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

Identify, Develop and Deploy

Yung-Li Lee

Contents 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 1. Fatigue Analysis & Testing in Design 2. Top Emerging Technologies 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 Yung-Li Lee

2. Validation by Testing

1. Design by Analysis

Expecting too much from FEA?

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

Contents 1. Fatigue Analysis & Testing in Design 2. Top 5 Emerging Technologies 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 Yung-Li Lee

Multiaxial fatigue analyses - overview (non-proportional loading)

strain history

theories of plasticity

stress history

load history

nonlinear transient analysis

stress & strain history

coordination transformation

critical plane search method

cycle counting & damage cal.

strain-based methods

(proportional & uniaxial loading) elastic transient analysis static or inertial relief analysis modal transient analysis

(non-proportional loading) elastic stress history

notch analysis stress-based methods

coordination transformation

critical plane search method

cycle counting & damage cal. (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 models a. 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 σ 1, σ 1e σ 1e - ε 1e curve

σ 1e - ε 1 curve

σ 1 − ε 1 curve

ε 1, ε 1e

• 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 ⎛σ log α NP = 0.705 ⎜ t,u ⎜σ ⎝ t,y 2

α NP

⎛ K ⎞ ⎛ Δε ⎞ = 1.6 ⎜ ⎟ ⎜ ⎟ ⎝ K′ ⎠ ⎝ 2 ⎠

⎞ ⎟ − 1.22 ⎟ ⎠ 2 (n −n′ )

⎛ K ⎞⎛ Δε ⎞ − 3.8 ⎜ ⎟⎜ ⎟ ⎝ K ′ ⎠⎝ 2 ⎠

(n−n′ )

+ 2.2

•Shamsaei, N. and Fatemi, A. (2010) “Effect of microstructure and hardness on non-proportional cyclic hardening coefficient and predictions,” Material Science and 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.

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

fNP

C = r ref T ⋅ σ 1,max

T

∫ ( sinξ (t ) ⋅ σ

1,max

)

(t) dt

0

• Itoh, T., Sakane, M., Ohnami, M., and Socie, D. F. (1995) “Nonproportional low cycle fatigue criterion for type 304 stainless steel,” Journal of Engineering Materials 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,” International Journal of Fatigue, 29, pp. 1162-1173.

2. Multiaxial fatigue damage model - two solutions 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

Yung-Li Lee

3. Choice of cycle counting methods - overview 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.

Yung-Li Lee

3. Choice of cycle counting methods - concept D

C

B

A 1000 800

Stress, MPa

600 400 200 0 -200 0

1

2

3

4

-400 -600 -800 -1000 normal stress

shear stress

5

6

Contents 1. Fatigue Analysis & Testing in Design 2. Top 5 Emerging Technologies in Fatigue Analyses 3. Their Applications and Challenges 3-1

Multiaxial Fatigue Analysis

3-2

Fatigue analysis of Welded Joints (seam welds & spot welds)

3-3

Thermal-Mechanical Fatigue Analysis

3-4

Fatigue Analysis of Rubbers

3-5

Bearing Fatigue Analysis 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. Dong Step 3: Establish unified growth behavior

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I. Structural stress approach by P. Dong Step 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

II. Structural stress approach by Fermer, et al. Step 2: Haigh’s diagram for mean stress correction

σa R = −1 R= −∞

R= 0

σar = σa + M1σm M1 = 0 R>1

−M1

−M2

0 M1 = 0.25

σa + M2σm 1+ M2

R= 0.5

σar

1

I

−

σar = (1+ M1 )

1

M1 = 0

+

σm

M2 = 0.097

Yung-Li Lee

II. Structural stress approach by Fermer, et al. 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 1. Fatigue Analysis & Testing in Design 2. Top 5 Emerging Technologies 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 Yung-Li Lee

Concept of TMF

Influences on TMF: 1. Dwell time 2. Strain rate 3. Creep 4. Stress relaxation 5. Aging 6. Softening 7. etc.

Combined loading (TMF, LCF, HCF, various influences)

Real component

TMF Applications

EVP material model

1) 2)

Taira’s damage model Sehitoglu’s damage model

Contents 1. Fatigue Analysis & Testing in Design 2. Top 5 Emerging Technologies 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 Yung-Li Lee

Fatigue of rubber components

Contents 1. Fatigue Analysis & Testing in Design 2. Top 5 Emerging Technologies 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 Rubber Components

3-5

Bearing Fatigue Analysis Yung-Li Lee

Bearing fatigue

Contact Pressure

y

τ max

z

Conclusions 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.

Yung-Li Lee

QUESTIONS ???

BACKUP MATERIALS

Overview of fatigue analysis of spot welds - II

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)

Yung-Li Lee Spot welds

36

Ultimate strength of spot welds - II

Spacing

Weld Size

Galvannealed Tensile Shear

DP590

Loading mode

Ultimate Strength

Material Type Galvannealed MS6000

Cross Tension

Adhesive

Thickness

Edge distance

MS-CD-457A

Yung-Li Lee

Design of experiments 25

TS-D+-N-1-H-TA Load, P(kN)

20 15 10 5 0 0

2

4

6

8

10

12

14

Displacement, u(mm)

DOE No.

Factory D (mm) E (mm) No.

UTS (kN)

UTS-A (kN)

S (mm)

Spec. No.

#1

#2

#1

#2

DOE 1 DOE 2 DOE 3 DOE 4

2I 2J 2K 2L

5.0 5.0 5.0 5.0

10 45 10 45

15 29 44 15

2 2 2 2

9.32 10.09 10.77

9.75 10.08 9.16 11.26

11.06 12.01 11.22 12.07

9.93 11.53 10.99 12.29

DOE 5 DOE 6 DOE 7 DOE 8

2M 2N 2O 2P

6.0 6.0 6.0 6.0

10 45 10 45

29 44 15 29

2 2 2 2

12.41 13.37 10.15 11.95

12.29 14.45 12.28 13.51

11.32 14.01 12.05 12.90

8.71 12.82 12.27 14.28

DOE 9 DOE 10 DOE 11 DOE 12

2Q 2R 2S 2T

7.0 7.0 7.0 7.0

45 10 45 10

44 29 15 44

2 2 2 2

16.90 13.19 14.78 13.74

16.34 15.72 11.81

13.51 12.77 16.12 10.83

14.74 12.72 12.84 11.92

Yung-Li Lee