advances in fatigue analysis technologies

Advances in Fatigue Analysis Technologies

Dr. Yung-Li Lee, Technical Fellow

Chrysler Group LLC

Presented

at

SAE Fatigue Design & Evaluation (FD&E) Committee Meeting

Auburn Hills, Michigan

on

Tuesday, October 19, 2010

Yung-Li Lee

Identify, Develop and Deploy

1. Fatigue Analysis & Testing in Design

2. Technology Advances in Fatigue Analyses

3. Their Applications and Challenges

3-1 Multiaxial Fatigue Analysis

3-2 Fatigue Analysis of Welded Joints

3-3 Thermal-Mechanical Fatigue Analysis

3-4 Fatigue Analysis of Rubbers

3-5 Bearing Fatigue Analysis

3-6 Vibration Fatigue

3-7 Probabilistic micro-structural fatigue modeling

Contents


2. Top Emerging Technologies in Fatigue Analyses







Contents

Yung-Li Lee

Expecting too much from FEA?

(Source: Machine Design by Engineers for Engineers, Paul Dvorak, July 10, 2008)

1. D

esig

n by

Ana

lysi

s

2. V

alid

atio

n by

Tes

ting


2. Top 5 Emerging Technologies in Fatigue Analyses







Contents

Yung-Li Lee

Multiaxial fatigue analyses - overview

strain history

theories of

plasticity

stress history

load history

nonlinear transient analysis

stress & strain history

elastic transient analysis

elastic stress history

static or inertial relief

analysis

modal transient analysis

strain-based methods

stress-based methods

notch analysis

coordination transformation

critical plane search method

cycle counting & damage cal.

(non-proportional loading)

(proportional & uniaxial loading)

coordination transformation

critical plane search method

cycle counting & damage cal.

(non-proportional loading)

(proportional & uniaxial loading)

Multiaxial fatigue analyses – three challenges

1. Multiaxial notch analysis based on pseudo stresses

a. Hoffmann-Seeger method (1989)

b. Buczynski-Glinka method (1995)

c. Barkey-Socie-Hsia method (1994)

d. Lee-Chiang-Wong method (1995)

2. Deficiencies in multiaxial fatigue damage modelsa. Nonproportional hardening (NP) effect

b. Loading path effect

3. Choice of cycle counting methods

a. Uniaxial cycle counting techniques

b. Multiaxial cycle counting techniques

1. Multiaxial notch analysis – LCW’s 2-step concept

curve ε-σ e1

e1

e11 σ,σ

e11 ε,ε

curve εσ 11 −

curve ε-σ 1e1curve ε-σ e

1e1

e11 σ,σ

e11 ε,ε

curve εσ 11 −

curve ε-σ 1e1

• Lee, Y.L., Chiang, Y.J. and Wong, H.H. (1995) “A Constitutive Model for Estimating Multiaxial Notch Strains,” ASME Journal of Engineering Materials and Technology, Vol. 117, pp. 33-40.

• R. Gu and Y. Lee (1997) " A New Method for Estimating Non-proportional Notch-Root Stresses and Strains,“ ASME Journal of Engineering Materials and Technology, Vol. 119, pp. 40-44.

2. Multiaxial fatigue damage model - not accounting for NP hardening effect

•Shamsaei, N. and Fatemi, A. (2010) “Effect of microstructure and hardness on non-proportional cyclic hardening coefficient and predictions,” Material Scienceand Engineering, A 527, pp. 3015-3024.• Borodii, M.V. and Shukaev, S.M. (2007)” Additional cyclic strain hardening and its relation to material structure, mechanical characteristics, and lifetime,”International Journal of Fatigue, 29, pp. 1184-1191.

1.22σσ

0.705αlogyt,

ut,NP −⎟

⎟⎠

⎞⎜⎜⎝

⎛=

( ) ( )

2.22Δε

KK3.8

2Δε

KK1.6α

nnnn22

NP +⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛

′−⎟

⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

′=

′−′−

2. Multiaxial fatigue damage model - not accounting for loading path effect

• Itoh, T., Sakane, M., Ohnami, M., and Socie, D. F. (1995) “Nonproportional low cycle fatigue criterion for type 304 stainless steel,” Journal of EngineeringMaterials and Technology, Vol. 117, pp. 285-292.• Lee, Y.L., Tjhung, T., and Jordan, A. (2007) “A life prediction model for welded joints under multiaxial variable amplitude loading histories,” InternationalJournal of Fatigue, 29, pp. 1162-1173.

( )( )∫ ⋅⋅

=T

0max1,ref

max1,NP dt(t)σtsinξ

σTCf r

2. Multiaxial fatigue damage model - two solutions

Yung-Li Lee

Solution #1 – Strain-based model + plasticity model enhancement +

uniaxial rainflow cycle counting

1. Tanaka’s 4th order tensor + Y. Jiang’s plasticity model (a modified Armstrong-Frederick

model)

Solution #2 – Stress-based model + equivalent stress/strain amplitude

parameter + multiaxial rainflow cycle counting 1. Itoh’s equivalent strain amplitude or LTJ’s equivalent stress amplitude + multiaxial RF

counting

3. Choice of cycle counting methods - overview

Yung-Li Lee

1. “Signed” equivalent stress/strain approach

2. Extension of Matsuishi and Endo’s reversal counting

approach (1968)

a. Maximum von Mises strain range (Wang-Brown, 1996)

b. Maximum von Mises stress range (Lee-Tjhung-Jordan, 2007)

c. Maximum fracture-based stress range (Dong-Wei-Hong, 2010)

1. Matsuishi, M. and Endo, T. (1968) “Fatigue of metals subjected to varying stress,” presented to the Japan Society of Mechanical Engineers, Fukuoka, Japan.

2. Wang, C. H. and Brown, M. W. (1996) “Life Prediction Techniques for Variable Amplitude Multiaxial Fatigue – Part 1: Theories,” Journal of Engineering Materials and Technology, Vol. 118, pp. 367-370.

3. Lee, Y.L., Tjhung, T., and Jordan, A. (2007) “A Life Prediction Model for Welded Joints under Multiaxial Variable Amplitude Loading,” International Journal of Fatigue, Vol. 29, pp. 1162-1173.

4. Dong, P., Wei, Z., Hong, J. K. (2010) “A path-dependent cycle counting method for variable-amplitude multi-axial loading,” International Journal of Fatigue, Vol. 32, pp. 720-734.

3. Choice of cycle counting methods - concept

-1000-800-600-400-200

0200400600800

1000

0 1 2 3 4 5 6

Stre

ss, M

Pa

normal stress shear stress

A B DC





3-2 Fatigue analysis of Welded Joints (seam welds & spot welds)




Contents

Yung-Li Lee

Overview of fatigue analysis of seam welds - I

1. Nominal Stress Approach

a. Design Codes e.g., British standards, IIW recommendations, FKM-Guideline, etc.

2. Structural Stress Approach (Geometrical Stress or Hot Spot Stress)

a. Dong’s approach

b. Fermer’s approach

3. Local Stress Approach

Yung-Li Lee

Stress definition

Yung-Li Lee

I. Structural stress approach by P. Dong

Step 1: nodal force -> unit line weld stress Step 2: Calculate the stress intensity factor

Yung-Li Lee

I. Structural stress approach by P. DongStep 3: Establish unified growth behavior

Yung-Li Lee

I. Structural stress approach by P. DongStep 4: Define S-N curve from Paris’ law

Yung-Li Lee

II. Structural stress approach by Fermer, et al.

Step 1: FE stresses based on the mesh rules

Yung-Li Lee


mσ

aσ

R −∞=

1R>1M−

1R −=0R=

0.5R=

+− 0

I

arσ1

0M1=

0M1=2M− 1

( )2

m2a1ar M1

σMσM1σ++

+=m1aar σMσσ +=

0.25M1 = 0.097M2 =

Step 2: Haigh’s diagram for mean stress correction

Yung-Li Lee


Step 3: Empirical S-N curves

Yung-Li Lee

Pros and cons of using the structural stress approach

Advantages

• Manufacturing and residual effects are directly included in the database.

• A large empirical database exists for structural steels.

• It is easy to calculate the structural stress parameters and is FE mesh independent.

Limitations

• Residual stress effect due to a different manufacturing process is not taken into account

• Multiaxial fatigue is not appropriately considered.

Yung-Li Lee

Case study # 1

• H. Kang, Y. Lee, and X.J. Sun, “Effects of Residual Stress and Heat Treatment on Fatigue Strength of Weldments,” Materials Science & Engineering,A497, 2008, pp. 37-43.









Contents

Yung-Li Lee

Concept of TMF

Real componentCombined loading (TMF, LCF, HCF, various influences)

Influences on TMF:

1. Dwell time2. Strain rate3. Creep4. Stress relaxation5. Aging6. Softening7. etc.

TMF Applications

EVP material model 1) Taira’s damage model2) Sehitoglu’s damage model









Contents

Yung-Li Lee

Fatigue of rubber components







3-4 Fatigue Analysis of Rubber Components


Contents

Yung-Li Lee

Bearing fatigue

Contact Pressure

y

z

maxτ

1. CAE fatigue analysis can be the best tool used for A-to-B comparison.

2. CAE fatigue analysis results need to be verified and validated.

3. There is no universal solutions/answers to all the fatigue problems. So there is room for improvement in fatigue analysis technology.

4. Testing is always required in design.

5. What is the testing in design?

a) validation testing

b) reliability demonstration testing.

Conclusions

Yung-Li Lee

QUESTIONS ???

BACKUP MATERIALS

36

Yung-Li Lee

Overview of fatigue analysis of spot welds - II

Spot welds

1. Radaj’s and Zhang’s model (1989)

2. Swellam and Lawrence’s stress intensity factor model (1992)

3. Sheppard’s structural stress model (1993)

4. Rupp’s structural stress model (1995)

5. Y. Lee’s nominal stress model (1996)

6. Zhang’s stress intensity factor model (1997)

7. Lin-Pan’s local stress model (1999-2003)

8. Chao-Wang’s nominal stress model (2006-2009)

Ultimate strength of spot welds - II

Ultimate StrengthLoading mode

Tensile Shear

Cross Tension

Material Type

DP590

MS6000

Adhesive

Spacing

Edge distance

Weld Size

Thickness

MS-CD-457A

Galvannealed

Galvannealed

Yung-Li Lee

Design of experiments

UTS (kN) UTS-A (kN) DOE No.

Factory No. D (mm) E (mm) S (mm) Spec.

No. #1 #2 #1 #2 DOE 1 2I 5.0 10 15 2 9.32 9.75 11.06 9.93 DOE 2 2J 5.0 45 29 2 10.09 10.08 12.01 11.53 DOE 3 2K 5.0 10 44 2 - 9.16 11.22 10.99 DOE 4 2L 5.0 45 15 2 10.77 11.26 12.07 12.29

DOE 5 2M 6.0 10 29 2 12.41 12.29 11.32 8.71 DOE 6 2N 6.0 45 44 2 13.37 14.45 14.01 12.82 DOE 7 2O 6.0 10 15 2 10.15 12.28 12.05 12.27 DOE 8 2P 6.0 45 29 2 11.95 13.51 12.90 14.28

DOE 9 2Q 7.0 45 44 2 16.90 - 13.51 14.74

DOE 10 2R 7.0 10 29 2 13.19 16.34 12.77 12.72 DOE 11 2S 7.0 45 15 2 14.78 15.72 16.12 12.84 DOE 12 2T 7.0 10 44 2 13.74 11.81 10.83 11.92

TS-D+-N-1-H-TA

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Displacement, u(mm)

Loa

d, P

(kN

)

Yung-Li Lee

advances in fatigue analysis technologies

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