Issue 38

N.O. Larrosa et alii, Frattura ed Integrità Strutturale, 38 (2016) 266-272; DOI: 10.3221/IGF-ESIS.38.36 268 fracture is active but outside the area where crack blunting becomes significant. Negative Q values indicate lower constraint conditions compared to the reference field and positive Q values higher constraint conditions. A local approach to ductile fracture An alternative framework for constraint analyses and effective fracture toughness assessment is the application of failure models, often referred to as local approaches. Local approaches couple the loading history (stress-strain) near the crack-tip region with micro-structural features of the fracture mechanisms involved [12]. Since the fracture event is described locally, the mechanical factors affecting fracture are included in the predictions of the model. The parameters depend only on the material and not on the geometry, and this leads to improved transferability from specimens to structures than one- and two-parameter fracture mechanics methods [13]. A fracture model accounting for the ductile damage processes has been used to quantify the increased resistance of blunt defects relative to sharp ones and to demonstrate that a loss of constraint leads to an increase in the fracture properties of these materials. A phenomenological model [14] based on a stress modified fracture strain concept was used in [6,7] to construct J -R curves of notched compact tension C(T) and single edge tension SE(T). It has been demonstrated that true fracture strain for ductile materials is strongly dependent on the level of stress triaxiality [15-17]. The model used in this study therefore uses an exponential relationship between the true fracture strain, f  , and stress triaxiality: m e f exp - =              (3) where  and  are material constants obtained by fitting test data for smooth and notched bars and the triaxiality is: m e e 1 2 3 3          (4) where σ i (i=1-3) are principal stresses and σ e is the von Mises stress. Using a FE analysis technique, this model is implemented in a step-by step procedure in which at each loading step, the incremental damage, ∆ω , produced by incremental strain is assessed and added to the total damage, ω , produced in previous steps. The quantification of the incremental damage definition is performed in each finite element of the model as follows: p e i i i i i f , 1 ; =             (5) where p i   is the equivalent plastic strain increment and f  is determined by the local triaxiality in the element using Eq. (3). When the total damage becomes equal to unity ( ω =1), local failure is assumed to occur at the element and the initiation and propagation of a crack is simulated by reducing all the stress components to a sufficiently small value to make the contribution of the element to the resistance of the component negligible. It should be noted that this local approach with the simulation procedure briefly summarised above has been verified by comparison with experimental data on fracture toughness test specimens and pressurised pipes which serves as validation for this purpose. All material constants in Eq. (3) with the crack tip element size for the material and tensile properties used in this study were determined by the procedure and also verified with experimental data. More details on the numerical implementation of the model can be found in [6,7,18]. F INITE ELEMENT ANALYSIS shallow cracked SE(T) specimen and a deeply cracked C(T) specimen were modelled by means of 3-D finite elements. The relevant dimensions of these specimens and the pipe component assessed in this work are shown in Fig. 1. The material properties used in the numerical models are for an API X65 steel used in [6,19]. A