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

  • F. KhelilEmail author
  • M. Belhouari
  • B. Aour
  • N. Benseddiq
Technical Paper


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.


Stress intensity factor T-stress Biaxiality parameter FEM PMMA 

List of symbols


Crack length


Specimen thickness

An, Bm

Coefficients of the crack tip asymptotic field


Young’s modulus


Half height of the plate


Stress intensity factors in Mode I


Critical stress intensity factor of the first mode


Length of half specimen


Applied load on the specimen

Pi(r, θ)

Locations of virtual strain gages


Radial distance from the crack tip

r, θ

Polar coordinate components


Specimen width

x, y, z

Cartesian coordinates components

εxx, εyy

Normal strains in x and y direction

εx’x’, εy’y’

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


Shear strain in xy plane


Poisson’s ratio


Mass density


Shear modulus

σxx, σyy

Normal stresses in x and y directions


Shear stress in xy plane



Crack tip opening displacement


Finite element method


Hutchinson-Rice-Rosengren field


Linear elastic fracture mechanics


Poly(methyl methacrylate) (Plexiglas)


Quarter point element


Three-point bending specimen


Single edge notched tensile specimen


Stress intensity factor


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2016

Authors and Affiliations

  • F. Khelil
    • 1
    Email author
  • M. Belhouari
    • 1
  • B. Aour
    • 2
  • N. Benseddiq
    • 3
  1. 1.Department of Mechanical EngineeringUniversity Djillali LiabesSidi Bel AbbesAlgeria
  2. 2.Laboratory of Applied Biomechanics and Biomaterials (LABAB)ENP OranOranAlgeria
  3. 3.Lille Mechanics Laboratory (LML)University of Lille 1Villeneuve-d’AscqFrance

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