An analytical solution for double cantilever beam based on elastic–plastic bilinear cohesive law: Analysis for mode I fracture of fibrous composites

Abstract The most difficult problem in mode I fracture test for fibrous composites using double cantilever beam (DCB) specimen is to identify crack tip without ambiguity. Consequently to evaluate fracture toughness through compliance method is a tricky matter. This study was conducted to solve this problem by developing an analytical solution for DCB fibrous composite specimen tested for mode I fracture. Cohesive law was employed to model separation constitution of cracking. Based on this analytical solution, the length of fracture process zone (FPZ) can be evaluated. Compliance equations of DCB specimen which take FPZ length into consideration were provided. Therefore, R-curve can be directly obtained by differentiating the compliance with respect to crack length. The model was validated by DCB tests of parallel strand bamboo (PSB), a bamboo-based fibrous composite. Good agreement between the predicted and test load–displacement were achieved. It was found that the R-curve behavior of PSB is similar to that of many other fibrous composites, which undergoes a nonlinear increase stage during FPZ formation and then reaches a constant after FPZ fully developed. Finally, general solutions for common used linear-type cohesive laws are provided.

[1]  Filippo Berto,et al.  Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches , 2014 .

[2]  H. Shodja,et al.  An accurate semi-analytical method for an arbitrarily oriented edge or interior crack in an anisotropic homogeneous elastic solid , 2014 .

[3]  T.A.C.M. van der Put,et al.  A new fracture mechanics theory for orthotropic materials like wood , 2007 .

[4]  Huang Yuan,et al.  Suggestions to the cohesive traction–separation law from atomistic simulations , 2011 .

[5]  Nuno Dourado,et al.  Cohesive zone model and quasibrittle failure of wood: a new light on the adapted specimen geometries for fracture tests. , 2013 .

[6]  Stefanie Feih,et al.  Development of a user element in ABAQUS for modelling of cohesive laws in composite structures , 2006 .

[7]  H. Cui.  Simulation of ductile adhesive failure with experimentally determined cohesive law , 2016 .

[8]  R. Campilho,et al.  Interlaminar and intralaminar fracture characterization of composites under mode I loading , 2010 .

[9]  P. C. Paris,et al.  On cracks in rectilinearly anisotropic bodies , 1965 .

[10]  S. Goutianos,et al.  The application of J integral to measure cohesive laws under large-scale yielding , 2016 .

[11]  Anne Nagel,et al.  Fracture Mechanics An Introduction , 2016 .

[12]  J. Nairn,et al.  Measuring and Modeling Fiber Bridging: Application to Wood and Wood Composites Exposed to Moisture Cycling , 2016 .

[13]  O. Frazão,et al.  Measuring mode I cohesive law of wood bonded joints based on digital image correlation and fibre Bragg grating sensors , 2015 .

[14]  José Morais,et al.  A new data reduction scheme for mode I wood fracture characterization using the double cantilever beam test , 2008 .

[15]  T. Anderson,et al.  Fracture mechanics - Fundamentals and applications , 2017 .

[16]  Brian N. Cox,et al.  The determination of crack bridging forces , 1991, International Journal of Fracture.

[17]  F. Grytten,et al.  Determination of a cohesive law for delamination modelling - Accounting for variation in crack opening and stress state across the test specimen width , 2016 .

[18]  A. Morais.  A new fibre bridging based analysis of the Double Cantilever Beam (DCB) test , 2011 .

[19]  Nuno Dourado,et al.  Size effect in quasibrittle failure: Analytical model and numerical simulations using cohesive zone model , 2011 .

[20]  Bent F. Sørensen,et al.  Cohesive law and notch sensitivity of adhesive joints , 2002 .

[21]  Tove Jacobsen,et al.  Large scale bridging in compos-ites: R-curve and bridging laws , 1998 .

[22]  Bent F. Sørensen,et al.  Determination of cohesive laws by the J integral approach , 2003 .

[23]  José Morais,et al.  A numerical study on the SEN-TPB test applied to mode I wood fracture characterization , 2011 .

[24]  M. D. Thouless,et al.  Use of mode-I cohesive-zone models to describe the fracture of an adhesively-bonded polymer-matrix composite , 2005 .

[25]  E. Dill,et al.  Theory of Elasticity of an Anisotropic Elastic Body , 1964 .

[26]  F. Scarpa,et al.  On the asymptotic crack-tip stress fields in nonlocal orthotropic elasticity , 2014 .

[27]  Huang Dongsheng,et al.  Experimental study on stress–strain relationships and failure mechanisms of parallel strand bamboo made from phyllostachys , 2015 .

[28]  Hiroshi Yoshihara,et al.  Simple estimation of critical stress intensity factors of wood by tests with double cantilever beam and three-point end-notched flexure , 2007 .

[29]  Oded Rabinovitch,et al.  Debonding analysis of fiber-reinforced-polymer strengthened beams : Cohesive zone modeling versus a linear elastic fracture mechanics approach , 2008 .

[30]  G. I. Barenblatt.  THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE , 1962 .

[31]  L. P. Canal,et al.  A multi-scale based cohesive zone model for the analysis of thickness scaling effect in fiber bridging , 2017 .

[32]  Bent F. Sørensen,et al.  Mode I intra-laminar crack growth in composites — modelling of R-curves from measured bridging laws , 2001 .

[33]  S. Sanchez-Saez,et al.  Influence of the cohesive law shape on the composite adhesively-bonded patch repair behaviour , 2016 .

[34]  A. Waas,et al.  The influence of adhesive constitutive parameters in cohesive zone finite element models of adhesively bonded joints , 2009 .

[35]  M. D. Thouless,et al.  Mixed-mode fracture analyses of plastically-deforming adhesive joints , 2001 .

[36]  D. S. Dugdale.  Yielding of steel sheets containing slits , 1960 .

[37]  V. Chalivendra.  Mode-I crack-tip stress fields for inhomogeneous orthotropic medium , 2008 .

[38]  Joël Cugnoni,et al.  Delamination detection and characterisation of bridging tractions using long FBG optical sensors , 2007 .