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Estimation of fatigue crack initiation in the very high cycle fatigue regime for AA7075-T6 alloy using crystal plasticity finite element method

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Abstract

Fatigue crack initiation (FCI) in the very high cycle fatigue (VHCF) regime for an AA7075-T6 alloy has been estimated by introducing fatigue indicator parameters (FIPs) serving as the driving force for FCI via crystal plasticity finite element model (CPFEM). Extreme value distribution (EVD) of FIPs is computed based on the statistical volume elements extracted in the material microstructure by DREAM.3D software. The EVD is fitted to the Gumbel extreme distribution and the characteristic parameters are analyzed to evaluate the FCI driving force and the “hot-spot” of crack initiation for the AA 7075-T6 under cyclic straining in the VHCF regime. Moreover, the apparent Schmid factor (SF) of the slip system with the highest FIPs and equivalent grain size of the grains with the highest FIPs are calculated to estimate the possibility of crack initiation, and the effects of grain size on the FCI are discussed. Representative ultrasonic fatigue experiments for three stress levels corresponding to the cyclic strain magnitude of 0.254%, 0.289%, and 0.312% are conducted to verify the estimation of fatigue crack formation via CPFEM simulation. The accumulated plastic slip was found to be a necessary condition for forming fatigue cracks, in addition, the fatigue cracks with higher SF and in the larger grain size were more likely to originate. FIPs extreme distributions parameters were also assessed to agree well with the experimental results.

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Abbreviations

FCI:

Fatigue crack initiation

VHCF:

Very high cycle fatigue

CPFEM:

Crystal plasticity finite element model

EVD:

Extreme value distribution

SVEs:

Statistical volume elements

SF:

Schmid factor

HCF:

High cycle fatigue

FIPFS :

Fatemi–Socie FIPs

RVE:

Representative volume element

LCF:

Low cycle fatigue

IHG:

Microstructurally small crack

CRSS:

Critical resolved shear stress

UMAT:

User-defined material subroutine

F e :

Elastic deformation gradients

F p :

Plastic deformation gradients

L p :

Plastic velocity gradient

\(\dot{\gamma }^{(\infty )}\) :

Dislocation slip rate on the αth slip system

s (α) :

Slip direction on the αth active slip system

m (α) :

The normal direction of slip plane on the αth active slip system

\(\dot{F}^{p}\) :

The evolution rate of deformation gradient Fp

\(\mathrm{\dot{\gamma }}_{0}\) :

Reference shear strain rate

g α :

Drag stress of the slip system α

τ α :

Resolved shear stress of slip system α

χ α :

Cyclic kinematic hardening parameter

h i :

Material constants (i = 1,2)

r i :

Material constants (i = 1,2)

σ :

Second-order Cauchy stress tensor

C :

The 4th elasticity tensor

E e :

The elastic Green strain tensor

I :

Identity tensor

h α β :

Latent hardening parameter

R:

Stress ratio

C 11 :

Elastic constant of AA7075-T6

C 12 :

Elastic constant of AA7075-T6

C 44 :

Elastic constant of AA7075-T6

σ a :

Stress amplitude

ε a :

Strain amplitude

N f :

Fatigue fracture life

\(\Delta \gamma_{p}^{\max }\) :

Maximum cyclic plastic shear strain range

σ max :

Peak normal stress

σ y :

Macroscopic yield strength of the material

k :

Material constant

α n :

The inverse measure of the dispersion

n :

Sample size

u n :

The largest characteristic value of the sampled population

j :

The rank order of the FIPs

R 2 :

Regression coefficient

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Acknowledgements

The authors are grateful for the supports provided by the National Natural Science Foundation of China (91860206), Shaanxi Province Key Research and Development Program (2019KW-063), and thank you for the contribution of Zhi Qin from Northwestern Polytechnical University.

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Authors and Affiliations

  1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, China

    Bin Li, Tao Gao & Hongqian Xue

  2. ICD, P2MN, LASMIS, The University of Technology of Troyes, CNRS FRE2019, Troyes, France

    Zhidan Sun

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  1. Bin Li
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  2. Tao Gao
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BL Methodology, Writing, original draft, review and editing. ZS Editing and review; HX Resources, Funding acquisition; TG Data curation, experiments.

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Correspondence to Hongqian Xue or Zhidan Sun.

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Handling Editor: M. Grant Norton .

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Li, B., Gao, T., Xue, H. et al. Estimation of fatigue crack initiation in the very high cycle fatigue regime for AA7075-T6 alloy using crystal plasticity finite element method. J Mater Sci 57, 10649–10663 (2022). https://doi.org/10.1007/s10853-021-06790-5

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