An energy-based fatigue life model for proportional and nonproportional loading conditions

This research examines the capability of a lately developed energy-based fatigue damage parameter1 to assess fatigue life of various metallic materials subjected to proportional and non-proportional loading conditions. The proposed damage is defined based on (i) shear and axial stress and strain components responsible for cracking/ modes of failure dominantly Case A and Case B, (ii) energy-based fatigue coefficients analogous to Coffin-Manson's coefficients, (iii) corresponding fatigue lives of components failed under axial and torsional loading conditions, and (iv) total elastic-plastic energy calculated from stress-strain hysteresis loops. For the latter, the modified Mroz cyclic plasticity model has been employed to calculate the hysteresis energy. Using this model in conjunction with the proposed damage parameter, fatigue lives of different materials have been predicted and then compared with reported experimental data in the literature. The predicted fatigue lives based on the proposed damage model were found in very good agreement as compared with experimental fatigue data of various metallic materials of Al 7075-T6, AISI 304, SAE 1045, 1% Cr-Mo-V steel, Inc 718 and Haynes 188 tested under both proportional and non-proportional loading conditions.

Loading Conditions and Paths

Proportional Loading

Plots and diagrams for proportional loading.

Nonproportional loading

Plots and diagrams for nonproportional loading.

Various nonproportional loading paths

90 degrees out of phase, box, two boxes, and cross loading path plots.

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Proposed Fatigue Life Model

Total strain-life equation (Δε-N or Coffin-Manson)

Log-log plot of the strain amplitude vs the reversals to failure.

Energy-life equation (ΔE-N)

Plot of the change in force vs the number of cycles.

Flowchart of steps for estimating the fatigue life.

Plot of delta sigma vs delta epsilon.

  • Cyclic energy calculation
    • Tension, Torsion or Proportional loading
      • Variable Material Property (VMP) method (Jahed et al. (1997) )
  • Nonproportional loading
    • An incremental cyclic plasticity model

For more information see: Autofretaged and Pressurized tubes (Jahed, 1997), Rotating disks (Jahed, 2000), Unloading behaviour of a thermoplastic disk (Jahed, 2001).

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Cyclic Plasticity Models

Multi-surface cycle plasticity model: proposed by Mroz (1967), modified by Garud (1981)
  1. Yield function: von Mises
  2. Flow rule: normality condition
  3. Hardening rule: kinematic hardening rule of Mroz and Garud

Comparative representation of Mroz's and Garud's cyclic plasticity models:

Diagram comparing Mroz's and Garud's cyclic plasticity models.

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Application of The Proposed Life Model to Nonproportional Loading

Verification of cyclic plasticity model used in this research for nonproportional loading
  • 1% Cr-Mo-V Steel

Loading: Out of Phase φ=135° εa=1.01 Υa=1.52

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Verification of plastic energy calculation of the cyclic plasticity model

  • 1% Cr-Mo-V Steel
  • 7075-T6 Al

Graph of the proposed model of plastic energy vs the Garud model of plastic energy.

Energy-life curves and corresponding energy-based fatigue properties
Curve fitting of energy-life data points

  • Logarithmic fitting (E=a Log(N) + b)
  • Direct fitting (E=C Nd )
  B C Bs Cs E'e E'f W'e W'f
1% CrMoV -0.112 -0.765 -0.1034 -0.782 3.658 1139.3 3.3712 2674.78
Al7075-T6 -0.141 -0.6908 -0.118 -0.586 9.686 669.34 7.3889 320.53
SAE 1045 -0.183 -0.5446 -0.1855 -0.548 3.779 446.1 3.110 402.08
AISI 304 -0.234 -0.510 -0.216 -0.472 4.041 247.8 4.405 448.26
Haynes 188 -0.170 -0.818 -0.613 -0.801 3.552 719.2

3.653

1685.4
Inc 718 -0.127 -0.844 -0.134 -0.896 12.53 6573.7 11.26

8930.2

List of upcoming graphs:

1% Cr-Mo-V Steel (Upper and lower life limit)

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AL7075-T6

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SAE 1045

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AISI 304

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Haynes 188

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Conclusion

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For more information about experimental data refer to the reference 2.
 

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References:

  1. Noban M, Jahed H, Varvani A, “The choice of cyclic plasticity models in fatigue life assessment of 304 and 1045 steel alloys based on the critical plane-energy fatigue damage approach,” International Journal of Fatigue, 43 (2012) 217–225;

  2. Noban M, Jahed H, Ibrahim E, Ince A, “Load path sensitivity and fatigue life estimation of 30CrNiMo8HH,” International Journal of Fatigue, 37, (2012), Pages 123-133;

  3. Noban, M., Jahed, H., Winkler, S., Ince, A., “Fatigue characterization and modeling of 30CrNiMo8HH under multiaxial loading,” Materials Science and Engineering A 528 (6), (2011), 2484-2494;

  4. Jahed H, Noban M, " Fatigue of Electroformed Nickel ", Journal of Failure Analysis and Prevention, J (2009) 9:549–557

  5. Jahed H, Varvani-Farahani A, "Upper and lower fatigue limits calculation using energy- based fatigue properties", Int Jnl Fatigue 2006;28:467-473


 

  1. Jahed H, Varvani A, Noban M and Khalaji I, "An energy-based fatigue life assessment model for various metallic materials under proportional and non-proportional loading conditions", Int Jnl Fatigue 2007;29:647-655