advanced software for integrated probabilistic damage tolerance analysis including ... · advanced...

Copyright 2010 Southwest Research Institute

Advanced Software for Integrated Probabilistic Damage Tolerance Analysis

Including Residual Stress Effects

R. Craig McClungMichael P. Enright

Yi-Der LeeWuwei Liang

Southwest Research InstituteSimeon H. K. Fitch

Mustard Seed Software

AeroMat 2010Bellevue, Washington

June 21-24, 2010

Copyright 2010 Southwest Research Institute2

Acknowledgments

• Funding provided byFederal Aviation Administration (FAA)• Grant 05-G-005

Air Force Research Laboratory (AFRL)• DUS&T Contract No. F336150325203• SBIR Contract No. FA8650-10-M-5110

–Via Scientific Forming Technologies Corporation


Introduction

• Damage tolerance analysis plays an increasingly important role in assuring integrity and reliability of components

Address threat of potential manufacturing or material anomalies

• Increasing requirement for accurate, efficient fatigue crack growth (FCG) life analysis methods

• Special challenge: Many possible locations for fatigue cracks to appear

For example, hard alpha anomalies in titanium rotors

• Probabilistic damage tolerance methods can address this threat, but introduce additional efficiency challenges


“Engineering” Approach to Damage Tolerance Analysis

• CharacteristicsPre-programmed SIF solutions for simple geometriesSophisticated FCG equations with load interaction models

• AdvantagesVery fast execution timesDetailed load history analysis

• DisadvantagesSIF solutions are often for simple constant or linear stress profilesMust manually transfer (and interpret) stress and geometry information from component model to fracture model


New Computational Approach

• Goal: User-friendly balance of accuracy and efficiency• Sophisticated GUI with direct interface to 2D/3D FE

models to extract and visualize geometry/stress information

• Automated construction of optimum simple fracture model geometry

• New weight function SIF solutions to address complex stress gradients

• Residual stresses (surface or bulk) addressed via weight function solutions

• Advanced FCG algorithms directly integrated with probabilistic analysis algorithms to calculate reliability


2D Finite Element Model Interface in DARWIN

• Import, visualize 2D FE model & stresses

• Use mouse to build engineering FCG model

Place initial crackLocate and size plate

• GUI extracts all stress and dimension information for fracture calculation


3D Finite Element Model Interface

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


Automatic Fracture Model Generation: Goal and Motivation

• GoalGiven…

• 2D FE model with stress results• Initial crack location

Automatically determine (no user input)• Initial crack type• Orientation & size for idealized fracture

mechanics plate model giving accurate FCG life results

• FCG life for specified initial crack size

• MotivationReduce variability and errors in the analysis process introduced by the human operatorReduce human time for analysis

• Especially important for large numbers of calculations


Automatic Fracture Model Strategy

• General rules that can be applied to any initial crack location in any general 2D model, set within a rigorous logical framework

• Addresses the effects of finite component boundariescurved front and side surfacescorners of various anglescrack transitionscomplex stress fieldsembedded, surface, and corner cracks

• GUI provides visualization for user review of the generated models


Automatic Fracture Model Examples

Automatically generated fracture mechanics plates for six representative crack locations

Circles are estimates of critical crack size

2D axisymmetric finite element mesh


Automatic Fracture Model Examples


x

y

• QR(ξ0, η)

• Q(ξ, η)

• Q*(0, η)

• Q’(ξ0, η0)yQ (-ξ, η) •

• xQ (ξ, -η)

c

a t

W

12

New Weight Function Stress Intensity Factor Solutions

• Calculate effect of actual FE stress field on SIF• New family of univariant & bivariant SIF solutions developed

Embedded, surface, corner, and through cracks in plates

• Calibrated with accurate 3D numerical reference solutions • Special algorithms to improve computational efficiency


Life Contour Maps

• Use auto-plate capability to build FM model at every node in the FE model

• Calculate FCG life for user-specified (fixed) initial crack size at each node

Stress Contours Life Contours


Life Contour Maps

• Life contour maps provide guidance for calculation of reliability as well as for design revision

• Stress contour hot spots and life contour hot spots may be different, due to geometry influences

Stress Contours Life Contours

15

DARWIN® Overview Design Assessment of Reliability With INspection

Probabilistic Fracture Mechanics

Probability of DetectionAnomaly Distribution

Finite Element Stress Analysis

Material Crack Growth Data

NDE Inspection Schedule

Pf vs. Cycles

Risk Contribution FactorsLife Scatter

Stress Scatter


Zone-Based Risk Assessment

• In probabilistic damage tolerance, we need to calculate not merely the FCG life, but the overall probability of fracture for the component, given all the potential locations that a crack could occur

• Discretize component into zones based on similar anomaly distribution, stress, lifetime

Place crack at life-limiting location in the zone• 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 given an anomaly” is probabilistic FCG calculation

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

of zones increases), risk converges down to “exact” answer (~numerical integration)

1

2 3 4

m

5 6 7


Next Automation Step: Reliability Calculation

• Use “auto-plate” to generate FCG model at many locations in the component

• Use life contour map to guide automated zone breakup• Give special attention to efficiency: do as few FCG life

calculations as possible for adequate accuracy

ac

a

NTarget N

P(a)

P(N)

Pf

ac

a

NTarget N

P(a)

P(N)

Pf


Residual Stress Issues

• Residual stresses can introduce significant uncertaintyWhat are the magnitudes of the residual stresses?How might these residual stresses change with cycles/temperature?How might the fracture critical locations change with RS effects?What are the anticipated fatigue lifetimes at these locations?

• Challenges:Assess fatigue life at many different locationsCombine complex service stress fields with complex RS fieldsAddress uncertainty in residual stressesIntegrate total risk of fracture over the entire component

18

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0 0.02 0.04 0.06 0.08 0.1

Depth (inches)

Res

idua

l Str

ess

(ksi

)

baseline200 min60 min10 min600 minaverageupperlower

Variability in Residual Stress SP and LSP in Ti-6Al-4V

Prevey et al., Proc. 17th Heat Treating Society Conf./Expo.

and 1st Int. Heat Treating Symp., ASM, 1998, pp. 3-12.

±8 ksi envelope

-140

-120

-100

-80

-60

-40

-20

0

20

0 0.002 0.004 0.006 0.008 0.01 0.012

Depth (inches)

Res

idua

l Str

ess

(ksi

)

baseline10 min

60 min200 min

600 minaverageupper

lower±10 ksi envelope

Shot Peening Laser Shock Peening

19


Effect of Residual Stress Variability on Fatigue Life

R = 0.1 Ti-6Al-4V

60

70

80

90

100

110

120

10000 100000 1000000

Cycles to Failure

Max

Stre

ss (k

si)

LPBSPDARWIN SP .003DARWIN LPB .003LPB -9 ksiLPB +9 ksiSP -9 ksiSP +9 ksi

These life calculations assume zero initiation life and include a small-crack model 20


(Local) Residual Stress Regions in DARWIN

RS Region

• The RS region is defined by the gradient distance and orientation 21


Exploratory Study of Local RS Variability

Shot Peening

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 50000 100000 150000 200000 250000 300000 350000 400000

Crack Growth Life, Flights

Prob

abili

ty

CDF (90 ksi Max Stress)CDF (80 ksi Max Stress)CDF (70 ksi Max Stress)Estimated Values (90 ksi)Estimated Values (80 ksi)Estimated Values (70 ksi)

• Residual stress is currently modeled as a deterministic quantity in DARWIN

• The influence of residual stress variability on crack growth life was explored by linking the NESSUS probabilistic code with DARWIN

• Stress amplitude was modeled as a normally distributed random variable

-140

-120

-100

-80

-60

-40

-20

0

20

0 0.002 0.004 0.006 0.008 0.01 0.012

Depth (inches)

Res

idua

l Str

ess

(ksi

)

baseline10 min

60 min200 min

600 minaverageupper

lower

22


Effect of Local Residual Stress Variability on Fatigue Life for LSP

Laser Shock Peening

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 200000 400000 600000 800000

Crack Growth Life, Flights

Prob

abili

ty

CDF (110 ksi Max Stress)CDF (100 ksi Max Stress)CDF (90 ksi Max Stress)Estimated Values (110 ksi)Estimated Values (100 ksi)Estimated Values (90 ksi)

23


DARWIN Treatment of Material Processing Residual Stresses

• USAF SBIR phase I program currently in progressProject Title – “Integrated Processing and Probabilistic Lifing Models for Superalloy Turbine Disks”Project Manager – Rollie Dutton, Air Force Research LaboratoryPrime Contractor – Ravi Shankar, Wei-Tsu Wu, Scientific Forming Technologies Corporation (SFTC)

• Primary objective: Establish link between DARWIN and SFTC DEFORM software

Phase 1 focus for DARWIN – demonstrate proof of concept model for linking residual stress predictions from DEFORM with probabilistic fracture risk assessment capability in DARWINWill also evaluate links with other DEFORM variables (microstructure, defect location/orientation) in preparation for potential Phase II project

24


DEFORM-DARWIN SBIR

• Phase 1 statusA residual stress interface is being established between DEFORM and DARWIN

• Residual stress files are transferred from DEFORM to DARWIN using SIESTA neutral file standard

• Service stress files can be transferred from DEFORM or other FE codes (e.g., ANSYS, ABAQUS, MARC) using existing DARWIN capabilities

The interface has been successfully implemented in DARWIN

DEFORMDARWIN

Service StressNeutral file

Residual StressNeutral file

ANSYS

DEFORMDARWIN



ANSYS

25


DARWIN Stress Superposition Approach for Residual Stresses



stress gradient

Service Stress

0.0 0.2 0.4 0.6 0.8 1.0-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

Residual Stress

Combined stress

Residual stress analysisDARWIN Stress ExtractionNormalized Distance

Nor

mal

ized

Stre

ssService StressNeutral file


stress gradient

Service Stress

0.0 0.2 0.4 0.6 0.8 1.0-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

Residual Stress

Combined stress

Residual stress analysisDARWIN Stress ExtractionNormalized Distance

Nor

mal

ized

Stre

ss

26


DARWIN Enhancements for Material Processing Residual Stresses

Input

Output

27


DARWIN Enhancements for Material Processing Residual Stresses (cont)

28


DARWIN Demonstration Example

• The DARWIN residual stress superposition capability was demonstrated for a realistic engine disk

• Objectives:Demonstrate that DARWIN could correctly combine service and residual stress values from files that were in the SIESTA format (i.e., format used for DEFORM output files)Correctly apply combined stress values to deterministic crack growth life and fracture risk computations

• To verify the result, crack growth life and fracture risk values were computed for two sets of input data

Service and “residual” stresses combined in a single set of SIESTA formatted files prior to use in DARWINService and “residual” stresses in separate sets of SIESTA formatted files that were combined during run time using the enhanced version of DARWIN developed under this projectAgreement was observed, which indicates that DARWIN is ready for use with DEFORM output files

29


Influence of “Residual Stress” on Life Contour Values in DARWIN

Without Residual Stress With Residual Stress

Stress

Life

30


Some Potential Future Steps

• Develop formal methods to treat residual stress variability in DARWIN (and effects on fracture risk)

• Develop probabilistic models for residual stress variability as a function of uncertainties in manufacturing processes

• Address residual stress relaxation and redistribution due to thermal, monotonic load, cyclic load, and crack growth mechanisms

McClung, FFEMS 30 (2007):173-205

31


Summary

• DARWIN provides an accurate, efficient, user-friendly method to perform structural reliability assessments of 2D and 3D components

Automated fatigue crack growth analysisProbabilistic damage tolerance analysis

• DARWIN facilitates analysis of engineered (local) residual stress effects on fatigue crack growth life

• Development of a DEFORM-DARWIN interface is underway to address bulk residual stress effects on fatigue crack growth life and reliability

• Residual stresses introduce multiple uncertainties into structural reliability analysis

These can be addressed through probabilistic analysis, but more work is needed

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