Microstructure evolution and enhanced fatigue behavior in the Mg-10Li-5Zn-0.5Er alloys micro-alloyed with Yb

In this paper,(0.2-1 wt%)Yb was added to improve the tensile properties and high-cycle fatigue behavior of the as-cast and as-extruded Mg-10Li-5Zn-0.5Er alloys.It is found that Yb mainly affects the mechanical properties of the alloy by changing the grain size,type and morphology of the second phases.Yb mainly exists in the formation of Mg_(2)Yb and Mg-Zn-Yb phases in the metallographic structure.With the addition of Yb,the grains are refined and these Yb-containing phases replace the large-sized MgLiZn phase to be enriched at the grain boundaries.While the addition of excess Yb reduces the number of small-sized MgLiZn phases in the grain,thus reducing the alloys’mechanical performance.After extrusion,the small-sized MgLiZn phase is refined and the number increases,which effectively improves the tensile and fatigue strength of the alloy.The fatigue strength is mainly affected by the number and morphology of the second phase,positively correlated with the strength.Balanced in grain size and number and size of second phases,the extruded alloy with 0.2Yb added exhibits excellent mechanical properties with the yield strength,ultimate tensile strength and elongation of 292 MPa,303 MPa and 11.7%,and an fatigue strength of 130 MPa.

A PRIMAL-DUAL FIXED POINT ALGORITHM FOR MULTI-BLOCK CONVEX MINIMIZATION

We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. Compared with similar works, the parameters in PDFP are easier to choose and are allowed in a relatively larger range. We will extend PDFP to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block prob- lems and illustrates how practical and fully splitting schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier （ADMM） are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be also solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm.