PSI - Issue 13

1622 Yuri Petrov et al. / Procedia Structural Integrity 13 (2018) 1620–1625 Yuri Petrov/ Structural Integrity Procedia 00 (2018) 000–000 3 In (1) stress ( , ) is a time-dependent stress and @ is the ultimate stress for the studied material. Criterion (1) also contains linear size parameter , which was firstly introduced as a fracture process parameter by Neuber (1937) and Novozhilov (1969). This parameter can be interpreted in various ways, however the approach used in this work supposes to be the fracture process zone size, indicating minimal increment of the crack length. According to this interpretation the linear size can be calculated using formula = 2 $ B % %B ⁄ , where $% is the critical stress intensity factor. The criterion (1) considers history of stresses since time integration is involved. It is considered that the dynamic fracture cannot take place instantly, as specific microscopic preparatory processes precede macroscopic fracture, observed experimentally. These preparatory processes are usually associated with the local stress relaxation caused by micro-cracking near the macro-crack tip and it can be generally represented by a special characteristic relaxation time, which is called incubation time and should be treated as material property. This parameter can be assessed experimentally and provides possibility to take into account essentially nonlinear irreversible microscopic fracture processes while solving linearly stated problem. The developed simulation scheme is based on finite element method in a two-dimensional formulation. ANSYS solver and custom routines are used to obtain the stress field surrounding the crack tip and to check the fracture condition (1). The numerical scheme is designed to solve symmetrical crack propagation problems: crack path coincides with line of symmetry and specimen is split into two equal halves; load is supposed to be applied symmetrically too. Node release technique is used in order to implement crack tip movement: when condition (1) holds in a particular node, the displacement constraint is removed from this node and the crack tip travels to the next node. This way, minimal crack length increment equals size of the element, and thus distance between nodes lying on the crack path should be at least as small as in order to apply (1) correctly. Stress intensity factor is calculated using J-integral. 2.2. Examples of the incubation approach application The fracture criterion (1) has been successfully applied in order to study dynamic crack propagation in various loading conditions. Figure 1 shows experimental and numerically obtained crack trajectories for quasistatic and pulse loading (Bratov and Petrov (2007), Kazarinov et al. (2014)). Experimental results by Ravi-Chandar and Knauss (1984a) and Fineberg et al. (1992) were investigated.

Fig. 1. Crack extension versus time for dynamic (a) and quasistatic (b) loading. Experiments and simulations using incubation time criterion.

Additionally, results on crack onset modelling can be found elsewhere (Petrov and Morozov (1994)). Further we will prove that the incubation time approach makes it possible to investigate dynamic crack movement for a wide variety of loading conditions – from quasistatic to high rate and short pulse loading of samples using only one extra material