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FEM Techniques Comparison for SIF Computing of Cracked Plate

  • Research Article - Mechanical Engineering
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Abstract

The main purpose of this paper is to perform a computation comparison of stress intensity factor ‘SIF’ evaluation in case of cracked thin plate with aluminum alloy 7075-T6 and 2024-T3 used in aeronautics structure under uniaxial loading. This evaluation is based on finite element method with a virtual power principle through two techniques: the extrapolation and \({G - \theta}\) . The first one consists to extrapolate the nodal displacements near the cracked tip using a refined triangular mesh with T3 and T6 special elements, while the second, consists to determine the energy release rate G through \({G - \theta}\) method by potential energy derivation which corresponds numricaly to elastic solution post-processing of a cracked solid by a contour integration computation via Gauss points. The SIF obtained results from extrapolation and \({G - \theta}\) methods will be compared to analytical solution in particular case. To illustrate the influence of the meshing kind and the size of integration contour position, simulations are presented and analyzed.

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Abbreviations

A:

Elasticity tensor modulus

\({C(\underline 0 )}\) :

Represents all the admissible free displacement (m)

\({C(\underline u ^D )}\) :

Represent all the admissible imposed displacement (m)

e 1, e 2, e 3 :

Unit vector of displacement near the crack tip (m)

\({f_{ij}^{\left( I \right)}}\), \({f_{ij}^{\left( II \right)}}\) and \({f_{ij}^{\left( III \right)}}\) :

Are the angular repartition functions

f(b):

Is the correction factor

\({\left\{F \right\}}\) :

Is the vector of generalized forces (N)

G :

The energy release rate (J)

\({\left[ K \right]}\) :

Is the stiffness matrix of structure

K I , K II :

Stress intensity factor of first and second mode (MPa.m 0.5)

\({\underline t }\) and \({\underline n}\) :

Are tangent and normal direction to the crack

\({u^\varepsilon}\) :

Displacement during infinitesimal perturbation \({\varepsilon}\) (m)

\({u^\varepsilon}\) :

Displacement of the nearest node lips to the crack tip (m)

\({C(\underline u (B))}\) :

Displacement during infinitesimal perturbation \({\varepsilon}\) (m)

w p :

Total potential energy (J)

w ext :

Potential energy of external forces f (J)

\({\partial a}\) :

Increment of surface correspondents to crack extension

\({\Gamma _e^T }\) :

Represent a portion of the element E e border situated on S T

\({\theta }\) :

Is the eventual propagation crack angle from its initial direction (rad)

\({\sigma ^\varepsilon}\) :

Stresses during infinitesimal perturbation \({\varepsilon}\) (Pa)

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Correspondence to Elkahina Sari.

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Sari, E., Zergoug, M. FEM Techniques Comparison for SIF Computing of Cracked Plate. Arab J Sci Eng 40, 1165–1171 (2015). https://doi.org/10.1007/s13369-015-1567-3

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