Predictions of fracture resistance of spruce wood under mixed mode loading using non-local fracture theory and numerical modelling
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Bialystok University of Technology, Department of Mechanical Engineering, Bialystok, Poland
Submission date: 2022-10-30
Final revision date: 2022-11-29
Acceptance date: 2022-11-29
Online publication date: 2023-01-08
Publication date: 2023-01-30
Corresponding author
Marek Romanowicz   

Department of Mechanical Engineering, Bialystok University of Technology, Wiejska 45c, 15-351, Bialystok, Poland
Journal of Theoretical and Applied Mechanics 2023;61(1):147-162
A novel analytical model to predict fracture resistance of a quasi-brittle material, like wood, is presented. The model is based on a scaling parameter introduced into the non-local fracture theory to take into account the specimen size effect on the development of the damage zone. An expression for length of the critical process zone, which can be used in damage tolerant design of wooden structures is derived from this theory. The model is validated with mixedmode bending tests. A numerical analysis using cohesive elements is performed to understand the role of specimen size in the development of the damage zone. The analytical predictions of the fracture resistance and the critical process zone length for wood are compared with numerical results and experimental data available in the literature.
Alfano G., Crisfield M.A., 2001, Finite element interface models for the delamination anaylsis of laminated composites:Mechanical and computational issues, International Journal for Numerical Methods in Engineering, 50, 1701-1736.
Barenblatt G.I., 1962, The mathematical theory of equilibrium cracks in brittle fracture, Advances in Applied Mechanics, 7, 55-129.
Bazant Z.P., Kazemi M.T., 1990, Size effect in fracture of ceramics and its use to determine fracture energy and effective process zone length, Journal of the American Ceramic Society, 73, 1841-1853.
Bennati S., Fisicaro P., Valvo P.S., 2013a, An enhanced beam-theory model of the mixed-mode bending (MMB) test. Part I: Literature review and mechanical model, Meccanica, 48, 443-462.
Bennati S., Fisicaro P., Valvo P.S., 2013b, An enhanced beam-theory model of the mixed-mode bending (MMB) test. Part II: Applications and results, Meccanica, 48, 465-484.
Benzeggagh M.L., Kenane M., 1996,Measurement of mixed mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus, Composites Science and Technology, 56, 439-449.
Camanho P.P., Dávila C.G., 2002, Mixed-mode decohesion finite elements for the simulation of delamination in composite materials, Technical Report NASA/TM-2002-211737, National Aeronautics and Space Administration, USA.
de Moura M.F.S.F., Oliveira J.M.Q., Morais J.J.L., Xavier J., 2010, Mixed-mode I/II wood fracture characterization using the mixed-mode bending test, Engineering Fracture Mechanics, 77, 144-152.
Dourado N., Morel S., de Moura M.F.S.F., Valentin G., Morais J., 2008, Comparison of fracture properties of two wood species through cohesive crack simulations, Composites Part A, 39, 415-427.
Dugdale D.S., 1960, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, 8, 100-104.
Morel S., Dourado N., Valentin G., 2005, Wood: a quasibrittle material. R-curve behavior and peak load evaluation, International Journal of Fracture, 131, 385-400.
Mróz Z., Seweryn A., 1998, Non-local failure and damage evolution rule: Application to a dilatant crack model, Journal of Physics IV, 8, 257-268.
Novozhilov V.V., 1969, On the necessary and sufficient criteria for brittle strength, Prikladnaja Matematika i Mekhanika, 33, 212-222.
Oliveira J.M.Q., de Moura M.F.S.F., Silva M.A.L., Morais J.J.L., 2007, Numerical analysis of the MMB test for mixed-mode I/II wood fracture, Composites Science and Technology, 67, 1764-1771.
Pedersen M.U., Clorius C.O., Damkilde L., Hoffmeyer P., 2003, A simple size effect model for tension perpendicular to the grain, Wood Science and Technology, 37, 125-140.
Phan N.A., Morel S., Chaplain M., 2016, Mixed-mode fracture in a quasi-brittle material: R-curve and fracture criterion: Application to wood, Engineering Fracture Mechanics, 156, 96-113.
Reeder J.R., Crews J.H., 1990, Mixed-mode bending method for delamination testing, AIAA Journal, 28, 1270-1276.
Romanowicz M., 2019, A non-local stress fracture criterion accounting for the anisotropy of the fracture toughness, Engineering Fracture Mechanics, 214, 544-557.
Seweryn A., Mróz Z., 1998, On the criterion of damage evolution for variable multiaxial stress states, International Journal of Solids and Structures, 35, 1589-1616.
Sih G.C., Paris P.C., Irwin G.R., 1965, On cracks in rectilinearly anisotropic bodies, International Journal of Fracture Mechanics, 1, 189-203.
Wang Y., Williams J.G., 1992, Corrections for mode II fracture toughness specimens of composites materials, Composites Science and Technology, 43, 251-256.
Williams J.G., 1989, End corrections for orthotropic DCB specimens, Composites Science and Technology, 35, 367-376.
Xie D., Biggers S.B., 2006, Progressive crack growth analysis using interface element based on the virtual crack closure technique, Finite Elements in Analysis and Design, 42, 977-984.
Xie J., Waas A.M., Rassaian M., 2016a, Closed-form solutions for cohesive zone modeling of delamination toughness tests, International Journal of Solids and Structures, 88-89, 379-400.
Xie J., Waas A.M., Rassaian M., 2016b, Estimating the process zone length of fracture tests used in characterizing composites, International Journal of Solids and Structures, 100, 111-126.
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