Don’t Let it Break - Southwest Research Institute...• “Classical” failures (LCF, creep, etc.) are trending down FAA and engine Manufacturers are addressing the potential for

Copyright 2015 Southwest Research Institute

Don’t Let it Break: Using Probabilistic Fracture Mechanics to Transform the

Material and Structural Design Process

R. Craig McClung Southwest Research Institute

San Antonio, Texas

Mechanical, Aerospace, and Biomedical Engineering Department University of Tennessee, Knoxville

4 November 2015

Introductions Copyright 2015 Southwest Research Institute®

Introduction to Southwest Research Institute

2

• Independent organization • Established in 1947 • $549M revenue in FY2014 • 60%/40% government/industry projects • 2780 staff members in 10 technical divisions

San Antonio, Texas

UTK MABE Seminar Copyright 2015 Southwest Research Institute®

Sioux City disk failure was the catalyst for unprecedented levels of industry/FAA cooperation regarding rotor safety … FAA Ti Initiative AIA Rotor Integrity Sub-Committee (RISC) established to develop new lifing strategies

ACCIDENT UAL 232, July 19, 1989 - Sioux City, Iowa

• DC10-10 crashed on landing • In-Flight separation of Stage 1 Fan Disk • Failed from cracks out of material anomaly - Hard Alpha produced during melting • Life Limit: 18,000 cycles. Failure: 15,503 cycles. • 112 fatalities • FAA Review Team Report (1991) recommended: - Changes in Ti melt practices, quality controls - Improved manufacturing and in-service inspections - Lifing Practices based on damage tolerance

Driving Force – Sioux City Titanium Hard Alpha

3


Pensacola failure motivated expansion of industry/FAA cooperation RISC Activities Focused on Surface Damage Tolerance Methodology Development Spawned FAA Enhanced In-Service Inspection and Rotor Manufacturing Initiatives

ACCIDENT DL 1288, July 6, 1996 - Pensacola, Florida

• MD-88 engine failure on take-off roll • Pilot aborted take-off • Stage 1 Fan Disk separated; impacted cabin • Failure from abusively machined bolthole • Life Limit: 20,000 cycles. Failure: 13,835 cycles. • 2 fatalities • NTSB Report recommended ... - Changes in inspection methods, shop practices - Fracture mechanics based damage tolerance

Driving Force – Pensacola Surface Damage

4


Perspective

Modern aircraft engines have excellent reliability and safety records Nevertheless, uncontained disk failures do occasionally occur Industry and FAA have been working to reduce these failure rates Recent experience shows primary causal factors for uncontained

failures are inherent material anomalies, and manufacturing and maintenance/usage induced anomalies • “Classical” failures (LCF, creep, etc.) are trending down

FAA and engine Manufacturers are addressing the potential for unanticipated anomalies by implementing a Damage Tolerance Philosophy

5


Retirement Life Inspection Requirements

Nominal Conditions Anomalous Conditions

Safe Life (Fatigue) Damage Tolerance

Enhanced Life Management Process

Damage Tolerance Complements Safe Life Methods

6


“Damage Tolerance” Concept

Assuming that an undetected crack exists in the structure, how many load cycles are required to grow the crack to failure?

The crack is often assumed to exist in the most critical location and orientation

The size of the assumed crack is often based on NDE considerations The largest crack that cannot

be reliably found Number of Cycles

Crac

k Le

ngth

Assumed initial crack size

Final crack size at failure

“Safe Life”

7


Probabilistic Damage Tolerance

Cannot assume that every rotor has a rogue anomaly in the worst location • This is unrealistic and too conservative

Probabilistic Damage Tolerance Analysis (PDTA) is a feasible alternative

PDTA determines • The unconditional risk of fracture (following established fatigue crack

growth analysis principles) based on the assumption that a rare anomaly is present in the component

• The probability that a rare anomaly is, in fact, present in the component • The probability that the anomaly and resulting crack will not be found

during inspections PDTA determines risk of fracture by considering all these factors The risk of fracture is managed via the design process to acceptably

low levels based on calibration to historical experience

8

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9

Probabilistic Fracture Mechanics Methodology


Development of Advisory Material

Specific damage tolerance methods for specific anomaly types have been developed and documented by the FAA in a series of Advisory Circulars • AC 33.14-1 (2001) – titanium hard alpha • AC 33.70-1 (2009) – general guidance for life-limited parts • AC 33.70-2 (2009) – hole features

10


Overall FAA/RISC Vision

Damage Tolerance Methodology

Inherent Flaws (Melt related, etc) Induced Flaws

Titanium Hard Alpha

Manufacturing

Analytical Method: Probabilistic FM Calculated Risk < DTR

Ni Anomalies Maintenance/ Service

Current Focus

• Analysis Tool calibrated by Test Case • Criteria Calibrated by Experience

• Circular holes • Attachment slots • Smooth surfaces • Other…? Analytical Method:

Probabilistic FM Calculated Risk < DTR

• Analysis Tool calibrated by Test Case • Criteria Calibrated by Experience

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As RISC and the FAA developed the enhanced life management process, they saw that further research and development (R&D) was needed to address shortfalls in technology and data

SwRI (guided by RISC) proposed to the FAA and was awarded a series of R&D grants to address these shortfalls • Enhanced predictive tool capability (DARWIN) • Supplementary material/anomaly behavior

characterization and modeling Goal to provide direct support for implementation and improvement of advisory material such as AC 33.14

Origins of DARWIN

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SwRI is program manager U.S. engine companies are

steering committee, major subcontractors • GE Aviation • Honeywell • Pratt & Whitney • Rolls-Royce Corp. (USA)

Activities coordinated with Rotor Integrity Sub-Committee (RISC) of Aerospace Industries Association (AIA)

Research Program Team

13


Hard Alpha Anomalies in Titanium Components

Initial RISC and TRMD focus on Hard Alpha (HA) anomalies in titanium rotors • Small brittle zone in

microstructure • Alpha phase stabilized

by N accidentally introduced during melting

AC 33.14 (2001) addressed only HA

Early DARWIN versions (1.x, 2.x, 3.x) were focused on titanium rotor alloys and 2D axisymmetric models

14


Surface Damage: Circular Holes in All Rotor Materials

The scope of FAA, RISC, and SwRI efforts expanded following the Pensacola incident (1996) to address surface damage due to manufacturing

Initial focus to define process and anomaly distribution for machined holes, leading to release of AC 33.70-2 in 2009

Later DARWIN versions (beginning with 4.x) addressed AC 33.70-2

DARWIN capabilities expanded to address surface cracks on 3D models in all rotor materials

15


How DARWIN Was Developed

DARWIN is the result of extensive collaboration between SwRI, engine companies, and agencies

RISC and FAA defined fundamental approaches Steering Committee (SC) partners (GE, P&W, Rolls-Royce,

Honeywell) defined specific requirements, provided input on algorithms, and requested convenience features

SwRI developed methods and software, and performed initial verification of software

SC performed further verification and validation through comparison with internal company codes and experience

SC and licensees provided feedback on ease of use SwRI performed bug fixes and enhancements as needed

16


What DARWIN Does

“Design Assessment of Reliability With INspection”

Calculate fatigue crack growth life for specific stress history, specific material properties, and specific initial crack size at specified location in component geometry

• DARWIN can also include crack formation life calculation

Calculate probability of fracture for the component considering uncertainties in the initial crack (anomaly) size and frequency, the stress magnitudes, the life calculation itself, the time of in-service inspection(s), and the probability that the inspection(s) will detect an existing crack

17


Inherent Anomalies Surface Damage

Zone-Based Risk (Volume) Feature-Based Risk (Area)

Random Anomaly

DARWIN Analysis Modes

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DARWIN Interface with Finite Element Models

Input finite element files • Geometry model • Stress results (multiple

load steps)

File translators currently available for ANSYS & ABAQUS

• Execute directly from GUI • Includes element filtering

2D (axisymmetric) for inherent anomalies

3D for surface damage View FE models in

DARWIN GUI

19


Fracture Mechanics Basics: Stresses at Crack Tip

Stresses near crack tips are described by

• Note that σ ∞ as r 0 • The strength of this singular field scales with K • K is called the “stress intensity factor”

K has units such as ksi√in or MPa√m This is different from a stress concentration factor

• K describes the “driving force” for crack extension Failure (complete fracture) occurs when K exceeds a critical

value, Kc (nominally a material property)

termsotherfr

Kijij += )(θσ

21


Fracture Mechanics Basics: Stress Intensity Factor

The stress intensity factor can be calculated from the general form

K = βσ√πa where a = crack size σ = remote (applied) stress β = a function of body geometry and crack

geometry

DARWIN K solutions employ the weight function (WF) formulation, which uses the actual stress normal to the crack plane in the corresponding uncracked body

σ∞

a

22

( )∫=c

dxxxWK0

)( σ


Weight Function Crack Models in DARWIN

Two classes of geometries • Cracks in plates • Cracks at holes

Weight function formulation • Univariant or Bivariant

Crack fronts are elliptical or straight Automatic transitioning

CC11 SC30

TC11 TC12

EC05 EC05

CC08 SC18 TC13 CC10

CC09 SC31

EC04 EC04

SC29

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Fracture Mechanics Basics: Fatigue Crack Growth Rate

Under fatigue loading (applied cyclic stresses described by ∆σ), the driving force for FCG is ∆K

∆K is related to the FCG rate per cycle, da/dN

The simplest fatigue crack equation is the Paris relationship (more complex expressions are often used)

∆K = β∆σ√πa

1e-009

1e-008

1e-007

1e-006

1e-005

0.0001

0.001

0.01

1 10 100

M2GC11AB01N1 R = 0.1 thk = 0.5 ref: 1M2GC11AB01N2 R = 0.7 thk = 0.5 ref: 1M2GC11AB01N3 R = 0.4 thk = 0.5 ref: 1Fit for R = 0.1Fit for R = 0.7Fit for R = 0.4

∆K

da/dN = C(∆K)m da

/dN

24


Fracture Mechanics Basics: Fatigue Crack Growth Life

The crack growth equation can be integrated between initial and final crack sizes to determine the FCG life

The initial crack size may be the anomaly size

The final crack size is determined from the known applied stresses and the failure criterion, K = Kc

The FCG life is generally very sensitive to the initial crack size

∫ ∆=

af

ai mFCG KCdaN )(

25


Superimpose simple fracture model on complex component geometry • Capture key dimensions and stresses

Idealized Fracture Mechanics Model

26

m

7

Retrieve stresses along line

Finite Element Model


Zones and fracture models easily created in GUI using mouse Select elements where initial crack might occur Define specific initial crack location Create and size a plate for the fracture model

Fracture Model and Zone Creation for 2D Models

27


Automatic Fracture Model Generation

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Given 2D FE model, stress results, initial crack location,

Automatically determine (no user input) orientation & size for idealized fracture mechanics plate model giving accurate FCG life results

Address the effects of • finite component boundaries • curved front and side surfaces • corners of various angles • crack transitions • complex stress fields • embedded, surface, and corner cracks

Reduce time, variability, and errors in the analysis process introduced by the human operator


Automatic Fracture Model Examples

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Stress Contours Life Contours

• Generate fracture model at each FE node using the DARWIN auto-plate algorithm, and compute FCG lifetime to failure for fixed initial crack size

• Display all life results using conventional contouring methods

Life Contours

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3D FE Model Interface for Surface Damage

1. Load 3D FE model

2. Select crack location & show principal stress plane

3. Slice 3D model to reveal 2D crack growth plane

4. Build 2D fracture model

31

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32

Probabilistic Fracture Mechanics Methodology

Copyright 2015 Southwest Research Institute® 32


DARWIN Implementation of Probabilistic Damage Tolerance Analysis

33


Anomaly Distribution

# of anomalies per volume/area of material as function of anomaly size Library of default anomaly distributions per AC 33.14-1 and AC 33.70-2

34


r

θ

b

depth = 2b* depth ratio

r

θ

b

depth = 2b* depth ratio

2D & 3D Anomalies in DARWIN

Anomaly distributions associated with titanium hard alpha are described in AC 33.14-1 • 2D, spherical

Additional parameters may be required to define inherent anomalies in other materials • 3D, ellipsoid • Six DOF(all potentially

random variables) Length Width aspect ratio Depth aspect ratio Three rotation angles

Multiple (competing) anomaly types can be addressed

r

Z

Length= 2b

width = 2b* width ratio

b

r

Z

Length= 2b

width = 2b* width ratio

b

γ1

r

Z

θ

γ2

γ3

γ1

r

Z

θ

γ2

γ3

1j =

2j =

j n=

AnomalyLocation

AnomalyType

Number ofAnomalies

Pore

NMP

Other

1j =

2j =

j n=

AnomalyLocation

AnomalyType

Number ofAnomalies

Pore

NMP

Other

35


Probability of Detection Curve

Define probability of NDE crack detection as function of crack size Can specify different PODs for different zones, schedules Built-in POD library (AC 33.14-1 and AC 33.70-2) or user-defined POD

36


Random Inspection Time

“Opportunity Inspections” during on-condition maintenance Inspection time modeled with Normal distribution or CDF table Can link inspection times to previous inspections

37


Summary of Basic DARWIN Random Variables

Initial Anomaly Area

Crack Detection (POD)

Inspection Time Stress scatter

• FE modeling error & usage variability

Life Scatter • Material variability & life model error • Separate formation and growth values

( )1 min max

( ) ( )1

( ) ( )X

D a D amaxF a a a aD a D amin max

−= − ≤ ≤

−

( ) ( )0detectedP POD a f a da∞

= ⋅∫

1 10 100 1,000 10,000 100,000 1,000,0000.001

0.01

0.1

1

10

100

Defect Area Size (mils^2)

Num

ber o

f Def

ects

POD (1-1 #3 FBH)

1,000 2,000 3,000 5,000 10,000 20,000 30,000 50,000 100,0000

0.2

0.4

0.6

0.8

1

Defect Area Size (mils^2)

POD

38


Zone-Based Risk Assessment

Define zones based on similar stress, inspection, anomaly distribution, lifetime

Total probability of fracture for zone: • (probability of having an anomaly) x (POF given an anomaly) • Anomaly probability determined by

anomaly distribution, zone volume • POF assuming an anomaly computed

with Monte Carlo sampling or advanced methods

POF for disk = sum of zone probabilities As individual zones become smaller

(number of zones increases), risk converges down to “exact” answer

1

2 3 4

m

5 6 7

39


m

7

Retrieve stresses along line

Finite Element Model

Place the initial crack at the “worst-case” location in the zone

Calculate the FCG life using the simple fracture mechanics model for this location

Fracture Mechanics Model for Zone Risk Calculations

40


Manual Zoning of Impeller Model

41


Manual Zoning: Risk Contribution Factors

Identify regions of component with highest risk Refine manual zones as needed to achieve convergence

42


Automatic Zoning of Impeller Model

43


Automatic Zoning: Risk Contours

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0

50

100

150

200

250

COM

PUTA

TION

TIM

E (S

EC)

CPU Time % Error

Pf - with inspection

COMPUTATIONAL METHOD

MC100,000

IS100SAMPLES

MC10,000

IS400

ERRO

R M

AGN

ITU

DE

5%

10%

15%

20%

25%

0%

DARWIN Probabilistic Methods

Monte Carlo: Converges to exact answer but can be inefficient Life Approximation Function: MC shortcut for no stress scatter Importance Sampling: Superior accuracy with fewer samples

45


Output: Risk vs. Flight Cycles

46


Design Target Risk (DTR)

47

Calculated risk of fracture for each component must be less than specified “Design Target Risk” (for example, 10-9 per flight for titanium hard alpha)

If Risk > DTR, risk reduction is required through redesign or inspection

Components

Risk

Maximum Allowable

Risk

10-9

Risk Reduction Required

C A B


Integrated Computational Materials Engineering (ICME)

The goal of ICME is to optimize materials, manufacturing processes, and component design through integration of computational processes into a holistic system

48


How is Life/Risk Influenced by the Manufacturing Process?

The material/manufacturing process (chemistry, forging, heat treating, machining, etc.) can influence FCG life and fracture risk in several different ways: • Forming residual stresses in the component • Changing the material microstructure changing material properties • Creating anomalies • Changing the location, orientation, and shape of material anomalies

49


ICME and ICSE

ICME needs to be extended beyond the design of manufacturing processes to direct use in the design of engineering components

“Integrated Computational Structural Engineering” (ICSE)

Residual Stresses Microstructure

Material Anomalies

Risk of Component Fracture

Manufacturing Process Simulation Probabilistic Damage Tolerance Analysis

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Integration with Manufacturing Process Simulation

Link DEFORM output with DARWIN input • Finite element geometry (nodes and elements) • Finite element stress, temperature, and strain results • Residual stresses at the end of processing / spin test • Location specific microstructure / property data • Tracked location and orientation of material anomalies

51


Numerical Simulation of Material Processing

Residual Stresses Microstructure

Anomaly Tracking and Deformation

52


Residual Stress Modeling in DEFORM

Residual stresses caused by non-uniform thermal, phase transformation and inelastic deformation during thermo-mechanical processing

Uncontrolled tensile residual stresses result in • dimensional control – distortion • premature failure – limits life

Controlled compressive residual stresses are beneficial Need to optimize thermo-mechanical processing Visco-elastic-plastic model predicts thermal,

elastic, plastic, creep strain and residual stresses.

53


Heat Treatment Modeling

Quenching after solution heat treat introduces substantial residual stresses 54


Effect of Material Processing Residual Stress on FCG Life

Stress

Life

Without Residual Stress With Residual Stress

55


Effect of Material Processing Residual Stress on Fracture Risk

Life

Without Residual Stress With Residual Stress

Risk

56


Modeling Random Residual Stresses in DARWIN

DEFORM

NESSUS

DARWIN

Stress Results Files

residual stress DOE n contour

residual stress DOE 1 contour

DOE

Gaussian Process Response Surface

Model

57


Principal Components Analysis for Residual Stresses Along Crack Path

Training data

Mode shapes

58


Material Microstructure

Common engineering metals are “polycrystalline” and consist of many (zillions of) different “grains” where each grain has its own crystalline orientation and boundaries

The material microstructure (e.g., grain size) is a function of the time-temperature history of the metal

Microstructure has a direct impact on material properties such as strength, ductility, and resistance to fatigue crack formation and growth

The processing history of the metal is optimized to obtain desired material properties

59


Grain Size Modeling in DEFORM Empirical – JMAK Method

Input: • Initial average grain size distribution • Strain, temperature, strain rate history • Grain growth equations • Recrystallization kinetics

Dynamic Metadynamic Static

Output: • Location-specific grain size contours • Percentage recrystallization

( ) 1010010

101010 cRTQdad

mnh

drx += /exp.εε

60


Component level JMAK Model Grain Size and Recrystallization

Courtesy – Carmel Forge

61


Influence of Grain Size Scaling on Life & Risk

ANSYS ABAQUS DEFORM

DEFORM

DARWIN

Stress Results

Files

Grain Size Results

File grain size contours

service stress contours

62


Microstructure-Based Fatigue Crack Growth Model

' 'y f

Esξ4σ ε d

=

( )b

b1/b

EK2sξ

dNda /2

/11

∆= −

∆K: Stress Intensity Range E: Young’s Modulus s: Dislocation Cell Size d: Dislocation Barrier Spacing σy′ : Cyclic Yield Stress εf′: Fatigue Ductility b: Fatigue Exponent D: Grain Size

1/3

00

Dd dD

=

63

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Influence of Grain Size Scaling on Crack Growth Rate

*

*da D dafdN D dN

=

grain size contours

crack growth rate multiplier

C=1.56 x 10-11

n2=3.66

Nominal values:


Location-Specific Grain Size Scaling Effect on Life & Risk

Life

Without Grain Size Scaling With Grain Size Scaling

Risk

a=0.01”

65

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Linking Materials and Lifing: Some Specific Needs

Link microstructure and lifing properties Link processing analysis with life analysis Probabilistic models linking

material/microstructural variability at relevant length scales to variability in fatigue/fracture/life properties and risk

Microstructure-property models that are computationally efficient and robust • Suitable for integration into the overall

optimization process, including linkages to probabilistic lifing codes

Microstructure

Processing

Lifing Properties

Life Prediction

Reliability


Closing Comments

The DARWIN software tool is being used today by many aircraft engine manufacturers to design and manage life and fracture risk in both commercial and military engines

DARWIN is also being used today as an ICME research platform to explore the extension of manufacturing technology into structural design

Probabilistic damage tolerance is the key enabling technology

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Documents

Don’t Let it Break - Southwest Research Institute...• “Classical” failures (LCF, creep, etc.) are trending down FAA and engine Manufacturers are addressing the potential for