Development of multi-phase-field crack model for crack propagation in polycrystal

2014 ◽  
Vol 03 (02) ◽  
pp. 1450009 ◽  
Author(s):  
Kento Oshima ◽  
Tomohiro Takaki ◽  
Mayu Muramatsu
Keyword(s):  
Grain Boundary ◽  
Crack Propagation ◽  
Phase Field ◽  
Crack Surface ◽  
Crack Path ◽  
Boundary Energy ◽  
Crack Model ◽  
Grain Boundary Energy ◽  
Basic Characteristics ◽  
Multi Phase

It is vitally important to ensure the safety of brittle materials. Therefore, it is essential to deeply understand the interaction of the material's microstructure and crack propagation. In this study, we constructed a multi-phase-field crack model which can express crack propagation in polycrystal. To evaluate the basic characteristics of the developed model, we performed two-dimensional crack propagation simulations in a bicrystal where a crack enters an inclined grain boundary by changing the ratio of the grain boundary energy to the crack surface energy. As a result, it is confirmed that the model can reasonably determine the crack path, depending on those conditions. Furthermore, by performing crack propagation simulations in a polycrystal, it is concluded that the model can properly express transgranular and intergranular cracks.

Fractional phase-field crystal modelling: analysis, approximation and pattern formation

2020 ◽  
Vol 85 (2) ◽  
pp. 231-262
Author(s):  
Mark Ainsworth ◽  
Zhiping Mao
Keyword(s):  
Pattern Formation ◽  
Grain Boundary ◽  
Fractional Order ◽  
Phase Field ◽  
Boundary Energy ◽  
Classical Case ◽  
Experimental Measurements ◽  
Grain Boundary Energy ◽  
Material Interface ◽  
Phase Field Crystal

Abstract We consider a fractional phase-field crystal (FPFC) model in which the classical Swift–Hohenberg equation (SHE) is replaced by a fractional order Swift–Hohenberg equation (FSHE) that reduces to the classical case when the fractional order $\beta =1$. It is found that choosing the value of $\beta $ appropriately leads to FSHE giving a markedly superior fit to experimental measurements of the structure factor than obtained using the SHE ($\beta =1$) for a number of crystalline materials. The improved fit to the data provided by the fractional partial differential equation prompts our investigation of a FPFC model based on the fractional free energy functional. It is shown that the FSHE is well-posed and exhibits the same type of pattern formation behaviour as the SHE, which is crucial for the success of the PFC model, independently of the fractional exponent $\beta $. This means that the FPFC model inherits the early successes of the FPC model such as physically realistic predictions of the phase diagram etc. and, therefore, provides a viable alternative to the classical PFC model. While the salient features of PFC and FPFC are identical, we expect more subtle features to differ. The prediction of grain boundary energy arising from a mismatch in orientation across a material interface is another notable success of the PFC model. The grain boundary energy can be evaluated numerically from the PFC model and compared with experimental measurements. The grain boundary energy is a derived quantity and is more sensitive to the nuances of the model. We compare the predictions obtained using the PFC and FPFC models with experimental observations of the grain boundary energy for several materials. It is observed that the FPFC model gives superior agreement with the experimental observation than those obtained using the classical PFC model, especially when the mismatch in orientation becomes larger.

Phase Field Model of Grain Growth Using Quaternions

2012 ◽  
Vol 715-716 ◽  
pp. 776-781
Author(s):  
Santidan Biswas ◽  
Indradev Samajdar ◽  
Arunansu Haldar ◽  
Anirban Sain
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Boundary Energy ◽  
Scaling Law ◽  
Phase Field Model ◽  
Polycrystalline Sample ◽  
Mechanical Processing ◽  
Grain Boundary Energy ◽  
Grain Orientations

The microstructure of a material determines its mechanical properties. Since microstructure can be tailored by thermo-mechanical processing of the metal, it is important to understand how the microstructure evolves under thermo-mechanical processing. We have constructed a phase field formalism to study recrystallization and grain growth in polycrystalline material. A unique feature of our model is that the Euler Angles (φ1,φ,φ2), obtained from Electron Back Scattered Diffraction (EBSD) data of a polycrystalline sample can be taken as an input to our model. In our model, the grain orientations at discrete grid points are represented by a non-conserved vector field, namely a quaternion. The free energy used for the evolution of the local orientations contains bulk energy for various preferred grain types and grain boundary energy. The grain orientations evolve in time following a Langevin dynamics. So far we have established that the rate of grain growth follows the usual L ~ t1/2scaling law when the grain boundary energy is independent of the misorientation angle between neighboring grains. Work on other aspects of this model is in progress.

Phase Field Simulation for Abnormal Growth of Grains by the In-Homogeneous Grain Boundary Energy

2019 ◽  
Vol 944 ◽  
pp. 747-752
Author(s):  
Yan Wu ◽  
Er Wei Qin ◽  
Qing Yu
Keyword(s):  
Magnesium Alloy ◽  
Grain Boundary ◽  
Phase Field ◽  
Boundary Energy ◽  
Annealing Treatment ◽  
Grain Boundary Energy ◽  
Abnormal Growth ◽  
Phase Field Models ◽  
Field Simulation ◽  
Az31 Mg Alloy

The phase field models have been built to study the influence of the nonuniform grain boundary energy for abnormal growth of grains in the AZ31 magnesium alloy in the real time and space. The simulated results show that if the grains of a certain orientation with low grain boundary energy in the AZ31 Mg alloy, abnormal grain growth will occur after annealing treatment, and only if the local low grain boundary energy is less than 0.98σ0, can the certain grains grow abnormally in the microstructure.

Effect of Grain Boundary Energy in Recrystallization Simulation by Phase Field Method

2020 ◽  
Vol 993 ◽  
pp. 953-958
Author(s):  
Yan Wu ◽  
Ren Chuang Yan ◽  
Er Wei Qin ◽  
Wei Dong Chen
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Boundary Energy ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Grain Boundary Energy ◽  
Average Grain Size

In this paper, the effect of grain boundary energy in AZ31 Mg alloy with multi-order parameters phenomenological phase field model has been discussed during the progress of recrystallization. The average grain size of the recrystallization grain at a certain temperature and a certain restored energy but various grain boundary energies have been studied, and the simulated results show that the larger the grain boundary energy is, the larger the average grain size will be, and the speed of grain growth will increase with the increase of grain boundary energy. Additionally, temperature will also increase the grain growth rate.

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