Cohesive crack tip modelling: size-scale transition from ductile to brittle failure

Carpinteri, Alberto

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 1, pp. 59-79

Résumé

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 (\( K_{I} = K_{IC} \)).