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Kinetics
Published in H. K. D. H. Bhadeshia, Bainite in Steels, 2015
In an ideal scenario, a phase-field model is able to compute quantitative aspects of the evolution of microstructure without explicit intervention, and gives a visual impression of the development of microstructure. The key advantage is that there is no tracking of individual interfaces and that many physical phenomena can be simultaneously modelled within the framework of irreversible thermodynamics. The subject has been widely reviewed11 but a presentation which is intended to be simple without compromising derivations is available for detailed study (Qin and Bhadeshia, 2011). The intention here is to focus on bainite, with only a cursory introduction to the method.
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Published in Adedeji B. Badiru, Vhance V. Valencia, David Liu, Additive Manufacturing Handbook, 2017
Microstructure will be predicted using phase field models, and properties will be predicted using crystal plasticity and dislocation dynamics. The incorporation of process optimization, data mining, and UQ will guide the AM process to yield optimized properties and performance. Results of simulations will be validated against measured material properties and data acquired from real-time in situ process monitors using design of experiments. Integrated in-process sensing, monitoring, and control technologies will be developed to ensure the end-processed material properties and component performance. The material being studied is 316L steel.
A phase-field study on a eutectic high-entropy alloy during solidification
Published in Philosophical Magazine Letters, 2021
Boina Sagar, Krishanu Biswas, Rajdip Mukherjee
Solidification is defined as the transformation of a liquid phase to a crystalline solid phase when the liquid is cooled below the equilibrium melting temperature. It has technological importance in fields such as casting and welding. The idea to develop phase-field models for the solidification process started with the development of a three-dimensional dendrite for an isothermal transformation of a single-component system [23]. Subsequently, a number of models have been developed for various phase transformations in binary alloy systems such as eutectic reactions [6]. A phase-field model describes a microstructure by detailing compositional domains and interfaces with phase-field variables. The free-energy density values required for the model were calculated using the commercially available thermodynamic modelling software, Thermo-Calc version 2017a. In general, there are two types of phase-field variables: conserved variables and non-conserved variables. A three-phase KKS model [24] has been implemented in MOOSE which uses kernels for the phase-field equations as well as the KKS constraint equations [25]. The module in MOOSE which is based on the KKS model, incorporates tilting functions that are used to prevent the formation of a spurious third phase at a two-phase interface [26].
Three-dimensional phase field modeling of progressive failure in aramid short fiber reinforced paper
Published in Mechanics of Advanced Materials and Structures, 2022
Song Zhou, Tong Wang, Xiaodi Wu, Zhi Sun, Yan Li, Filippo Berto
In the recent years, a new kind of fracture phase field model has drawn attentions of scientists [29]. The phase field model has been widely applied to brittle fracture [30, 31], dynamic fracture [32, 33], Viscoelastic fracture [34, 35], cohesive zone model based fracture [36–38], etc. The phase field model is developed from the well-known Francfort-Marigo variational principle [39], and has been widely applied to composite laminates [29, 40]. Alessi et al., proposed a new phase field model for the modeling of failure in lamina [41]. Bleyer et al., proposed a double phase field model to capture the failures of fiber and matrix in lamina [42]. Natarajan et al., proposed an anisotropic phase field model for variable stiffness lamina [43]. In the above phase field models, only simple failure mechanisms in lamina can be handled, and it normally requires dense meshes to account for the rapid changing of the phase field’s gradient when modeling arbitrary cracking processes. However, it results in huge computational expenses since phase field model is nonlinear and extensive iteration is required to find the solution [44]. Ziaei-Rad et al., proposed an explicit phase field model based GPU parallel computation acceleration technique for dynamic failure processes [45]. In comparison with implicit phase field model, explicit phase field model does not require nonlinear iteration, nor the requirement of storing large-sized matrix, thus has higher efficiency. Ren et al., proposed an explicit phase field model with higher efficiency but comparable accuracy with implicit model [33]. Wang et al., proposed an explicit phase field model for quasi-static compression failure process and shearing failure process [46]. Zhang et al., proposed a smeared crack model for composite laminates under microscopic length scale, such that the complicated failure process in composite can be modeled using a unified phase field model [37]. For laminate with multiple layers, Zhang et al., further proposed a phase field-cohesive element combined modeling technique to reduce the computational expense, and thus the method has higher efficiency [44, 47–49]. The explicit phase field models proposed by Zhang et al., show great advantages in comparison with existing phase field models, the models have higher efficiency and are capable of handling large sized models with up to tens of millions of DOFs.