Browse > Article
http://dx.doi.org/10.12989/sem.2017.61.3.371

On the mixed-mode crack propagation in FGMs plates: comparison of different criteria  

Nabil, Benamara (Laboratory of Materials and Reactive Systems, Mechanical Engineering Department, Djillali Liabes University of Sidi Bel-Abbes)
Abdelkader, Boulenouar (Laboratory of Materials and Reactive Systems, Mechanical Engineering Department, Djillali Liabes University of Sidi Bel-Abbes)
Miloud, Aminallah (Laboratory of Materials and Reactive Systems, Mechanical Engineering Department, Djillali Liabes University of Sidi Bel-Abbes)
Noureddine, Benseddiq (Mechanics Laboratory of Lille)
Publication Information
Structural Engineering and Mechanics / v.61, no.3, 2017 , pp. 371-379 More about this Journal
Abstract
Modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics. In this paper, two crack growth criteria and the respective crack paths prediction in functionally graded materials (FGM) are compared. The maximum tangential stress criterion (${\sigma}_{\theta}-criterion$) and the minimum strain energy density criterion (S-criterion) are investigated using advanced finite element technique. Using Ansys Parametric Design Language (APDL), the variation continues in the material properties are incorporated into the model by specifying the material parameters at the centroid of each finite element. In this paper, the displacement extrapolation technique (DET) proposed for homogeneous materials is modified and investigated, to obtain the stress intensity factors (SIFs) at crack-tip in FGMs. Several examples are modeled to evaluate the accuracy and effectiveness of the combined procedure. The effect of the defects on the crack propagation in FGMs was highlighted.
Keywords
functionally graded materials; maximum tangential; strain energy density; crack propagation; displacement extrapolation technique; stress intensity factor;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
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.