Effects of size and slenderness on ductility of fracturing structures

The ductility of an elastic structure with a growing crack may be defined a s the ratio of the additional load-point displacement that is caused by the crack at the moment of loss of stability under displacement control to the elastic displacement at no crack at the moment of peak load. The stability loss at displacement control is known to occur when the load-deflection cu rve of the whole structural system with the loading device (characterized b y a spring) reaches a snapback point. Based on the known stress intensity f actor as a function of crack length, the well-known method of linear elasti c fracture mechanics is used to calculate the load-deflection curve and det ermine the states of snapback and maximum loads. An example of a notched th ree-point bend beam with a growing crack is analyzed numerically. The ducti lity is determined and its dependence of the structure size, slenderness, a nd stiffness of the loading device is clarified. The family of the curves o f ductility versus structure size at various loading device stiffnesses is found to exhibit at a certain critical stiffness a transition from bounded single-valued functions of D to unbounded two-valued functions of D. The me thod of solution is general and is applicable to cracked structures of any shape. The flexibility (force) method can be adapted to extend the ductilit y analysis to structural assemblages provided that the stress intensity fac tor of the cracked structural part considered alone is known. This study le ads to an improved understanding of ductility, which should be useful mainl y for design against dynamic loads.