Local strain energy density to predict mode II brittle fracture in Brazilian disk specimens weakened by V-notches with end holes

Abstract The present paper reports some experimental, theoretical and numerical results on brittle fracture of notched components made of Polymethylmethacrylate (PMMA). First, fracture experiments were carried out at room temperature on V-notches with end holes (VO-notches) under mode II loading by means of a recently proposed disk-type specimen, called the Brazilian disk containing central VO-notches (VO-BD specimen) made of PMMA for different notch angles and various notch radii. Then, the well-established averaged strain energy density (SED) criterion over the specified control volume which embraces the notch border was formulated and employed to predict theoretically the experimental fracture loads. The center of the control volume is located on the notch edge, where the principal stress reaches its maximum value. The correct orientation is obtained by a rigid rotation of the crescent-shaped volume while the size depends on the fracture toughness and the ultimate strength of the material. This methodology has been already used in the literature to analyze U- and V-shaped notches subject to different loading modes with very good results and advantages with respect to classic approaches. In this contribution it was demonstrated that SED works well also on VO-notches under pure mode II loading.

[1]  A. R. Torabi,et al.  Failure assessment of notched polycrystalline graphite under tensile-shear loading , 2011 .

[2]  Andrea Carpinteri,et al.  Buckling and fracture behaviour of cracked thin plates under shear loading , 2011 .

[3]  Hans Albert Richard,et al.  Influence of the root radius of crack-like notches on the fracture load of brittle components , 2006 .

[4]  Filippo Berto,et al.  High-temperature fatigue strength of a copper–cobalt–beryllium alloy , 2014 .

[5]  Filippo Berto,et al.  Brittle failure of inclined key‐hole notches in isostatic graphite under in‐plane mixed mode loading , 2013 .

[6]  David Taylor,et al.  The theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading , 2008 .

[7]  E. M. Morozov,et al.  Calculation of the energy J-integral for bodies with notches and cracks , 2004 .

[8]  Y. Alizadeh,et al.  The effect of notch depth on J-integral and critical fracture load in plates made of functionally graded aluminum–silicone carbide composite with U-notches under bending , 2010 .

[9]  Paolo Livieri,et al.  A new path independent integral applied to notched components under mode I loadings , 2003 .

[10]  Morten Strandberg,et al.  Fracture at V-notches with contained plasticity , 2002 .

[11]  A. Kifani,et al.  Fracture toughness of high strength steel using the notch stress intensity factor and volumetric approach , 2003 .

[12]  Filippo Berto,et al.  Brittle fracture of sharp and blunt V-notches in isostatic graphite under torsion loading , 2012 .

[13]  Filippo Berto,et al.  Brittle fracture of U-notched graphite plates under mixed mode loading , 2012 .

[14]  Andrei Kotousov,et al.  Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates , 2010 .

[15]  A. R. Torabi,et al.  Stress-based criteria for brittle fracture in key-hole notches under mixed mode loading , 2015 .

[16]  Dai-heng Chen,et al.  Investigation of failure criteria for a sharp notch , 2008 .

[17]  F. Berto,et al.  Some Expressions for the Strain Energy in a Finite Volume Surrounding the Root of Blunt V-notches , 2005 .

[18]  Filippo Berto,et al.  Coupled fracture mode of a cracked disc under anti-plane loading , 2014 .

[19]  Zohar Yosibash,et al.  Failure initiation at a blunt V-notch tip under mixed mode loading , 2008 .

[20]  Filippo Berto,et al.  Fatigue strength of a fork-pin equivalent coupling in terms of the local strain energy density , 2008 .

[21]  Zdeněk Knésl,et al.  A criterion of V-notch stability , 1991 .

[22]  Filippo Berto,et al.  Fatigue strength of severely notched specimens made of Ti–6Al–4V under multiaxial loading , 2015 .

[23]  A. R. Torabi,et al.  Mode II Brittle Fracture Assessment of Key-Hole Notches by Means of the Local Energy , 2016 .

[24]  G. Sih.  Strain-energy-density factor applied to mixed mode crack problems , 1974 .

[25]  Filippo Berto,et al.  Local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches , 2009 .

[26]  Ali Reza Torabi.  Closed-form expressions of mode I apparent notch fracture toughness for key-hole notches , 2014 .

[27]  Andrea Carpinteri,et al.  Stress intensity factors and fatigue growth of surface cracks in notched shells and round bars: two decades of research work , 2013 .

[28]  Andrea Carpinteri,et al.  Surface cracks in fatigued structural components: a review , 2013 .

[29]  Filippo Berto,et al.  High temperature fatigue tests of un-notched and notched specimens made of 40CrMoV13.9 steel , 2014 .

[30]  Ali Reza Torabi,et al.  Fracture analysis of U-notched disc-type graphite specimens under mixed mode loading , 2014 .

[31]  David Taylor,et al.  A finite fracture mechanics approach to structures with sharp V-notches , 2008 .

[32]  A. R. Torabi,et al.  Investigation of mixed mode brittle fracture in rounded-tip V-notched components , 2010 .

[33]  Filippo Berto,et al.  Fatigue strength of structural components under multi-axial loading in terms of local energy density averaged on a control volume , 2011 .

[34]  A. R. Torabi,et al.  Brittle fracture in rounded-tip V-shaped notches , 2010 .

[35]  T. Marrow,et al.  An approach to calculate the J‐integral by digital image correlation displacement field measurement , 2012 .

[36]  G. Pluvinage,et al.  Influence of notch radius and microstructure on the fracture behavior of Al–Zn–Mg–Cu alloys of different purity , 2010 .

[37]  Jaime Planas,et al.  The cohesive crack concept: application to PMMA at −60 °C , 2005 .

[38]  Paolo Livieri,et al.  Use of J-integral to predict static failures in sharp V-notches and rounded U-notches , 2008 .

[39]  Manuel Elices,et al.  Cracking in PMMA containing U‐shaped notches , 2000 .

[40]  Pietro Cornetti,et al.  A Finite Fracture Mechanics approach to V-notched elements subjected to mixed-mode loading , 2013 .

[41]  G. Pluvinage,et al.  On characteristic lengths used in notch fracture mechanics , 2013, International Journal of Fracture.

[42]  Guy Pluvinage,et al.  Stress field near a large blunted tip V-notch and application of the concept of the critical notch stress intensity factor (NSIF) to the fracture toughness of very brittle materials , 1994 .

[43]  A. R. Torabi,et al.  Pure shear fracture study in a brittle graphite material containing a U-notch , 2014 .

[44]  Andrei Kotousov,et al.  Fracture in plates of finite thickness , 2007 .

[45]  Dominique Leguillon,et al.  Strength or toughness? A criterion for crack onset at a notch , 2002 .

[46]  Fatigue life of steel notched elements including the complex stress state , 2013 .

[47]  A. R. Torabi,et al.  Determination of mode II fracture toughness for U-shaped notches using Brazilian disc specimen , 2010 .

[48]  F. Berto,et al.  Strain energy density to assess mode II fracture in U-notched disk-type graphite plates , 2014 .

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

[50]  Andrei Kotousov,et al.  On higher order terms and out-of-plane singular mode , 2011 .

[51]  Filippo Berto,et al.  Brittle failures from U- and V-notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite-size volumes , 2009 .

[52]  A. Kotousov,et al.  Three dimensional finite element mixed fracture mode under anti-plane loading of a crack , 2012 .

[53]  F. Berto,et al.  Mixed mode fracture assessment of U-notched graphite Brazilian disk specimens by means of the local energy , 2014 .

[54]  Andrzej Seweryn,et al.  Brittle fracture criterion for structures with sharp notches , 1994 .

[55]  Andrei Kotousov,et al.  Induced out-of-plane mode at the tip of blunt lateral notches and holes under in-plane shear loading , 2012 .

[56]  Zohar Yosibash,et al.  Failure criteria for brittle elastic materials , 2004 .

[57]  L. Pook.  A 50‐year retrospective review of three‐dimensional effects at cracks and sharp notches , 2013 .

[58]  Andrei Kotousov.  On stress singularities at angular corners of plates of arbitrary thickness under tension , 2005 .

[59]  Filippo Berto,et al.  A synthesis of Polymethylmethacrylate data from U-notched specimens and V-notches with end holes by means of local energy , 2013 .

[60]  Filippo Berto,et al.  A comparison among some recent energy- and stress-based criteria for the fracture assessment of sharp V-notched components under Mode I loading , 2014 .

[61]  A. R. Torabi,et al.  Experimental verification of RV-MTS model for fracture in soda-lime glass weakened by a V-notch , 2011 .

[62]  Filippo Berto,et al.  A review of the volume-based strain energy density approach applied to V-notches and welded structures , 2009 .

[63]  E. Barati,et al.  A new practical equation for evaluation of strain-energy density distribution and J-integral in plates with blunt V-notches under bending loading , 2013 .

[64]  Filippo Berto,et al.  Brittle fracture of sharp and blunt V-notches in isostatic graphite under pure compression loading , 2013 .

[65]  Filippo Berto,et al.  Multiaxial fatigue of V-notched steel specimens: a non-conventional application of the local energy method , 2011 .

[66]  A. R. Torabi,et al.  Compressive brittle fracture in V-notches with end holes , 2014 .

[67]  Filippo Berto,et al.  The effects of different boundary conditions on three-dimensional cracked discs under anti-plane loading , 2015 .

[68]  Paolo Lazzarin,et al.  A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notches , 2001 .

[69]  G. Pluvinage,et al.  Notch fracture toughness of high-strength Al alloys , 2013 .

[70]  George A. Gogotsi,et al.  Fracture toughness of ceramics and ceramic composites , 2003 .

[71]  A. R. Torabi,et al.  Brittle fracture in V-notches with end holes , 2015 .

[72]  Filippo Berto,et al.  Rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: Theoretical bases and applications , 2010 .

[73]  Andrea Carpinteri,et al.  A notch multiaxial-fatigue approach based on damage mechanics , 2012 .