13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- describe the failure in the brittle or transition region. It quantifies the probability of cleavage fracture based on the weakest link theory and the Griffith criterion. Due to the absence of an initial macroscopic crack and a rather small stress triaxiality compared to fracture mechanic specimens, large parts of the SPT specimen undergo high plastic deformations even if brittle fracture is finally observed. In any case, the evolution of ductile damage precedes failure. Therefore, it is necessary to account for the influence of ductile damage when identifying material properties from the measured load displacement curves of the SPT. In this paper, fracture toughness values are predicted solely by numerical simulation of fracture mechanics tests using material parameters identified from the SPT. A non-local formulation of a ductile damage model is used in combination with a modified Beremin model to characterize the fracture behavior of pressure vessel steels in the transition region. 2. Damage models 2.1. Non-local ductile damage model When standard continuum damage models are implemented numerically using the finite element method, they exhibit a high sensitivity of the results to the spatial discretization size [9][10]. Material softening due to the evolution of damage localizes in a small portion of the model that is controlled by the finite element mesh, i.e. the finite element size becomes an additional model parameter. As a consequence, it is generally not possible to use the same damage model parameters in dissimilar FE models with very different element sizes. A common idea of different methods to reduce the mesh sensitivity of damage models is to account for the influence of the surrounding material at a given material point in the constitutive equations. This results in a formulation that introduces a characteristic length scale into the model. Non-local formulations [11][12] of damage models may be divided in to three main types: formulations of the integral type, explicit gradient formulations and implicit gradient models. The continuum damage model established by Gurson and modified by Tvergaard and Needleman (GTN, [13]-[15]) provides the basis for the constitutive equations applied in the present work. It was developed to describe the growth and coalescence of initially present or later nucleating voids in isotropic ductile materials. The GTN model accounts for the growth, nucleation and coalescence of voids. It consists of the yield condition and evolution equation for the two relevant internal variables. The change of the void volume fraction is determined by the growth of existing voids and the nucleation of voids in the matrix. Motivated by the approach of generalized continua, the GTN continuum damage model is modified by replacing the dilatational part of the plastic strain rate by its non-local spatial average in the evolution equation for the growth of existing voids. ( ) 1 ε = − nl G p f f All other equations of the GTN model remain untouched. For the considered case of elastic strains being small compared to plastic strains, the change of the micro-volume becomes an additional degree of freedom. The local behavior is sustained for the elastic case. The non-local dilatational part of the plastic strain rate is treated as an additional independent field quantity that is governed by the partial differential equation of the Helmholtz type
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