1) School of Energy and Power Engineering, Beihang University, Beijing 100191, China
2) the Collaborative Innovation Center for Advanced Aero-Engine (CICAAE), Beijing 100191, China;
Cite this article:
Shiwei HAN, Duoqi SHI, Xiaoguang YANG, Guolei MIAO. COMPUTATIONAL STUDY ON MICROSTRUCTURE-SENSITIVE HIGH CYCLE FATIGUE DISPERSIVITY. Acta Metall Sin, 2016, 52(3): 289-297.
Empirical approaches to characterize the variability of high cycle fatigue have been widely used. However, little is understood about the intrinsic relationship of randomness of microstructure attributes on the overall variability in high cycle fatigue. The ability of quantifying the dispersivity of high cycle fatigue with physics based computational methods has great potential in design of minimum life and can aid in the improvement of fatigue resistance. To investigate the effects between microstructure attributes and high cycle fatigue dispersivity, the microstructure-sensitive extreme value probabilistic framework is introduced. First, the Voronoi algorithm is used to construct random polycrystalline microstructure representative volume elements. Different kinds of periodic boundary conditions are proposed to simulate the interior and surface constraints in polycrystalline microstructure representative volume elements. Then mechanical responses of both interior and surface microstructure representative volume elements under different strain amplitudes are simulated by internal state variable based crystal plasticity. The fatigue indicator parameter is introduced to characterize the driving force for fatigue crack formation dominated by maximum shear plastic strain amplitude. By computing a limited number of random polycrystalline microstructure representative volume elements, the distributions of fatigue indicator parameter under different strain amplitudes are obtained and analyzed with extreme value probability theory. The study with a kind of titanium alloy with material grade TC4 supports that the high cycle fatigue dispersivity increases with the decrease of the strain amplitude, especially under elastic limit. The extreme value of fatigue indicator parameter from random polycrystalline microstructure representative volume elements correlates well with the Gumbel extreme value distribution. Besides, the lower the average stress under different strain amplitudes, the fewer grains in polycrystalline microstructure representative volume element yield. Moreover, the grains on surface tend to have higher probability to initiate fatigue cracks and lower dispersivity in fatigue crack formation.
Fig.3 Periodic boundary condition (a) full infinite space (interior) (b) half infinite space (surface)
Fig.4 Probability density distribution of grain volume (k--shape parameter, q--scale parameter)
Fig.5 Frequency distribution of standard deviation in grain volumes within each microstructure representative volume element (RVE)
Case number
Strain amplitude Δε
Δε p (under monotonic tension)
Spatial constraint
1
0.45%
0
Interior
2
0.50%
0
Interior
3
0.60%
0.0145%
Interior
4
0.70%
0.0489%
Interior
5
0.70%
0.0489%
Surface
Table 1 Computational parameters for microstructure RVEs
Fig.6 Monotonic tensile curve and corresponding plastic strain increment Δε p for TC4 alloy
Fig.7 Probability density distributions of grain-averaged fatigue indicator parameter (FIP) in primary α phase grains at different strain amplitudes Δε
Fig.8 Distributions of mean and standard deviation of grain-averaged FIP within each microstructure RVE at different Δε
Fig 9 Distributions of mean and standard deviation of grain- averaged FIP in interior and surface microstructure RVEs at 0.70% strain amplitude
Fig 10 Extreme value distributions of grain-averaged FIP in each microstructure RVE at different D e(P--accumulative probability)
Fig 11 Extreme value distribution of grain- averaged FIP in each microstructure RVE at 0.45% stain amplitude
Case number
un
bn
bn/un
R2
1
5.6×10-7
3.410×10-6
6.0842
0.7934
2
1.6×10-4
2.090×10-4
1.3025
0.9064
3
3.9×10-3
3.862×10-4
0.0976
0.9675
4
7.3×10-3
6.541×10-4
0.0896
0.9808
5
8.2×10-3
7.046×10-4
0.0859
0.9910
Table 2 Fitting parameters of Gumbel distribution
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