An incompatible singular elastic element for two- and three-dimensional crack problems

Abstract

A new 3 node singular finite element has been derived. This element is incompatible and has to be used in conjunction with incompatible 4 node quadrilateral elements. An extension to three dimensional problems is also presented. This element is used to compute the stress intensity factor along the crack border in a wire with a semi elliptical surface crack subject to tension and for a large variety of elliptical shapes.

High Strength Steels Fracture Toughness Variation by the Media

“…Until a depth of cracks an around 0.5 times the radius R, it is observed quite good accordance between the predictions of both equations. It is worth noting that, for greater depths of crack, as it is the case of those observed by us in prestressing wires, the value of stress intensity factor calculated from the equation of Levan [8] is much higher than that one calculated by the equation of Astiz [7]. For so acute cracks in cylindrical specimens it has not been found a rupture criterion that allows considering in a simple manner.…”

“…For the case of a cylindrical geometry of the material, the calculation of the stress intensity factor and the criterion of fracture can be calculated through Astiz, Valiente and Elices's equation [1,7] or through Levan and Royer's equation [8]. The above mentioned authors have assumed that cracks along the whole perimeter of the specimen are formed and the superficial cracks have semi-ellipse shape (Figure 4).…”

Stress intensity factors for cracked cold-drawn steel wires under tensile loading

“…1(a), 1(b), and the maximum SIF value was obtained at the crack center C, according to the results given by Astiz [8]. Following a well known purely linear elastic solution in the vicinity of σ app σ app σ app σ app a 3D crack with an arbitrary curved front [9], the calculation of the SIF can be based on 2D plane strain hypothesis on the longitudinal section of a cracked cold-drawn steel wire under tensile loading, fig.…”

Stress intensity factor solutions for a cracked bolt loaded by a nut

“…This hypothesis has been justified theoretically and numerically, although the size of this domain of validity may be very small. In any case the importance of this decision in stress intensity values is very small, because the errors due to the choice are never higher than 3-4 percent [2,3,13,14,45].…”