scholarly journals Phase-Field Modeling Fracture in Anisotropic Materials

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Haifeng Li ◽  
Wei Wang ◽  
Yajun Cao ◽  
Shifan Liu
Keyword(s):  
Fracture Surface ◽  
Crack Propagation ◽  
Phase Field ◽  
Phase Field Model ◽  
Elastic Strain Energy ◽  
Critical Energy ◽  
Phase Field Method ◽  
Mixed Mode Fracture ◽  
Critical Energy Release Rate ◽  
Degradation Rates

The phase-field method is a widely used technique to simulate crack initiation, propagation, and coalescence without the need to trace the fracture surface. In the phase-field theory, the energy to create a fracture surface per unit area is equal to the critical energy release rate. Therefore, the precise definition of the crack-driving part is the key to simulate crack propagation. In this work, we propose a modified phase-field model to capture the complex crack propagation, in which the elastic strain energy is decomposed into volumetric-deviatoric energy parts. Because of the volumetric-deviatoric energy split, we introduce a novel form of the crack-driving energy to simulate mixed-mode fracture. Furthermore, a new degradation function is proposed to simulate crack processes in brittle materials with different degradation rates. The proposed model is implemented by a staggered algorithm and to validate the performance of the phase-field modelling, and several numerical examples are constructed under plane strain condition. All the presented examples demonstrate the capability of the proposed approach in solving problems of brittle fracture propagation.

scholarly journals Phase-Field Model for the Simulation of Brittle-Anisotropic and Ductile Crack Propagation in Composite Materials

2021 ◽  
Author(s):  
Christoph Herrmann ◽  
Daniel Schneider ◽  
Ephraim Schoof ◽  
Felix Schwab ◽  
Britta Nestler
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Compressive Load ◽  
Phase Field Model ◽  
Model Parameters ◽  
Ductile Crack ◽  
Critical Energy Release Rate ◽  
Compression Load

In this work, a small-strain phase-field model is presented, which is able to predict crack propagation in systems with anisotropic brittle and ductile constituents. To model the anisotropic brittle crack propagation, an anisotropic critical energy release rate is used. The brittle constituents behave linear-elastically, in a transversely isotropic manner. Ductile crack growth is realised by a special crack degradation function, depending on the accumulated plastic strain, which is calculated by following the J2-plasticity theory. The mechanical jump conditions are applied in solid-solid phase transition regions. The influence of the relevant model parameters on a crack, propagating through a planar brittle-ductile interface, and furthermore a crack developing in a domain with a single anisotropic brittle ellipsoid, embedded in a ductile matrix, is investigated. We demonstrate that important properties, concerning the mechanical behaviour of grey cast iron, such as the favoured growth of cracks along the graphite lamellae and the tension-compression load asymmetry of the stress-strain response, are covered by the model. The behaviour is analysed on basis of a simulation domain consisting of three differently oriented elliptical inclusions, embedded in a ductile matrix, which is subjected to tensile and compressive load. The used material parameters correspond to graphite lamellae and pearlite.

scholarly journals A Bayesian estimation method for variational phase-field fracture problems

2020 ◽  
Vol 66 (4) ◽  
pp. 827-849 ◽  
Author(s):  
Amirreza Khodadadian ◽  
Nima Noii ◽  
Maryam Parvizi ◽  
Mostafa Abbaszadeh ◽  
Thomas Wick ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Phase Field ◽  
Measurement Data ◽  
Estimation Method ◽  
Reference Value ◽  
Solid Material ◽  
Critical Energy ◽  
Field Method ◽  
Phase Field Method ◽  
Critical Energy Release Rate

Abstract In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values.

scholarly journals Phase-Field Model for the Simulation of Brittle-Anisotropic and Ductile Crack Propagation in Composite Materials

Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 4956
Author(s):  
Christoph Herrmann ◽  
Daniel Schneider ◽  
Ephraim Schoof ◽  
Felix Schwab ◽  
Britta Nestler
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Compressive Load ◽  
Phase Field Model ◽  
Model Parameters ◽  
Ductile Crack ◽  
Critical Energy Release Rate ◽  
Compression Load

In this work, a small-strain phase-field model is presented, which is able to predict crack propagation in systems with anisotropic brittle and ductile constituents. To model the anisotropic brittle crack propagation, an anisotropic critical energy release rate is used. The brittle constituents behave linear-elastically in a transversely isotropic manner. Ductile crack growth is realised by a special crack degradation function, depending on the accumulated plastic strain, which is calculated by following the J2-plasticity theory. The mechanical jump conditions are applied in solid-solid phase transition regions. The influence of the relevant model parameters on a crack propagating through a planar brittle-ductile interface, and furthermore a crack developing in a domain with a single anisotropic brittle ellipsoid, embedded in a ductile matrix, is investigated. We demonstrate that important properties concerning the mechanical behaviour of grey cast iron, such as the favoured growth of cracks along the graphite lamellae and the tension–compression load asymmetry of the stress–strain response, are covered by the model. The behaviour is analysed on the basis of a simulation domain consisting of three differently oriented elliptical inclusions, embedded in a ductile matrix, which is subjected to tensile and compressive load. The material parameters used correspond to graphite lamellae and pearlite.

Phase Field Model for Influence of Edge Dislocation on Precipitation

2011 ◽  
Vol 415-417 ◽  
pp. 1482-1485
Author(s):  
Chuang Gao Huang ◽  
Ying Jun Gao ◽  
Li Lin Huang ◽  
Jun Long Tian
Keyword(s):  
Edge Dislocation ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Second Phase ◽  
Free Energy Function ◽  
Phase Nucleation ◽  
Good Agreement

The second phase nucleation and precipitation around the edge dislocation are studied using phase-field method. A new free energy function is established. The simulation results are in good agreement with that of theory of dislocation and theory of non-uniform nucleation.

Modeling crack propagation in heterogeneous granite using grain-based phase field method

2021 ◽  
pp. 103203
Author(s):  
Xunjian Hu ◽  
Xiaonan Gong ◽  
Ni Xie ◽  
Qizhi Zhu ◽  
Panpan Guo ◽  
...  
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method

scholarly journals Study of the Fracture Behavior of Tetragonal Zirconia Polycrystal with a Modified Phase Field Model

Materials ◽  
2020 ◽  
Vol 13 (19) ◽  
pp. 4430 ◽  
Author(s):  
Jingming Zhu ◽  
Jun Luo ◽  
Yuanzun Sun
Keyword(s):  
Phase Transformation ◽  
Crack Propagation ◽  
Phase Field ◽  
Fracture Behavior ◽  
Tetragonal Zirconia ◽  
Finite Size ◽  
Phase Field Model ◽  
Crack Tip ◽  
Propagation Mode ◽  
Tetragonal Zirconia Polycrystal

The superior fracture toughness of zirconia is closely correlated with stress-induced martensitic phase transformation around a crack tip. In this study, a modified phase field (PF) model coupling phase transformation and fracture is proposed to study the fracture behavior and toughening effect of tetragonal zirconia polycrystal (TZP). The stress-induced tetragonal to monoclinic (t–m) phase transformation around a static or propagating crack is characterized with PF simulations. It is shown that the finite size and shape of the transformation zone under different loads and ambient temperatures can be well predicted with the proposed PF model. The phase transformation may decrease the stress level around the crack tip, which implies the toughening effect. After that, crack propagation in TZP is studied. As the stress field is perturbed by the phase transformation patterns, the crack may experience deflection and branching in the propagation process. It is found that the toughness of the grain boundaries (GBs) has important influences on the crack propagation mode. For TZP with strong GBs, the crack is more likely to propagate transgranularly while, for TZP with weak GBs, intergranular crack propagation is prevalent. Besides that, the crystal orientation and the external load can also influence the topology of crack propagation.

Application of Interface-Tracking Method Based on Phase-Field Model to Numerical Analysis of Isothermal and Thermal Two-Phase Flows

2007 ◽  
Author(s):  
Naoki Takada
Keyword(s):  
Phase Field ◽  
Density Ratio ◽  
Phase Field Model ◽  
Field Method ◽  
Diffuse Interface ◽  
Phase Field Method ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Two Phase Flows ◽  
Two Phase

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, the applicability of two versions of Navier-Stokes phase-field method (NS-PFM) was examined, combining NS equations for a continuous fluid with a diffuse-interface model based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

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