An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

Abstract

Brittle and ductile dynamic fracture in solids is a complex mechanical phenomenon which attracted much attention from both engineers and scientists due to its technological interests. Modeling cracks in dynamic cases based on a discontinuous description is difficult because it needs additional criteria for branching and widening. Due to the very short time scales and the spatial complexity of the dynamic problem, its experimental analysis is still very difficult. Therefore, researchers still have to rely on numerical simulations to find a deeper explanation for many observed phenomena. This study is set out to investigate the effect of plasticity on dynamic fracture propagation. On the other hand, the diffuse phase-field formulation makes it possible to initiate, propagate, arrest or even branch cracks while satisfying the basic principles of thermodynamics. An implicit, staggered elastoplastic version of the phase-field approach was implemented in the commercial finite element code Abaqus through the UEL option. By means of simple examples we show that localized ductile deformations first increase both resistance and toughness. Then, after a maximum value, the resistance starts to decrease with a significant increment in energy dissipation. By favoring shear deformation over tensile failure the fracture pattern changes. First the branching disappears, then the crack propagation angle changes and becomes a shear band. Finally, we observed the increment of the instantaneous dynamic stress intensity factor during the acceleration stage of the crack without introducing a rate dependent critical fracture energy. We explained this phenomenon with the increasing roughness of the fracture surface.

Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion

“…One of its major flaws is that due to the quadratic setting it does not have an initial elastic threshold. Some authors tried to correct this flaw by adding an initial elastic threshold (Miehe et al, 2016;Molnár et al, 2020;Wu and Huang, 2020), however in all of the cases the crack surface calculated from the damage topology overestimates the theoretical value by more than 20%, which makes this method somewhat unreliable. On the other hand Pham et al (2011) proposed a description with the damage variable entering the surface only with a linear term.…”

“…Though there are other methods to obtain a positive damage rate (e.g., bound constrained non-linear optimization techniques (Amor et al, 2009;Farrell and Maurini, 2017;Wu, 2018b), augmented Lagrangian (Lorentz and Godard, 2011;Wheeler et al, 2014) or penalization methods (Gerasimov and Lorenzis, 2019)), due to its simplicity the history field of Miehe et al (2010b) is the most frequently used (Wu and Huang, 2020). More details about the Abaqus implementation can be found in our previous papers (Molnár and Gravouil, 2017;Molnár et al, 2020).…”

“…where H is the elastic (undamaged) strain energy history used in the staggered schemes (Miehe et al, 2010b;Molnár and Gravouil, 2017;Molnár et al, 2020) and η is a scalar multiplier. There are other methods to determine an optimal time step size.…”

A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine

“…These works have been aimed at both commercial finite element packages, such as COMSOL [ 30 ], and open-source platforms like FEniCS [ 31 ]. The development of phase field fracture implementations in the commercial package Abaqus has received particular attention [ 32 , 33 , 34 , 35 , 36 , 37 , 38 ], due to its popularity in the solid mechanics community. However, these works require the use of multiple user subroutines, most often including a user element (UEL) subroutine.…”

PSBFEM-Abaqus: Development of User Element Subroutine (UEL) for Polygonal Scaled Boundary Finite Element Method in Abaqus

“…Kumbhar et al [6] implemented the element based smoothed finite element method (CSFEM) by the UEL subroutines. Molnar et al [31] implemented an implicit, staggered elastoplastic version of the phase-field approach Abaqus through the UEL.…”