Stress Intensity Factor for Dynamic Cracking of Composite Material by X-FEM Method
The work involves develops attended by a numerical
execution of the eXtend Finite Element Method premises a
measurement by the fracture process cracked so many cracked plates
an application will be processed for the calculation of the stress
intensity factor SIF. In the first we give in statically part the
distribution of stress, displacement field and strain of composite plate
in two cases uncrack/edge crack, also in dynamical part the first six
modes shape. Secondly, we calculate Stress Intensity Factor SIF for
different orientation angle θ of central crack with length (2a=0.4mm)
in plan strain condition, KI and KII are obtained for mode I and mode
II respectively using X-FEM method. Finally from crack inclined
involving mixed modes results, the comparison we chose dangerous
inclination and the best crack angle when K is minimal.
[1] Benzley, S.E. (1974) Representation of singularities with isoparametric
finite elements. International Journal for Numerical Methods in
Engineering, 8, 537–545.
[2] Atluri, S.N., Kobayashi, A.S. and Nakagaki, M. (1975b) An assumed
displacement hybrid finite element model for linear fracture mechanics.
International Journal of Fracture, 11(2), 257–271.
[3] Gifford, N.L. and Hilton, P.D. (1978) Stress intensity factors by
enriched finite elements. Engineering Fracture Mechanics, 20, 485–296.
[4] Belytschko, T. and Black, T. (1999) Elastic crack growth in finite
elements with minimal remeshing. International Journal of Fracture
Mechanics, 45, 601–620.
[5] Moes, N., Gravouil, A. and Belytschko, T. (2002) Non-planar 3D crack
growth by the extended finite element and level sets–Part I: Mechanical
model. International Journal for Numerical Methods in Engineering, 53,
2549–2568.
[6] Griffith A.A. The Phenomena of Rupture and Flow in Solids.
Philosophical Transactions of the Royal Society of London 1920, Vol.
A-221:163-198.
[7] Irwin, GR. Analysis of stresses and strains near the end of a crack
traversing a plate. Journal of Applied Mechanics 1957. 24: 361-364.
[8] Erdogane F , Paris P. A critical analysis of crack propagation laws 1963.
Journal of Basic Engineering, Transaction of the American Society of
Mechanical Engineers. p 528-534.
[9] Rice, JR. Plane strain deformation near a crack tip in a power law
hardening material. Journal of the Mechanics and Physics of Solids
1968. vol.16: 1-12.
[10] Erdogan F and Civelek M. B. Crack problems for a rectangular sheet
and infinite strip. Internationa l Journal of Fracture 1982. 19:139-159.
[11] Babuska I, Melenk J. The partition of unity method. International
Journal for Numerical Methods in Engineering 1997. Vol. 40:727–758.
[12] Prabel, B., Marie, S. and Combescure, A. (2007) Using the X-FEM
method to model the dynamic propagation and arrest of cleavage cracks
in ferritic steel. Engineering Fracture Mechanics, 75(10), 2984–3009.
[13] Soheil Mohammadi. 2012 . XFEM Fracture Analysis of Composites,
First Edition. John Wiley & Sons, Ltd. Published 2012 by John Wiley &
Sons, Ltd.
[14] Dolbow, J.E. and Nadeau, J.C. (2002) On the use of effective properties
for the fracture analysis of microstructured materials. Engineering
Fracture Mechanics, 69, 1607–1634.
[15] Wells, and Barst. (2003) The condition of fast fracture in aluminium
alloys with particular reference to comet failures. British Welding
Research Association Report.
[16] Nagashima, T. and Suemasu, H. (2006) Stress analysis of composite
laminates with delamination using XFEM. International Journal of
Computational Methods, 3, 521–543.
[17] Bayesteh, H. and Mohammadi, S. (2012) Fracture analysis of orthotropic
functionally graded materials by XFEM. Journal of Composites, Part B.
[18] Asadpoure, A., Mohammadi, S. and Vafai, A. (2006) Modeling crack in
orthotropic media using a coupled finite element and partition of unity
methods. Finite Elements in Analysis and Design, 42(13), 1165–1175.
[19] Asadpoure, A. and Mohammadi, S. (2007) A new approach to simulate
the crack with the extended finite element method in orthotropic media.
International Journal for Numerical Methods in Engineering, 69, 2150–
2172.
[1] Benzley, S.E. (1974) Representation of singularities with isoparametric
finite elements. International Journal for Numerical Methods in
Engineering, 8, 537–545.
[2] Atluri, S.N., Kobayashi, A.S. and Nakagaki, M. (1975b) An assumed
displacement hybrid finite element model for linear fracture mechanics.
International Journal of Fracture, 11(2), 257–271.
[3] Gifford, N.L. and Hilton, P.D. (1978) Stress intensity factors by
enriched finite elements. Engineering Fracture Mechanics, 20, 485–296.
[4] Belytschko, T. and Black, T. (1999) Elastic crack growth in finite
elements with minimal remeshing. International Journal of Fracture
Mechanics, 45, 601–620.
[5] Moes, N., Gravouil, A. and Belytschko, T. (2002) Non-planar 3D crack
growth by the extended finite element and level sets–Part I: Mechanical
model. International Journal for Numerical Methods in Engineering, 53,
2549–2568.
[6] Griffith A.A. The Phenomena of Rupture and Flow in Solids.
Philosophical Transactions of the Royal Society of London 1920, Vol.
A-221:163-198.
[7] Irwin, GR. Analysis of stresses and strains near the end of a crack
traversing a plate. Journal of Applied Mechanics 1957. 24: 361-364.
[8] Erdogane F , Paris P. A critical analysis of crack propagation laws 1963.
Journal of Basic Engineering, Transaction of the American Society of
Mechanical Engineers. p 528-534.
[9] Rice, JR. Plane strain deformation near a crack tip in a power law
hardening material. Journal of the Mechanics and Physics of Solids
1968. vol.16: 1-12.
[10] Erdogan F and Civelek M. B. Crack problems for a rectangular sheet
and infinite strip. Internationa l Journal of Fracture 1982. 19:139-159.
[11] Babuska I, Melenk J. The partition of unity method. International
Journal for Numerical Methods in Engineering 1997. Vol. 40:727–758.
[12] Prabel, B., Marie, S. and Combescure, A. (2007) Using the X-FEM
method to model the dynamic propagation and arrest of cleavage cracks
in ferritic steel. Engineering Fracture Mechanics, 75(10), 2984–3009.
[13] Soheil Mohammadi. 2012 . XFEM Fracture Analysis of Composites,
First Edition. John Wiley & Sons, Ltd. Published 2012 by John Wiley &
Sons, Ltd.
[14] Dolbow, J.E. and Nadeau, J.C. (2002) On the use of effective properties
for the fracture analysis of microstructured materials. Engineering
Fracture Mechanics, 69, 1607–1634.
[15] Wells, and Barst. (2003) The condition of fast fracture in aluminium
alloys with particular reference to comet failures. British Welding
Research Association Report.
[16] Nagashima, T. and Suemasu, H. (2006) Stress analysis of composite
laminates with delamination using XFEM. International Journal of
Computational Methods, 3, 521–543.
[17] Bayesteh, H. and Mohammadi, S. (2012) Fracture analysis of orthotropic
functionally graded materials by XFEM. Journal of Composites, Part B.
[18] Asadpoure, A., Mohammadi, S. and Vafai, A. (2006) Modeling crack in
orthotropic media using a coupled finite element and partition of unity
methods. Finite Elements in Analysis and Design, 42(13), 1165–1175.
[19] Asadpoure, A. and Mohammadi, S. (2007) A new approach to simulate
the crack with the extended finite element method in orthotropic media.
International Journal for Numerical Methods in Engineering, 69, 2150–
2172.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:67268", author = "S. Lecheb and A. Nour and A. Chellil and H. Mechakra and N. Hamad and H. Kebir", title = "Stress Intensity Factor for Dynamic Cracking of Composite Material by X-FEM Method", abstract = "The work involves develops attended by a numerical
execution of the eXtend Finite Element Method premises a
measurement by the fracture process cracked so many cracked plates
an application will be processed for the calculation of the stress
intensity factor SIF. In the first we give in statically part the
distribution of stress, displacement field and strain of composite plate
in two cases uncrack/edge crack, also in dynamical part the first six
modes shape. Secondly, we calculate Stress Intensity Factor SIF for
different orientation angle θ of central crack with length (2a=0.4mm)
in plan strain condition, KI and KII are obtained for mode I and mode
II respectively using X-FEM method. Finally from crack inclined
involving mixed modes results, the comparison we chose dangerous
inclination and the best crack angle when K is minimal.
", keywords = "Stress Intensity Factor (SIF), Crack orientation,
Glass/Epoxy, natural Frequencies, X-FEM.", volume = "8", number = "5", pages = "813-7", }
