PSI - Issue 7

Stanislav Žák et al. / Procedia Structural Integrity 7 (2017) 254 – 261

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Stanislav Žák et al. / Structural Integrity Procedia 00 (201 7 ) 000 – 000

1. Introduction Due to material inhomogeneities, microstructure and texture, real shear-mode fatigue cracks almost never locally propagate in one direction on the microscale level and the crack flanks are not smooth even if the global (macroscopic) crack propagation is planar (Pokluda et al. (2014) ; Vojtek et al. (2016); Zerres and Vormwald (2014)). This also holds for fatigue precracks generated under mode I loading in the near-threshold region, where the precrack path and front are particularly sensitive to microstructural features (Pokluda and Šandera (2010)). Perhaps the most important fatigue characteristic related to crack propagation is the crack-growth threshold. In the last years, many authors attempted to review the state-of-the-art and the progress in this field (Pokluda et al. (2014); Richard et al. (2005); Zerbst et al. (2016)). It is well known that, in the mode II loading case, the increasing roughness of the crack faces during the crack growth can significantly reduce the values of remote effective SIF Δ K II,eff while the tortuosity of the precrack front can reduce the value of effective threshold Δ K IIth,eff (Pokluda et al. (2014)). However, the quantitative assessment of these geometrical shielding effects is rather difficult and thus only rarely reported (e. g. Beretta et al. (2011); Faber and Evans (1983); Gross and Mendelsohn (1989)). In a series of papers devoted to experimental determination of effective shear-mode thresholds in metallic materials and their theoretical background (Pokluda and Pippan (2005); Pokluda et al. (2014 ); Vojtek et al. (2016)), the authors showed the basic importance of the effective (local) mode II component also for mode III and mixed mode II+III loading cases. Therefore, only the plausible determination of this component of the general I+II+III local mixed mode loading produced by the real 3D tortuous precrack fronts can give a sufficiently relevant comparison of experimental and theoretical values of shear- mode fatigue thresholds. This article presents results of numerical and analytical modelling of crack-tip shielding effects and calculation of the local k II – component of the mixed I+II+III local loading mode produced by 3D tortuosity of the fatigue precrack under remote pure mode II loading. The results will be used for correction of the value of previously measured effective threshold Δ K IIth, eff for the polycrystalline ARMCO iron (Vojtek et al. (2015)) and its comparison with the theoretical data for the iron single crystal obtained from multiscale models.

Nomenclature a

length of smooth part of crack projected length of crack length of the rough crack part length of one crack front asperity

a p

Δ a d m

loading force

F

local mode I, II and III stress intensity factors remote mode II stress intensity factor

k I, II, III

K II K IIe

theoretical value of mode II stress intensity factor related to emission of dislocations

Δ K II,eff Δ K IIth,eff

remote effective range of mode II stress intensity factor remote effective fatigue threshold for mode II loading

L R

matrix of direction cosines

cyclic ratio

linear roughness

R L

linear roughness of crack front obtained from fractured ARMCO iron specimens

R L,Fe

specimen thickness standard stress tensor transformed stress tensor

t

T σ T σ

*

specimen width

w

position along the crack front in direction of z-axis crack kink angle (maximal crack kink angle)

z

α ( α m)

crack twist angle

β

stress tensor components where i, j = x; y; z

σ ij