Issue 50

P. Livieri et alii, Frattura ed Integrità Strutturale, 50 (2019) 613-622; DOI: 10.3221/IGF-ESIS.50.52 613 Stress intensity factor for small embedded cracks in weldments Paolo Livieri University of Ferrara, Department of Engineering, Italy paolo.livieri@unife.it Fausto Segala University of Ferrara, Department of Mathematic, Italy fausto.segala@unife.it A BSTRACT . In the present work, the stress intensity factor (SIF) of embedded small cracks placed at the weld toe is calculated by means of two procedures based on the Oore-Burns integral. In the first approach, the defect is considered as a circular disk and the SIF is evaluated by means of the Oore- Burns weight function. By taking advantage of a suitable change of variable, the singularity of the weight function on the crack border can be removed. In this way, the numerical evaluation of the SIF is possible without the use of specific integration algorithms, although the nominal stress field becomes singular when the crack approaches a V-sharpe notch. As an example, the obtained equations are applied to a defect located in the neighbourhood of a weld toe with an opening angle of 135 degrees under mode I loading. Subsequently, for a crack similar to a star domain with a border expressed by means of the Fourier series, the SIF is given by means of an explicit equation based on the Oore-Burns weight function. K EYWORDS . Weight function; Stress intensity factor; Three-dimensional crack; Weld. Citation: Livieri, P., Segala, F., Stress intensity factor for small embedded cracks in weldments, Frattura ed Integrità Strutturale, 50 (2019) 613-622. Received: 19.07.2019 Accepted: 17.08.2019 Published: 01.10.2019 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION he safety factors in the presence of a defect can be verified by the knowledge of the stress intensity factor (SIF) evaluated for an elastic linear material [1]. As proposed by Bueckner [2] and Rice [3], the SIF calculation can be performed by means of the weight function technique. The numerical analysis is reduced to an evaluation of an integral exactly over the region covered by the crack. This method can be applied both for two-dimensional models (crack as a line) or for three-dimensional problems (crack as a surface). In the literature for two-dimensional cracks, there are many formulations in closed form obtained with different methodologies [4]. However, for the three-dimensional cracks, the number of proposed solutions is poor (see, for example, bibliographical references [5–6]). In fact, in many cases the use of T