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Closed-Form Solutions of Stress Intensity Factors for Semi-elliptical Surface Cracks in a Cylindrical Bar Under Pure Tension

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Abstract

In this work, the stress intensity factors (SIFs) for a wide range of semi-elliptical surface cracks with different inclination angles in a cylindrical bar subjected to pure tension were investigated numerically. The main parameters considered to evaluate the SIFs were the crack size ratio \((a\big / d)\), the crack aspect ratio \((a\big /c)\), and the crack inclination angle \((\theta )\). The dual-boundary element method implemented in software BEASY was used to compute the SIF values for cracks. Furthermore, the general closed-form solutions were proposed to evaluate the corresponding SIFs for Mode I, Mode II and Mode III types of fracture through curve fitting approaches. These solutions can provide accurate and reliable values of stress intensity factors for a crack on a cylindrical bar under pure tension in a rapid way compared to those obtained using computational models. In addition, these results can be used as inputs for failure studies and life evaluations of cracked cylinder under working conditions.

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Abbreviations

a :

Depth of crack

c :

Half-length of crack

\(c^{'}\) :

Half-length of distance between intersections of crack front with cylinder surface

\(\sigma _{0}\) :

Applied tension to the cylindrical bar

d :

Diameter of cylindrical bar

r :

Radius of cylindrical bar

L :

Length of cylindrical bar

\(\theta \) :

Crack inclination angle

E :

Modulus of Elasticity

\(\nu \) :

Poisson’s ratio

s :

Crack front arc-length

h :

Element size

\(\varphi \) :

Parametric angle of ellipse

Q :

Shape factor for elliptical crack

\(K_\mathrm{I}\) :

Mode I, SIF

\(K_\mathrm{II}\) :

Mode II, SIF

\(K_\mathrm{III}\) :

Mode III, SIF

\(F_{RM}\) :

Normalized SIFs for surface crack in the cylinder

\(f_{S}\) :

Normalized value for SIFs at \(\varphi =\pi /2\) for Mode I and III and \(\varphi =\varphi _{0}\) for Mode II

\(f_{\theta }\) :

Inclination-correction factor

g :

Curve fitting function

CPE:

Corner points on the ellipse

DPE:

Deepest point on ellipse

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Acknowledgements

The authors wish to thank the Ministry of Higher Education, Malaysia, through the High Impact Research Grant (UM.C/625/1/HIR/MOHE/ENG/33).

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Authors and Affiliations

  1. Centre of Advanced Manufacturing and Materials Processing, Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, 50603, Malaysia

    M. K. Ramezani & S. Ramesh

  2. Department of Mechanical Engineering, University of Pertamina, Jakarta, 12220, Indonesia

    J. Purbolaksono

  3. Sir Lawrence Wackett Aerospace Research Centre, School of Engineering, RMIT University, Melbourne, VI, 3000, Australia

    R. Das

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  1. M. K. Ramezani
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  3. J. Purbolaksono
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Ramezani, M.K., Ramesh, S., Purbolaksono, J. et al. Closed-Form Solutions of Stress Intensity Factors for Semi-elliptical Surface Cracks in a Cylindrical Bar Under Pure Tension. Acta Mech. Solida Sin. 35, 344–356 (2022). https://doi.org/10.1007/s10338-021-00286-0

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  • DOI: https://doi.org/10.1007/s10338-021-00286-0

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