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E. Maggiolini et alii, Frattura ed Integrità Strutturale, 25 (2013) 117-123; DOI: 10.3221/IGF-ESIS.25.17 117 Special Issue: Characterization of Crack Tip Stress Field On numerical integration for effective stress assessment at notches Enrico Maggiolini, Paolo Livieri University of Ferrara (Italy) Roberto Tovo University of Ferrara (Italy) A BSTRACT . This paper presents a numerical method for non-local stress assessment by means of a general FE tool and the local stress field. Unlike usual calculations by means of a numerical PDE solver, a more general numerical integration is used. Different solutions are compared theoretically and numerically by evaluating the results obtained by two different FEM commercial software. The application of the non-local tension field is applied to the strength assessment of notches, welded joints and cracks. K EYWORDS . Implicit gradient; Local tension field; Notches; Welding; Fatigue. I NTRODUCTION n real applications, it is usual for an engineer to deal with strength assessment at stress raisers, i.e. notches, welding or cracks. There are several theories and approaches explaining how to tackle such problems, but, sometimes, the proposed approaches are difficult to use. In particular, it is often impossible to apply the “non-local” effective stress values without a particular software tool because many procedures require the integration of a specific Partial Differential Equation to calculate the non-local stress field. The goal of this research is to find a method for the evaluation of the non-local field in a fast and simple way, by using the local stress field available in all FEM software. For this purpose, both Comsol Multiphysics and Ansys numerical software were used and compared. Comsol has a pre-loaded module for an ordinary differential equation solution (Helmholtz equation) that can be used to calculate stress for non-local resistance, and even has an integration procedure for a general user-defined integral evaluation all-over the investigated domain. Alternatively, Ansys only has the possibility to compute and export the nodal coordinates and nodal results turned out from a conventional local structural analysis. The final aim is to compute a non-local stress field by means of a sound conventional local stress analysis. I MPLICIT GRADIENT METHOD he authors recently presented a new way to estimate the fatigue life of notched structures and welded joints based on the Implicit Gradient [1, 2]. This method is particularly suitable for a numerical estimation of the component fatigue life dependent on their geometry. The idea is very simple and enables application of the average damage originally formulated in the 1930s by Neuber [3], referred to as a geometry where fatigue crack propagation is on the bisector of the notch direction. This idea succeeds in attaining the fatigue limit of a plane component with notches by simple manual calculation [3,4]; on the other I T

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