On the application of the volume free strain energy density method to blunt V-notches under mixed mode condition

Abstract This work investigates the possibility to apply the strain energy density method, as regards blunt V-notches under mixed loading condition, through finite element models with a free mesh pattern. It is worth underlining that the conventional procedure for the application of this method to this kind of components requires two different numerical simulations. A first simulation is needed to define the point of maximum of the first principal stress field along the notch fillet whose position represents an input for a second simulation to build the control volume in the right position to apply the method. Several numerical analyses were carried out to compare the conventional procedure of the method with this new procedure that allows the application of the method as a post-processing tool. The main advantage of this new procedure applied to components without stress singularity is that, by accepting an error that depends on the mesh refinement, the efforts of designers and researchers and the calculation time are decreased. The error in evaluating the SED value has been found to have a zero average value with a standard deviation of 1% and a maximum absolute value of 4.5% having a ratio between the main geometrical parameters of the control volume and the average mesh size comprised in the following range 3 m i n R 0 ; γ / 2 / Size averaged ≤ 5 . Dealing with this kind of components, the calculation time decreases by at least 50% requiring one simulation instead of the two requested by the conventional procedure.

[1]  F. Berto,et al.  Evaluation of the Effect of the TIG-Dressing Technique on Welded Joints through the Strain Energy Density Method , 2020 .

[2]  F. Berto,et al.  Application of an average strain energy density criterion to obtain the mixed mode fracture load of granite rock tested with the cracked asymmetric four-point bend specimens , 2017, Theoretical and Applied Fracture Mechanics.

[3]  Filippo Berto,et al.  Fracture assessment of U-notches under three point bending by means of local energy density , 2011 .

[4]  F. Berto,et al.  Fatigue strength of blunt V-notched specimens produced by selective laser melting of Ti-6Al-4V , 2017, Theoretical and Applied Fracture Mechanics.

[5]  F. Berto,et al.  Strain energy density evaluation with free coarse mesh model , 2020 .

[6]  Filippo Berto,et al.  Some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints , 2008 .

[7]  P. Carraro,et al.  An efficient energy-based approach for the numerical assessment of mode I NSIFs in isotropic and orthotropic notched plates , 2020 .

[8]  Cetin Morris Sonsino,et al.  Recent developments in local concepts of fatigue assessment of welded joints , 2009 .

[9]  F. Berto,et al.  A generalized strain energy density criterion for mixed mode fracture analysis in brittle and quasi-brittle materials , 2015 .

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

[11]  Filippo Berto,et al.  Three-dimensional linear elastic distributions of stress and strain energy density ahead of V-shaped notches in plates of arbitrary thickness , 2004 .

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

[13]  F. J. Gómez,et al.  Fracture assessment of U-notches under mixed mode loading: two procedures based on the ‘equivalent local mode I’ concept , 2007 .

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

[15]  Cetin Morris Sonsino,et al.  Fatigue assessment of welded joints by local approaches Second edition , 2007 .

[16]  A. R. Torabi,et al.  Local strain energy density to predict mode II brittle fracture in Brazilian disk specimens weakened by V-notches with end holes , 2015 .

[17]  J-integral evaluation for U- and V-blunt notches under Mode I loading and materials obeying a power hardening law , 2007 .

[18]  M. Elices,et al.  Local strain energy to assess the static failure of U-notches in plates under mixed mode loading , 2007 .

[19]  Michael Vormwald,et al.  Advanced Methods of Fatigue Assessment , 2013 .

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

[21]  F. Berto,et al.  Fatigue assessment of high strength welded joints through the strain energy density method , 2020 .

[22]  Filippo Berto,et al.  Coupled fracture modes of discs and plates under anti‐plane loading and a disc under in‐plane shear loading , 2016 .

[23]  Filippo Berto,et al.  Multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading , 2013 .

[24]  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 .

[25]  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 .

[26]  D. Radaj.  State-of-the-art review on the local strain energy density concept and its relation to the J-integral and peak stress method , 2015 .

[27]  Paolo Lazzarin,et al.  The Equivalent Strain Energy Density approach re-formulated and applied to sharp V-shaped notches under localized and generalized plasticity , 2002 .

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

[29]  F. Berto,et al.  On the applicability of ASED criterion for predicting mixed mode I+II fracture toughness results of a rock material , 2017 .

[30]  F. Berto,et al.  Rapid strain energy density evaluation for V-notches under mode I loading conditions , 2020 .

[31]  Wolfgang Fricke,et al.  Experiences and recommendations for numerical analyses of notch stress intensity factor and averaged strain energy density , 2016 .

[32]  Paolo Lazzarin,et al.  Fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values , 2005 .

[33]  F. Berto,et al.  Geometry effects on fracture trajectory of PMMA samples under pure mode-I loading , 2016 .

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

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

[36]  Shun-Peng Zhu,et al.  Evaluation and comparison of critical plane criteria for multiaxial fatigue analysis of ductile and brittle materials , 2018, International Journal of Fatigue.

[37]  Filippo Berto,et al.  A generalised notch stress intensity factor for U-notched components loaded under mixed mode , 2008 .

[38]  Paolo Lazzarin,et al.  A notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry , 2003 .

[39]  F. Berto,et al.  Francis-99: Evaluation of the strain energy density value for welded joints typical of turbine runner blades , 2019, Journal of Physics: Conference Series.

[40]  Filippo Berto,et al.  Fatigue assessment of welded joints under slit-parallel loading based on strain energy density or notch rounding , 2009 .

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

[42]  G. Meneghetti,et al.  Averaged strain energy density estimated rapidly from nodal displacements by coarse FE analyses: Cracks under mixed mode loadings , 2020 .

[43]  W. Fricke.  IIW guideline for the assessment of weld root fatigue , 2013, Welding in the World.

[44]  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 .

[45]  F. Berto,et al.  From Neuber’s Elementary Volume to Kitagawa and Atzori’s Diagrams: An Interpretation Based on Local Energy , 2005 .

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

[47]  C. M. Sonsino,et al.  A notch stress intensity approach to assess the multiaxial fatigue strength of welded tube‐to‐flange joints subjected to combined loadings , 2004 .

[48]  Filippo Berto,et al.  Local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading , 2008 .

[49]  Wolfgang Fricke,et al.  Comparison of different structural stress approaches for fatigue assessment of welded ship structures , 2005 .

[50]  Filippo Berto,et al.  Evaluation of the Strain Energy Density Value without the Construction of the Control Volume in the Preprocessing Phase of the Finite Element Analysis , 2019 .