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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Table 1. Range of the GTN parameters. Parameter

Parameter

Value range

Yield surface multiplier Yield surface multiplier Initial void volume fraction Critical void volume fraction Failure void volume fraction Mean strain for nucleation

1.5

(fixed) (fixed)

1 q 2 q

1

0.0005-0.001

0 f c f

0.1-0.25 0.3-0.5 0.12-0.22

f f

n 

Standard deviation

0.05

(fixed)

n S

Volume fraction for void nucleation 0.005-0.015 The simulations were performed with MSC.Marc Software using 50 µm element size in the crack propagation environment. The results of the 90 simulations compared to the test curve are illustrated in Figure 3 for the NT1 specimen (with 1mm notch), which was used to determine the GTN parameters. n f

Fig. 3. Dimensions of notched flat tensile specimens.

The second step is to use this data to train the ANN program. In this process, the input data is divided into three sets: training, validation, and verification, but since Bayesian regularization has been applied, the validation domain has been moved to the training set. Also, both the input and output parameter sets were between -1 and 1, therefore there was no need to scale them. It is important to note that the number of neurons in the hidden layer should be set to a value between the input and output parameter numbers, but it may exceed these numbers, but care should be taken that the program cannot generalize the results. Due to the characteristics of the curve, the displacement values were taken for given force values (8 force values: 3100, 3000, 2900, 2800, 2700, 2600, 2500, 2400 N). A trial-and-error approach was used to estimate the number of hidden neurons. For different numbers of hidden neurons, the ANN was generated ten times and the errors of the test samples were calculated. Then both the errors and the number of hidden neurons were compared for the different ANNs, and the lowest number of hidden neurons that still gave a satisfactory result was chosen for the final ANN. The procedure showed that a hidden layer of 30 neurons was a reasonable choice. Thus, the ANN (8-30-5) was structured with 8 neurons in the input layer (displacement values for 8 given force values), 30 neurons in the hidden layer and 5 neurons in the output layer. The neurons in the output layer represent the damage parameters to be identified ( n c f n n f , f , f , , f  ). Thereafter the optimal GTN parameter can be obtained from the trained ANN. The other two specimens (2 and 4 mm notch) were simulated with the ideal GTN parameter set determined from the ANN, and the parameters defined above were verified. The results of the simulation compared with the tests are shown in the Fig. 4, where the specified GTN parameters are included.