Crack tip plastic zone under Mode I, Mode II and mixed mode (I+II) conditions

The shape and size of the plastic zone around the crack tip are analyzed under pure mode I, pure mode II and mixed mode (I+II) loading for small scale yielding and for both plane stress and plane strain conditions. A new analytical formulation is presented to determine the radius of the plastic zone in a non-dimensional form. In particular, the effect of T-stress on the plastic zone around the crack tip is studied. The results of this investigation indicate that the stress field with a T-stress always yields a larger plastic zone than the field without a T-stress. It is found that under predominantly mode I loading, the effect of a negative T-stress on the size of the plastic zone is more dramatic than a positive T-stress. However, when mode II portion of loading is dominating the effect of both positive and negative T-stresses on the size of the plastic zone is almost equal. For validating the analytical results, several finite element analyses were performed. It is shown that the results obtained by the proposed analytical formulation are in very good agreements with those obtained from the finite element analyses.

[1]  J. Willis,et al.  Matched asymptotic expansions in nonlinear fracture mechanics—III. In-plane loading of an elastic perfectly-plastic symmetric specimen , 1977 .

[2]  N. P. Andrianopoulos,et al.  Experimental study of the T-criterion in ductile fractures , 1983 .

[3]  Majid R. Ayatollahi,et al.  Crack-tip constraint in mode II deformation , 2002 .

[4]  N. P. Andrianopoulos,et al.  The mises elastic-plastic boundary as the core region in fracture criteria , 1982 .

[5]  Theo Fett,et al.  Stress intensity factors and T-stress for internally cracked circular disks under various boundary conditions , 2001 .

[6]  R. Narasimhan,et al.  J-Dominance in Mixed Mode Ductile Fracture Specimens , 1997 .

[7]  S. M. Khan,et al.  Analysis of mixed mode crack initiation angles under various loading conditions , 2000 .

[8]  J. Rice,et al.  Limitations to the small scale yielding approximation for crack tip plasticity , 1974 .

[9]  M. Benguediab,et al.  Estimation of the plastic zone by finite element method under mixed mode (I and II) loading , 2007 .

[10]  Jiping Zhang,et al.  Effects of notch radius and anisotropy on the crack tip plastic zone , 1987 .

[11]  G. Sih.  SOME BASIC PROBLEMS IN FRACTURE MECHANICS AND NEW CONCEPTS , 1973 .

[12]  K. S. Kim,et al.  The minimum plastic zone radius criterion for crack initiation direction applied to surface cracks and through-cracks under mixed mode loading , 2004 .

[13]  A. J. Carlsson,et al.  Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials , 1973 .

[14]  L. Bian.  Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials , 2007 .

[15]  Yuh J. Chao,et al.  Quantification of constraint on elastic–plastic 3D crack front by the J–A2 three-term solution , 2001 .

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

[17]  X. Kong,et al.  Effect of triaxial stress on mixed-mode fracture , 1995 .

[18]  James D. Lee,et al.  The constant stress term , 1995 .

[19]  Majid R. Ayatollahi,et al.  On mixed mode loading of a single edge notched specimen , 1996 .

[20]  J. Hancock,et al.  The effect of non-singular stresses on crack-tip constraint , 1991 .

[21]  J. Hutchinson,et al.  The relation between crack growth resistance and fracture process parameters in elastic-plastic solids , 1992 .

[22]  Norman A. Fleck,et al.  The mode I crack growth resistance of metallic foams , 2001 .

[23]  M.R.M. Aliha,et al.  Mixed mode fracture in soda lime glass analyzed by using the generalized MTS criterion , 2009 .

[24]  Wolfgang Brocks,et al.  Quantification of constraint effects in elastic-plastic crack front fields , 1998 .

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

[26]  B. Parida,et al.  Determination of the size of crack-tip plastic zone in a thin sheet under uniaxial loading , 1985 .

[27]  A. Garlick,et al.  The form of crack tip plastic zones , 1984 .

[28]  L. Gorbatikh,et al.  Closed-Form Solutions for the Mode ii Crack tip Plastic Zone Shape , 2003 .

[29]  G. Harmain,et al.  Fatigue crack-tip plasticity revisited — The issue of shape addressed , 1997 .

[30]  M. Ayatollahi,et al.  Mixed mode brittle fracture in PMMA—An experimental study using SCB specimens , 2006 .

[31]  J. W. Hancock,et al.  J-Dominance of short cracks in tension and bending , 1991 .

[32]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

[33]  J. Hancock,et al.  Two-Parameter Characterization of Elastic-Plastic Crack-Tip Fields , 1991 .

[34]  Majid R. Ayatollahi,et al.  Determination of T-stress from finite element analysis for mode I and mixed mode I/II loading , 1998 .

[35]  Viggo Tvergaard,et al.  Effect of T-Stress on mode I crack growth resistance in a ductile solid , 1994 .

[36]  C. Shih,et al.  Family of crack-tip fields characterized by a triaxiality parameter—I. Structure of fields , 1991 .

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

[38]  T. Khraishi,et al.  Analytical Solutions for Crack Tip Plastic Zone Shape Using the Von Mises and Tresca Yield Criteria: Effects of Crack Mode and Stress Condition , 2004 .

[39]  V. G. Ukadgaonker,et al.  A new criterion for fracture initiation , 1995 .

[40]  Marwan K. Khraisheh,et al.  A new criterion for mixed mode fracture initiation based on the crack tip plastic core region , 2004 .