PSI - Issue 28

Yuri Petrov et al. / Procedia Structural Integrity 28 (2020) 1975–1980 Yuri Petrov/ Structural Integrity Procedia 00 (2019) 000–000

1977

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1 8 1 % %&' 8 ( ( , ( ) ( ( ≥ ) )&* "

(1), where ( , ) is a time-dependent tearing stress, " is ultimate stress for the studied material and stands for the incubation time. Criterion (1) also contains linear size parameter , which was firstly introduced by Neuber (1937), Novogilov (1969). This parameter is treated as the fracture process zone size, coinciding with the minimal distance the crack tip can travel. The linear size can be calculated using the formula = 2 ! + " "+ (2), where !" is the critical stress intensity factor for the studied material. In the case of stationary crack or intact sample we calculate fracture time as well as critical amplitudes of external loads according to the incubation time approach (1)-(2), which is known as an effective tool to predict characteristics of fracture in both homogenous and non homogenous materials (Petrov et al (2010), Bragov et al (2012)). The incubation time fracture model implies natural discretization of the fracture process, since minimal fracture zone size is introduced. This feature makes the condition (1) embedment into the numerical methods a relatively simple task as the majority of the numerical schemes are based on the medium discretization. The numerical scheme used in the work is built on the FEM software ANSYS with external custom libraries controlling the solution flow, the criterion (1) check and managing the crack propagation. The developed scheme is able to solve two dimensional problems with symmetry: the crack path should coincide with the symmetry line. This way, nodes lying on the crack path are constrained in a direction normal to the crack path and crack propagation is implemented through node releasing when condition (1) holds. Element size along the crack path is chosen to be /3 from accuracy and mesh sensitivity considerations and thus four nodes are released for the crack to propagate the distance. Material is supposed to be linear and elastic, and thus the specimens’ behavior can be described by Lame equations and Hooke’s law: (3). At time = 0 the specimens are supposed to be stress free and velocities of all points of the body are supposed to be zero. The trapezoidal pressure pulse ( ) is applied to the initial crack (see figure 1 for details) and this way, the initial and boundary conditions are the following: 1⃗( , 0) = 0; , , - % .⃗ ( , 0) = 0 ++ ( ∈ Γ 0 , ) = ( ) 0+ ( ∈ Γ 0 , ) = 0 + ( ∈ Γ + , ) = 0, 0+ ( ∈ Γ + , ) = 0 – symmetry condition (4) + # + = ( + )∇ # (∇ ∙ 1⃗) + ∆ # #$ = #$ ∇ ∙ 1⃗ + F # $ + $ # G 3. Numerical scheme