Numerical study on crack propagation in linear elastic multiphase composite materials using phase field method

2018 ◽  
Vol 36 (1) ◽  
pp. 307-333 ◽  
Author(s):  
Xiang Li ◽  
Dongyang Chu ◽  
Yue Gao ◽  
Zhanli Liu
Keyword(s):  
Crack Initiation ◽  
Damage Threshold ◽  
Field Method ◽  
Point Of View ◽  
Phase Field Method ◽  
Content Type ◽  
Linear Elastic ◽  
Multiphase Composites ◽  
Complex Crack ◽  
Void Pores

PurposeThe purpose of this paper is to develop an efficient numerical method to study the complex crack initiation and propagation in linear elastic multiphase composites.Design/methodology/approachA phase field method is developed to study the complex fracture behavior in multiphase composites. A damage threshold is introduced for referring crack initiation in the proposed method. The damage threshold is assigned as a material property so that different composite components possess different thresholds. In this manner, smooth transition from crack initiation to propagation is revealed.FindingsThe proposed method is used to investigate complex crack evolution in mesoscale cementitious composite, which consists of aggregates, matrix and void pores. From a mesoscale point of view, it is found that cracks prefer to evolve within the matrix phase. As a crack encounters an aggregate, it tends to bypass the aggregate and evolve along the interface. Cracks tend to avoid to penetrate through aggregates. Also, cracks tend to be attracted by void pores. From a mesoscale point of view, it is revealed that the elastic modulus and strength of concrete models are closely related to porosity.Originality/valueA criterion with a damage threshold is introduced to the proposed method. The criterions with and without a damage threshold are compared with each other in details. The proposed method is proven to be a useful tool to study mechanical behavior and crack evolution of brittle multiphase composites.

Crack kinking and tunneling simulation for the single-fiber composite under transverse tension based on phase-field method

2020 ◽  
Vol 55 (5-6) ◽  
pp. 145-158
Author(s):  
Leying Song ◽  
Songhe Meng ◽  
Chenghai Xu ◽  
Guodong Fang ◽  
Qiang Yang ◽  
...  
Keyword(s):  
Numerical Model ◽  
Crack Initiation ◽  
Phase Field ◽  
Three Dimensional ◽  
Field Method ◽  
Fiber Reinforced Composites ◽  
Phase Field Method ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Transverse Tension

Virtual tests for a single-fiber–reinforced composite model subjecting to transverse tension are carried out based on a phase-field method considering a varying interface toughness parameter. Without pre-treating the crack initiation location and propagation path, the complete fracture process is realized for the first time in a three-dimensional numerical model, including nucleation cracks on the fiber/matrix interface at the free end, tunneling cracks along the fiber axis, and kinked interface cracks deviating from the interface and penetrating into the matrix. The numerically calculated crack propagation process is in good agreement with the in situ observations in the literature, indicating that the present model provides a good real-time quantitative numerical method for three-dimensional fracture analysis of fiber-reinforced composites. Tunneling cracks tend to cause macroscopic interface debonding and fiber pull-out. The interface tunneling crack initiation and the transition to the steady state inside the model are captured and analyzed in the numerical model. Kinked interface cracks can merge with other matrix cracks, forming a macroscopic transverse crack fracture mode. The kinking behaviors affected by the initial crack size and the interface properties are investigated. This study for the detailed crack propagation is helpful in understanding the toughening mechanism of fiber-reinforced composites under transverse tension.

The numerical modeling of cell freezing in binary solution under subcooling conditions

2019 ◽  
Vol 30 (6) ◽  
pp. 3005-3025
Author(s):  
Przemysław Smakulski ◽  
Sławomir Pietrowicz ◽  
Jun Ishimoto
Keyword(s):  
Numerical Modeling ◽  
Free Energy ◽  
Numerical Calculation ◽  
Phase Field ◽  
Field Method ◽  
Energy Functional ◽  
Phase Field Method ◽  
Phase Front ◽  
Content Type ◽  
Free Energy Functional

Purpose This paper aims to describe and investigate the mathematical models and numerical modeling of how a cell membrane is affected by a transient ice freezing front combined with the influence of thermal fluctuations and anisotropy. Design/methodology/approach The study consists of mathematical modeling, validation with an analytical solution, and shows the influence of thermal noises on phase front dynamics and how it influences the freezing process of a single red blood cell. The numerical calculation has been modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional. Findings The results show an influence scale on directional phase front propagation dynamics and how significant are stochastic thermal noises in micro-scale freezing. Originality/value The numerical calculation has modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional.

scholarly journals On the choice of parameters in the phase field method for simulating crack initiation with experimental validation

2016 ◽  
Vol 197 (2) ◽  
pp. 213-226 ◽  
Author(s):  
T. T. Nguyen ◽  
J. Yvonnet ◽  
M. Bornert ◽  
C. Chateau ◽  
K. Sab ◽  
...  
Keyword(s):  
Crack Initiation ◽  
Phase Field ◽  
Experimental Validation ◽  
Field Method ◽  
Phase Field Method

Optimal shape design of flux barriers in IPM synchronous motors using the phase field method

2014 ◽  
Vol 33 (3) ◽  
pp. 998-1016 ◽  
Author(s):  
Jae Seok Choi ◽  
Takayuki Yamada ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki ◽  
Heeseung Lim ◽  
...  
Keyword(s):  
Phase Field ◽  
Numerical Technique ◽  
Optimization Method ◽  
Field Method ◽  
Phase Field Method ◽  
Content Type ◽  
Synchronous Motors ◽  
Diffuse Interfaces ◽  
Interior Permanent Magnet ◽  
Rotor Flux

Purpose – The purpose of this paper is to present an optimization method for flux barrier designs in interior permanent magnet (IPM) synchronous motors that aims to produce an advantageous sinusoidal flux density distribution in the air-gap. Design/methodology/approach – The optimization is based on the phase field method using an Allen-Cahn equation. This approach is a numerical technique for tracking diffuse interfaces like the level set method based on the Hamilton-Jacobi equation. Findings – The optimization results of IPM motor designs are highly dependent on the initial flux barrier shapes. The authors solve the optimization problem using two different initial shapes, and the optimized models show considerable reductions in torque pulsation and the higher harmonics of back-electromotive force. Originality/value – This paper presents the optimization method based on the phase field for the design of rotor flux barriers, and proposes a novel interpolation scheme of the magnetic reluctivity.

Phase-field modeling of multicomponent and multiphase flows in microfluidic systems: a review

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Somnath Santra ◽  
Shubhadeep Mandal ◽  
Suman Chakraborty
Keyword(s):  
Phase Field ◽  
Order Parameter ◽  
Multiphase Flows ◽  
Field Method ◽  
Phase Field Method ◽  
Phase Field Modeling ◽  
Field Function ◽  
Content Type ◽  
Forcing Function ◽  
Field Modeling

Purpose The purpose of this study is to perform a detailed review on the numerical modeling of multiphase and multicomponent flows in microfluidic system using phase-field method. The phase-field method is of emerging importance in numerical computation of transport phenomena involving multiple phases and/or components. This method is not only used to model interfacial phenomena typical to multiphase flows encountered in engineering and nature but also turns out to be a promising tool in modeling the dynamics of complex fluid-fluid interfaces encountered in physiological systems such as dynamics of vesicles and red blood cells). Intrinsically, a priori unknown topological evolution of interfaces offers to be the most concerning challenge toward accurate modeling of moving boundary problems. However, the numerical difficulties can be tackled simultaneously with numerical convenience and thermodynamic rigor in the paradigm of the phase field method. Design/methodology/approach The phase-field method replaces the macroscopically sharp interfaces separating the fluids by a diffuse transition layer where the interfacial forces are smoothly distributed. As against the moving mesh methods (Lagrangian) for the explicit tracking of interfaces, the phase-field method implicitly captures the same through the evolution of a phase-field function (Eulerian). In contrast to the deployment of an artificially smoothing function for the interface as used in the volume of a fluid or level set method, however, the phase-field method uses mixing free energy for describing the interface. This needs the consideration of an additional equation for an order parameter. The dynamic evolution of the system (equation for order parameter) can be described by Allen–Cahn or Cahn–Hilliard formulation, which couples with the Navier–Stokes equation with the aid of a forcing function that depends on the chemical potential and the gradient of the order parameter. Findings In this review, first, the authors discuss the broad motivation and the fundamental theoretical foundation associated with phase-field modeling from the perspective of computational microfluidics. They subsequently pinpoint the outstanding numerical challenges, including estimations of the model-free parameters. They outline some numerical examples, including electrohydrodynamic flows, to demonstrate the efficacy of the method. Finally, they pinpoint various emerging issues and futuristic perspectives connecting the phase-field method and computational microfluidics. Originality/value This paper gives unique perspectives to future directions of research on this topic.

scholarly journals К теории формирования крупных трещин в хрупких твердых телах

2021 ◽  
Vol 63 (7) ◽  
pp. 923
Author(s):  
Ю.А. Хон ◽  
П.В. Макаров
Keyword(s):  
Crack Initiation ◽  
Uniform Distribution ◽  
Phase Field ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Field Method ◽  
Phase Field Method ◽  
Spatial And Temporal Scales ◽  
Brittle Solids ◽  
Nonlinear Parabolic

A model of the large cracks formation in brittle solids is formulated taking into account different space-time scales of crack accumulation during deformation. Within the framework of the phase field method, a system of two coupled nonlinear parabolic equations is obtained that describe the deformation of a loaded medium during crack initiation on two spatial and temporal scales. The conditions are found under which the uniform distribution of cracks becomes unstable. The development of instability is accompanied by the formation of large cracks.

Environmental cell studies of deformation and fracture

1990 ◽  
Vol 48 (4) ◽  
pp. 516-517
Author(s):  
H. K. Birnbaum ◽  
I. M. Robertson
Keyword(s):  
National Laboratory ◽  
Argonne National Laboratory ◽  
Damage Threshold ◽  
Chromatic Aberration ◽  
Good Choice ◽  
Point Of View ◽  
Deformation And Fracture ◽  
Environmental Cell ◽  
Gas Molecules ◽  
The University

Studies of the effects of hydrogen environments on the deformation and fracture of fcc, bcc and hep metals and alloys have been carried out in a TEM environmental cell. The initial experiments were performed in the environmental cell of the HVEM facility at Argonne National Laboratory. More recently, a dedicated environmental cell facility has been constructed at the University of Illinois using a JEOL 4000EX and has been used for these studies. In the present paper we will describe the general design features of the JEOL environmental cell and some of the observations we have made on hydrogen effects on deformation and fracture.The JEOL environmental cell is designed to operate at 400 keV and below; in part because of the available accelerating voltage of the microscope and in part because the damage threshold of most materials is below 400 keV. The gas pressure at which chromatic aberration due to electron scattering from the gas molecules becomes excessive does not increase rapidly with with accelerating voltage making 400 keV a good choice from that point of view as well. A series of apertures were placed above and below the cell to control the pressures in various parts of the column.

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