1 |
ANSYS, Inc. (2009), Programmer's Manual for Mechnical APDL, Release 12.1.
|
2 |
Barsoum, R.S. (1974), "On the use of isoparametric finite element in linear fracture mechanics", Int. J. Numer. Meth. Eng., 10, 25-37.
|
3 |
Becker, T.L. Jr., Cannon, R.M. and Ritchie, R.O. (2001), "Finite crack kinking and T-stresses in functionally graded materials", Int. J. Solid. Struct., 38(32-33), 5545-5563.
DOI
|
4 |
Benamara, N., Boulenouar, A. and Aminallah, M. (2017), "Strain energy density prediction of mixed-mode crack propagation in functionally graded materials", Period. Polytech. Mech. Eng. (in press)
|
5 |
Benouis, A., Boulenouar, A., Benseddiq, N. and Serier, B. (2015), "Numerical analysis of crack propagation in cement PMMA, Application of SED approach", Struct. Eng. Mech., 55 (1), 93-109.
DOI
|
6 |
Bouchard, P.O., Bay, F. and Chastel, Y. (2003), "Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria", Comput. Meth. Appl. Mech. Eng., 192, 3887-3908.
DOI
|
7 |
Bouchard, P.O., Bay, F., Chastel, Y. and Tovena, I. (2000), "A modified J-integral for functionally graded materials crack propagation modelling using an advanced remeshing", Comput. Meth. Appl. Mech. Eng., 189, 723-742.
DOI
|
8 |
Boulenouar, A., Benouis, A. and Benseddiq, N. (2016), "Numerical modelling of crack propagation in cement PMMA: comparison of different criteria", Mater. Res., 19(4), 846-855.
DOI
|
9 |
Boulenouar, A., Benseddiq, N. and Mazari, M. (2013a), "Strain energy density prediction of crack propagation for 2D linear elastic materials", Theor. Appl. Frac. Mech., (67-68) 29-37.
|
10 |
Boulenouar, A., Benseddiq, N. and Mazari, M. (2013b), "Twodimensional numerical estimation of stress intensity factors and crack propagation in linear elastic analysis", Eng. Technol. Appl. 5, 506-510.
|
11 |
Boulenouar, A., Benseddiq, N., Mazari, M. and Benamara, N. (2014), "FE model for linear-elastic mixed mode loading: Estimation of sifs and crack propagation", J. Theor. Appl. Mech., 52 (2), 373-383.
|
12 |
Burlayenko, V.N., Altenbach, H., Sadowski, T. and Dimitrova, S.D. (2016), "Computational simulations of thermal shock cracking by the virtual crack closure technique in a functionally graded plate", Comput. Mater. Sci., 116, 11-21.
DOI
|
13 |
Chen, J., Wu, L. and Du, S. (2000), "A modified J-integral for functionally graded materials", Mech. Struct. Mach., 54, 301-306.
|
14 |
EL-Desouky, A.R. and EL-Wazery, M.S. (2013), "Mixed mode crack propagation of Zirconia/Nickel functionally graded materials", Int. J. Eng., 26(8), 885-894.
|
15 |
Cotterell, B. and Rice, J.R. (1980), "Slightly curved or kinked cracks", Int. J. Fract., 16(2), 155-169.
DOI
|
16 |
Dag, S. (2006), "Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach", Eng. Fract. Mech., 73, 2802-2828.
DOI
|
17 |
Dag, S., Arman, E.E. and Yildirim, B. (2010), "Computation of thermal fracture parameters for orthotropic functionally graded materials using Jk-integral", Int. J. Solid. Struct., 47, 3480-3488.
DOI
|
18 |
Erdogan, F. and Sih, G.C. (1963), "On the crack extension in plates under plane loading and transverse shear", J. Basic Eng., 85, 519-27.
DOI
|
19 |
Erdogan, F. and Wu, B.H. (1997), "The surface crack problem for a plate with functionally graded properties", ASME J. Appl. Mech., 449-456.
|
20 |
Gu, P. and Asaro, R.J. (1997), "Crack deflection in functionally graded materials", Int. J. Solid. Struct., 34(24), 3085-3098.
DOI
|
21 |
Hosseini, S.S., Bayesteh, H. and Mohammadi, S. (2013), "Thermo-mechanical XFEM crack propagation analysis of functionally graded materials", Mater. Sci. Eng.-A, 561, 285-302.
DOI
|
22 |
Hussain, M.A., Pu, S.L. and Underwood, J. (1993), "Strain energy release rate for a crack under combined mode I and mode II", Eds. Paris, P.C. and Irwin, G.R., Fracture Analysis, ASTM STP 560, Philadelphia.
|
23 |
Kidane, A., Chalivendra, V.B., Shukla, A. and Chona, R. (2010), "Mixed mode dynamic crack propagation in graded material under thermomechanical loading", Eng. Fract. Mech., 77, 2864-2880.
DOI
|
24 |
Kim, J.H. and Paulino, G.H. (2003a), "Mixed-mode J-integral formulation and implementation using graded finite elements for fracture analysis of non-homogeneous orthotropic materials", Mech. Mater., 35, 107-128.
DOI
|
25 |
Kim, J.H. (2003), "Mixed-mode crack propagation in functionally graded materials", Ph.D. Thesis, University of Illinois at Urbana-Champaign, Illinois.
|
26 |
Kim, J.H. and Paulino, G.H. (2002), "Finite element evaluation of mixed mode stress intensity factors in functionally graded materials", Int. J. Numer. Meth. Eng., 53, 1903-1935.
DOI
|
27 |
Kim, J.H. and Paulino, G.H. (2003 b), "The interaction integral for fracture of orthotropic functionally graded materials: evaluation of stress intensity factors", Int. J. Solid. Struct., 40, 3967-4001.
DOI
|
28 |
Kim, J.H. and Paulino, G.H. (2004), "Simulation of crack propagation in functionally graded materials under mixed-mode and non-proportional loading", Int. J. Mech. Mater. Des., 1(1), 63-94.
DOI
|
29 |
Kim, J.H. and Paulino, G.H. (2005), "Mixed-mode crack propagation in functionally graded materials", Mater. Sci., Trans Tech Publ., 492, 409-414.
|
30 |
Kim, J.H. and Paulino, G.H. (2007), "On fracture criteria for mixed-mode crack propagation in functionally graded materials", Mech. Adv. Mater. Struct., 14, 227-244.
DOI
|
31 |
Lee, Y.D. and Erdogan, F. (1994), "Residual/thermal stresses in FGM and laminated thermal barrier coatings", Int. J. Fract., 69(2), 145-165.
DOI
|
32 |
Ma, L., Wang, Z.Y. and Wu, L.Z. (2010), "Numerical simulation of mixed-mode crack propagation in functionally graded materials", Mater. Sci., 631-632, 121-126.
|
33 |
Palaniswamy, K. and Knauss, W.G. (1978), "On the problem of crack extension in brittle solids under general loading", Ed. Nemat-Nasser, S., Mechanics Today, Vol. 4, Pergramon Press.
|
34 |
Sabuncuoglu, B., Dag, S. and Yildirim, B. (2012), "Three dimensional computational analysis of fatigue crack propagation in functionally graded materials", Comput. Mater. Sci., 52, 246-252.
DOI
|
35 |
Raju, I.S. and Newman, J.C. (1979), "Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates", Eng. Fract. Mech., 11(4), 817-829.
DOI
|
36 |
Rashid, M.M. (1988), "The arbitrary local mesh replacement method: An alternative to remeshing for crack propagation analysis", Comput. Meth. Appl. Mech. Eng., 154, 133-150.
|
37 |
Rybicki, E.F. and Kanninen, M.F. (1977), "A finite element calculation of stress intensity factors by a modified crack closure integral", Eng. Fract. Mech., 9, 931-938.
DOI
|
38 |
Shih, C.F., DeLorenzi, H.G. and German, M.D. (1967), "Crack extension modeling with singular quadratic isoparametric elements", Int. J. Fract., 12, 647-651.
|
39 |
Sih, G.C. (1973), Mechanics of Fracture 1: a Special Theory of Crack Propagation, Noordhoff International Publishing, Leyden.
|
40 |
Sih, G.C. (1974), "Strain energy-density factor applied to mixed mode crack problem", Int. J. Fract., 10(3), 305-321.
DOI
|
41 |
Sih, G.C. (1975), Three dimensional crack problems, Mechanics of fracture, V. 2, Noordhoff, Netherlands.
|
42 |
Topal, S. and Dag, S. (2013), "Hygrothermal fracture analysis of orthotropic functionally graded materials using JK-Integralbased bethods", Math. Probl. Eng., Article ID 315176, 11.
|