On higher order terms and out-of-plane singular mode

Abstract It is well known that in a plate weakened by a through-the-thickness crack and subjected to remote anti-symmetric loading (mode II), the Poisson’s effect leads to the generation of a coupled out-of-plane singular mode (mode O). Recent theoretical and numerical analyses have demonstrated that this effect also occurs in plates weakened by pointed V-notches, and it can play an important role in failure initiation especially in the case of large notch opening angles. Dealing with cracked plates the influence of higher order terms tied to mode II loading on the out-of-plane singular mode has not been investigated until now. The aim of this paper is to fill this gap with an accurate analysis of mode II higher order terms and their effects on mode O.

[1]  Yuichi Kawagishi,et al.  Experimental evaluation of stress field around crack tip by caustic method , 2001 .

[2]  G. Sih,et al.  An approximate three-dimensional theory of plates with application to crack problems☆ , 1970 .

[3]  F. J. Gómez,et al.  Fracture of U-notched specimens under mixed mode: Experimental results and numerical predictions , 2009 .

[4]  Satyandra K. Gupta,et al.  Evaluation of stress field parameters in fracture mechanics by photoelasticity—Revisited , 1997 .

[5]  Z. Bažant,et al.  Surface singularity and crack propagation , 1979 .

[6]  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 .

[7]  A. Kotousov,et al.  A crack closure model of fatigue crack growth in plates of finite thickness under small-scale yielding conditions , 2009 .

[8]  Andrei Kotousov,et al.  On the Presence of the Out–of–Plane Singular Mode Induced by Plane Loading With KII = KI = 0 , 2011 .

[9]  Andrei Kotousov,et al.  Effect of the thickness on elastic deformation and quasi-brittle fracture of plate components , 2010 .

[10]  A. Korsunsky,et al.  Evaluation and analysis of residual stresses due to foreign object damage , 2007 .

[11]  Mode I intersonic crack propagation in poroelastic media , 2008 .

[12]  On the Singularity Induced by Boundary Conditions in a Third-Order Thick Plate Theory , 2002 .

[13]  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 .

[14]  Zhongmin Jin,et al.  A crack at the interface between a Kane-Mindlin plate and a rigid substrate , 1997 .

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

[16]  David M. Parks,et al.  Antisymmetrical 3-D stress field near the crack front of a thin elastic plate , 1989 .

[17]  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 .

[18]  M. Williams,et al.  On the Stress Distribution at the Base of a Stationary Crack , 1956 .

[19]  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 .

[20]  L. P. Pook,et al.  Some implications of corner point singularities , 1994 .

[21]  J. Benthem.  State of stress at the vertex of a quarter-infinite crack in a half-space , 1977 .

[22]  Chi-Hung Huang,et al.  Corner stress singularities in a high-order plate theory , 2004 .

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

[24]  F. Berto,et al.  On Higher Order Terms in the Crack Tip Stress Field , 2010 .

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

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

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

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

[29]  Andrea Spagnoli,et al.  Self-similarity and fractals in the Paris range of fatigue crack growth , 2005 .

[30]  Bhushan Lal Karihaloo,et al.  Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element , 2004 .

[31]  Andrei Kotousov,et al.  Transverse singular effects in V-shaped notches stressed in mode II , 2010 .

[32]  Wanlin Guo,et al.  Equivalent thickness conception for corner cracks , 2010 .

[33]  Luboš Náhlík,et al.  The effect of a free surface on fatigue crack behaviour , 2010 .

[34]  Bhushan Lal Karihaloo,et al.  An overview of a hybrid crack element and determination of its complete displacement field , 2007 .

[35]  Wanlin Guo,et al.  The out-of-plane constraint of mixed-mode cracks in thin elastic plates , 2007 .