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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initiation when the time of fracture is relatively small (fig.1) showed a strong difference from the critical SIF measured in the quasi-static tests. This certainly contradicts the classical Griffith-Irwin approach. Dynamic crack initiation is a complicated physical phenomenon and therefore both efficient and robust computational techniques and innovative fracture models are required to predict and to investigate corresponding dynamic fracture effects. Nomenclature

mass density � acceleration body force density position vectors of the particle position vectors of the neighbouring particle ℋ spherical neighbourhood of the particle x vector state force vector state deformation vector state � ultimate tensile stress of the material y normal stress value ���� bond stress fracture process zone size/fracture cell size incubation time scaling coefficient 2. Peridynamics

In the present work peridynamic approach (Silling (2000), Silling et al (2007)) was used to study the problem of dynamic crack initiation. According to the peridynamic theory, the body is represented as a set of discrete particles with essentially non-local interaction rules. According to the theory the medium balance equations are written without spatial differential operators and thus objects with discontinuities (e.g. cracks) can be investigated with higher accuracy. A well-known state based ordinary material model was used (Silling et al (2007)), for which an equation of motion is as follows: � � � � � � � � �� �〈 � 〉 � �� �〈 � 〉 � � � � �� � ℋ (1) where � � , � � � , � � are mass density, acceleration and body force density, respectively; is the position vector of any neighbor of the particle in its spherical neighborhood ℋ , which is determined as a sphere with a certain radius called horizon and with center at . A vector state maps the vectors into the vectors as well as the second-order tensor (difference between them is that vector state can be a nonlinear or discontinuous function and therefore it’s something more general than a second-order tensor). � � � is the force vector state function, which maps the deformation vector state into the force-vector state � � (in the angle brackets, 〈 � 〉 , we indicate the bond (interaction between two particles), on which a force state operates). Peridynamic simulations in this work were conducted using an ordinary state based linear peridynamic solid material (Silling et al (2007)) in the open-sourced software Peridigm (Parks et al (2012)), which is developed by Sandia National Laboratories. 3. Incubation time criterion of fracture. Since the classical approach to the crack initiation problem is based on the static critical values of stress intensity factor, it is not able to describe the effects of dynamic crack initiation. Thus, a different approach was used in this