PSI - Issue 13

Yuri Petrov et al. / Procedia Structural Integrity 13 (2018) 1620–1625 Yuri Petrov/ Structural Integrity Procedia 00 (2018) 000–000

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1. Introduction

Research in the area of dynamic crack propagation is of key importance for the dynamic fracture mechanics. From the one hand the dynamic crack propagation problems are able to reveal fundamental properties of the dynamic fracture processes. While from the other hand unstable dynamic crack growth can be also encountered in engineering applications (Kanninen and O’Donoghue (1995)). Experimental investigation of the dynamically propagating cracks requires complicated measurement techniques since the crack tip movement is controlled by transient stress and strain fields. Considerable success in analytical studies of the dynamically propagating cracks was achieved in the second half of the 20 th century (Broberg (1964), Kostrov (1975), Freund (1998), Slepyan (1976)). Phenomenon of the propagating cracks has been also studied experimentally (Ravi-Chandar and Knauss (1984a, 1984b, 1984c), Fineberg et al. (1992), Rosakis et al. (1984), Kobayashi and Dally (1977)). Solid mechanics does not provide any a priori given fracture criteria, and development and application of models, capable of fracture prediction is one of the key problems of fracture mechanics. Energy based fracture theory was introduced by Griffith (1921) and was then modified using the concept of stress intensity factor (SIF) $ (first fracture mode is addressed in the paper). According to Irwin’s fracture criterion (Irwin (1957)) a crack becomes unstable if $ equals to some critical value $% , which is a material property. This approach is able to reliably predict the crack onset for a case of quasistatic loading, however many experiments, (e.g. by Ravi-Chandar and Knauss (1984a)), demonstrated that $ can be significantly higher than $% for the case of dynamic load application. Irwin’s criterion is conventionally modified for the case of dynamically loaded cracks introducing notion of the dynamic stress intensity factor and rate dependence of its critical value: $ & ( , ( ), - ) = $ &% / $ & ( )̇1. This approach provides the following equation for the crack tip motion: $ & ( , ( ), ( ), ( )) = $3 ( ( )), where ( ) is the crack length and ( ) is the crack tip velocity correspondingly. The right side of this equation is a functional, which represents dependence of the stress intensity factor on the crack velocity ( − dependence further in the text). This dependence is regarded as a material property and is implied to be unique for a given material. This dependence has to be determined experimentally a priory in order to make the conventional theoretical model applicable. Experimental procedures for the − dependence assessment are complicated, since both crack tip movement and corresponding stress field in the crack tip vicinity should be registered using high-speed photography. This dependence was determined for a number of materials in works by Rosakis et al. (1984), Dally (1979), etc., who regarded this curve as a unique material property. However, the − curve was found to be dependent on the specimen shape (Kalthoff (1983), Kobayashi and Dally (1977)) and moreover, in works by Ravi-Chandar and Knauss (1984c) is reported to be not dependent on the crack velocity, since considerable variation of the values was observed for the cracks propagating with constant velocities. Thus, the above mentioned experimental results are obviously contradictory and cause ambiguity. In this paper the crack propagation phenomenon is studied using the incubation time fracture model – the approach based on the time characteristics of the dynamic fracture process and finite element method. This approach makes it possible to evade controversy of the − dependence and moreover, to numerically obtain different variants (shapes) of this curve for various specimen types and loading conditions. 2. Simulation approach 2.1. Incubation time fracture criterion We apply an approach based on the concept of material incubation time taken as a scale level dependent material constant that was firstly put forward by Petrov (1991). The corresponding incubation time fracture model was proposed in Petrov and Utkin (1989), Petrov (1991), Petrov and Morozov (1994). According to this approach fracture at point and time occurs if the following inequality holds: 6 7 ∫ 9 9 :7 & 6 ∫ ( ′, ′) ′ ′ ≥ ? ? :& @ , (1).