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On the mode I and II failure of three Cameroonian hardwoods with orthotropy rate evaluation

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Abstract

This work uses the M-theta method on a new proposed specimen called "I-specimen" for the numerical modeling of cracks on some tropical hardwoods in general and in particular on some Cameroonian woods. The finite element analysis of fracture in an orthotropic medium is developed. The fracture algorithm is introduced in a finite element software Cast3M and, with an incremental orthotropic formulation, the simulation of crack growth is computed. Using this method, stress intensity factors and energy release rate are calculated for Mode I and II failures. The energy release rate and stress intensity factors are numerically deduced using “I-specimen” to characterize three Cameroonian hardwoods under mode I and II loading for different crack growths. The specimen used has better characteristics than other samples generally used in the literature and its geometry is very simple to define. The proposal of a new geometry that can guarantee the reproduction of the different failure modes while exhibiting some stability of the crack parameters G and K during propagation was evaluated and compared to other specimens given by the fracture mechanics literature. For each fracture mode, the influence of the orthotropy rate parameters on the energy release rate was investigated.

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Abbreviations

\(a\) :

Crack length

\(M\) :

M-integral defined on surface domain

\(S\) :

Two-dimensional cracked body

\(C\) :

Integration path on the crack edges

\(\Gamma\) :

Integration crown

\(\overrightarrow{n}\) :

Outward unit normal

\(\overrightarrow{\theta }\) :

Vector field

\((x\), \(y)\) :

Cartesian coordinates

\((r\), θ\()\) :

Polar coordinates

\(\mu\) :

Loading angle

α, κ:

Orthotropy rate

\({C}_{I}\), \({C}_{II}\) :

Elastic compliances in opening and shear mode

\({E}_{j}\) :

Elastic modulus in direction j

\(\upsilon\) :

Poisson’s ratio

\({P}_{j}\), \({q}_{j}\) :

Roots of characteristic equation

\(\overrightarrow{{F}_{I}}\), \(\overrightarrow{{F}_{II}}\) :

Mechanic loads on crack edges in modes I and II

\({u, \varepsilon }_{ij}^{u}\), \({\sigma }_{ij}^{u}\) :

Real displacements, strains, and stresses

\({v, \varepsilon }_{ij}^{v}\),\({\sigma }_{ij}^{v}\) :

Auxiliary displacements, strains, and stresses

\(w\) :

Strain energy density

\(J\) :

Rice’s integral

\({G}_{I}\) , \({G}_{II}\) :

Energy release rates in opening and shear modes

\({G}_{IC}\) , \({G}_{IIC}\) :

The separation work rates in opening and shear modes

\({K}_{I}\) , \({K}_{II}\) :

Stress intensity factors corresponding to the real fields

ENS:

End Notched Shear

SENT:

Single-Edge-Notched Tensile

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Acknowledgements

The authors wish to gratefully acknowledge the wood’s pool of UR-2MSP (Research Unit of Mechanics and Modelling of Physical Systems), Faculty of Sciences, University of Dschang, Cameroon, for the facilities given during this work.

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Authors and Affiliations

  1. Faculté Des Sciences, UR-2MSP (Unité de Recherche de Mécanique Et de Modélisation Des Systèmes Physique), Université de Dschang, BP 067, Dschang, Cameroun

    Hervice Kouefouet, Jeanne Sandrine Mabekou & Pierre Kisito Talla

  2. Université Clermont Auvergne, Clermont Auvergne INP, CNRS, Institut Pascal, 63000, Clermont-Ferrand, France

    Rostand Moutou Pitti

  3. IRT, CENAREST, BP 14070, Libreville, Gabon

    Rostand Moutou Pitti

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  1. Hervice Kouefouet
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  2. Jeanne Sandrine Mabekou
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  3. Rostand Moutou Pitti
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  4. Pierre Kisito Talla
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Contributions

KH wrote the main manuscript text, collected data and prepared figures, MJ Sandrine arrange the manuscript, MP Rostand review the manuscript and prepared figures, TPK review the manuscript.

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Correspondence to Hervice Kouefouet.

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Kouefouet, H., Mabekou, J.S., Pitti, R.M. et al. On the mode I and II failure of three Cameroonian hardwoods with orthotropy rate evaluation. Eur. J. Wood Prod. (2024). https://doi.org/10.1007/s00107-024-02058-2

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