Enhanced Strength and Plasticity of CoCrNiAl0.1Si0.1 Medium Entropy Alloy via Deformation Twinning and Microband at Cryogenic Temperature

The synthesis of lightweight yet strong-ductile materials has been an imperative challenge in alloy design. In this study, the CoCrNi-based medium-entropy alloys (MEAs) with added Al and Si were manufactured by vacuum arc melting furnace subsequently followed by cool rolling and anneal process. The mechanical responses of CoCrNiAl0.1Si0.1 MEAs under quasi-static (1 × 10−3 s−1) tensile strength showed that MEAs had an outstanding balance of yield strength, ultimate tensile strength, and elongation. The yield strength, ultimate tensile strength, and elongation were increased from 480 MPa, 900 MPa, and 58% at 298 K to 700 MPa, 1250 MPa, and 72% at 77 K, respectively. Temperature dependencies of the yield strength and strain hardening were investigated to understand the excellent mechanical performance, considering the contribution of lattice distortions, deformation twins, and microbands. Severe lattice distortions were determined to play a predominant role in the temperature-dependent yield stress. The Peierls barrier height increased with decreasing temperature, owing to thermal vibrations causing the effective width of a dislocation core to decrease. Through the thermodynamic formula, the stacking fault energies were calculated to be 14.12 mJ/m2 and 8.32 mJ/m2 at 298 K and 77 K, respectively. In conclusion, the enhanced strength and ductility at cryogenic temperature can be attributed to multiple deformation mechanisms including dislocations, extensive deformation twins, and microbands. The synergistic effect of multiple deformation mechanisms lead to the outstanding mechanical properties of the alloy at room and cryogenic temperature.

Development of a physically-informed neural network interatomic potential for tantalum

Large-scale atomistic simulations of materials heavily rely on interatomic potentials, which predict the system energy and atomic forces. One of the recent developments in the field is constructing interatomic potentials by machine-learning (ML) methods. ML potentials predict the energy and forces by numerical interpolation using a large reference database generated by quantum-mechanical calculations. While high accuracy of interpolation can be achieved, extrapolation to unknown atomic environments is unpredictable. The recently proposed physically-informed neural network (PINN) model significantly improves the transferability by combining a neural network regression with a physics-based bond-order interatomic potential. Here, we demonstrate that general-purpose PINN potentials can be developed for body-centered cubic (BCC) metals. The proposed PINN potential for tantalum reproduces the reference energies within 2.8 meV/atom. It accurately predicts a broad spectrum of physical properties of Ta, including (but not limited to) lattice dynamics, thermal expansion, energies of point and extended defects, the dislocation core structure and the Peierls barrier, the melting temperature, the structure of liquid Ta, and the liquid surface tension. The potential enables large-scale simulations of physical and mechanical behavior of Ta with nearly first-principles accuracy while being orders of magnitude faster. This approach can be readily extended to other BCC metals.

Convergence of solutions of Hamilton–Jacobi equations depending nonlinearly on the unknown function

Motivated by the vanishing contact problem, we study in the present paper the convergence of solutions of Hamilton–Jacobi equations depending nonlinearly on the unknown function. Let H ⁢ ( x , p , u ) {H(x,p,u)} be a continuous Hamiltonian which is strictly increasing in u, and is convex and coercive in p. For each parameter λ > 0 {\lambda>0} , we denote by u λ {u^{\lambda}} the unique viscosity solution of the Hamilton–Jacobi equation H ⁢ ( x , D ⁢ u ⁢ ( x ) , λ ⁢ u ⁢ ( x ) ) = c . H\big{(}x,Du(x),\lambda u(x)\big{)}=c. Under quite general assumptions, we prove that u λ {u^{\lambda}} converges uniformly, as λ tends to zero, to a specific solution of the critical Hamilton–Jacobi equation H ⁢ ( x , D ⁢ u ⁢ ( x ) , 0 ) = c {H(x,Du(x),0)=c} . We also characterize the limit solution in terms of Peierls barrier and Mather measures.

Weak KAM Theory and Forcing Equivalence

This chapter describes weak Kolmogorov-Arnold-Moser (KAM) theory and forcing relation. One change from the standard presentation is that one needs to modify the definition of Tonelli Hamiltonians to allow different periods in the t component. The chapter points out an alternative definition of the alpha function, namely, one can replace the class of minimal measures with the class of closed measures. It then considers a dual setting which corresponds to forward dynamic. It also looks at elementary solutions, static classes, and Peierls barrier. In many parts of the proof, the chapter studies the hyperbolic property of a minimizing orbit, for which the concept of Green bundles is very useful.

Variational construction of positive entropy invariant measures of Lagrangian systems and Arnold diffusion

We develop a variational method for constructing positive entropy invariant measures of Lagrangian systems without assuming transversal intersections of stable and unstable manifolds, and without restrictions to the size of non-integrable perturbations. We apply it to a family of $2\frac{1}{2}$ degrees of freedom a priori unstable Lagrangians, and show that if we assume that there is no topological obstruction to diffusion (precisely formulated in terms of topological non-degeneracy of minima of the Peierls barrier), then there exists a vast family of ‘horseshoes’, such as ‘shadowing’ ergodic positive entropy measures having precisely any closed set of invariant tori in its support. Furthermore, we give bounds on the topological entropy and the ‘drift acceleration’ in any part of a region of instability in terms of a certain extremal value of the Fréchet derivative of the action functional, generalizing the angle of splitting of separatrices. The method of construction is new, and relies on study of formally gradient dynamics of the action (coupled parabolic semilinear partial differential equations on unbounded domains). We apply recently developed techniques of precise control of the local evolution of energy (in this case the Lagrangian action), energy dissipation and flux.

Action-Minimizing Curves for Tonelli Lagrangians

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.