Mode III fracture of an arbitrary oriented crack in two dimensional functionally graded material

In this paper, a two dimensional functionally graded material (2D-FGM) under an anti-plane load with an internal crack is considered. The crack is oriented in an arbitrary direction. The material properties are assumed to vary exponentially in two planar directions. The problem is analyzed and solved by two different methods namely Fourier integral transforms with singular integral equation technique, and then by the finite element method. The effects of crack orientation, material non-homogeneity, and other parameters on the value of stress intensity factor (SIF) are studied. Finally, the obtained results for Mode III stress intensity factor of different methods are compared.     

No directed fractal percolation in zero area

We consider the fractal percolation process on the unit square with fixed decimation parameterN and level-dependent retention parameters {p _k}; that is, for allk ⩾ 1, at thek th stage every retained square of side lengthN ¹⁻ k is partitioned intoN ² congruent subsquares, and each of these is retained with probabilityp _k. independent of all others. We show that if Π_k p _k =0 (i.e., if the area of the limiting set vanishes a.s.), then a.s. the limiting set contains no directed crossings of the unit square (a directed crossing is a path that crosses the unit square from left to right, and moves only up, down, and to the right).     

交联1，4－顺式聚丁二烯的取向结晶

用ＷＡＸＤ和ＳＡＸＳ研究交联１，４－顺式聚丁二烯的取向结晶．结果表明：该试样在拉伸状态时，形成折叠链片晶，而不是伸直链纤维晶．片晶之间不断产生新的片晶，使长周期减小，并且片晶的横向尺寸不断增大，由此导致结晶度增大．     

The influence of short-chain branching on the creep behavior of oriented polyethylene,and its effect on the efficiency of crosslinking by electron irradiation

Studies have been made of the creep behavior of oriented (15:1) polyethylenes containing 0.4 and 1.3 butyl branches per 1000 C atoms. Increasing the branch concentration reduces significantly the creep strain and the equilibrium strain rate. The data have been fitted to an established model comprising two thermally activated processes in parallel, relating to the amorphous network at low stress, and the crystal phase at high stress. Analysis based on this model indicates the similarity between branching, entanglements, and crosslinks on the creep response. The creep behavior of electron-beam-irradiated materials shows that increasing the branch concentration makes the polyethylene more susceptible to mainchain scission, indicated by increased creep flow rates at higher stress, consistent with previous rubber elasticity studies. Irradiation in an acetylene atmosphere with low (< 1 Mrad) doses is shown to reduce the creep rates at all accessible stresses, and this attributed to an increase in crosslinking compared with scission. © 1994 John Wiley & Sons, Inc.     

聚（对羟基苯甲酸－对苯二甲酸双酚A酯）的液晶结构与相变

用ＤＳＣ、ＷＡＸＤ和热台偏光显微镜等研究了热处理和外力作用对标题共聚酯液晶微观结构和序态结构的影响。对出现的双玻璃化转变现象进行了讨论     

On the number of matchings of graphs formed by a graph operation

Let G be a simple graph. Define R(G) to be the graph obtained from G by adding a new vertex e* corresponding to each edge e = (a,b) of G and by joining each new vertex e* to the end vertices a and b of the edge e corresponding to it. In this paper, we prove that the number of matchings of R(G) is completely determined by the degree sequence of vertices of G.     

On nice and injective-nice tournaments

One way of defining an oriented colouring of a directed graph $\overrightarrow{G}$ is as a homomorphism from $\overrightarrow{G}$ to a target directed graph $\overrightarrow{H}$, and an injective oriented colouring of $\overrightarrow{G}$ can be defined as a homomorphism from $\overrightarrow{G}$ to a target directed graph $\overrightarrow{H}$ such that no two in-neighbours of a vertex of $\overrightarrow{G}$ have the same image. Oriented colourings may be constructed using target directed graphs that are nice, as defined by Hell et al. (2001). We extend the work of Hell et al. by considering target graphs that are tournaments, characterizing nice tournaments, and proving that every nice tournament on $n$ vertices is $k$-nice for some $k\le n+2$. We also give a characterization of tournaments that are nice but not injective-nice.