PSI - Issue 52

Made Wiragunarsa et al. / Procedia Structural Integrity 52 (2024) 583–593 Wiragunarsa et al. / Structural Integrity Procedia 00 (2023) 000–000

584

2

used in dynamics problems Libersky et al. [1993], impact problems Randles and Libersky [1996], Stellingwerf and Wingate [1993], Johnson et al. [1996], Vidal et al. [2007], geometrically nonlinear structural analysis Lin et al. [2014], Naceur et al. [2015], Lin et al. [2018], and large strain solid dynamics Lee et al. [2017, 2019]. In fracture mechanics, SPH has advantages in saving modelling time and improving flexibility compared to mesh based methods, which was implemented for damage and fracture of shells, elastoplastic damage and fracture, and mixed-mode fracture modelling Ming et al. [2015], Grellier et al. [2016]. In Tazoe et al. [2020], a new method was reported using the Smoothed Particle Hydrodynamics (SPH) technique for fatigue crack propagation prediction, called SPH-Fatigue. The method calculates the stress intensity factor and solves the fatigue crack propagation problem with particle models. A hypothesis of the continuity of the crack-front line is considered, and a method for dealing with the crack merging problem was proposed. The validity of the proposed method is confirmed by comparing the numerical solution with the result of a fatigue test. Another work by Tazoe and Yagawa [2021] proposed a method based on C0 continuous crack-front line. The detailed application of the chained crack-front line concept to crack propagation problems was discussed, including crack separation and merging phenomena. They also present a detailed algorithm for crack propagation with the chained crack front line and verify the method by comparing computed results with experimental ones. An e ffi cient fatigue crack growth model using the smoothed particle hydrodynamics (SPH) method was developed by Wiragunarsa et al. [2021]. The crack is represented using the particle interaction-based crack model, in which the crack propagates between the two particles. The interaction of two particles will be deactivated if the fracture criterion is reached at the crack tip. The study used linear elastic fracture mechanics and Paris’s law for calculating crack increment. The location of maximum principal stress determined the crack growth direction, and the stress intensity factor was calculated using the J-integral method. The results were compared with available data in the literature, and the study found that no special treatment was needed for handling singularity at the crack tip. Besides, the algorithm to predict the crack growth direction could be built with minimal e ff ort. Another work reported the SPH for fatigue crack growth analysis using the pseudo-spring algorithm. This algorithm stops the interactions between the crack-front particle and its critical neighbours. These critical neighbours are the ones that have the largest axial stresses in the pseudo-springs Ganesh et al. [2022]. Based on the literature study that reported the SPH for crack growth analysis, the crack modelling technique can be grouped into particle-deletion and interaction deletion techniques. This research aims to analyse and compare the performance of particle and interaction deletion techniques for the crack growth simulation. The conservation of momentum and deformation gradient will be discretised using the updated Lagrangian SPH formulation. The Jameson-Schmidt-Turkel (JST) stabilisation is added to the discretised momentum equation to achieve nodal stability. The JST stabilisation for the SPH can be found in Lee et al. [2016]. An explicit two-stage total variation diminishing Runge-Kutta (TVD RK) time integrator is adopted to update the properties at every time step. Finally, the stress intensity factor will be compared with the available data in the literature Murakami [1987].

2. Governing equation

2.1. Motion and deformation

The motion of a particle is governed using the rate of change of linear momentum with respect to the current configuration, as represented in Equation 1. Variable p is the linear momentum per unit of volume, σ is the Cauchy stress, and s is the external force per unit of volume.

∂ p ∂ t − ∇ ·

σ T

= s

(1)