Effects of Size and Slenderness on Ductility of Fracturing Structures

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Abstract
The ductility of an elastic structure with a growing crack may be defined as 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 curve of the whole structural system with the loading device (characterized by a spring) reaches a snapback point. Based on the known stress intensity factor as a function of crack length, the well-known method of linear elastic fracture mechanics is used to calculate the load-deflection curve and determine the states of snapback and maximum loads. An example of a notched three-point bend beam with a growing crack is analyzed numerically. The ductility is determined and its dependence of the structure size, slenderness, and stiffness of the loading device is clarified. The family of the curves of 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 method of solution is general and is applicable to cracked structures of any shape. The flexibility (force) method can be adapted to extend the ductility analysis to structural assemblages provided that the stress intensity factor of the cracked structural part considered alone is known. This study leads to an improved understanding of ductility, which should be useful mainly for design against dynamic loads.