Phase Field: A Methodology to Model Complex Material Behavior

2018 ◽  
pp. 67-103
Author(s):  
José Luiz Boldrini
Keyword(s):  
Phase Field ◽  
Material Behavior ◽  
Complex Material ◽  
Model Complex

Mathematical Modelling of Materials Behavior Under Creep Conditions

2001 ◽  
Vol 54 (2) ◽  
pp. 107-132 ◽  
Author(s):  
J. Betten
Keyword(s):  
Experimental Data ◽  
Mathematical Modelling ◽  
Mechanical Behavior ◽  
Review Article ◽  
Material Behavior ◽  
Experimental Investigations ◽  
Rational Basis ◽  
Complex Material ◽  
Interpolation Methods ◽  
Materials Behavior

This article will provide a short survey of some recent advances in the mathematical modelling of materials behavior under creep conditions. The mechanical behavior of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behavior. This article presents certain principles, methods, and recent successful applications of tensor functions in creep mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. Finally, we have carried out our own experiments to examine the validity of the mathematical modelling. Furthermore, an overview of some important experimental investigations in creep mechanics of other scientists has been provided. There are 243 references cited in this review article.

Two-scale FE–FFT- and phase-field-based computational modeling of bulk microstructural evolution and macroscopic material behavior

2016 ◽  
Vol 305 ◽  
pp. 89-110 ◽  
Author(s):  
Julian Kochmann ◽  
Stephan Wulfinghoff ◽  
Stefanie Reese ◽  
Jaber Rezaei Mianroodi ◽  
Bob Svendsen
Keyword(s):  
Computational Modeling ◽  
Microstructural Evolution ◽  
Phase Field ◽  
Material Behavior

Computer Simulation of Phase Decomposition in Magnetic Materials Based on the Phase-Field Method

2005 ◽  
Vol 237-240 ◽  
pp. 593-602
Author(s):  
Toshiyuki Koyama
Keyword(s):  
Magnetic Materials ◽  
Phase Field ◽  
Materials Science ◽  
Field Method ◽  
Phase Field Method ◽  
Microstructure Changes ◽  
Diffusion Controlled ◽  
Model Complex ◽  
Field Methodology ◽  
Error Testing

During the last decade, the phase-field method has emerged across many fields in materials science as a powerful tool to simulate and predict complex microstructure evolutions. Since phase-field methodology has an ability to model complex microstructure changes quantitatively, it will be possible to search for the most desirable microstructure by using this method as a design simulation, i.e. through computer trial-and-error testing. In order to establish this methodology, the flexible quantitative modeling for various types of complex microstructure changes using the phase-field method must first be needed. In this study, as the typical examples for the modeling of the complex microstructure changes using phase-field method, recent simulation results for the diffusion controlled phase transformations and microstructure developments in magnetic materials are demonstrated.

scholarly journals Three Dimensional CS-FEM Phase-Field Modeling Technique for Brittle Fracture in Elastic Solids

2018 ◽  
Vol 8 (12) ◽  
pp. 2488 ◽  
Author(s):  
Sauradeep Bhowmick ◽  
Gui-Rong Liu
Keyword(s):  
Brittle Fracture ◽  
Phase Field ◽  
Three Dimensional ◽  
Coupled System ◽  
Field Method ◽  
Three Dimensions ◽  
Modeling Technique ◽  
Phase Field Method ◽  
Elastic Solids ◽  
Model Complex

The cell based smoothed finite element method (CS-FEM) was integrated with the phase-field technique to model brittle fracture in 3D elastic solids. The CS-FEM was used to model the mechanics behavior and the phase-field method was used for diffuse fracture modeling technique where the damage in a system was quantified by a scalar variable. The integrated CS-FEM phase-field approach provides an efficient technique to model complex crack topologies in three dimensions. The detailed formulation of our combined method is provided. It was implemented in the commercial software ABAQUS using its user-element (UEL) and user-material (UMAT) subroutines. The coupled system of equations were solved in a staggered fashion using the in-built non-linear Newton–Raphson solver in ABAQUS. Eight node hexahedral (H8) elements with eight smoothing domains were coded in CS-FEM. Several representative numerical examples are presented to demonstrate the capability of the method. We also discuss some of its limitations.

scholarly journals Shock-reshock of zirconium to explore the effect of microstructure on the alpha-omega phase transformation

2021 ◽  
Vol 250 ◽  
pp. 03010
Author(s):  
Benjamin M. Morrow ◽  
Juan P. Escobedo-Diaz ◽  
David R. Jones ◽  
Carl P. Trujillo ◽  
Daniel T. Martinez ◽  
...  
Keyword(s):  
Phase Transformation ◽  
Phase Field ◽  
Electron Backscatter Diffraction ◽  
Peak Stress ◽  
Relative Activity ◽  
Material Behavior ◽  
Omega Phase ◽  
Orientation Relationships ◽  
Final Microstructure ◽  
Backscatter Diffraction

Phase transformations play an important role in the mechanical behavior of materials subjected to extreme loading conditions. A series of shock-reshock experiments were fielded to determine whether the phase transitions in materials are significantly enhanced or inhibited by preexisting microstructural features. Polycrystalline zirconium samples were shock loaded using gas-gun plate impact and soft recovered to examine microstructure using electron backscatter diffraction (EBSD). Drive conditions were varied to study the (hcp) alpha to (hexagonal) omega solidsolid phase transformation. Recovered samples were then subjected to a second shock loading event to determine the change in material behavior as a function of pre-shock microstructure. Crystallography of phase fragments in the final microstructure showed that prior twinning (formed during the shock to a peak stress below the transition threshold) appeared to suppress omega formation/retention after reshock. Conversely, when a material was initially shocked into the omega phase field, retained-omega was not found to have a large impact on subsequent omega formation during reshock. This suggests that nucleation and growth of omega phase are important processes, and the relative activity of nucleation vs. growth processes is modified by a pre-existing substructure. Additionally, orientation relationships reveal a reverse transformation pathway (omega to alpha) dominates the final microstructure, suggesting significant grain growth in the omega phase field is possible even for dynamic timescales.

Sign in / Sign up

Export Citation Format

Share Document