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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
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
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
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
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
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
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
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
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.
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
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.
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
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.
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
Contents
Yung-Li Lee
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
Contents
Yung-Li Lee
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
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
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