PSI - Issue 47

Zoltán Bézi et al. / Procedia Structural Integrity 47 (2023) 646–653 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Following verification of the GTN parameters in the CT specimens, unloading were applied to the model to evaluate the ASTM E1820-20 standard, similar to the tests. The tests were carried out with the unload of 38%, but the optimum load values defined in the standard were considered in the evaluation. For the evaluation we used our improved version of the elastic compliance E1820 test analysis software made by NISTIR (Lucon (2022)). The simulations were carried out with the unloads considered optimal by the standard, which was also evaluated against the standard. The LLD-F curve and the J a − obtained from the standard evaluation are shown in Figure 7. Figure 7.b shows that the fracture toughness values match very well, but the evaluation requires time consuming modelling and standard evaluation. For this reason, a model was used that allows the continuous computation of the integral J in the finite element software.

Fig. 7. Simulation and test with standard evaluation (a) LLD-F curves (b) Fracture toughness curves.

4. Determination of fracture toughness with VCCT model Originally proposed by Rybicki and Kanninen (1977), the virtual crack closure (VCCT) method is based on linear elastic fracture mechanics. The basic assumption is that the energy required to propagate a crack is equal to the energy required to close the crack to its original length. Basically, the VCCT method simulates crack propagation by applying virtual constraints to nodes along the crack path. It first connects the nodes before the crack tip and then disconnects them after the fracture criterion is met, thus simulating crack propagation. The method was originally developed for the simulation of brittle fractures, where the fracture criterion is defined as the limit of the strain energy accumulated at the crack tip, but the modelling technique, in particular its finite element representation, allows to simulate also ductile crack propagation. An important step in the model development was to see how the advantages of the GTN and VCCT techniques described above can be applied in one model to determine the J Q fracture toughness value for a given material as accurately as possible using simulation tools. In this chapter, a finite-element simulation of the CT specimen presented in the previous section has been performed using a 2D plane-strain approach to compare the obtained crack propagation and J-integral values with those derived from standard tests. In the developed fracture mechanics model, the fracture criterion was defined based on the material-specific parameters obtained from the damage (GTN) model discussed above, thus combining the two methods. The resulting 2D model of the CT specimen is illustrated in Figure 8. The VCCT method requires a predefined crack path that is limited to the element boundaries. In general, smaller the distance between adjacent nodes, the more precise the prediction of the rate of release of the deformation energy, in our case the value of the J-integral. For this reason, reasonable changes have been made to the previously presented models used to simulate crack propagation to obtain more accurate results. For the CT specimens, the element size used along the crack front was 100 micrometers, which was modified to 25 micrometers. 2D linear four-node elements were used in the simulations, while the pins were assumed to be perfectly rigid. The boundary conditions used are the same as in the