We present a statistical study of serration behaviours in Pd 77.5 Cu 6 Si 16.5 , Ti 41 Zr 25 Be 26 Ag 8 , Zr 41.2 Ti 13.8 Cu 12.5 Ni 10.0 Be 22.5 and Fe 50 Ni 30 P 13 C 7 metallic glasses with different plasticity. The four samples show similar serration patterns in the beginning of yielding, and different patterns during later loading. These results indicate that the shear band initiation process in metallic glasses follow some similar dynamics. And the later serration process follows different dynamics and will lead to different plasticity. Here we interpret these serration behaviours from a perspective of inhomogeneity. The different serration patterns and shear band dynamics could be reasonably understood. The serration pattern of the Fe-based sample suggests that the brittleness of metallic glasses might result from a lower degree of inhomogeneity, and a less tendency of forming shear band intersections. This study might provide new experimental evidences for different microstructures (or inhomogeneity) and dynamic behaviours in metallic glasses with different plasticity.

SUMMARYThe Lagrangian method has become increasingly popular in numerical simulation of free surface problems. In this paper, after a brief review of a recent Lagrangian method, namely the particle finite element method, some issues are discussed and some improvements are made. The least-square finite element method is adopted to simplify the solving of the Navier-Stokes equations. An adaptive time method is derived to obtain suitable time steps. A mass correction procedure is imported to improve the mass conservation in long time calculations and time discretization scheme is adopted to decrease the pressure oscillations during the calculations.Finally, the method is used to simulate a series of examples and the results are compared with the commercial FLOW3D code.

SUMMARYThere are many challenges in the numerical simulation of liquid sloshing in horizontal cylinders and spherical containers using the finite element method of arbitrary Lagrangian-Eulerian (ALE) formulation: tracking the motion of the free surface with the contact points, defining the mesh velocity on the curved wall boundary and updating the computational mesh. In order to keep the contact points slipping along the curved side wall, the shape vector in each time advancement is defined to modify the kinematical boundary conditions on the free surface. A special function is introduced to automatically smooth the nodal velocities on the curved wall boundary based on the liquid nodal velocities. The elliptic partial differential equation with Dirichlet boundary conditions can directly rezone the inner nodal velocities in more than a single freedom. The incremental fractional step method is introduced to solve the finite element liquid equations. The numerical results that stemmed from the algorithm show good agreement with experimental phenomena, which demonstrates that the ALE method provides an efficient computing scheme in moving curved wall boundaries. This method can be extended to 3D cases by improving the technique to compute the shape vector.

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