PSI - Issue 28

Maksim Ignatev et al. / Procedia Structural Integrity 28 (2020) 1650–1654 M. Ignatev / Structural Integrity Procedia 00 (2020) 000–000

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work – the incubation time fracture criterion (Petrov and Utkin (1989), Petrov (1991), Petrov and Morozov (1994)). An idea of the structural approach (Novozhilov (1969)) is that there is a process zone of fracture and thus the structural block of a certain size will fail, if the average stress inside this block (averaged in space) exceeds the ultimate tensile stress of the material � : � � � � � �� � � � � � (2) where y � � � – normal stress value. Size of the structural block is determined from condition of the correspondence of the structural criterion to the classical approach within the framework of linear elastic fracture mechanics and this parameter is regarded as a material constant. Incubation time criterion is an extension of the structural criterion and it considers the average value of the stress variations both in space over the length of the structural block and in time over the characteristic time of fracture – the incubation time : � � � � � � � � � � �� �� � � � � �� � � (3) It is supposed that the fracture is not an instantaneous process, but on the contrary, a particular amount of time is needed for the preparatory processes (microcracking, coalescence of defects and pores, etc.) to develop and to cause the material failure. Parameter can be evaluated from various experiments on dynamic fracture via substitution of the stress history and fracture time to formula (3). Criterion (3) is known as an effective tool to predict critical parameters of fracture in both homogenous and non-homogenous materials (Petrov et al (2010), Bragov et al (2012)). In order to implement structural approach in peridynamics, a separate failure of the bonds is considered similarly to the classical failure criteria in peridynamics. Since this approach considers the stress field, it is necessary to introduce the concept of the bond stress ���� , which is assumed to be equal to the mean value of the stresses in the interacting elements. The failure of a structural block (or element) is interpreted as the failure of all bonds of the peridynamic particle occupying a volume in the form of a cube with an edge of size . If we consider the case when a critical stress is reached in the considered peridynamic particle, and its neighboring particle has even a zero-stress value, then the connection between them has to fail. Therefore, we obtain that the critical bond stress is equal to a half of the quasi static strength of material � . Due to the heterogeneity of the stress field at the crack tip, the average stress value on a structural block strongly depends on its size. In case of the inverse root asymptotic approximation of the stress field, it can be found that the critical value of the average stress on a structural element of the size is √ less than on the structural block of size . Considering all mentioned above the incubation time criterion of the bond failure can be written in the following form: � � � � � ���� � � � � с �√� (4) 4. Results. In the present work crack initiation tests from works by Ravi-Chandar and Knauss (1984a) were modelled using methods of peridynamic theory coupled with the incubation time fracture criterion. For this study 250 mm high, 150 mm wide and 3mm thick Homalite-100 specimen with a 25 mm long pre-notch was found to be appropriate, as reflected waves from the boundaries do not reach a crack tip during 80 s time period and this way do not influence the crack tip behavior. According to the developed numerical approach the crack initiation was considered at the moment, when the damage of at least 35% (Ha and Bobaru (2010)) was achieved in the next element after the crack tip.