Issue 42

G. Testa et alii, Frattura ed Integrità Strutturale, 42 (2017) 315-327; DOI: 10.3221/IGF-ESIS.42.33 317 Alternatively, continuum damage mechanics (CDM) provides a framework for constitutive modelling of damaged material in which some of the aforementioned issues can be avoided. In CDM, the damage variable accounts for the detrimental effects on the reference material properties caused by a generic damage state. Differently from the concept of porosity, the damage in CDM is not strictly defined for a specific micromechanism of failure, making it suitable for describing progressive deterioration caused by the development of inelastic deformation at different length scales. Bonora [14] proposed a damage model formulation for describing ductile damage evolution in different classes of metals and alloys. The model was successfully used to predict ductile rupture under different loading conditions and material microstructural states [15, 16]. One of the key feature of this model formulation is the capability to account for stress triaxiality effects on material ductility [17]. Recently, Carlucci et al. [18] used the Bonora damage model (BDM) to predict fracture resistance of flaw in girth weld pipes showing the possibility to use CDM in support of strain-based design procedure [19]. A major limitation to the use of advanced material modelling for structural assessment route of engineering components relies on the difficulties of the determination of material model parameters. In porosity-based micromechanical models, material model parameters, in most of the cases, do not have a physical meaning and are determined numerically by inverse calibration of selected laboratory-scale test results. This approach relies on the experience and sensitivity of the operator, which becomes a major cause of uncertainty in model parameters identification. In CDM, in general, fewer material model parameters are required. In the BDM, these parameters are four but can be reduced to two for quasi-static loading. In this work, the BDM was used to predict the strain limit capacity of X65 steel grade used for pipeline application. The procedure for the identification of damage model parameters is presented. Once determined, damage model parameters allow building the limit strain diagram (LSD) to predict strain capacity as a function of stress triaxiality. The solution is validated comparing the predicted limit strain with onset crack propagation data in SENT specimen. D AMAGE MODEL Formulation he Bonora Damage Model (BDM) is formulated in framework of continuum damage mechanics. The basic concept in CDM is that the constitutive response of the damaged material is described by the same set of equations of the undamaged material simply replacing the stress with the “effective” stress concept [20]: 1 D      (2) Here, D is the damage variable that, under the assumption of isotropic damage, is a scalar. The definition of the “effective” stress together with the principle of strain equivalence [21] leads to the following definition of damage as, 0 1 E D E    (3) where E  and 0 E are the effective and the reference Young modulus of the material, respectively. Assuming that the mechanical and thermal dissipations are uncoupled, the second principle of thermodynamics requires the mechanical dissipation to be positive: : 0 p ij k k ij YD A V         (4) k V  indicates the rate of internal variables, A k designates the associated variables, and -Y is the damage (elastic) strain energy release rate given by,   2 2 2 1 eq Y R E D      (5) where, T