Geodesic
Cohesive crack tip modelling: size-scale transition from ductile to brittle failure
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 1, pp. 59-79 
Carpinteri, Alberto. Cohesive crack tip modelling: size-scale transition from ductile to brittle failure. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 1, pp. 59-79. http://geodesic.mathdoc.fr/item/RLIN_1990_9_1_1_a9/
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Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

The nature of the crack and the structure behaviour can range from ductile to brittle depending on tensile strength and fracture toughness of the material, as well as on the size-scale of the solid body. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must consider energy dissipation both per unit of volume and per unit of crack area. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e., the transition from ductile to brittle global behaviour caused by increasing the size-scale and keeping the geometrical shape unchanged. For extremely brittle cases (e.g., initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap-back instability in the load-deflection path occurs. If the loading process is deflection-controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophical event tends to reproduce the classical LEFM-instability (\( K_{I} = K_{IC} \)).

[1] G. I. Barenblatt, The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-simmetric cracks. J. Appl. Math. Mech., 23, 1959, 622-636. | MR | Zbl

[2] Z. P. Bazant, Instability, ductility and size effect in strain-softening concrete. Journal of the Engineering Mechanics Division ASCE, 102, 1976, 331-344.

[3] B. A. Bilby - A. H. Cottrell - K. H. Swinden, The spread of plastic yield from a notch. Proc. R. Soc, A272, 1963, 304-314.

[4] L. Biolzi - S. Cangiano - G. P. Tognon - A. Carpinteri, Snap-back softening instability in high strength concrete beams. SEM-RILEM International Conference on Fracture of Concrete and Rock (Houston, Texas, June 17-19, 1987), S.P. Shah and S.E. Swartz (eds.), in press.

[5] A. Carpinteri, Notch sensitivity in fracture testing of aggregative materials. Eng. Fracture Mech., 16, 1982, 467-481.

[6] A. Carpinteri, Application of fracture mechanics to concrete structures. J. Struc. Div. (A.S.C.E.), 108, 1982, 833-848.

[7] A. Carpinteri, Statistical strength variation in materials with a random distribution of defects. Università di Bologna, Istituto di Scienza delle Costruzioni, 73, Bologna 1983.

[8] A. Carpinteri, Interpretation of the Griffith instability as a bifurcation of the global equilibrium. NATO Advanced Research Workshop on Application of Fracture Mechanics to Cementitious Composites (Evanston, Illinois, September 4-7, 1984), S. P. Shah (ed.), Martinus Nijhoff, 1985, 284-316.

[9] D. S. Dugdale, Yielding of steel sheets containing slits. J. Mech. Phys. Solids, 8, 1960, 100-104.

[10] C. Fairhurst - J. A. Hudson - E. T. Brown, Optimizing the control of rock failure in servo-controlled laboratory tests. Rock Mechanics, 3, 1971, 217-224.

[11] A. Hillerborg - M. Modeer - P. E. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 6, 1976, 773-782.

[12] G. Maier, On the unstable behaviour in elastic-plastic beams in flexure (in Italian). Istituto Lombardo, Accademia di Scienze e Lettere, Rendiconti, Classe di Scienze (A), 102, 1968, 648-677.

[13] J. R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech., 35, 1968, 379-386.

[14] K. Rokugo - S. Ohno - W. Koyanagi, Automatical measuring system of load-displacement curves including post-failure region of concrete specimens. International Conference on Fracture Mechanics of Concrete (Lausanne, Switzerland, October 1-3, 1985). In: F. H. Wittmann (ed.), Fracture Toughness and Fracture Energy of Concrete. Elsevier, Amsterdam 1986, 403-411.

[15] J.G. Rots - D.A. Hordijk - R. De Borst, Numerical simulation of concrete fracture in direct tension. Fourth Intern. Conf. on Numerical Methods in Fracture Mechanics (San Antonio, Texas, March 23-27, 1987), Pineridge Press, 1987, 457-471.

[16] H. Schreyer - Z. Chen, One-dimensional softening with localization. Journal of Applied Mechanics, 53, 1986, 791-797.

[17] H. Tada - P. Paris - G. Irwin, The Stress Analysis of Cracks Handbook. Del Research Corporation, St. Louis (Missouri) 1963, 2.16-17.

[18] M. P. Wnuk, Quasi-static extension of a tensile crack contained in a viscoelastic-plastic solid. Journal of Applied Mechanics, 41, 1974, 234-242 | Zbl