13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 3. Identification of material properties For a small initial void volume fraction of the investigated material ductile damage affects the behavior of the SPT specimen in a deformation state, where large equivalent plastic strains occur. Accordingly, the parameter identification is performed in two phases: First, the yield curve parameters are determined neglecting ductile damage. Here, the material is modeled as elasticplastic with the von Mises yield condition and the associated flow rule with isotropic hardening. Subsequently, the identification of the ductile damage parameter is carried out together with the adoption of a reduced number of yield curve parameters. 3.1. Identification of yield curves For the determination of yield curves from measured load-displacement curves of the SPT, a method was used, which does not require FEM calculations during the identification process. Instead, previously trained Neural Networks are used. The parameter determination is done by minimizing the difference between measured load-displacement curves and those approximated by the Neural Networks. The optimization algorithm simulated annealing (SA, [25]) was used. Details of the identification of yield curves can be found in [4]. 3.2. Identification of the parameters of the non-local ductile damage model The identification of damage parameters is done after the determination of the yield curve parameters, now with ductile damage taken into account. Here, the parallel optimization algorithms Appspack and Hopspack are used [26]-[28] . Both algorithms are based on Generating Set Search Methods (GSS, [29][30]), a class of derivative-free optimization methods. The asynchronous parallel implementations Appspack and Hopspack start FE-simulations on different processors; the algorithms are not waiting for the results of simultaneous calculations. 3.3. Identification of Weibull-parameters For the determination of the Weibull parameters load-displacement curves of experiments in which the specimens failed brittle are simulated by FEM and the stress state at the time of failure is analyzed. The calculated probabilities of cleavage fracture are adapted to the experimental distribution using the maximum likelihood method (ML, [31]-[33]). 3.4. Prediction of fracture mechanical properties Tests with fracture mechanics specimens are simulated to determine fracture toughness values. Here, the material behavior is described by the parameters of the implemented damage models that were previously identified from the SPT. The evaluation of the stress state in the fracture mechanics specimen provides the relation between Weibull stress and fracture toughness values in the brittle and the transition region, which allows the comparison with the Master Curve [34]. The determination of fracture mechanical parameters by numerical simulations of conventional fracture mechanics tests is based on the hypothesis that the crack initiation both in SPT specimens as well as in fracture mechanics specimens is accurately described by the same material models. In the brittle and transition region, critical fracture toughness values KIc are calculated from J-integral values if the Weibull stress reaches 5%, 50% and 95% probability of cleavage fracture.
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