Quantitative predictions of linear viscoelastic rheological properties of entangled polymers

The “dual constraint” model developed by Mead, Van Dyke et al. is here extended by inclusion of “early-time” contour-length fluctuations and constraint-release Rouse relaxation, and then evaluated by comparing its predictions with literature data for over 50 different linear and star polymers. By combining the reptation model of Doi and Edwards with contour-length fluctuations and constraint release, the model provides a systematic approach to prediction of the rheological properties of polymers. The parameters are taken from the literature and used consistently for linear polymers, star polymers, and their mixtures having the same chemical compositions. In most cases, the predictions of the model appears to agree well with data for monodisperse, bidisperse, and polydisperse linear and star polymers, except at low molecular weights. Received: 23 December 1999 Accepted: 28 March 2000     

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorK _Cand a second parameterT orA ₃,whereT andA ₃are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateG _Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.     

ON KARUSH-KUHN-TUCKER POINTS FOR A SMOOTHING METHOD IN SEMI-INFINITE OPTIMIZATION

We study the smoothing method for the solution of generalized semi-infinite optimiza-tion problems from(O.Stein,G.Still:Solving semi-infinite optimization problems withinterior point techniques,SIAM J.Control Optim.,42(2003),pp.769-788).It is shownthat Karush-Kuhn-Tucker points of the smoothed problems do not necessarily converge toa Karush-Kuhn-Tucker point of the original problem,as could be expected from resultsin(F.Facchinei,H.Jiang,L.Qi:A smoothing method for mathematical programs withequilibrium constraints,Math.Program.,85(1999),pp.107-134).Instead, they mightmerely converge to a Fritz John point.We give,however,different additional assumptionswhich guarantee convergence to Karush-Kuhn-Tucker points.     

最优值函数的方向导数

本文详细介绍了参数非线性规划问题最优值函数的方向导数的存在性、表示形式和有关的发展历史,本文不仅讨论了这一问题的经典结论,还叙述了最近二十年来的新结果。本文最后指出进一步研究的方向。     

A new constraint qualification condition

We introduce a new constraint qualification condition in mathematical programming which encompasses the Mangasarian-Fromovitz's condition and the constant rank condition of Janin. Contrarily to the Mangasarian-Fromovitz's condition, our condition is still satisfied when one translates equalities as double inequalities. It relies on the fact that linearization stability is easier to check with equalities than with inequalities.     

半晶聚对苯二甲酸乙二酯中的受限非晶相

当半晶聚对苯二甲酸乙二酯 (PET)的结晶度 (Xwc)处于一定范围内时 ,其物理老化后在差示扫描量热(DSC)曲线上的玻璃化转变区有吸热双峰出现 .通过对此吸热双峰分别与完全非晶试样和具有相当高Xwc 的半晶试样物理老化后在DSC曲线上出现的吸热单峰的比较 ,表明半晶PET中存在两种性质极为不同的非晶区 ,即自由非晶区和受限非晶区 .动态力学热分析 (DMTA)曲线上显示的损耗正切 (tanδ)双峰进一步证实了这两种不同非晶区的存在 .这两种不同非晶区的产生是由于试样中晶粒对非晶相中高分子链段活动性的不同限制作用所致 .研究发现 ,对于由冷结晶得到的半晶试样来说 ,出现两种不同非晶区所需的Xwc 上下限都随结晶温度 (Tc)的升高而增高 .还发现 ,在物理老化过程中 ,虽然非晶相的总量基本保持不变 ,但部分自由非晶区却逐渐转变为受限非晶区 .上述实验结果很好地符合Struik的“扩展玻璃化转变”模型 .     

Quality assurance and instrumentation

 The quality process for commercial analytical equipment starts with the selection of the vendor. It is recommended that vendors be selected who are recognized as having quality processes in place for instrument design, development, manufacturing, testing, service, and support, for example, ISO 9001 registration. When the instrument arrives in the laboratory, the installation process should follow well-documented procedures. This includes a visual inspection that the instrument is not damaged and checking that the instrument, documentation and accessories such as cables and tubings are complete. Before the instrument is used it should be verified that it meets functional and performance specification. During operation the instruments should be periodically inspected and tested, verified to meet performance, and calibrated. The instrument should be labeled with the calibration status, indicating the dates of the last successful and the next performance verification and calibration. Defective instruments should be removed from the testing area or should at least be labeled as being "out of order." Received 23 August 1995 Accepted 6 September 1995     

The development and application of guidance on equipment qualification of analytical instruments

 This paper describes the development of guidance for the equipment qualification (EQ) of analytical instruments. EQ is a formal process that provides documented evidence that an instrument is fit for its intended purpose and kept in a state of maintenance and calibration consistent with its use.     

Experimental studies of variable selection strategies based on constraint weights

Variable ordering heuristics that sample information before or during search in order to inform subsequent decisions have shown better performance and greater robustness than standard heuristics. One such strategy, the “weighted degree heuristic,” is based on weighting constraints according to their involvement in failure during search. A more recent approach uses “random probing” with restarting to gain information less subject to sampling bias. To date, these approaches have not been carefully analysed experimentally. In the present work, several important findings are presented, including a better delineation of the class of events that is sampled, an analysis of the importance of informed choices at the beginning of search, and a demonstration that random probing identifies sources of global contention effectively even when these are not clearly demarcated. These experiments show how empirical analysis can clarify subtle issues in the analysis of heuristic procedures for difficult search problems.     

Characterisation of flowability of cohesive powders by testing small quantities of weak compacts

Characterisation of flowability of small quantifies of cohesive powders is of great industrial interest, particularly for the pharmaceutical sec tors, where a limited amount of material is available or the material is not easily accessible. In this paper, ball indentation on a powder bed is evaluated for flow charaeterisation of small quantifies of cohesive powders at low levels of consolidation pressures. In parallel, the bulk powder is subjected to the common test method of unconfined direct compression. Analogous to indentation hardness testing, for which the indentation pressure is related to the flow stress, a constraint factor (C) is defined relating the unconfined yield stress and indentation pres sure. The constraint factors for the test powders have been evaluated, enabling an easy method to characterize the flow behaviour of cohesive powders.