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Mixed-mode I/II criterion based on combining Hill failure analysis and reinforcement isotropic solid model

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Abstract

Several failure criteria for fibrous and non-fibrous anisotropic materials were proposed after considering numerous implementations in various industries. Failure theories are classified as including or excluding distinct failure modes, and the majority of them do not account for intrinsic properties and loading mode mixites. In this context, theories include the gradual micromechanical transition from anisotropic to isotropic media embedding reinforcement, referred to as the “reinforcement isotropic solid model.” In other words, the reinforcement isotropic solid model ensures the independence of the fiber effects by modeling fibers as a proportion of the isotropic matrix's active stress. The Hill criterion, in conjunction with the reinforcement isotropic solid model, is employed to propose a new fracture criterion for mixed-mode I/II loading, referred to here as “Extended HILL.” Additionally, experimental results have been established to validate the failure criteria based on reinforcement in the isotropic solid mode. This criterion produces good agreement between the fracture limit curves and the experimental data.

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Abbreviations

\(C_{ij}\) :

Compliance matrix

\(E_{ij}\) :

Elastic modulus

\(G_{ij}\) :

Shear modulus

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

Mode I and II stress intensity factor

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

Mode I and II fracture toughness

\(n_{1} ,\,n_{2} ,\,n_{6}\) :

Effect coefficients

\(S_{ij} (i,j = 1,..,6)\) :

Compliance matrix

\(S\) :

Shear strength

T, R, L :

Tangential, radial and longitudinal orthotropy axis in of wood

\(X_{T} ,\,X_{C}\) :

Longitudinal failure stress strength

\(Y_{T} ,\,Y_{C}\) :

Transverse failure stress strength

\(\alpha\) :

Fiber direction

\(\varepsilon_{x} ,\varepsilon_{y} ,\gamma_{xy}\) :

Strain function

\(\theta\) :

Crack direction

\(\mu\) :

Roots of the characteristic equation

\(\nu_{ij}\) :

Poisson's ratio

\(\sigma_{ij}\) :

Crack-tip stress field

\(\phi ,\,\psi\) :

Airy stress function

ASER:

Augmented strain energy release rate

EHILL:

Extended Hill

EMTS:

Extended maximum tangential stress

FLC:

Fracture limited curve

FPZ:

Fracture process zone

RIS:

Reinforcement isotropic solid

LEFM:

Linear elastic fracture mechanics

SED:

Strain energy density

SER:

Strain energy release rate

MTS:

Maximum tangential stress

MPS:

Maximum principal stress

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Authors and Affiliations

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

    Shahab Zare Hosseinabadi, Mohammad Hossein Sabour & Mahdi Fakoor

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  1. Shahab Zare Hosseinabadi
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  2. Mohammad Hossein Sabour
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  3. Mahdi Fakoor
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Contributions

SZH contributed to software, validation, formal analysis, data curation, and writing original draft. MHS contributed to investigation, supervision, and writing review and editing. MF contributed to conceptualization, methodology, supervision, and writing review and editing.

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Correspondence to Mahdi Fakoor.

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Zare Hosseinabadi, S., Sabour, M.H. & Fakoor, M. Mixed-mode I/II criterion based on combining Hill failure analysis and reinforcement isotropic solid model. Acta Mech 234, 1437–1450 (2023). https://doi.org/10.1007/s00707-022-03456-4

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