Skip to main content
Log in

Stochastic Fracture Analysis of the Laminated Composite Plates Subjected to Different Types of Biaxially Applied Stresses by Implementing SXFEM

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

The stochastic investigation of fracture response of centrally cracked symmetric angle ply laminated composite plates subjected to different types of biaxially applied stresses by implementing stochastic extended finite element method (SXFEM) is carried out. The second-order perturbation technique is used in the framework of well-established extended finite element method to obtain the mean and coefficient of variance of mixed-mode stress intensity factors by random change in input parameters. The various system properties such as material elastic properties, lamination angle, loading, crack parameters like crack length and crack angle are modelled as independent, and they combine uncorrelated and correlated input random Gaussian variables. Typical numerical results are presented to examine the effect of various levels of uncertainties in biaxial load factors, fibre angle, crack eccentricity in X and/or Y direction, crack angles and crack lengths. The results obtained using SXFEM approach are compared with the results available in the published literature, and by performing Monte Carlo simulations, an excellent agreement is seen.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Akramin MRM, Alshoaibi A, Hadi MSA, Ariffin AK, Mohamed NAN (2007) Probabilistic analysis of linear elastic cracked structures. App Phys Eng 8(11):1795–1799

    MATH  Google Scholar 

  • Alkhateb H, Ostaz AA, Alzebdeh KI (2009) Developing a stochastic model to predict the strength and crack path of random composites. Compos Part B 40:7–16

    Article  Google Scholar 

  • Asadpoure A, Mohammadi S (2007) Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method. Int J Numer Methods Eng 69:2150–2172

    Article  MATH  Google Scholar 

  • Asadpoure A, Mohammadi S, Vafai A (2006a) Crack analysis in orthotropic media using the extended finite element method. Thin Walled Struct 44:1031–1038

    Article  Google Scholar 

  • Asadpoure A, Mohammadi S, Vafai A (2006b) Modelling crack in orthotropic media using a coupled finite element and partition of unity methods. Finite Elem Anal Des 42:1165–1175

    Article  Google Scholar 

  • Bellec J, Dolbow JE (2003) A note on enrichment functions for modelling crack nucleation. Commun Numer Methods Eng 19:921–932

    Article  MATH  Google Scholar 

  • Belytschko T, Chen H, Xu J, Zi G (2003) Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int J Numer Methods Eng 58:1873–1905

    Article  MATH  Google Scholar 

  • Belytschko T, Gracie R (2007) X-FEM applications to dislocations and interfaces. Int J Plast 23:1721–1738

    Article  MATH  Google Scholar 

  • Belytschko T, Gracie R, Ventura G (2005) A review of extended/generalized finite element methods for material modelling. Int J Fract 131:124–129

    Google Scholar 

  • Carloni C, Piva A, Viola E (2003) An alternative complex variable formulation for an inclined crack in an orthotropic medium. Eng Fract Mech 70:2033–2058

    Article  Google Scholar 

  • Chatzi EN, Hiriyur B, Waisman H, Smyth AW (2011) Experimental application and enhancement of the X-FEM–GA algorithm for the detection of flaws in structures. Comput Struct 89:556–570

    Article  Google Scholar 

  • Chen G, Rahman S, Park YH (2001a) Shape sensitivity analysis in mixed-mode fracture mechanics. Comput Mech 27(4):282–291

    Article  MATH  Google Scholar 

  • Chen G, Rahman S, Park YH (2001b) Shape sensitivity and reliability analyses of linear-elastic cracked structures. Int J Fract 112(3):223–246

    Article  Google Scholar 

  • Chopra PS, Wang PY, Hartz BJ (1974) Probabilistic prediction of multiple fracture under service conditions. Nucl Eng Des 28:446–458

    Article  Google Scholar 

  • Chowdhury SM, Song C, Gao W (2011) Probabilistic fracture mechanics by using Monte Carlo simulation and the scaled boundary finite element method. Eng Fract Mech 78:2369–2389

    Article  Google Scholar 

  • Duarte CA, Oden JT (1996) An H-p adaptive method using clouds. Comput Methods Appl Mech 139:237–262

    Article  MathSciNet  MATH  Google Scholar 

  • Ebrahimi SH, Mohammadi S, Asadpoure A (2008) An extended finite element (X-FEM) approach for crack analysis in composite media. Int J Civ Eng 6:198–207

    Google Scholar 

  • Gayathri P, Umesh K, Ganguli R (2010) Effect of matrix cracking and material uncertainty on composite plates. Reliab Eng Sys Safe 95:716–728

    Article  Google Scholar 

  • Ghorashi SS, Mohammadi S, Yazdi SRS (2011) Orthotropic enriched element free Galerkin method for fracture analysis of composites. Eng Fract Mech 78:1906–1927

    Article  Google Scholar 

  • Giner E, Sukumar N, Tarancon JE, Fuenmayor FJ (2009) An Abaqus implementation of the extended finite element method. Eng Fract Mech 76:347–368

    Article  Google Scholar 

  • Goldstein RV, Shifrin EI (2012) Conditions for Mode I crack deviation in orthotropic plane subjected to biaxial loading. Int J Eng Sci 61:36–47

    Article  MathSciNet  MATH  Google Scholar 

  • Hadlar A, Mahadavan S (2000) Probability reliability and statistical methods in engineering design. Wiley, New York

    Google Scholar 

  • Jones DL, Poulose PK, Liebowitz H (1986) The effects of biaxial loading on the fracture characteristics of several engineering materials. Eng Fract Mech 24(2):187–205

    Article  Google Scholar 

  • Kfouri P, Miller KJ (1977) The effect of load biaxiality on the fracture toughness parameters J and GA. Fracture 1977 Proceedings of the tCF4 Waterloo, Canada, University of Waterloo Press, vol 3. pp 241-245.

  • Lal A, Palekar SP (2016) Probabilistic fracture investigation of symmetric angle ply laminated composite plates using displacement correlation method. Curv Layer Struct 3(1):47–62

    Google Scholar 

  • Lal A, Palekar SP (2017) Stochastic fracture analysis of laminated composite plate with arbitrary cracks using X-FEM. Int J Mech Mater Des 13:195–228

    Article  Google Scholar 

  • Lee JD, Liebowitz H (1977) The nonlinear and biaxial effects on energy release rate, J-integral, and stress intensity factor. Eng Fract Mech 9:765–779

    Article  Google Scholar 

  • Lekhnitskii SG (1963) Theory of an anisotropic elastic body. Holden-Day, San Francisco

    MATH  Google Scholar 

  • Liebowitz H, Lee JD, Efus J (1978) Biaxial load effects in fracture mechanics. Eng Fract Mech 10:315–335

    Article  Google Scholar 

  • Lim WK, Choi SY, Sankar BV (2001) Biaxial load effects on crack extension in anisotropic solids. Eng Fract Mech 68:403–416

    Article  Google Scholar 

  • Lin YK, Yang JN (1993) On statistical moments of fatigue crack propagation. Eng Fract Mech 18(2):243–256

    Article  Google Scholar 

  • Meek C, Ainsworth RA (2015) The effects of load biaxiality and plate length on the limit load of a centre-cracked plate. Eng Fract Mech 147:306–317

    Article  Google Scholar 

  • Melenk JM, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139:289–314

    Article  MathSciNet  MATH  Google Scholar 

  • Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150

    Article  MathSciNet  MATH  Google Scholar 

  • Mohammadi S (2008) Extended finite element method for fracture analysis of structures. Blackwell, Oxford

    Book  MATH  Google Scholar 

  • Mohammadi S (2012) XFEM fracture analysis of composites. Wiley, London

    Book  Google Scholar 

  • Mostafavi M, Smith DJ, Pavier MJ (2011) Fracture of aluminium alloy 2024 under biaxial and triaxial loading. Eng Fract Mech 78:1705–1716

    Article  Google Scholar 

  • Motamedi D, Mohammadi S (2010) Dynamic crack propagation analysis of orthotropic media by the extended finite element method. Int J Fract 161:21–39

    Article  MATH  Google Scholar 

  • Nobile L, Carloni C (2005) Fracture analysis for orthotropic cracked plates. Compos Struct 68:285–293

    Article  Google Scholar 

  • Oladimeji MK (1981) Cracks emanating from a circular hole under biaxial load. Eng Fract Mech 15:391–405

    Article  Google Scholar 

  • Rahman S (1995) A stochastic model for elastic-plastic fracture analysis of circumferential through wall-cracked pipes subject to bending. Eng Fract Mech 52(2):265–288

    Article  Google Scholar 

  • Rahman S (2001) Probabilistic fracture mechanics: J-estimation and finite element methods. Eng Fract Mech 68:107–125

    Article  Google Scholar 

  • Rahman S, Chakraborty A (2011) Stochastic multi scale fracture analysis of three-dimensional functionally graded composites. Eng Fract Mech 78:27–46

    Article  Google Scholar 

  • Rahman S, Chen G (2005) Continuum shape sensitivity and reliability analyses of nonlinear cracked structures. Int J Fract 131(2):189–209

    Article  MATH  Google Scholar 

  • Sadd MH (2005) Elasticity: theory, applications, and numeric. Elsevier, London

    Google Scholar 

  • Sih GC, Paris PC, Irwin GR (1965) On cracks in rectilinearly anisotropic bodies. Int J Fract Mech 1:189–203

    Article  Google Scholar 

  • Sobey AJ, Blake JIR, Shenoi RA (2013) Monte Carlo reliability analysis of tophat stiffened composite plate structures under out of plane loading. Reliab Eng Syst Safe 110:41–49

    Article  Google Scholar 

  • Sukumar N, Prevost JH (2003) Modeling quasi-static crack growth with the extended finite element method, part–I, computer implementation. Int J Solids Struct 40:7513–7537

    Article  MATH  Google Scholar 

  • Sukumar N, Dolbow J, Devan A, Yvonnet J, Chinesta F, Ryckelynck D, Lorong P, Alfaro I, Martínez MA, Cueto E, Doblaré M (2005) Meshless methods and partition of unity finite elements. Int J Form Proces 8:409–427

    Article  Google Scholar 

  • Tabarraei A, Sukumar N (2007) Extended finite element method on polygonal and quadtree meshes. Comput Methods Appl Mech Eng 197:425–438

    Article  MathSciNet  MATH  Google Scholar 

  • Theocaris IS, Papadopoulos GA (1985) Crack-propagation trajectories under biaxial loading based on fracture criteria. J Franklin Inst 319:443–456

  • Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T (2014) Uncertainty quantification for multiscale modeling of polymer nano composites with correlated parameters. Compos part B 68:446–464

    Article  Google Scholar 

  • Wang SS, Yau JF, Corten HT (1980) A mixed mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity. Int J Fract 16:247–259

    Article  MathSciNet  MATH  Google Scholar 

  • Wu XF, Dzenis YA (2005) Experimental determination of probabilistic edge-delamination strength of a graphite-fiber/epoxy composite. Compos Struct 70:100–108

    Article  Google Scholar 

  • Yan X (2004) A numerical analysis of cracks emanating from a square hole in a rectangular plate under biaxial loads. Eng Fract Mech 71:1615–1623

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shailesh P. Palekar.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Palekar, S.P., Lal, A. Stochastic Fracture Analysis of the Laminated Composite Plates Subjected to Different Types of Biaxially Applied Stresses by Implementing SXFEM. Iran J Sci Technol Trans Mech Eng 46, 509–530 (2022). https://doi.org/10.1007/s40997-021-00434-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40997-021-00434-4

Keywords

Navigation