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Surface crack growth prediction under fatigue load using probabilistic S-version finite element model

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Abstract

The objective of this paper is to recognize the probabilistic distribution of crack growth and stress intensity factor for surface crack. A model with surface crack is subjected to arbitrary constant-amplitude loads. The model is analysed using probabilistic S-version finite element model (ProbS-FEM). In order to decide the probabilistic distribution, Latin hypercube sampling is embedded with ProbS-FEM. Simulation model is compared with experimental specimens. The specimens are prepared and investigated for fatigue testing. Good agreement between predictions, experiments, and previous numerical solutions shows that the developed approach can serve for a realistic reliability analysis of three-dimensional engineering structures.

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Abbreviations

\(a\) :

Initial crack depth

\(a /c\) :

Aspect ratio

\(b\) :

Length of specimen

\(B^{\text{G}}\) :

Deformation matrix for global

\(B^{\text{L}}\) :

Deformation matrix for local

\(c\) :

Initial crack length

\(C\) :

Paris coefficient \(c\)

\(C^{I}\) :

Constant of VCCM

\(D\) :

Material properties matrix

\({\text{d}}a\) :

Crack growth increment

\({\text{d}}a_{ \max}\) :

Maximum crack growth increment

\({\text{d}}a / {\text{d}}N\) :

Crack growth rate

\(E\) :

Modulus of elasticity

\(E\left[ {} \right]\) :

Mean operator

\(f\) :

Body force

\(F_{\text{G}}\) :

Force for global region

\(F_{\text{L}}\) :

Force for local region

\(F_{ \max}\) :

Maximum stress during loading cycle

\(F_{ \min}\) :

Minimum stress during loading cycle

\(G_{\text{Total}}\) :

Total energy release rate

\(G_{\text{I,II,III}}\) :

Energy release rate for modes I, II, and III

\(h\) :

Width of specimen

\(I\) :

Node number around the crack tip

\(K\) :

Stiffness matrix

\(K_{\text{IC}}\) :

Critical stress intensity factor

\(K_{\text{GG}}\) :

Stiffness matrix for global region

\(K_{\text{LL}}\) :

Stiffness matrix for local region

\(K_{\text{GL}}\) :

Stiffness matrix for overlay region

\(K_{\text{I,II,III}}\) :

Stress intensity factor for modes I, II, and III

\(n\) :

Fatigue power parameter

\(h\) :

Nodal force

\(P_{i}^{I}\) :

Failure probability

\(r\) :

Radius of crack growth

\(R\) :

Radius of crack front

\(S_{1}^{J}\) :

Area after crack front

\(S_{2}^{J}\) :

Area before crack front

\(t\) :

Thickness of specimen

\(u\) :

Displacement function

\(u^{\text{G}}\) :

Displacement function for global

\(u^{\text{L}}\) :

Displacement function for local

\({\text{Var}}\left[ {} \right]\) :

Variance operator

\(w^{J}\) :

Width of element parallel to the crack front

\(v_{i}^{I}\) :

Nodal displacement between the upper and lower crack surfaces

\(v_{i}\) :

Crack opening displacement at the crack surface

\(v\) :

Poisson’s ratio

\(\varDelta\) :

Width of the element in the radial direction

\(\Delta K_{\text{th}}\) :

Threshold value

\(\Delta K_{\text{eq}}\) :

Equivalent stress intensity factor

\(\Delta K_{{{\text{eq}}_{ \max} }}\) :

Maximum equivalent stress intensity factor

\(\varOmega^{\text{L}}\) :

Local mesh region

\(\varOmega^{\text{G}}\) :

Global mesh region

ε :

Strain

\(\varepsilon^{\text{L}}\) :

Strain for local region

\(\varepsilon^{\text{G}}\) :

Strain for global region

\(\theta\) :

Surface crack angle

\(\varphi_{0}\) :

Crack growth angle

σ :

Stress

\(\sigma_{3i}\) :

Cohesive stress at the local axis x3

\(\varGamma\) :

Boundary condition

\(\varGamma^{\text{GL}}\) :

Boundary condition at overlay region

\(\mu\) :

Shear modulus

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Acknowledgements

This study was funded by RDU170383 from Universiti Malaysia Pahang and Fundamental Research Grant Scheme (FRGS/1/2017/TK03/UMP/02/24) from Kementerian Pendidikan Malaysia with Number RDU170124.

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Authors and Affiliations

  1. Universiti Malaysia Pahang, 26600, Pekan, Pahang, Malaysia

    M. R. M. Akramin, M. S. Shaari & M. N. M. Husnain

  2. Universiti Kebangsaan Malaysia, 43650, Bangi, Selangor, Malaysia

    A. K. Ariffin

  3. Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, 278-8510, Japan

    Masanori Kikuchi

  4. Institute for Computer Science in Civil Engineering, Leibniz University Hannover, Hannover, Germany

    M. Beer

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  1. M. R. M. Akramin
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Correspondence to M. R. M. Akramin.

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Technical Editor: Paulo de Tarso Rocha de Mendonça, Ph.D.

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Akramin, M.R.M., Ariffin, A.K., Kikuchi, M. et al. Surface crack growth prediction under fatigue load using probabilistic S-version finite element model. J Braz. Soc. Mech. Sci. Eng. 40, 522 (2018). https://doi.org/10.1007/s40430-018-1442-8

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