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Appropriate fitted point on fracture limit curve of orthotropic materials to include the fracture process zone effects on mixed-mode I/II fracture criterion

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Abstract

The fracture phenomenon in orthotropic materials is associated with the formation of the fracture process zone at the crack tip. Several toughening mechanisms in this zone delay the fracture by absorbing energy. The activation of these mechanisms and the extent of their effects depend on the loading mode. In this paper, the behavior of the fracture process zone under different loading modes is investigated. In the following, considering the fracture process zone effects, a new mixed-mode I/II fracture criterion is presented to investigate the crack growth behavior of orthotropic materials. In this criterion, by extending the minimum strain energy density theory to orthotropic materials and fitting the fracture limit curve to a midpoint (a mixed-mode I/II point) instead of the pure mode I point, a greater portion of the energy absorbed in the fracture process zone is considered. To validate the presented criterion, the related fracture limit curves are compared with the available experimental data for laminated composites and wood species as orthotropic materials. The results show that the newly proposed criterion, unlike the available conservative ones, especially around predominantly mode II, is more compatible with the nature of the failure phenomena in orthotropic materials.

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Abbreviations

\(W\) :

Strain energy

\(\sigma_{ij}\) :

Stress field around the crack tip

\(\varepsilon_{ij}\) :

Strain field around the crack tip

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

Mode I and mode II stress intensity factor

\(K_{Ic}\) , \(K_{IIc}\) :

Mode I and mode II fracture toughness

\(K_{{I_{Mid} }}\) , \(K_{{II_{Mid} }}\) :

Mode I and mode II stress intensity factor of midpoint

\(r\) :

Distance from the crack tip

\(\theta\) :

Angle from the crack tip

\(\theta_{0}\) :

Crack initiation angle

\(\theta_{{0_{I} }}\), \(\theta_{{0_{II} }}\) :

Crack initiation angle under pure mode I and pure mode II loading

\(\theta_{{0_{I/II} }}\) :

Crack initiation angle under mixed-mode I/II loading

\(C_{ij}\) :

Components of compliance matrix for the plane stress conditions

\(C^{\prime}_{ij}\) :

Components of compliance matrix for the plane strain conditions

\(S\) :

Strain energy density factor

\(S_{c}\) :

Critical strain energy density factor

\(\rho\) :

Damage factor

\(\rho^{\prime}\) :

Modified damage factor

\(\alpha_{i} ,\;\;i = 1,2\) :

Inverse of defined damage factors

\(E_{i} ,\;\;i = 1,2,3\) :

Young’s moduli in the i direction

\(G_{ij}\) :

Shear modulus

\(\nu_{ij}\) :

Poisson’s ratio

FPZ:

Fracture process zone

SER:

Strain energy release

SED:

Strain energy density

MTS:

Maximum tangential stress

LEFM:

Linear-elastic fracture mechanics

SERR:

Strain energy release rate

SEM:

Scanning electron microscope

DCB:

Double cantilever beam

MMB:

Mixed-mode bending

ENF:

End-notched flexure

SIF:

Stress intensity factor

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Authors and Affiliations

  1. Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran

    Zahra Daneshjoo

  2. Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

    Mahdi Fakoor

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  1. Zahra Daneshjoo
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Correspondence to Zahra Daneshjoo.

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Daneshjoo, Z., Fakoor, M. Appropriate fitted point on fracture limit curve of orthotropic materials to include the fracture process zone effects on mixed-mode I/II fracture criterion. Acta Mech 234, 1489–1502 (2023). https://doi.org/10.1007/s00707-022-03468-0

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