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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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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DOI: https://doi.org/10.1007/s13369-015-1567-3