Outline ICRS Workshop on Stress Analysis Effects of ... Stress Analysis 7.pdfICRS Workshop on Stress Analysis Effects of Residual Stress and Use of Residual Stress Data 8th International

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

[email protected]

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


• 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

7

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





• Distortion



Using residual stress data tounderstand performance





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)

15

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

16

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)

17

-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

18

Progress check





• Distortion








19

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

20

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

21

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

22

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?

23

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

24

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

25

Progress check





• Distortion








A case study

A case study

26

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)

27

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

29

)()(

)()( 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

30

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.

31

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

32

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

33

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

34

Progress check





• Distortion








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

36

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 ( *)

37

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

38

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.

40

-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)

41

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


* independent of

Introduce *(r,z), compute

residual stress

RS in unflawed shell

43


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




• Distortion



Using residual stress data to understand performance




• Finite element analysis (using Eigenstrain)

46

Contact Information

Michael R. HillMechanical and Aeronautical EngineeringUniversity of CaliforniaOne Shields AvenueDavis, CA [email protected](530) 754-6178

Documents

Outline ICRS Workshop on Stress Analysis Effects of ... Stress Analysis 7.pdfICRS Workshop on Stress Analysis Effects of Residual Stress and Use of Residual Stress Data 8th International