ICRS Workshop on Stress AnalysisEffects of Residual Stress andUse of Residual Stress Data
8th International Conference on Residual Stress
August 5, 2008
Denver, CO
Michael R. Hill
Associate Professor
Mechanical and Aeronautical Engineering
University of California, Davis
President
Hill Engineering, LLC
McClellan, CA
2
Outline
Effects of residual stress
When to expect residual stress influences
Examples of influences:
• High-cycle fatigue
• Distortion
• Fatigue crack growth
• Stress corrosion cracking
Using residual stress data to understand performance
Qualitative explanations
Quantitative analysis methods
• Fatigue crack growth
• Eigenstrain and finite element analysis
3
Effects of residual stresses
Residual stresses play a significant role in failure mechanisms
Fatigue, Fracture, Stress corrosion cracking
Tensile RS decreased performance
Compressive RS increased performance
Residual stresses limit material thermal cycles
e.g., Ceramic composites, weld cracking
Residual stresses cause distortions
e.g., During machining of materials
Complicate material performance
e.g., Surface treatments
• Compressive RS in treatment zone
• Tensile RS outside treatment zone
• Can lead to, e.g., sub-surface crack
initiation (> 1 mm depth) From: M. J. Shepard, P. S. Prevéy, N. Jayaraman,
“Effects of surface treatment on fretting fatigue
performance of Ti-6Al-4V”, Proceedings of the 8th
National Turbine Engine High Cycle Fatigue
Conference, April 14-16, Monterey, CA, 2003.
Subsurfaceinitiation 1 mm
(–) Surface Stress
4
Residual stress affects long-life (HCF) fatigue behavior
Ref: Prof Drew Nelson, ME245, Stanford University
5
Residual stress affects long-life (HCF) fatigue behavior
Ref: Prof Drew Nelson, ME245, Stanford University
6
Background: Laser shock peening
Laser shock peening (LSP) is similar to shot peening, but with severalkey advantages:
Deeper extent of residual stress
Better surface finish
Lower cold work
Deterministic
LSP enhances performanceImproved resistance to fatigue initiation,fatigue crack growth, SCC
Lawrence
Livermore
National Lab
Metal Improvement
Company, Inc
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Rectangular, highly uniform laser beam intensity distribution is coupled to the part using an optical delivery system that preserves the uniform intensity
Peening pulses are applied sequentially in complete rows without the need for re-coating the surfaceablation layer
Background: LSP process is a spot-by-spot raster
8
Background: LSP enhances airfoil damage tolerance
First commercial application of LSP was thin leading edges ofTitanium fan blades
Compressive stress through the entire thickness balanced bytension outside peened region
Array of2 to 5 mmlaser spots
x
9
LSP residual stress affects edge crack growth
Near edge LSP stress greatly improvescrack growth resistance in Ti6Al4V
Compressive RS leads to improved FOD resistance
Treatment must put compressive stress where needed,tensile stress where not detrimental
x
Ruschau, et alInt J Fatigue, v21 (1999)
10
Tensile residual stresses drive stress-corrosion cracking
SCC in 1 inch thick 316 stainless butt-weld
LSP treatment applied to part of surface
Weld region bathed in 40% solution of MgCl2 at 155 °C
11
Distortion in machining driven by residual stress
Even for modest levels of residual stress (±70MPa (10 ksi))
12
Distortion from residual stress treatments
Change of airfoil shape from LSP
LSP Peen forming
13
Progress check
Effects of residual stress
When to expect residual stress influences
Examples of influences:
• High-cycle fatigue
• Distortion
• Fatigue crack growth
• Stress corrosion cracking
Using residual stress data tounderstand performance
Qualitative explanations
Quantitative analysis methods
• Fatigue crack growth
• Eigenstrain and finite element analysis
14
Ti6Al4V ( -annealed) Welds: Verifying Stress Relief
Double-vee TIG welds
25.4 mm thickness
Difficult microstructure
Contour method
Results useful for verifyingTSR prediction model
As-welded
PartiallyStress Relieved(800F, 24 hours)
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C-22 Welding Processes: Compare GTAW to RPEB
GTAW: 33 mm thick plate
High stress near surface (multipass)
RPEB: 25 mm thick plate
High stress near center (single pass)
Contour method
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t = 0.15 inch
W = 1.5 inch
d = 0.25 inch
-58 -29 0 29 58 ksi-400 -200 0 200 400 MPa
No LP
Peened Area Residual Stress Map
Tensile RS @
t/2, hole edge
Small compressive RS
High compressive RS
Pattern 1
Pattern 2
Pattern 3
d t
W
Laser peening pattern variations
Residual stress from various LSP patternsBSTOA Ti6Al4V open hole samples (contour stress measurement)
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-80
-60
-40
-20
0
20
40
60
0 0.5 1 1.5
As-machinedLP, Pattern 1LP, Pattern 2LP, Pattern 3
Re
sid
ua
l S
tre
ss
(k
si)
Distance across sample (inch)
104 105 106
30
35
40
45
50
55
60
65
70 As-machinedLP, Pattern 1LP, Pattern 2LP, Pattern 3Shot Peen
Cycles to Failure
Maxim
um
Str
ess (
ksi)
Open Hole SamplesK
t = 3.1
R = 0.1
Residual stress variations explain fatigue test results
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Progress check
Effects of residual stress
When to expect residual stress influences
Examples of influences:
• High-cycle fatigue
• Distortion
• Fatigue crack growth
• Stress corrosion cracking
Using residual stress data tounderstand performance
Qualitative explanations
Quantitative analysis methods
• Fatigue crack growth
• Eigenstrain and finite element analysis
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Weight-function methods: Concept
Allows calculation of stress intensity factor for:
Arbitrary crack-line stress distribution
Specific geometry
Specific set of boundary conditions
(2)(x) = stress field of interest
K(2)(a) = desired stress intensity factor
m(a,x) = the weight function
The weight function is derived via a simpler “reference” problem
where
K(1)(a) = the reference stress intensity factor, and
u(1)(a,x) = the reference crack opening shapeRef: XR Wu, Eng Fract Mech v20, 1984
K (2) (a) = (2) (x) m(a,x) dx
0
a
m(a,x) =
E
K (1)
u(1)
a
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Weight-function methods: Residual stress applications
Use crack-line opening stresses in uncracked body
From measurement
From simulation/model
Ref: XR Wu, Eng Fract Mech v20, 1984
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Weight-function methods: Take care with BCs
Must properly account for boundary conditions
Use wrong BCs, getwrong answer
Problems largest for
Edge cracks
Non-equilibruim stress
states (esp. bending)
Constraints near to
crack faces
Example
Geom: Edge cracked strip
BC: Two different cases___ Free boundaries, or
---- Clamped sides
Stress: 3 different fields Ref: XR Wu, Eng Fract Mech v20, 1984
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Weight-function methods: Take care with stress input
Residual stresses satisfy equilibrium(2)(x) must satisfy equilibrium to be useful
Small differences in (2)(x) can make large
differences in K(2)(a)
Example for edge-cracked strip
Does this seem correct?
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Weight-function methods: Take care with stress input
Residual stresses satisfy equilibrium(2)(x) must satisfy equilibrium to be useful
Small differences in (2)(x) can make large
differences in K(2)(a)
Example for edge-cracked strip
Incorrect
Correct
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Weight-function methods: Some advice
Use correct Weight FunctionMatch geometryMatch boundary conditions
Available in books and archival publications
Example:
Wu, XR and J Carlsson, 1991, Weight functions and stress intensity
factor solutions, 1st ed, New York: Pergamon Press
Use residual stresses that satisfy equilibrium
Experimental data often do not satisfy equilibrium and
must be adjusted
Benchmark analysis methods against available/reliable solutionsand data
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Progress check
Effects of residual stress
When to expect residual stress influences
Examples of influences:
• High-cycle fatigue
• Distortion
• Fatigue crack growth
• Stress corrosion cracking
Using residual stress data tounderstand performance
Qualitative explanations
Quantitative analysis methods
• Fatigue crack growth
• Eigenstrain and finite element analysis
A case study
A case study
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Case study: Effect of residual stresses on crack growth
Objectives:Develop a set of identicalRS bearing coupons
Characterize RS in coupons
Predict FCG behavior (LEFM)• Superposition (applied + residual stress)
Verify predictions
ASTM E647 C(T) couponsClad 7075-T6 Al, 4.8 mm thick, L-T
RS from Laser Shock Peening:Repeatable, deep compression
Applied to square region, both sides
Mostly negative KRS in crack path
Test program elementsResidual stress measurements (contour)
KRS measurements (slitting)
LEFM predictions
Crack growth tests
LSP Near
front face
(KRS Negative)
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Case study: Residual stress in LSP C(T) coupons
Contour provides RS on crack-plane
Replicate measurements (rep)
28
Contour method:
2-D residual stress distributionon crack plane
Thickness-average stressaffects crack growth
Thickness average residual stress2-D residual stress distribution
Case study: Residual stress results
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)()(
)()( aK
da
ad
aZ
Ea
RS
Case study: KRS measurement
Slitting (Crack compliance)
Schindler’s method for a thin rectangular plateSchindler, H.J. and P. Bertschinger. “Some Steps Towards Automation of the Crack Compliance Method to
Measure Residual Stress Distributions.” in Proc. 5th Int. Conference on Res. Stress. 1997. Linköping.
Strain gage
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Case study: RS measurement comparison
Cross check: Contour vs. Crack compliance
)()(:
)(:
,
*
,
atpulsesaCC
atContour
RSavg
RSavg
=+
)(:
)()(: ,
aKCC
aKWFatContour
RS
RSRSavg=+
* Schajer and Prime 2007, “Residual Stress Solution Extrapolation for the
Slitting Method using Equilibrium Constraints,” Journal of Engineering
Materials and Technology, 129(2), 227-232.
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Loading: constant amplitude applied load
Superposition of applied and residual stress intensity factors
Crack growth rate from Ktot, Rtot
NASGRO equation, available constants
da/dN = f( Ktot, Rtot)
Crack growth history determinedby numerical integration
Ktot(a) = [Kapp, max(a) + KRS(a)] [Kapp, min(a) + KRS (a)]
Rtot =
Kapp, min(a) + KRS(a)
Kapp, max(a) + KRS(a)
Case study: Crack growth prediction for C(T) coupons
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Case study: Crack growth prediction
Constant Pmax (0.98 kN for AM, 2.22 kN for LSP)
Rapp = 0.1 ( K increasing)
LSP
AM
LSP
AM
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Case study: Verify against experiment
Constant Pmax (0.98 kN for AM, 2.22 kN for LSP)
Rapp = 0.1 ( K increasing)
LSP
AM
LSP
AM
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Progress check
Effects of residual stress
When to expect residual stress influences
Examples of influences:
• High-cycle fatigue
• Distortion
• Fatigue crack growth
• Stress corrosion cracking
Using residual stress data tounderstand performance
Qualitative explanations
Quantitative analysis methods
• Fatigue crack growth
• Eigenstrain and finite element analysis
35
Eigenstrain
Refs: H. Reissner (1931), T. Mura (1982)
Use in residual stress problems:
Y. Ueda (inherent strain, 1975+), Hill (1997+), Korsunsky (2005+)
Residual stress exists without applied load
Strain is the source of residual stress
Result of mechanical or thermal operations
Eigenstrain
Net effect of all processing
Plastic, thermal, transformation strains
Spatially varying, second order tensor
Residual stress results fromeigenstrain, *
Ref: MR Hill, “Modeling of residual stress effects using eigenstrain,” ICF10979OR,
Proceedings 10th Inter. Conference on Fracture, Oahu, Hawaii, Dec 2001
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Residual stress is a function of eigenstrain
Constitutive Model
Equilibrium
“Elastic Response” function
• Linear function
• Material Dependent
• Geometry Dependent
Sectioning does notalter eigenstrain(elastic)
Stress release due to sectioning predicted
Elastic Response
=C:( *)
=0, n=0= f ( *)
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Eigenstrain Determination
Measure *(x,y,z) (Ueda’s Inherent Strain, Hill)
Measure residual stress, compute **(x,y,z) = -C-1: RS(x,y,z)
Full field, multi-component
Finite element simulation
e.g., autofrettage, hole expansion
Educated guess for *Physics-based assumptions
Combination
e.g., measure stress in regionof interest, spatially decay *to zero over some distance
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Eigenstrain Modeling
Eigenstrain can be included in FEM
Use thermal strain capability
Distribute anisotropic thermal strain coefficients (x,y,z) = *(x,y,z)
Impose T(x,y,z) = 1
Solve for equilibrium
Residual stress in different geometries
Same *, different finite element mesh
Method can be applied with elastic or elastic-plastic material
* must not cause general yield, since RS satisfies yield criterion
39
Continuously welded joints
Thermal history independent of z
Similar mechanical restraint
* independent of z
Double-sided weld
*(x,y) symmetric, max at center,
zero outside near-bead region
Educated guess forwelding *(x,y)
Example: Observations on Welds
Perp. (y)
Trans. (x)
Long. (z)
DirectTerms
*
x
y(i)(i)
Ref: MR Hill, MR, TL Panontin,
“Effect of Residual Stress on
Brittle Fracture Testing,” ASTM
STP 1332, T.L. Panontin and S.D.
Sheppard, Eds., American
Society for Testing and
Materials, 1998.
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-20000 -10000 0 10000 20000 30000
-1.5
-1.0
-0.5
Stress (psi)
0.0
Trans.
Perp.
Long.
y (in)
-5000
0
5000
10000
15000
20000
25000
30000
0
Str
es
s
(ps
i)
1 2 3 4 5 6
x (in)
7 8
Trans.
Long.
Perp. (y)
Trans. (x)
Long. (z)
Example: Representative Plate Weld Stress
Stress resembles experiments *
x
y(i)(i)
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Example 2: Fracture analysis of girth welded shell
Fracture of large diametergirth weld
Geometry
Cylindrical shellDo/t = 40, t = 25.4 mm
External flaw, a/t = 0.3
Axial load
Material
A516-70: high hardening Sy = 303 MPa
42
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1
Axial
Hoop
Radial
/ o
Distance from the inner surface (r/t)
Stress @ Weld Center
-0.2
0
0.2
0.4
0.6
0.8
1
-3 -2 -1 0 1 2 3
AxialHoop
/ o
Distance from the centerline (z/t)
Surface Stresses
Example 2: Fracture analysis of girth welded shell
* independent of
Introduce *(r,z), compute
residual stress
RS in unflawed shell
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Example 2: Fracture analysis of girth welded shell
Residual stress causes large initial KRS
At high loads, plastic deformation reduces KRS
Ductile fracture less sensitive to residual stressBrittle fracture more sensitive to residual stress
Ref: Panontin TL, Hill MR, 1996,
“The effect of residual stresses
on brittle and ductile fracture
initiation predicted by
micromechanical models,” Int J
Fracture 82(4): 317-333.
44
Example 3: Residual stress in removed coupon
Same *, different geometry
RS in uncracked SE(B) blank
Opening RS nearly unchanged
• Same driving force effect
"z-stress” RS altered
• Affects crack-tip constraint
Ref: TL Panontin, OS Niskioka, and MR Hill, "Fracture Assessments of
Welded Structures," Proceedings of the International Conference on
Computational Engineering Science, Atlanta, GA, October 6-9, 1998.
45
Summary
Residual stresses affect failure
When to expect residual stress influences
Examples of influences:
• High-cycle fatigue
• Distortion
• Fatigue crack growth
• Stress corrosion cracking
Using residual stress data to understand performance
Qualitative explanations
Quantitative analysis methods
• Fatigue crack growth
• Finite element analysis (using Eigenstrain)
46
Contact Information
Michael R. HillMechanical and Aeronautical EngineeringUniversity of CaliforniaOne Shields AvenueDavis, CA [email protected](530) 754-6178