Mixed mode (I and II) crack tip fields in bulk metallic glasses

Stationary crack tip fields in bulk metallic glasses under mixed mode (I and II) loading are studied through detailed finite element simulations assuming plane strain, small scale yielding conditions. The influence of internal friction or pressure sensitivity on the plastic zones. notch deformation, stress and plastic strain fields is examined for different mode mixities. Under mixed mode loading, the notch deforms into a shape such that one part of its surface sharpens while the other part blunts. Increase in mode If component of loading dramatically enhances the normalized plastic zone size, lowers the stresses but significantly elevates the plastic strain levels near the notch tip. Higher internal friction reduces the peak tangential stress but increases the plastic strain and stretching near the blunted part of the notch. The simulated shear bands are straight and extend over a long distance ahead of the notch tip under mode II dominant loading. The possible variations of fracture toughness with mode mixity corresponding to failure by brittle micro-cracking and ductile shear banding are predicted employing two simple fracture criteria. The salient results from finite element simulations are validated by comparison with those from mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass.

[1]  P. Donovan A yield criterion for Pd40Ni40P20 metallic glass , 1989 .

[2]  G. Ravichandran,et al.  Effect of Poisson’s ratio on crack tip fields and fracture behavior of metallic glasses , 2008 .

[3]  R. Narasimhan,et al.  A three-dimensional numerical study of mode I crack tip fields in pressure sensitive plastic solids , 2007 .

[4]  Reinhold H. Dauskardt,et al.  Mean stress effects on flow localization and failure in a bulk metallic glass , 2001 .

[5]  C. Schuh,et al.  Yield surface of a simulated metallic glass , 2003 .

[6]  R. Narasimhan,et al.  A finite element analysis of mixed-mode fracture initiation by ductile failure mechanisms , 1994 .

[7]  Saumyadeep Jana,et al.  Hardness and plastic deformation in a bulk metallic glass , 2005 .

[8]  Frank A. McClintock,et al.  PLASTICITY ASPECTS OF FRACTURE , 1971 .

[9]  C. Su,et al.  Plane strain indentation of a Zr-based metallic glass: Experiments and numerical simulation , 2006 .

[10]  C. Su,et al.  A theory for amorphous viscoplastic materials undergoing finite deformations, with application to metallic glasses , 2005 .

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

[12]  W. Johnson,et al.  Mechanical properties of Zr56.2Ti13.8Nb5.0Cu6.9Ni5.6Be12.5 ductile phase reinforced bulk metallic glass composite , 2001 .

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

[14]  Francisco Armero,et al.  Elastoplastic and Viscoplastic Deformations in Solids and Structures , 2004 .

[15]  J. Eckert,et al.  Difference in compressive and tensile fracture mechanisms of Zr59CU20Al10Ni8Ti3 bulk metallic glass , 2003 .

[16]  R. Raghavan,et al.  Plastic flow softening in a bulk metallic glass , 2006 .

[17]  Shigeru Aoki,et al.  A finite element study of the near crack tip deformation of a ductile material under mixed mode loading , 1987 .

[18]  Subra Suresh,et al.  Study of mechanical deformation in bulk metallic glass through instrumented indentation , 2001 .

[19]  R. Dauskardt,et al.  Mode II fracture behavior of a Zr-based bulk metallic glass , 2006 .

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

[21]  R. McMeeking,et al.  On criteria for J-dominance of crack-tip fields in large-scale yielding , 1979 .

[22]  R. Dauskardt,et al.  Enhanced Toughness Due to Stable Crack Tip Damage Zones in Bulk Metallic Glass , 1999 .

[23]  U. Ramamurty,et al.  Spherical indentation response of metallic glasses , 2004 .

[24]  R. Narasimhan,et al.  A Three-dimensional Numerical Study of Mixed Mode (I and II) Crack Tip Fields in Elastic–plastic Solids , 2005 .

[25]  Thomas J. R. Hughes,et al.  Encyclopedia of computational mechanics , 2004 .

[26]  U. Ramamurty,et al.  Temperature dependence of mechanical properties and pressure sensitivity in metallic glasses below glass transition , 2008 .

[27]  G. Ravichandran,et al.  Pressure-dependent flow behavior of Zr_41.2Ti_13.8Cu_12.5Ni_10Be_22.5 bulk metallic glass , 2003 .

[28]  S. K. Maiti,et al.  Theoretical and experimental studies on the extension of cracks subjected to concentrated loading near their faces to compare the criteria for mixed mode brittle fracture , 1983 .

[29]  Shigeru Aoki,et al.  Elastic-plastic fracture behavior of an aluminum alloy under mixed mode loading , 1990 .

[30]  J. G. Williams,et al.  Fracture under complex stress — The angled crack problem , 1984 .

[31]  John R. Rice,et al.  ON THE RELATIONSHIP BETWEEN CRITICAL TENSILE STRESS AND FRACTURE TOUGHNESS IN MILD STEEL , 1973 .

[32]  J. Lewandowski,et al.  Fracture toughness and notched toughness of bulk amorphous alloy: Zr-Ti-Ni-Cu-Be , 1998 .

[33]  U. Ramamurty,et al.  Mode I crack tip fields in amorphous materials with application to metallic glasses , 2007 .

[34]  J. F. Knott,et al.  The fracture behaviour of PMMA in mixed modes I and II , 1989 .

[35]  R. Narasimhan,et al.  An experimental investigation of constraint effects on mixed mode fracture initiation in a ductile aluminium alloy , 1999 .

[36]  W. Johnson,et al.  Shear bands and cracking of metallic glass plates in bending , 2003 .

[37]  W. Johnson,et al.  Fracture toughness and fatigue-crack propagation in a Zr–Ti–Ni–Cu–Be bulk metallic glass , 1997 .

[38]  J. Rice,et al.  Elementary engineering fracture mechanics , 1974 .

[39]  Albert S. Kobayashi,et al.  Elastic-Plastic Fracture , 1979 .

[40]  Lallit Anand,et al.  On H. Hencky’s Approximate Strain-Energy Function for Moderate Deformations , 1979 .

[41]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[42]  T. Hufnagel,et al.  Mechanical behavior of amorphous alloys , 2007 .

[43]  C. Shih,et al.  Small-Scale Yielding Analysis of Mixed Mode Plane-Strain Crack Problems , 1974 .

[44]  Frans Spaepen,et al.  A microscopic mechanism for steady state inhomogeneous flow in metallic glasses , 1977 .

[45]  A. Argon Plastic deformation in metallic glasses , 1979 .