Issue 16

F. Carta et alii, Frattura ed Integrità Strutturale, 16 (2011) 34-42; DOI: 10.3221/IGF-ESIS.16.04 39 Geometrically linear analyses were performed to find, for each crack length analyzed, the value of K corresponding to the maximum load of the test. The stress intensity factor range  K was then calculated according to the load ratio used in the experiments. The Mode I, II and III stress intensity factors are calculated using the contour integral method and they showed a limited variability with the distance of the contour from the crack tip. The K II and K III parameters assume always values close to zero, therefore the crack propagation is Mode I-dominated. For each size of the defect an average value of the K factor was calculated across the thickness (see Fig. 10). Figure 10 : K value in 4 different positions of the crack tip across a doubler and a stiffener. After a study of convergence based on analysis between various discretization solutions, a modeling with linear solid elements was chosen (see Tab.1), in this way through a mobile partition (see Fig. 11) with good density of elements near to the fracture tip (see Fig. 7), a good compromise between the convergence of the numerical results in terms of stress intensity factor and acceptable computation times was achieved. Element Characteristics K 1 [MPa  m] Process Time 2 K Deviation 3 [%] Shell Linear 1771.3 5.2 3.46 Shell Parabolic (QPNT) 1780.5 33.1 3.99 Solid Linear 1780.7 7.4 4.01 Solid Parabolic (QPNT) 1712 100 0 1 Values obtained by the solver taking into account the follow conditions of analysis: - Same configuration of loads and constraints; - Same crack length ( a = 42,71 mm ); - Same element dimensions in the plane of extension of the skin in the panel; 2 Normalized values in respect to computation time with modeling elements Solid Parabolic (QPNT) 3 The deviations were assessed against the best geometric discretization (with Solid Parabolic elements - QPNT) Table 1 : Comparison between the discretization solutions considered in the FE study (QPNT is Quarter-Point Node Technique). Figure 11 : The mobile partition around the crack tip.