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On the efficiency of the numerical evaluation of fracture parameters using a virtual strain gage method

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Abstract

A simple method, called the virtual strain gage method, is proposed for an accurate numerical evaluation of the stress intensity factor, the T-stress and the biaxiality parameter β. This method is based on the optimal positions of virtual strain gages located near a crack tip so that the effect of dominant singular strains are canceled. The applicability of the proposed method is examined for quasi-static and low-velocity impact loading conditions on an epoxy three-point bending specimen and PMMA single edge notched specimen. The effects of the loading conditions, the geometry configuration and the length of the crack were presented and discussed. A good agreement has been found between the results of the proposed method and those of the numerical and experimental data previously published. In addition, it is noticed that the proposed method is an alternative and more advantageous then the extrapolation method because of its simplicity and accurate results.

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Abbreviations

a :

Crack length

B :

Specimen thickness

A n , B m :

Coefficients of the crack tip asymptotic field

E :

Young’s modulus

h :

Half height of the plate

K I :

Stress intensity factors in Mode I

K IC :

Critical stress intensity factor of the first mode

L :

Length of half specimen

P :

Applied load on the specimen

P i (r, θ):

Locations of virtual strain gages

r :

Radial distance from the crack tip

r, θ :

Polar coordinate components

W :

Specimen width

x, y, z :

Cartesian coordinates components

ε xx , ε yy :

Normal strains in x and y direction

ε x’x’ , ε y’y’ :

Normal strains in relative to a rotated coordinate system (x’, y ’)

γ xy :

Shear strain in x–y plane

ν :

Poisson’s ratio

ρ :

Mass density

µ :

Shear modulus

σ xx , σ yy :

Normal stresses in x and y directions

τ xy :

Shear stress in x–y plane

CTOD:

Crack tip opening displacement

FEM:

Finite element method

HRR:

Hutchinson-Rice-Rosengren field

LEFM:

Linear elastic fracture mechanics

PMMA:

Poly(methyl methacrylate) (Plexiglas)

QPE:

Quarter point element

TPB:

Three-point bending specimen

SENT:

Single edge notched tensile specimen

SIF:

Stress intensity factor

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Authors and Affiliations

  1. Department of Mechanical Engineering, University Djillali Liabes, BP 89, City Benmhidi, 22000, Sidi Bel Abbes, Algeria

    F. Khelil & M. Belhouari

  2. Laboratory of Applied Biomechanics and Biomaterials (LABAB), ENP Oran, El Mnaour, BP 1523, 31000, Oran, Algeria

    B. Aour

  3. Lille Mechanics Laboratory (LML), University of Lille 1, Scientific city, BP 90179, 59653, Villeneuve-d’Ascq, France

    N. Benseddiq

Authors
  1. F. Khelil
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  2. M. Belhouari
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  3. B. Aour
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  4. N. Benseddiq
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Correspondence to F. Khelil.

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Technical Editor: Eduardo Alberto Fancello.

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Khelil, F., Belhouari, M., Aour, B. et al. On the efficiency of the numerical evaluation of fracture parameters using a virtual strain gage method. J Braz. Soc. Mech. Sci. Eng. 39, 589–599 (2017). https://doi.org/10.1007/s40430-016-0520-z

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  • DOI: https://doi.org/10.1007/s40430-016-0520-z

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