PSI - Issue 13

Lapin V.N. et al. / Procedia Structural Integrity 13 (2018) 1171–1176 Lapin V.N. and Cherny S.G. / Structural Integrity Procedia 00 (2018) 000–000

1174

4

Рис. 2. (a) Normalized Stress Intensity Factors for the initial frature calculated numerically (solid line) and analytically in Lazarus et al. (2008) (dashed line): 2 – K II / K I ; 3 – K III / K I .; (b) Kinking angle at the first step of the fracture propagation: 0 – Experiment; 1 – 2DMTS; 2 3D MTS; 3 – MVG; 4 – implicit method with β = 0 . 5 . Solid lines corresponds with distributions calculated here, dashed and dotted ones are obtained in Lazarus et al. (2008).

3. Simulation and comparison with the experiment

3.1. Problem statement

The problem statement described in Buchholz et al. (2004) and Lazarus et al. (2008) is used to verify the implicit criterion. The geometry of the specimen in 3PB test is shown in Fig. 1. The parameters of the specimen are as follows: length L c = 0 . 260 m , 2 L e = 0 . 24 m , thickness t = 0 . 01 m , width W = 0 . 06 m , crack length L f = 0 . 02 , angle of the inclined planes of the initial crack is γ = 45 ◦ . Parameters of the material used for the simulation are taken from Lazarus et al. (2008) where experiments under PMMA specimen with Young modulus E = 2 . 8 GPa and Poisson ratio ν = 0 . 38 was performed. The specimens are subject to a cyclic lateral force of F = 2 . 4 kN and the stress ratio of the cyclic loading is R = 0.1. Since the only direction of the fracture propagation is considered the particular value of the force is not important here. Since the greatest change in the propagation direction is observed in the first step, we will compare the kinking angle at the very beginning of the propagation. Four criteria are used to verify the implicit one. They are 2DMTS of Erdogan and Sih (1963), 3D MTS of Schollmann et al. (2002) and MVK, MVG criteria that were applied to the considered problem in Lazarus et al. (2008). Elastic equilibrium equation were solved by boundary element method incorporated in the model of the fracture propagation Shokin at al. (2015), Cherny at al. (2016). The computation mesh that covers the surface of the specimen consists of N = 1000 elements with N Lc = 28 elements in L -direction, N T = 8 elements in t -direction and N W = 7 elements in W direction (see Fig 1, b) . The increment of the crack was ∆ L = 0 . 001 m , that is, 1 / 60 from the width of the sample. All criteria of the fracture propagation use values of SIF calculated for the fracture at the initial or at the first step. To separate the errors caused by the quality of SIF calculation and the influence of the criterion itself the dimensionless values of SIF K II / K I and K III / K I that were calculated here and by Lazarus et al. (2008) for the initial fracture are shown in the Fig. 2, a). The main difference is observed in the surface vicinity but Lazarus et al. (2008) note that the results for the points located at the free surface shall be disregarded. Fig. 2 shows the distribution of the kink angle at the first step of the crack propagation, calculated here and by Lazarus et al. (2008) by the various propagation criteria.. It is seen that the error in calculating K III cause the error in the kink angle calculated by 3DMTS of Schollmann et al. (2002) criterion. Whereas the 3.2. The first step of the propagation