Advanced Software for Integrated Probabilistic Damage Tolerance Analysis Including Residual Stress Effects Residual Stress Summit 2010 Tahoe City, California September 26-29, 2010 Michael P. Enright R. Craig McClung Yi-Der Lee Wuwei Liang Southwest Research Institute Simeon H. K. Fitch Mustard Seed Software
Acknowledgments Funding provided by Federal 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 2
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 3
Engineering Approach to Damage Tolerance Analysis Characteristics Pre-programmed SIF solutions for simple geometries Sophisticated FCG equations with load interaction models Advantages Very fast execution times Detailed load history analysis Disadvantages SIF solutions are often for simple constant or linear stress profiles Must manually transfer (and interpret) stress and geometry information from component model to fracture model 4
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 5
2D Finite Element Model Interface in DARWIN Import, visualize 2D FE model & stresses Use mouse to build engineering FCG model Place initial crack Locate and size plate GUI extracts all stress and dimension information for fracture calculation 6
3D Finite Element Model Interface 1. Load 3D FE model 3. Slice 3D model to reveal 2D crack growth plane 2. Select crack location & show principal stress plane 4. Build 2D fracture model 7
Automatic Fracture Model Generation: Goal and Motivation Goal Given 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 Motivation Reduce variability and errors in the analysis process introduced by the human operator Reduce human time for analysis Especially important for large numbers of calculations 8
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 boundaries curved front and side surfaces corners of various angles crack transitions complex stress fields embedded, surface, and corner cracks GUI provides visualization for user review of the generated models 9
Automatic Fracture Model Examples 2D axisymmetric finite element mesh Automatically generated fracture mechanics plates for six representative crack locations Circles are estimates of critical crack size 10
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 11
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 12
DARWIN Overview Design Assessment of Reliability With INspection Anomaly Distribution NDE Inspection Schedule Probability of Detection Finite Element Stress Analysis Probabilistic Fracture Mechanics Pf vs. Cycles Stress Scatter Life Scatter Material Crack Growth Data Risk Contribution Factors 13
Typical Random Variables Associated with Assessment of Fracture Risk Applied Stress Stress Scatter Anomaly Location Anomaly Area (Initial) Life Scatter Shop Visit Time Probability of Detection
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) m 1 2 3 4 5 6 7 15
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 P f a P(N) a c P(a) Target N N 16
Multiple Types of Anomalies In some materials, fatigue lifetimes exhibit a multi-modal distribution arising from different formation mechanisms Studies of at AFRL have shown that different failure populations are associated with subsurface or surface crack formation at non-metallic particles or pores Established system reliability methods can be used to predict the probability of failure of a component with multiple anomaly types Life PDFs for single anomalies of each type must be known (parent dists) p ( ) = [ p ] P F d i 1 1 ln 1 λv i i i ( ) = 1 exp λv P F d i i i i 1 P( N i ) measured life parent distribution
Influence of Multiple Anomalies of a Single Type System ( ) i j P Fd ( ) P d j PDF ( i j 1 ) P F d = PDF ( j 1 ) P d = j =1 j = 2 PDF ( ) i j 2 P F d = 1 d j PDF P ( d j = 2 ) PDF ( i j n ) P F d = 2 PDF P ( d j = n ) d j j = n n d j
DARWIN Provides Treatment for Multiple Types of Anomalies Anomaly Location Anomaly Type Number of Anomalies Pore j =1 NMP j = 2 Other j = n Probability of failure considering type, location, and multiple anomalies m m p 1 ( 1 ) 1 exp ( ) F = pi = λivi P Fi d 1 i= 1 i= 1
Residual Stress Issues Residual stresses can introduce significant uncertainty What 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 locations Combine complex service stress fields with complex RS fields Address uncertainty in residual stresses Integrate total risk of fracture over the entire component 20
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. 20 Residual Stress (ksi) 0-20 -40-60 -80-100 -120 Depth (inches) 0 0.002 0.004 0.006 0.008 0.01 0.012 baseline 10 min 60 min 200 min 600 min average upper ±10 ksi envelope lower Residual Stress (ksi) 10 0-10 -20-30 -40-50 -60-70 Depth (inches) 0 0.02 0.04 0.06 0.08 0.1 baseline 200 min 60 min 10 min 600 min ±8 ksi envelope average upper lower -140-80 Shot Peening Laser Shock Peening 21
Effect of Residual Stress Variability on Fatigue Life Max Stress (ksi) 120 110 100 90 80 LPB SP DARWIN SP.003 DARWIN LPB.003 LPB -9 ksi LPB +9 ksi SP -9 ksi SP +9 ksi R = 0.1 Ti-6Al-4V These life 70 calculations assume zero initiation 60 life and 10000 100000 1000000 include a small-crack model Cycles to Failure 22
(Local) Residual Stress Regions in DARWIN RS Region The RS region is defined by the gradient distance and orientation 23
Exploratory Study of Local RS Variability 1.20 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 Probability 1.00 0.80 0.60 0.40 0.20 Shot Peening 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 (ksi) 20 0-20 -40-60 -80-100 -120-140 Depth (inches) 0 0.002 0.004 0.006 0.008 0.01 0.012 baseline 10 min 60 min 200 min 600 min average upper lower 0.00 0 50000 100000 150000 200000 250000 300000 350000 400000 Crack Growth Life, Flights 24
Effect of Local Residual Stress Variability on Fatigue Life for LSP 1.20 1.00 Laser Shock Peening 0.80 Probability 0.60 0.40 0.20 0.00 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) 0 200000 400000 600000 800000 Crack Growth Life, Flights 25
DARWIN Treatment of Material Processing Residual Stresses USAF SBIR phase I program currently in progress Project Title Integrated Processing and Probabilistic Lifing Models for Superalloy Turbine Disks Project Manager Rollie Dutton, Air Force Research Laboratory Prime 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 DARWIN Will also evaluate links with other DEFORM variables (microstructure, defect location/orientation) in preparation for potential Phase II project 26
DEFORM-DARWIN SBIR Phase 1 status A 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 ANSYS DEFORM Service Stress Neutral file Residual Stress Neutral file DARWIN 27
DARWIN Stress Superposition Approach for Residual Stresses Service Stress Neutral file Residual Stress Neutral file stress gradient Normalized Stress 2.0 1.6 1.2 0.8 0.4 0.0-0.4 Service Stress Combined stress Residual Stress DARWIN Stress Extraction -0.8 0.0 0.2 0.4 0.6 0.8 1.0 Normalized Distance Residual stress analysis 28
DARWIN Enhancements for Material Processing Residual Stresses Input Output 29
DARWIN Enhancements for Material Processing Residual Stresses (cont) 30
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 DARWIN Service 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 project Agreement was observed, which indicates that DARWIN is ready for use with DEFORM output files 31
Influence of Residual Stress on Life Contour Values in DARWIN Stress Life Without Residual Stress With Residual Stress 32
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 33
Summary DARWIN provides an accurate, efficient, user-friendly method to perform structural reliability assessments of 2D and 3D components Automated fatigue crack growth analysis Probabilistic 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 34