Size-effects induced bifurcation phenomena during multiple cohesive crack propagation

Abstract The nonlinear behavior of concrete-like materials in tension is characterised by strain-softening. Phenomena involving the localisation of strain caused by strain softening can be analysed accurately through the so-called “cohesive crack model” which uses the length of the fictitious crack as a control variable. In this approach, the length of the process zone is not fixed and the ratio between this length and the length of the specimen decreases with increasing size-scale. This phenomenon is evident even for small changes in size. It can explain why, in four point shear test, a critical size is observed, below which a secondary crack starts to propagate. This is a size-related phenomenon of bifurcation of equilibrium path, which is predicted by the cohesive crack model and confirmed experimentally. The theoretical results obtained by means of the cohesive crack model involving two cracks are in good agreement with experimental results.

[1]  G. Maier,et al.  Equilibrium Branching Due to Flexural Softening , 1973 .

[2]  Silvio Valente,et al.  Experimental and Numerical Fracture Modelling of a Gravity Dam , 1994, SP-143: New Experimental Techniques for Evaluating Concrete Material & Structural Performance.

[3]  D. C. Drucker,et al.  Conventional and Unconventional Plastic Response and Representation , 1988 .

[4]  Alberto Carpinteri,et al.  Size-Scale Transition from Ductile to Brittle Failure , 1988 .

[5]  Surendra P. Shah,et al.  Application of fracture mechanics to cementitious composites , 1985 .

[6]  Surendra P. Shah,et al.  Fracture of Concrete and Rock , 1989 .

[7]  A. Carpinteri,et al.  Mixed mode fracture of concrete , 1991 .

[8]  Quoc-Son Nguyen,et al.  Bifurcation and post-bifurcation analysis in plasticity and brittle fracture , 1987 .

[9]  G. Maier.  Incremental plastic analysis in the presence of large displacements and physical instabilizing effects , 1971 .

[10]  Alberto Carpinteri,et al.  Interpretation of the Griffith Instability as a Bifurcation of the Global Equilibrium , 1985 .

[11]  Z. Bažant,et al.  Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories , 1993 .

[12]  S. Nemat-Nasser,et al.  Unstable growth of tension cracks in brittle solids: Stable and unstable bifurcations, snap-through, and imperfection sensitivity , 1980 .

[13]  Alberto Carpinteri,et al.  Size Effects on Strength, Toughness, and Ductility , 1989 .

[14]  Silvio Valente,et al.  Is mode II fracture energy a real material property , 1993 .

[15]  Z. Bažant.  FRACTURE MECHANICS OF CONCRETE STRUCTURES , 1992 .

[16]  D. S. Dugdale.  Yielding of steel sheets containing slits , 1960 .

[17]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .