. Furthermore, a description of the test program thatis being conducted to characterize the irreversible portion ofthe constitutive model, along with some representative results,which demonstrate the full history-dependence of the materialresponse has been discussed. Future efforts will involve fullycharacterizing the irreversible portion of the material model

NASA/TM—2009-215827 21

both uniaxially and biaxially, as well as carrying out a coupledexperimental/analytical study to characterize the damageportions of the material behavior. This method will then belinked to appropriate diagnostic methods through state-awareness systems to provide a full-featured structural healthmonitoring system.

References

(Adams, 2004) D.E. Adams. “Diagnosis and Prognosis inStructural Systems,” A short course, Ohio AerospaceInstitute, 2004.

(Arnold et al., 2001) S.M. Arnold, A.F. Saleeb, M.G. Castelli .“A General Reversible Hereditary Constitutive Model: PartII Application to Titanium Alloys,” JEMT, Vol. 123, pp.65–73, 2001.

(Arnold, 2006) S.M. Arnold. “Paradigm Shift in Data Contentand Informatics Infrastructure Required for GeneralizedConstitutive Modeling of Materials Behavior,” MRSBulletin, December, pp. 1013–1021, 2006.

(Dowling, 1999) N.E. Dowling. Mechanical Behavior ofMaterials: Engineering Methods for Deformation, Fracture,and Fatigue, Prentice Hall, New Jersey, 1999.

(Fatemi and Yang, 1998) A. Fatemi and L. Yang. “CumulativeFatigue damage and life prediction theories: a survey of thestate of the art of homogeneous materials,” Int. J. ofFatigue, Vol. 20, No. 1, pp. 9–34, 1998.

(Grandt, 2004) A.F. Grandt. “Fundamentals of StructuralIntegrity,” John Wiley & Sons, 2004.

(Hess, 2002) A. Hess. “The Prognostic Requirement forAdvanced Sensors and Nontraditional DetectionTechnologies,” DARPA/DSO Prognosis Bidder’sConference, Alexandria, VA, 2002.

(Lemaitre and Chaboche, 1990) J. Lemaitre and J.L.Chaboche. Mechanics of Solid Materials, CambridgeUniversity Press, 1990.

(MDMC, 2006) MDMC. www.mdmc.net , Cambridge, UnitedKingdom, 2006.

(Odqvist, 1936) F. Odqvist. Theory of Creep Under the Actionof Combined Stresses with Applications to HighTemperature machinery,” Proc. Royal Swedish Institute forEngineering Research, N. 141, 1936.

(Rytter, 1993) A. Rytter, “Vibration based inspection of civilengineering structures,” Ph. D. Dissertation, Department ofBuilding Technology and Structural Engineering, AalborgUniversity, Denmark, 1993.

(Saleeb and Wilt, 1993) A.F. Saleeb, and T.E. Wilt. “Analysisof the Anisotropic Viscoplastic Damage Response of

Composite Laminates-Continuum Basis andComputational Algorithms,” International Journal forNumerical Methods in Engineering, 36(10), pp. 1629,1993.

(Saleeb, et al., 2001) A.F. Saleeb, S.M. Arnold, M.G. Castelli,T.E. Wilt, and W.E. Graf. “A General HereditaryMultimechanism-Based Deformation Model WithApplication to The Viscoelastoplastic Response ofTitanium Alloys, Int. Jnl. of Plasticity, Vol. 17, No. 10, pp.1305–1350, 2001.

(Saleeb and Arnold, 2001) A.F. Saleeb, and S.M. Arnold. ‘‘AGeneral Reversible Hereditary Constitutive Model: Part ITheoretical Developments,” JEMT, Vol. 123, pp. 51–64,2001.

(Saleeb, et al., 2002) A.F. Saleeb, A.S. Gendy, T.E. Wilt.“Parameter-Estimation Algorithms for Characterizing AClass of Isotropic and Anisotropic Viscoplastic MaterialModels,” Int. Jnl. of the Mechanics of Time DependentMaterials, Vol. 6, No. 4, pp. 323–361, 2002.

(Saleeb and Arnold, 2004) A.F. Saleeb and S.M. Arnold.“Specific Hardening Function Definition andCharacterization of A Multimechanism GeneralizedPotential-Based Viscoelastoplasticity Model,” Int. Jnl. ofPlasticity, Vol. 20, pp. 2111–2142, 2004.

(Saleeb, et al., 2004) A.F. Saleeb, J.R. Marks, T.E. Wilt, andS.M. Arnold. “Interactive Software for Material ParameterCharacterization of Advanced Engineering ConstitutiveModels,” Adv. Eng. Software, Vol. 35, pp. 383–398, 2004.

(Saleeb and Wilt, 2005) A.F. Saleeb, and T.E. Wilt. OnExtending the Capabilities of COMPARE to IncludeMaterial Damage, NASA/CR—2005-213815, 2005.

(Saleeb and Ponnaluru, 2006) A.F. Saleeb, and G.K.Ponnaluru. Enhancement of the Feature ExtractionCapability in Global Damage Detection Wavelet Theory,NASA/CR—2006-21225, May 2006.

(Saleeb and Prabhu, 2002) A.F. Saleeb, and M. Prabhu. DefectLocalization Capability of a Global Detection Scheme:Spatial Pattern Recognition Using Full-Field VibrationTest Data in Plates, NASA/CR—2002-211685, Aug. 2002.

(Skrzypek and Hetnarski, 2000) J. Skrzypek and R. Hetnarski.Plasticity and Creep, Theory, Examples, and Problems,CRC Press, 2000.

(Springer, 2004) Springer, JOM, Volume 56, Issue 3, 2004.(Z-mat, 2006) Z-mat Library, http://www.nwnumerics.com/Z-

mat/, Seattle, WA, 2006.

NASA/TM—2009-215827 22

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14. ABSTRACTHerein a general, multimechanism, physics-based viscoelastoplastic model is presented in the context of an integrated diagnosis andprognosis methodology which is proposed for structural health monitoring, with particular applicability to gas turbine engine structures. Inthis methodology, diagnostics and prognostics will be linked through state awareness variable(s). Key technologies which comprise theproposed integrated approach include (1) diagnostic/detection methodology, (2) prognosis/lifing methodology, (3) diagnostic/prognosislinkage, (4) experimental validation, and (5) material data information management system. A specific prognosis lifing methodology,experimental characterization and validation and data information management are the focal point of current activities being pursued withinthis integrated approach. The prognostic lifing methodology is based on an advanced multimechanism viscoelastoplastic model whichaccounts for both stiffness and/or strength reduction damage variables. Methods to characterize both the reversible and irreversible portionsof the model are discussed. Once the multiscale model is validated the intent is to link it to appropriate diagnostic methods to provide a full-featured structural health monitoring system.15. SUBJECT TERMSStructural health monitoring; Diagnostics; Prognosis; Experimental; Modeling; Damage; Reversible; Irreversible

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