Computational study on microstructure evolution and magnetic property of laser additively manufactured magnetic materials

Additive manufacturing (AM) offers an unprecedented opportunity for the quick production of complex shaped parts directly from a powder precursor. But its application to functional materials in general and magnetic materials in particular is still at the very beginning. Here we present the first attempt to computationally study the microstructure evolution and magnetic properties of magnetic materials (e.g. Fe-Ni alloys) processed by selective laser melting (SLM). SLM process induced thermal history and thus the residual stress distribution in Fe-Ni alloys are calculated by finite element analysis (FEA). The evolution and distribution of the $\gamma$-Fe-Ni and FeNi$_3$ phase fractions were predicted by using the temperature information from FEA and the output from CALculation of PHAse Diagrams (CALPHAD). Based on the relation between residual stress and magnetoelastic energy, magnetic properties of SLM processed Fe-Ni alloys (magnetic coercivity, remanent magnetization, and magnetic domain structure) are examined by micromagnetic simulations. The calculated coercivity is found to be in line with the experimentally measured values of SLM-processed Fe-Ni alloys. This computation study demonstrates a feasible approach for the simulation of additively manufactured magnetic materials by integrating FEA, CALPHAD, and micromagnetics.Comment: 20 pages, 15 figure

A phase-field model of relaxor ferroelectrics based on random field theory

A mechanically coupled phase-field model is proposed for the first time to simulate the peculiar behavior of relaxor ferroelectrics. Based on the random field theory for relaxors, local random fields are introduced to characterize the effect of chemical disorder. This generic model is developed from a thermodynamic framework and the microforce theory and is implemented by a nonlinear finite element method. Simulation results show that the model can reproduce relaxor features, such as domain miniaturization, small remnant polarization and large piezoelectric response. In particular, the influence of random field strength on these features are revealed. Simulation results on domain structure and hysteresis behavior are discussed and compared with related experimental results.Comment: 8 figure

Multiscale examination of strain effects in Nd-Fe-B permanent magnets

We have performed a combined first-principles and micromagnetic study on the strain effects in Nd-Fe-B magnets. First-principles calculations on Nd2Fe14B reveal that the magnetocrystalline anisotropy (K) is insensitive to the deformation along c axis and the ab in-plane shrinkage is responsible for the K reduction. The predicted K is more sensitive to the lattice deformation than what the previous phenomenological model suggests. The biaxial and triaxial stress states have a greater impact on K. Negative K occurs in a much wider strain range in the ab biaxial stress state. Micromagnetic simulations of Nd-Fe-B magnets using first-principles results show that a 3-4% local strain in a 2-nm-wide region near the interface around the grain boundaries and triple junctions leads to a negative local K and thus decreases the coercivity by ~60%. The local ab biaxial stress state is more likely to induce a large loss of coercivity. In addition to the local stress states and strain levels themselves, the shape of the interfaces and the intergranular phases also makes a difference in determining the coercivity. Smoothing the edge and reducing the sharp angle of the triple regions in Nd-Fe-B magnets would be favorable for a coercivity enhancement.Comment: 9 figure

Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

Phase-field modeling of paramagnetic austenite-ferromagnetic martensite transformation coupled with mechanics and micromagnetics

A three-dimensional phase-field model is proposed for simulating the magnetic martensitic phase transformation. The model considers a paramagnetic cubic austenite to ferromagnetic tetragonal martensite transition, as it occurs in magnetic Heusler alloys like Ni2 MnGa, and is based on a Landau 2-3-4 polynomial with temperature dependent coefficients. The paramagnetic-ferromagnetic transition is recaptured by interpolating the micromagnetic energy as a function of the order parameter for the ferroelastic domains. The model is numerically implemented in real space by finite element (FE) method. FE simulations in the martensitic state show that the model is capable to correctly recapture the ferroelastic and -magnetic microstructures, as well as the influence of external stimuli. Simulation results indicate that the paramagnetic austenite to ferromagnetic martensite transition shifts towards higher temperatures when a magnetic field or compressive stress is applied. The dependence of the phase transition temperature shift on the strength of the external stimulus is uncovered as well. Simulation of the phase transition in magnetocaloric materials is of high interest for the development of energy-efficient magnetocaloric cooling devices

Modeling and simulation of sintering process across scales

Sintering, as a thermal process at elevated temperature below the melting point, is widely used to bond contacting particles into engineering products such as ceramics, metals, polymers, and cemented carbides. Modelling and simulation as important complement to experiments are essential for understanding the sintering mechanisms and for the optimization and design of sintering process. We share in this article a state-to-the-art review on the major methods and models for the simulation of sintering process at various length scales. It starts with molecular dynamics simulations deciphering atomistic diffusion process, and then moves to microstructure-level approaches such as discrete element method, Monte--Carlo method, and phase-field models, which can reveal subtle mechanisms like grain coalescence, grain rotation, densification, grain coarsening, etc. Phenomenological/empirical models on the macroscopic scales for estimating densification, porosity and average grain size are also summarized. The features, merits, drawbacks, and applicability of these models and simulation technologies are expounded. In particular, the latest progress on the modelling and simulation of selective and direct-metal laser sintering based additive manufacturing is also reviewed. Finally, a summary and concluding remarks on the challenges and opportunities are given for the modelling and simulations of sintering process.Comment: 45 pages, 38 figure