Papers by Keyword: Phase Field

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Authors: Rainer Falkenberg
Abstract: The fracture mechanics assessment of materials exposed to harmful environments requires the understanding of the interaction between the soluted species and the affected mechanical behaviour. With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase field approach is presented with an embrittlement-based coupling mechanism showing the influence on crack patterns and fracture toughness. Within the phase field approach the modeling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies such as curvilinear crack patterns, without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations. The simulation of showcases demonstrates crack initiation and crack propagation aiming for the determination of stress-intensity factors and crack-resistance curves.
Authors: Tansel T. Arif, Rong Shan Qin
Abstract: The phase field method is rapidly becoming the method of choice for simulating the evolution of solid state phase transformations in materials science. Within this area there are transformations primarily concerned with diffusion and those that have a displacive nature. There has been extensive work focussed upon applying the phase field method to diffusive transformations leaving much desired for models that can incorporate displacive transformations. Using the current model, the formation of martensite, which is formed via a displacive transformation, is simulated. The existence of a transformation matrix in the free energy expression along with cubic symmetry operations enables the reproduction of the 24 grain variants of martensite. Furthermore, upon consideration of the chemical free energy term, the model is able to utilise both the displacive and diffusive aspects of bainite formation, reproducing the autocatalytic nucleation process for multiple sheaves using a single phase field variable. Transformation matrices are available for many steels, one of which is used within the model.
Authors: Bartek Wierzba, Marek Danielewski, Andrzej Nowotnik, Jan Sieniawski
Abstract: In this paper we couple the bi-velocity with the phase field method. It deals with: (1) the different mobility of the components in the two-phase zone; (2) nonzero steps of molar volumes for each component from phase to phase and (3) the composition dependent interdiffusion coefficients. The method allows to determine the average stress field during the diffusion process, the kinetics of the reactions and estimate the entropy production. The paper presents the numerical computations of diffusion in th eNiAlCr system. The results can serve as a basis in designing gradient coatings of extended life time.
Authors: Hui Chang, Chun Li Huang, Bin Tang, Rui Hu, Jin Shan Li, Hong Zhong
Abstract: A phase field model has been developed to simulate the dendritic growth of Ti-Ni alloy subjected to a strong magnetic field. The influence of a strong magnetic field on the microstructure morphology and its evolution was successfully investigated by the model. The effect of the magnetic field intensity on the dendritic evolution has been further discussed. The simulating results revealed that with greater magnetic field intensity, the primary dendritic arms and the side branches were easier to coarsen. Besides, the dendritic tip growth rate increased with increasing magnetic field intensity, while the curvature radius had an opposite tendency. The microstructure evolution under a strong magnetic field was also studied combined with solidification thermodynamics theory. The results indicate that, the temperature of equilibrium solidification of Ti-Ni alloy changes with the presence of a strong magnetic field, and the morphology of dendritic grains will be affected eventually.
Authors: Jin Jun Tang, Jian Zhong Jiang, Chun Hua Tang, Li Qun Hou, Liang Jun Fei
Abstract: In this study W was found to have strong effects on solidification structure of the binary alloy. Based 0.5 W0、W0 and 1.5W0 base W0, three conditions with free energy base W equal to 0.5 W0, W0 and 1.5W0 respectively were computed. The results showed that the variation of energy base contributed a lot to the development of side branches of equiaxed dendrite structures, the lower W, the more developed side branches, the higher W, the more restrained side branches. Furthermore, the effects of boundary layer thickness δ on solidification structures were also studied. It is found that when the layer thickness δ is as small as Δx/0.94, computational errors occurred at the base of the dendrite and when the layer thickness δ is as big as Δx/0.54, some irreal phenomena, such as coarsened dendrite trunks and maladjusted side branches, could be caused. Further study on space step Δx showed that bigger space steps made higher computational errors. It is given that the relationships among phase-field perturbation, space step and solidification structure.
Authors: Xun Feng Yuan, Yan Yang
Abstract: The phase field model coupling with the concentration field and flow field is used to simulate the dendrite growth during isothermal solidification of Fe-C alloy in a forced flow. The effects of flow velocity on the dendrite growth are studied. The results indicate that with introducing the forced flow, the upstream secondary dendrite arm space decreases, the downstream secondary dendrite arm space increases. As flow velocity increases, the side branch at the upstream regions become bulky and tilt, the side branch at the downstream regions degenerated and even disappear, the length of upstream dendrite arm increases linearly, the length of downstream dendrite arm decreases parabolically. Meanwhile, the solute concentration of upstream dendrite tip increases slowly first, then decreases, the solute concentration of downstream dendrite tip increases monotonously.
Authors: H. Zapolsky, G. Demange, Rafal Abdank-Kozubski
Abstract: The phase-field method is a very powerful tool to model the phase transformation and microstructural evolution of solids at mesoscopic scale. However, several important phenomena, like defect formation, grain boundary motion, or reconstructive phase transitions require an atomic scale study. Recently an approach called the quasi-particle approach, based on the Atomic Density Function theory was developed to incorporate the atomic-level crystalline structures into standard continuum theory for pure and multicomponent systems. This review focuses on the description of different computational methods used to model microstructural evolution and self-assembly phenomena at mesoscopic and atomistic scales. Various application examples of these methods are also presented.
Authors: Yan Wu, Si Xia, Bernie Ya Ping Zong
Abstract: A phase field model has been established to simulate the grain growth of AZ31 magnesium alloy containing spherical particles with different sizes and contents under realistic spatial-temporal scales. The expression term of second phase particles are added into the local free energy density equation, and the simulated results show that the pinning effect of particles on the grain growth is increased when the contents of particles is increasing, which is consistent with the law of Zener pinning. There is a critical particle size to affect the grain growth in the microstructure. If the size of particles is higher than the critical value, the pinning effect of particles for grain growth will be increased with further decreasing the particle size; however the effect goes opposite if the particle size is lower than the critical value.
Authors: Yong Sheng Li, Yan Zhou Yu, Xiao Lin Cheng, Guang Chen
Abstract: The phase field simulation of interface movement and interdiffusion microstructure in a binary diffusion couples was developed. The diffusion couples with nonequilibrium concentration for single phase or single phase and two-phase including the temperature and mobility effects were studied. It’s shown that the interface movement and the atoms diffusion direction were determined by the magnitude of relative concentration difference between the initial concentration and the equilibrium concentration, the distance of interface movement and interdiffusion flux increases as the temperature or the mobility increasing, and the large mobility makes the particles coarsening faster.
Authors: Ruho Kondo, Yuichi Tadano, Kazuyuki Shizawa
Abstract: A coupled model based on crystal plasticity and phase field theories that express both plastic anisotropy of HCP metals and expansion/shrinkage of twin-bands is proposed in the present study. In this model, the difference of the hardening rate in each slip system is expressed by changing their dislocation mobility as a numerical parameter defined in the crystal plasticity framework. The stress calculated via crystal plasticity analysis becomes to the driving force of multi-phase filed equations that express the evolution of twin bands of several variants, which include both the growth and shrinkage. Solving this equation set, the rate of twinning/detwinning and the mirror-transformed crystal basis in the twinned/detwinned phase are obtained and then, crystal plasticity analysis is carried out again. Using the present model, a uniaxial cyclic loading simulation along [0001] direction on the specimen including two variants of twin-bands is carried out by means of finite element method (FEM). The results show that the detwinning stress decreases with increase of the pre-tensioned strain. This is caused by a residual compression stress resulting from the twin shearing that occurs in the vicinity of two twin boundaries approaching each other.
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