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Verification of reinforcement isotropic solid model in conjunction with maximum shear stress criterion to anticipate mixed mode I/II fracture of composite materials

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Abstract

In the present research, a new criterion based on maximum shear stress (MSS) theory is developed for fracture investigation of orthotropic materials under mixed mode I/II loading. The crack is assumed to be embedded both along and across the fibers in the isotropic matrix. Self-similar crack propagation is assumed based on experimental observations and the reinforcement isotropic solid (RIS) concept is utilized for theoretical derivation of the criterion. In this model, an istropic crack tip stress field is assumed and the effects of fibers are supposed as stress reduction factors. The superiority of employing MSS theory in conjunction with RIS model is proved by derivation of a direct MSS-based mixed mode fracture criterion with respect to the orthotropic crack tip stress field. Verification of the results is performed by comparison of the fracture limit curves with available experimental mixed mode fracture data.

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Abbreviations

\(C_{ij} \) :

Components of compliance matrix

\({C}'_{ij} \) :

Components of compliance matrix in plane strain condition

\(C_{ij}^{{\text {off-axis}}} \) :

Off-axis components of compliance matrix

\(C_{ij}^{{\text {on-axis}}} \) :

On-axis components of compliance matrix

\(c_{t} ,c_{n} \) :

Extensional and sliding compliance of a damaged body

\(E_{ij} \) :

Young’s modulus

\(E_{L} ,E_{R} ,E_{T} \) :

Longitudinal, Radial and Tangential Young’s modulus for wood specimens

\(f_{ij} (\theta ),g_{ij} (\theta )\) :

Angular functions

\(G_{ij} \) :

Shear modulus of composite material

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

Mode I and mode II stress intensity factors

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

Mode I and mode II fracture toughness

\(K_{\mathrm{I}}^{{\mathrm{kink}}} ,K_{{\mathrm{II}}}^{{\mathrm{kink}}} \) :

Mode I and mode II stress intensity factors at the tip of the crack kink

L, R, T :

Longitudinal, Radial and Tangential orthotropy axes in wood specimen

\(n_{i} \) :

Reinforcement factor

r :

Distance from crack tip

\(V_{f} ,V_{m} \) :

The volume fraction of fibers and the matrix in a composite

x, y :

Global coordinate system

\(\alpha _{ij} \) :

Related to crack kink angle

\(\beta _{i}\)  (i = 1...6):

Damage coefficient in the theoretical criteria

\(\theta \) :

Arbitrary angle to show stress state in crack tip

\(\lambda \) :

Dimensionless parameters

\(\nu _{{\textit{LR}}} \) :

Poisson’s ratio in RL direction

\(\nu _{{\textit{LT}}} \) :

Poisson’s ratio in TL direction

\(\nu _{{\textit{TR}}} \) :

Poisson’s ratio in RT direction

\(\xi _{i}\)  (i = 1...3):

Reinforcement factor

\(\rho _{i} \,\) :

Damage factor in fracture criteria

\(\sigma _{ij}^{{\mathrm{iso}}} \) :

Isotropic stress tensor

\(\sigma _{ij}^{{\mathrm{ortho}}} \) :

Orthotropic stress tensor

\(\tau \) :

Shear stress

\(\tau _{{\textit{cr}}} \) :

Critical Shear stress

\(\varphi \) :

Crack-Fiber angle

\(\chi \) :

Dimensionless parameters

\(\psi \) :

Airy stress function

ASER:

Augmented strain energy release rate

EMSS:

Extended maximum shear stress

FEM:

Finite element method

MPS:

Maximum principal stress

MSS:

Maximum shear stress

MTS:

Maximum tangential stress

RIS:

Reinforcement isotropic solid

RIS–MSS:

Reinforcement isotropic solid–maximum shear stress criterion

SED:

Strain energy density

SER:

Strain energy release rate

SIFs:

Stress intensity factors

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Authors and Affiliations

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

    Sadra Shahsavar & Mahdi Fakoor

  2. Norwegian University of Science and Technology, Trondheim, Norway

    Filippo Berto

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  1. Sadra Shahsavar
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  2. Mahdi Fakoor
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  3. Filippo Berto
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Correspondence to Mahdi Fakoor.

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Shahsavar, S., Fakoor, M. & Berto, F. Verification of reinforcement isotropic solid model in conjunction with maximum shear stress criterion to anticipate mixed mode I/II fracture of composite materials. Acta Mech 231, 5105–5124 (2020). https://doi.org/10.1007/s00707-020-02810-8

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