Induced out-of-plane mode at the tip of blunt lateral notches and holes under in-plane shear loading

As it is well known the Poisson's effect in a cracked plate subjected to anti-symmetric plane loading leads to the generation of a coupled out-of-plane singular mode. Recent theoretical and numerical analyses have shown that this effect is present also in plates weakened by sharp V-notches and might play a role in failure initiation phenomena of notched plates subjected to Mode II loading, especially in the presence of a large notch opening angle. Dealing with blunt notches with a large notch radius, and not just with sharp notches, the presence or not of an out-of-plane mode does not appear to have been systematically investigated in the past. The main aim of this work is to confirm the existence of the stress field associated with the out-of-plane mode (Mode O) and to describe its main features in the presence of a notch radius significantly different from zero. The analyses include U-notches, as well as circular and elliptic holes. The strain energy density in a 3D control volume is utilized to identify the most critical zone (with respect to failure initiation) through the plate thickness at the notch tip.

[1]  Analysis of the stress field in front of a notch , 1998 .

[2]  Andrei Kotousov,et al.  Stress singularities resulting from various boundary conditions in angular corners of plates of arbitrary thickness in extension , 2006 .

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

[4]  D. Radaj.  T‐stress corrected notch stress intensity factors with application to welded lap joints , 2010 .

[5]  X. Yao,et al.  Recent application of caustics on experimental dynamic fracture studies , 2011 .

[6]  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 .

[7]  Paolo Lazzarin,et al.  Cracks and notches: analogies and differences of the relevant stress distributions and practical consequences in fatigue limit predictions , 2001 .

[8]  J. Gálvez,et al.  An embedded cohesive crack model for finite element analysis of mixed mode fracture of concrete , 2006 .

[9]  Andrei Kotousov,et al.  Out‐of‐plane singular stress fields in V‐notched plates and welded lap joints induced by in‐plane shear load conditions , 2011 .

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

[11]  Filippo Berto,et al.  Control volumes and strain energy density under small and large scale yielding due to tension and torsion loading , 2008 .

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

[13]  Filippo Berto,et al.  Fatigue‐relevant stress field parameters of welded lap joints: pointed slit tip compared with keyhole notch , 2009 .

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

[15]  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 .

[16]  D. A. Hills,et al.  Asymptotic characterisation of nearly-sharp notch root stress fields , 2004 .

[17]  V. Doquet,et al.  3D shear-mode fatigue crack growth in maraging steel and Ti-6Al-4V , 2010 .

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

[19]  D. Radaj,et al.  Theoretical fatigue-effective notch stresses at spot welds , 2001 .

[20]  Andrea Carpinteri,et al.  Notched shells with surface cracks under complex loading , 2006 .

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

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

[23]  Wanlin Guo,et al.  Three-dimensional elastic stress fields near notches in finite thickness plates , 2000 .

[24]  Wanlin Guo,et al.  The influence of Poisson’s ratio on thickness-dependent stress concentration at elliptic holes in elastic plates , 2008 .

[25]  Paul C. Paris,et al.  Elastic field equations for blunt cracks with reference to stress corrosion cracking , 1967 .

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

[27]  M. Ayatollahi,et al.  Analysis of a new specimen for mixed mode fracture tests on brittle materials , 2009 .

[28]  Eann A. Patterson,et al.  Optical analysis of crack tip stress fields: a comparative study , 2004 .

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

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

[31]  L. P. Pook.  Finite element analysis of corner point displacements and stress intensity factors for narrow notches in square sheets and plates , 2000 .

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

[33]  Wanlin Guo,et al.  Three-dimensional stress concentrations at elliptic holes in elastic isotropic plates subjected to tensile stress , 2007 .

[34]  Chongdu Cho,et al.  The concentration of stress and strain in finite thickness elastic plate containing a circular hole , 2008 .

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

[36]  Paolo Lazzarin,et al.  A generalized stress intensity factor to be applied to rounded V-shaped notches , 2006 .

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

[38]  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 .

[39]  Andrei Kotousov,et al.  Three-dimensional stress constraint in an elastic plate with a notch , 2002 .

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

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

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

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

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

[45]  M. Elices,et al.  GENERALIZED SIZE EFFECT EQUATION FOR QUASIBRITTLE MATERIALS , 1997 .

[46]  E. Patterson,et al.  A study of residual caustics generated from fatigue cracks , 1997 .

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

[48]  Andrea Carpinteri,et al.  Sickle‐shaped surface crack in a notched round bar under cyclic tension and bending , 2009 .

[49]  M. Pavier,et al.  The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading , 2001 .

[50]  Pook.  Crack profiles and corner point singularities , 2000 .

[51]  L. P. Pook.  A finite element analysis of cracked square plates and bars under antiplane loading , 2003 .