Further examination of the criterion for crack initiation under mixed-mode I+III loading

Mixed-mode fracture presents spectacular, scale-independent, pattern formation in nature and engineering applications. The criteria for crack initiation and growth under such mixed mode loading, however, are not well established. This work is aimed at exploring the failure criteria and the pattern formation under combined modes I and III. Specific designs of specimens based on boundary element simulations are considered with the aim of examining crack path selection at nucleation, threshold behavior of crack front fragmentation and, spacing of fragmentation. Experimental investigations with these specially designed geometries show that there does not exist a threshold ratio of $$K_{III}^{\infty }/K_{I}^{\infty }$$KIII∞/KI∞ below which a crack will propagate smoothly without fragmenting into facets. The crack front is shown to fragment immediately as soon as it is perturbed by a small amplitude mode III loading. The experimental results show further that spacing of the fragmentation is set not by any intrinsic length scale of the material, but by the characteristic dimension of the driving crack and the global loading.

[1]  E. Sommer.  Formation of fracture ‘lances’ in glass , 1969 .

[2]  M. Williams,et al.  Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension , 1952 .

[3]  Huajian Gao,et al.  On perturbations of plane cracks , 1998 .

[4]  G. I. Barenblatt,et al.  On brittle cracks under longitudinal shear , 1961 .

[5]  Alain Karma,et al.  Helical crack-front instability in mixed-mode fracture , 2010, Nature.

[6]  J. Wiebesiek,et al.  Comparison of predictions by mode II or mode III criteria on crack front twisting in three or four point bending experiments , 2008 .

[7]  R. Salganik,et al.  Brittle fracture of solids with arbitrary cracks , 1974 .

[8]  A. Karma,et al.  Theoretical analysis of crack front instability in mode I þ III , 2011 .

[9]  K. Ravi-Chandar,et al.  Criterion for initiation of cracks under mixed-mode I + III loading , 2010 .

[10]  R. Goldstein,et al.  Fracture structure near a longitudinal shear macrorupture , 2012 .

[11]  M. Cooke,et al.  Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate , 1996 .

[12]  Songshan Li,et al.  Singularity-reduced integral equations for displacement discontinuities in three-dimensional linear elastic media , 1998 .

[13]  S. Li,et al.  Symmetric weak-form integral equation method for three-dimensional fracture analysis , 1998 .

[14]  G. Irwin.  ANALYSIS OF STRESS AND STRAINS NEAR THE END OF A CRACK TRAVERSING A PLATE , 1957 .

[15]  J. Leblond.  Crack paths in three-dimensional elastic solids. i: two-term expansion of the stress intensity factors—application to crack path stability in hydraulic fracturing , 1999 .

[16]  Wolfgang G. Knauss,et al.  An observation of crack propagation in anti-plane shear , 1970 .

[17]  A. A. Griffith.  The Phenomena of Rupture and Flow in Solids , 1921 .

[18]  K. J. Miller,et al.  Mixed mode (I+III) fatigue thresholds in a forging steel , 1989 .