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Microstructure-Dependent Model for Calculating the Growth Rate of Physically Small and Long Fatigue Cracks

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Strength of Materials Aims and scope

Based on the structural concept of threshold stress intensity factor ranges, the model, describing the growth kinetics of physically small and long cracks, was constructed. The model permits the calculation of lifetime on the growth of physically small and long cracks at regular cyclic uniaxial loads by the data on static mechanical characteristics and a microstructure of the initial material. The model validity was corroborated by fracture toughness results in symmetric cyclic plane bending of VT3-1 titanium alloy specimens in different microstructural states. Calculated kinetic fatigue fracture diagrams are in good agreement with experimental results.

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Abbreviations

a, c, h :

hexagonal close-packed (hcp) crystal lattice parameters

b :

Burgers vector (\( \overline{b} \)) module

d :

linear dimension of the microstructure element responsible for the fatigue strength of a material [grain size, maximum depth of a microstructurally short crack (MSC), minimum depth of a physically small crack (PSC)]

E :

elastic modulus

ΔK :

stress intensity factor (SIF) range

K Imax :

maximum SIF of the mode I cycle

ΔK th,d :

threshold SIF range for MSC

ΔK th,l :

threshold SIF range for PSC

ΔK th :

threshold SIF range for long cracks (LC)

ΔK th,eff :

effective threshold SIF range

ΔK T :

SIF range for the PSC-to-LC growth

l :

surface half-penny crack depth

l s :

intermediate PSC depth at σ a = σ–1

l i :

intermediate PSC depth at σ–1 < σ a < σ p

l ′ i :

final PSC depth (initial LC depth)

l t :

final LC depth (fatigue fracture criterion)

M :

Taylor factor (M = 1/m s )

m s :

Schmid factor (m = cos φ cos γ)

φ:

slip plane normal–load direction angle

γ:

slip direction–load direction angle

μ:

Poisson’s ratio

N :

number of load cycles

R :

stress ratio

r p,c :

cyclic plastic zone size

σ a :

cycle stress amplitude

σmax :

maximum cycle stress

σ–1 :

endurance limit at the symmetric load cycle

σ p :

proportionality limit

σ f :

internal friction stress in the crystal lattice

Y, Y 1, Y 2 :

geometric factors (SIF correction)

References

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Authors and Affiliations

  1. Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine

    O. M. Herasymchuk

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  1. O. M. Herasymchuk
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Translated from Problemy Prochnosti, No. 2, pp. 48 – 60, March – April, 2015.

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Herasymchuk, O.M. Microstructure-Dependent Model for Calculating the Growth Rate of Physically Small and Long Fatigue Cracks. Strength Mater 47, 257–267 (2015). https://doi.org/10.1007/s11223-015-9656-9

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  • DOI: https://doi.org/10.1007/s11223-015-9656-9

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