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Relationship Between the Threshold Stress Intensity Factor Ranges of the Material and the Transition From Short to Long Fatigue Crack

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Strength of Materials Aims and scope

A relationship between the threshold stress intensity factor ranges of the material is established for microstructurally short, physically small and long fatigue cracks depending on the microstructure at a symmetrical loading cycle. The threshold stress intensity factor ranges calculated by the proposed concept for titanium alloy VT3-1 in different structural states agree well with those determined experimentally. The criteria are proposed for the transition from a small to a long fatigue crack depending on the level of the applied load amplitude. In the whole range of the load amplitudes, the condition when a reversible plastic zone at the crack tip reaches the grain size is taken as a criterion for the transition from a physically small to a long fatigue crack. In the high cycle fatigue region, the physically small crack growth range is to be divided into two areas because of a change in the mechanisms of the physically small crack growth upon the attainment by the stress intensity factor range of the threshold value for the long crack.

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Abbreviations

a, c, h :

hexagonal close packed (HCP) crystal lattice parameters

b :

Burgers vector (\( \overrightarrow{b} \)) magnitude

d :

linear dimension of the structural element responsible for the fatigue strength of the given material (grain size, maximum dept of the microstructurally short crack (MSC), minimum depth of the physically small crack (PSC)

E :

modulus of elasticity

ΔK :

stress intensity factor (SIF) range

K max :

maximum SIF of the cycle

ΔK th,d :

threshold SIF range for a MSC

ΔK th,l :

threshold SIF range for a PSC

ΔK th :

threshold stress intensity factor range for a long crack (LC)

ΔK th,in :

intrinsic threshold SIF range

ΔK th,eff :

effective threshold SIF range for a LC

ΔK T :

SIF range corresponding to the transition from a PSC and a LC

l :

semicircular surface crack depth

l s :

transitional PSC depth corresponding to the fatigue limit σ-1

l i :

transitional PSC depth at σ-1 < σ a ≤ σp

l ' i :

final PSC depth (initial LC depth)

M :

Taylor factor (M = 1/m)

m :

Schmid factor (m = cos φcos γ)

φ:

angle between the normal to the slip plane and load σ a direction γ angle between the slip direction and load σ a direction

μ:

Poisson’s ratio

R :

cycle stress ratio

r p,c :

reversible plastic zone size

σ a :

stress amplitude of load cycle

σ max :

maximum stress of load cycle

σ1 :

fatigue limit at symmetric loading cycle

σ p :

proportionality limit

σ f :

internal friction stress in the crystal lattice

U :

crack opening factor

Y 1, Y 2 :

geometrical factors (shape functions)

Y 1 k d :

plastic zone effect factor

Y 2 k d :

crack closure factor

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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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Translated from Problemy Prochnosti, No. 3, pp. 77 – 95, May – June, 2014.

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Herasymchuk, O.M. Relationship Between the Threshold Stress Intensity Factor Ranges of the Material and the Transition From Short to Long Fatigue Crack. Strength Mater 46, 360–374 (2014). https://doi.org/10.1007/s11223-014-9558-2

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