A New Mixed-Mode Fracture Criterion for Orthotropic Materials,Based on Strength Properties

Abstract

In this paper, a new methodology for modelling the fracture process zone in cracked wooden structures has been proposed. Implementing this method for modelling the crack tip damage zone could help to establish a new criterion applicable for assessing the fracture of cracked wood specimens under combined mode I/II loading. This criterion involves a damage factor representing the material softening effect due to microcrack existence and growth in the fracture process zone. For calculation of this damage factor, it is not necessary to investigate the complex and non-linear analysis of material behaviour in the damage zone. The approach proposed makes it possible to express an analytical relation for the damage factor as a function of tensile strength along and across the wood fibres. The novelty of this work is that the given method enables not only the arbitrary orientation effects of the original crack with respect to wood fibres but also the T-stress effects in crack growth initiation to be considered. To demonstrate the effectiveness of this method, different case studies have been investigated, and the results obtained by applying the new criterion are compared with available experimental data.

Keywords

mixed-mode fracture wood orthotropic materials damage zone tensile strength

Get full access to this article

View all access options for this article.

References

Wood as an engineering material, in Wood hand-book, 1999 (Forest Products Laboratory, Forest Service, United States Department of Agriculture, US Government Printing Office, Washington, DC).

Smith

Landis

Gong

Fracture and fatigue in wood , 2003 (Wiley Chichester, UK).

Vasic

Application of fracture mechanics to wood , PhD Thesis, University of New Brunswick, Fredriction, New Brunswick, Canada, 2000.

Pluvinage

Azari

Kadi

Dlouhy

Kozak

Effect of ferritic microstructure on local damage zone distance associated with fracture near notch. Theor. Appl. Fracture Mech. 1999, 31, 149–156.

Smith

Vasic

Fracture behavior of softwood. Mech. Mater. 2003, 35, 803–815.

Vasic

Smith

Bridging crack model for fracture of wood. Engng Fracture Mech. 2002, 69, 745–760.

Landis

E. N.

Vasic

Davids

W. G.

Parrod

Coupled experiments and simulations of microstructural damage in wood. Expl Mech. 2002, 42 1–6.

Bostrom

Method for determination of the softening behavior of wood and applicability of a non-linear fracture mechanics model. Report TVBM-1012, Lund University, Sweden 1992.

Mall

Murphy

J. E.

Criterion for mixed mode fracture in wood. J. Engng Mech. 1983, 109(3), 680–690.

10.

E. M.

Application of fracture mechanics to anisotropic plates. J. Appl. Mech. 1976, 34(4), 967–974.

11.

Sih

G. C.

Strain-energy density factor applied to mixed mode crack problems. Int. J. Fracture 1974, 10, 305–321.

12.

Griffith

A. A.

The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. Lond. 1921, 221, 163–197.

13.

Jernkvist

L. O.

Fracture of wood under mode loading I. Derivation of fracture criteria. Engng Fracture Mech. 2001, 68, 549–563.

14.

Jernkvist

L. O.

Fracture of wood under mode loading, II: Experimental investigation of Picea abies. Engng Fracture Mech. 2001, 68, 565–576.

15.

Romanowicz

Seweryn

Verification of a non-local stress criterion for mixed mode fracture in wood. Engng Fracture Mech. 2008, 75(10), 3141–3160.

16.

Smith

D. J.

Ayatollahi

M. R.

Pavier

M. J.

The role of T-stress in brittle fracture for linear elastic materials under mixed mode loading. Fatigue Fracture Engng Mater. Struct. 2001, 24, 137–150.

17.

Ayatollahi

M. R.

Pavier

M. J.

Smith

D. J.

Determination of T-stress from finite element analysis for mode I and mixed mode loading. Int. J. Fracture 1998, 91, 283–298.

18.

Gowhari

A. R.

Fakoor

General mixed mode I/II fracture criterion for wood considering T-stress effects. Mater. Des. 2010, 31, 4461–4469.

19.

Nemat-Nasser

Horii

Overall moduli of solids with microcracks: Load induced anisotropy. J. Mech. Phys. Solids 1983, 31(2), 155–171.

20.

Nemat-Nasser

Hori

Micromechanics: overall properties of heterogeneous materials , 2nd edition, 1999 (Elsevier, Amsterdam/Lausanne/New York/Oxford).

21.

Gambarotta

Logomarsino

A microcrack damage model for brittle materials. Int. J. Solids Struct. 1993, 30, 177–198.

22.

Budiansky

O'Connell

R. J.

Elastic moduli of cracked solid. Int. J. Solids Struct. 1976, 12, 81–97.

23.

Sih

G. C.

Paris

P. C.

Irwin

G. R.

On cracks in rectilinearly anisotropic bodies. Int. J. Fracture Mech. 1965, 1(3), 189–203.

24.

Fowell

R. J.

The chevron cracked Brazilian disc test - geometrical considerations for practical rock fracture toughness measurement. Int. J. Rock Mech. Min. Sci. 1993, 30(7), 521–524.

25.

Fowell

R. J.

The use of cracked Brazilian disc for rock fracture investigations. Int. J. Rock Mech. Min. Sci. 1994, 31(6), 571–579.

26.

Capurso

Sacchi

Una condizione di plasticita per solidi anisotropi. Technical Report 512, I.S.T.C., Politecnico di Milano, 1970.

27.

Nova

Zaninetti

An investigation into the tensile behaviour of a schistose rock. Int. J. Rock Mech. Min. Sci. Geomech. 1990, 27(4), 231–242.

28.

Mindess

Benture

Crack propagation in notched wood specimens with different grain orientations. Wood Sci. Technol. 1986, 20, 145–155.

29.

Hunt

D. G.

Croager

W. P.

Mode II fracture toughness of wood measured by a mixed-mode test method. J. Mater. Sci. Lett. 1982, 1, 77–79.

30.

Hutchinson

J. W.

Kinking of a crack out of an interface. Trans ASME, J. Appl. Mech. 1989, 56, 270–278.