Sage Journals: Discover world-class research

Abstract

An analytical study of delamination fracture in two-dimensional functionally graded multilayered non-linear elastic split cantilever beam configurations is carried out. The beam is made of an arbitrary number of adhesively bonded longitudinal vertical layers, which have different thicknesses and material properties. Besides, the material is two-dimensional functionally grade in the cross-section of each layer. A vertical delamination crack is located arbitrary along the beam width. The beam is loaded eccentrically in tension by a force applied at the free end of the right-hand crack arm. The delamination fracture is studied in terms of the strain energy release rate. A comparison with the J-integral approach is carried out for verification. The results, yielded by the two analyses, are identical. The solutions obtained are used to evaluate the influences of crack location, material gradients and non-linear behaviour of material on the delamination fracture in the split cantilever beam under consideration. The distribution of the J-integral value along the crack front is analyzed too. It is found that the strain energy release rate can be reduced by appropriate selection of the material gradients in the design stage of two-dimensional functionally graded multilayered beams.

Keywords

Multilayered beam two-dimensional functionally graded material delamintion crack material non-linearity

Get full access to this article

View all access options for this article.

References

Bohidar

S.K.

Sharma

and Mishra

P.R.

, Functionally graded materials: A critical review, International Journal of Research 1 (2014), 289–301.

Broek

, Elementary Engineering Fracture Mechanics, Springer, 1986.

Bykov

Yu.V.

Egorov

S.V.

Ermeev

A.G.

and Holoptsev

V.V.

, Fabrication of metal-ceramic functionally graded materials by microwave sintering, Inorganic Materials: Applied Research 3 (2012). doi:10.1134/S20751133120300057.

Chakrabarty

, Theory of Plasticity, Elsevier Butterworth-Heinemann, Oxford, 2006.

Gasik

M.M.

, Functionally graded materials: Bulk processing techniques, International Journal of Materials and Product Technology 39 (2010), 20–29.

Hirai

and Chen

, Recent and prospective development of functionally graded materials in Japan, Mater Sci. Forum 308-311 (1999), 509–514.

Hutchinson

and Suo

, Mixed mode cracking in layered materials, Adv Appl Mech 64 (1992), 804–810.

Liang

Jun

, The effect of the lattice parameter of functionally graded materials on the stress field near crack tip, Strength, Fracture and Complexity: An International Journal 4 (2006), 105–116.

Liu

Hai-Tao

Zhou

Zhen-Gong

and Wu

Jian-Guo

, Non-singular anti-plane fracture theory of two parallel cracks within non-local functionally graded piezoelectric materials, Strength, Fracture and Complexity: An International Journal 10 (2017), 23–38.

10.

C.F.

Lim

C W.

and Chen

W.Q.

, Semi-analytical analysis for multi-dimensional functionally graded plates: 3-D elasticity solutions, Int. J. Num. Meth. Engng 79 (2009), 25–44.

11.

Lubliner

, Plasticity Theory (Revised edition), University of California, Berkeley, CA, 2006.

12.

Nemat-Allal

M.M.

Ata

M.H.

Bayoumi

M.R.

and Khair-Eldeen

, Powder metallurgical fabrication and microstructural investigations of Aluminum/Steel functionally graded material, Materials Sciences and Applications 2 (2011), 1708–1718.

13.

Pan

Shi-Dong

Feng

Ji-Cai

Zhou

Zhen-Gong

and Zhi

Wu-Lin

, Four parallel non-symetric Mode – III cracks with different lengths in a functionally graded material plane, Strength, Fracture and Complexity: An International Journal 5 (2009), 143–166.

14.

Panigrahi

Brajesh

and Pohit

Goutam

, Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230 (2016), 1468–1497.

15.

Paulino

G.C.

, Fracture in functionally graded materials, Engng Fract Mech 69 (2002), 1519–1530.

16.

Petrov

V.V.

, Non-linear incremental structural mechanics, M.: Infra-Injeneria (2014).

17.

Rizov

V.I.

, Non-linear analysis of delamination fracture in functionally graded beams, Coupled Systems Mechanics 6 (2017), 97–111.

18.

Rizov

V.I.

, Analytical study of elastic-plastic longitudinal fracture in a functionally graded beam, Strength, Fracture and Complexity: an International Journal 10 (2017), 11–22.

19.

Rizov

V.I.

, Delamination fracture in a functionally graded multilayered beam with material nonlinearity, Archive of Applied Mechanics 87 (2017), 1037–1048.

20.

Rizov

V.I.

, Non-linear elastic delamination of multilayered functionally graded beam, Multidiscipline Modelling in Materials and Structures 13 (2017), 434–447.

21.

Rizov

V.I.

, Delamination analysis of a multilayered functionally graded beam exhibiting material non-linearity, International Journal of Structural Stability and Dynamics (2017). doi:10.1142/S0219455418500517.

22.

Suresh

and Mortensen

, Fundamentals of Functionally Graded Materials, IOM Communications Ltd, London, 1998.

23.

Tang

C.Y.

Tsui

C.P.

Wei

and Wang

Z.W.

, Damage analysis on a graded porous bicomposite structure using FEM, Strength, Fracture and Complexity: An International Journal 7 (2011), 241–252.

24.

Tilbrook

M.T.

Moon

R.J.

and Hoffman

, Crack propagation in graded composites, Composite Science and Technology 65 (2005), 201–220.

25.

Torki

M.E.

and Reddy

J.N.

, Buckling of functionally-graded beams with partially delaminated piezoelectric layers, International Journal of Structural Stability and Dynamics 16 (2016), 1450104.

26.

Upadhyay

A.K.

and Simha

K.R.Y.

, Equivalent homogeneous variable depth beams for cracked FGM beams; compliance approach, Int. J. Fract. 144 (2007), 209–213.

27.

Zhang

X.F.

Tang

G.J.

and Shen

Z.B.

, Stress intensity factors of double cantilever nanobeams via gradient elasticity theory, Engng. Fract. Mech. 105 (2013), 58–64.

Non-linear elastic analysis of delamination in two-dimensional functionally graded multilayered beams

Abstract

Keywords

Get full access to this article

References