PSI - Issue 48

Bernadett Spisák et al. / Procedia Structural Integrity 48 (2023) 326–333 Spisák et al / Structural Integrity Procedia 00 (2023) 000 – 000

331

6

Based on these simulations, it can be said that using an exact replication of the measurement geometry, the GTN parameters work well for mini-CT samples too. Therefore, later the GTN parameters determined with NT specimens can be used for the modified VCCT simulation method. 5. Aplication of the modified VCCT model to determine fracture toughness The crack closure method or two-step crack closure technique is based on Irwin's crack closure integral. The method assumes that the  E energy released from the crack when the crack length ( a) is extended by  a to a+  a is equal to the energy required to close the crack. Therefore, the forces required to close the crack are equal to the forces acting on the top and bottom surfaces of the closed crack. The virtual crack closure method (VCCT) is based on the same assumptions as the crack closure method. In addition, it assumes that the  a crack extension from a+  a to a+2  a does not significantly change the state at the crack tip. Hence, when the crack tip is located at node k , the displacements behind the crack tip at node i are approximately equal to the displacements behind the crack tip at node l when the crack tip is located at node i, for the better understanding this idea is illustrated on Fig. 6. (Krueger (2004)).

Fig. 6. VCCT theoretical representation.

In principle, an energy value must be defined at which the crack propagation can be initiated. This idea has been modified and adapted so that the energy is not the driving force for propagation, but the critical failure value, which is defined by the GTN method. In this way, the actual crack propagation can be simulated and at the same time the J integral values and the actual crack length can be determined. For this a subroutine was developed. In two type of subroutine was combined. The first is the so called ucrack_directgrowth subroutine which allows the user to specify a crack growth criterion. The basic concept if it is, that the current crack front node will grow if the variable igrow is set to 1. In this part the driving force of cracking can be chosen from the VCCT (driving force is the energy release rate, G ) and the Lorenzi method (driving force is the J-integral). Furthermore, the subroutine contains the number of the node along the crack front and the accumulated growth for each front node. The aim was to modify this driving force, therefore other subroutines were also implemented which are the followings:  uactive: it is used to either activate or deactivate elements in the model. In this step the void volume fraction of the elements nearby to the crack front is taken out.  newsv: with this the new values of the state variable to be defined at the end of the current step can be set. In this part the void volume fraction of the elements which are close to the crack front and are still in front of it are compared to the critical void volume. If their value is higher then the crack would propagate.  uedinc:it is called at the end of each increment and the necessary information are saved in the memory (e.g. number of crack front node, value of J-integral, size of element)  upstno: is used to write the results out into the post file. With the combination of these subroutines the driving force of the crack propagation can be modified to the critical void volume fraction and the crack tip can be changed continuously, therefore the J-integral is calculated at every timestep.