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Fatigue Crack Tip Plasticity for Inclined Cracks

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Abstract

The evaluation of the crack tip deformation is essential to the estimation of crack growth under either static or cyclic loading. A 3-D elastic–plastic finite element analysis was developed to simulate the crack tip deformation along mixed mode inclined edge cracks in a steel plate subjected to either monotonic or cyclic loading at selected R-ratios. In this paper, two types of crack configurations were investigated: inclined cracks with equal inclined lengths (EICL) and inclined cracks with equal horizontal projection length (ECHP). The development of the monotonic (Δm) and cyclic (Δc) crack tip plastically zones and the monotonic (CTOD) and cyclic (ΔCTOD) crack tip opening displacements were traced to find the effect of the crack inclination angle, which significantly affected the size and shape of the crack tip plastic zone. The finite element results compared well with the analytical results based on modified Dugdale’s model. It was observed that Mode II has a significant effect on the plastic zone in the case of equal inclined crack length (EICL), i.e., Mode II increases as the crack angle decreases. Also, it is interesting to note that for the EICL case, the magnitude of Δc is delayed to appear with decreasing the inclination angle, for example, for θ = 90° the cyclic plastic zone appeared at Δσ = 103.32 MPa, while for θ = 45° the cyclic plastic zone appeared at Δσ = 132.84 MPa. Whereas, the variation of monotonic and cyclic plastic zone size in the equal crack horizontal projection (ECHP) case is not affected by the crack inclination angle. Furthermore, it was observed that the static crack tip opening displacement (CTOD) and the cyclic (ΔCTOD) are independent of the crack inclination angle in case of ECHP, due to such cracks take into consideration the effect of inclination angle through its length.

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Abbreviations

w:

Plate width

h:

Plate height

t:

Plate thickness

σ:

Applied stress

KI, KII :

Stress intensity factors for modes I and II, respectively

ΔK:

Stress intensity factor range

a:

Crack length

θ:

Angle made by the crack measured in a clockwise direction from the loading axis

R:

Stress ratio

CTOD:

Monotonic crack tip opening displacement normal to the crack face

CTSD:

Monotonic crack tip sliding displacement

CTODR :

Resultant of monotonic normal and sliding opening displacements

ΔCTODR :

Resultant of cyclic normal and sliding opening displacements

Y:

Geometry correction factor

Δm:

Monotonic plastic zone size (MPZS)

Δc:

Cyclic plastic zone size (CPZS)

FCG:

Fatigue crack growth

εy :

Engineering tensile yield strain

σy :

Engineering tensile yield strength

µ:

Poisson’s ratio

E:

Young’s modulus

ECHP:

Equal crack horizontal projection

EICL:

Equal inclined crack length

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Authors and Affiliations

  1. Civil and Environmental Engineering, University of Missouri, Columbia, MO, 65211, USA

    Hesham El-Emam, Alaaeldin Elsisi & Hani Salim

  2. Civil Engineering, Jazan University, Jazan, Kingdom of Saudi Arabia

    Hossam Sallam

Authors
  1. Hesham El-Emam
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  2. Alaaeldin Elsisi
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  3. Hani Salim
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  4. Hossam Sallam
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Correspondence to Hesham El-Emam.

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Hesham El-Emam and Hossam Sallam—On leave from Materials Engineering Department, Zagazig University, Zagazig, Egypt.

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El-Emam, H., Elsisi, A., Salim, H. et al. Fatigue Crack Tip Plasticity for Inclined Cracks. Int J Steel Struct 18, 443–455 (2018). https://doi.org/10.1007/s13296-018-0016-z

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