Unified Curve

R5) is consistent with OH having a narrower spatial distribution than The unified curve... 

R5) is consistent with OH having a narrower spatial distribution than e g. The unified curve for G(H2)/f(H2) and G(H202)/f(H202) in Fig. 1 may therefore be a somewhat fortuitous result of the spatial distributions of the radicals and the rate constants of their reactions with one another. If, as proposed by LaVerne and Pimblott [17], process 1(b) is an important contributor to g(H2), then there should also be a significant initial yield of H2O2 resulting from the reaction of 0 ( D) with H2O, but there is no experimental evidence for such a yield. 

New local fracture approach called the Unified Curve has been developed that has similarities to the Master Curve... 

The Russian predictive embrittlement method is based primarily on test reactor data and utilizes the shift in CVN impact energy properties essentially at the 47 J temperature (PNAE, 1989). The effects of Cu, P and O (E > 0.5 MeV) are included in the method. A new local approach called the Unified Curve (similar to the Master Curve method) for assessing vessel integrity has recently has been added for structural analysis purposes (Margolin et ai, 2007). Additionally, an IAEA activity on embrittlement prediction for WWER-440 RPVs was completed (IAEA, 2005), with the published IAEA report providing recommended guidelines based on a larger database than previously available. 

Figure 4.9 shows a plot of viscosity versus shear rate at three different temperatures, 17S°C, 190°C, and 20S°C, for one grade of LDPE, namely, 24FS040 with a MFI of 4 ( 190°C and 2.16 k. In order to obtain a unified master curve of 1) X MFI versus y/MFI, it is essential to obtain MFI values at different temperatures but the same loading conditions, namely, 17S°C and 2.16 kg as well as 205°C and 2.16 kg. The equation discussed in Sec. 4.2.4 is used to obtain these effective MFI values at 17S°C and 20S°C, knowing the MFI at 190°C. Using the appropriate MFI values with each of the curves in Fig. 4.9, a plot of 7) X MFI versus -y/MFI was generated as shown in Fig. 4.10. This unified curve is then temperature independent but dependent only on the MFI testing load condition of 2.16 kg. When a plot of X MFI versus y/MFI is to be generated at a different load condition, Eq. (4.9) is used for obtaining the MFI at the required load condition.

The master rheogram for SBS is given in Fig. 4.31. This unified curve has been produced [77] using limited data from a single source [39]. The 27 data points included have been taken from viscosity versus shear rate curve spanning 6 temperatures between 110°C and 210 C and covering a shear-rate range from 0.1 to 1000/s (Table B2 of Appendix B). 

The master rheogram for ethylene-vinyl acetate (EVA) is shown in Fig. 4.34. This unified curve was obtained [77] from limited data on just one grade of EVA, namely, ALAIHON EA A 3185. The viscosity versus shear rate data were available [40,41] at seven temperatures between 60°C and 125°C, covering a shear-rate range from 0.01 to 500/s (Table B2 of ipendix B). 

Figure 5.4 shows a plot of t) X MFI versus y/MFI for four LDPE melts. In the low-shear-r jegion of 10 -10/s, the coalescence is rather poor. A plot of (q X MFI)/(Af,/M ,) versus (W,/JI ) ( V/MFI) for the same four LDPE melts is found to give a unified curve as shown in Fig. 5.5. Figures 5.6 and 5.7 show...

Normal stress difference data are not as extensively avaUable as the shear viscosity data. The plots, therefore, do not contain the abundance of data as in the unified curves for shear viscosity. The approach here was to establish the curve profile more than prove the validity of the unifying technique which, in the case of shear viscosity, has been conclusively shown to hold and the logic for the development of the unified curve in the case of the elastic material function runs on parallel lines. The unified curves provide the easiest way of getting an estimate of the elasticity of polymer melts simply through knowWge of their MFl. 

It has been shown in Gupter 4 that a unified curve, indqiendent of temperature and grade for each generic type of polymer, can be generated by plotting t) X MFI versus y/MFL Based on Eq. (S3), it is natural to expect that t) versus curves could also be coalesced by using MFI as a convenient shift factor. Thus, i X MFI vmsus [Pg.191]

In Giapters 4 and S, a number of unified curves have been presented for a variety of polymers of different generic types. These curves can be readily used for generating specific matraial parameter versus shear rate curves at any required tenqierature of interest merely fiom the knowled of the MFI at that temperature. As ASTM test conditions [1 ] have to be conferred to during MFI test measurements, the MFI at the ASTM test tmnperature needs to be convoted to the MFI value at the required temperature of interest. This could be done through the use of the modified Anfaenhis-type Eq. (4.14) or the modified (Williams-Landel-Ferry) WLF-type Eq. (4.15) described in Sec. 4.2.4. 

If the loading condition of the obtained MFI does not correspond to that in the unified curve, then a new MFI value ought to be calculated using Eq. (4.9) given in Sec. 4.2.2. 

The plot of material parameter versus shear rate under die requited conditions can then be readily obtained by substituting the correct value of MFI in the unified curve. 

In order to simplify the final step in generating the required material parameter versus shear rate curves from by the above procedure, appropriate rheological models have been suggested for fitting the unified curves. 

Hguro 6.1 Evaluation of Genml Rheological model constants for unified curves of viscoitity versus ear rate. 

Tlie liquid-crystalline hydroxy benzoic acid/poly(ethylene terephthalate) (HBA/PET) copolymer master rheogram given in Fig. 4.37, however, is not amenable to a curve fit by any of the models discussed above. The reason is because the shape of the unified curve for this liquid-crystalline copolymer is radically different from those obtained for other thermoplastics. There are two shear-thinning regions separated by a short plateau as can be seen in Fig. 4.37. A new equation of the following form is thus suggested [12] ... 

A plot of Ni versus (y/MFI) on a log-log scale would suffice to obtain a unified curve when various grades of polymers of a generic type all have broad and regular molecular-weight distributions or, alternatively, all have narrow mo-lecular-weigiht distributions. If a unique curve is to be obtained which is independent of the width of molecular-weight distribution, n a correction term is to be included so that a plot of Ni versus has... 

Normal stress difference data are not as extensively available nor easily determinable as shear viscosity data. Unified curves predicted through Eqs. (6.11) or (6.14) thus provide the easiest method of getting a reasonable estimate of the elasticity of polymer melts simply through the knowledge of the MFI. 

Shenoy, A. V. and Saini, D. R., Rheological models for unified curves for simplified design calculations in polymer processing, RheoL Acta, 23, 368-377 (1984). 

Figure 8.3 Unified curve showing the variation of the compaction force (F) with the rate of plate separation (-Ai).

In the case of extensional viscosity, unified curves have been presented for a limited number of cases and the data used for coalescence are also-limited. Because of the difficulties in measurement of extensional viscosity, the reliability of the data is often questionable. Because the original data cannot be as trustworthy as in the case of shear viscosity or complex viscoaty data, the master curves of extensional data should be looked at in the same light. In the case dt shear viscosify, the master rheograms for the filled polymers have been shown to be the same as those for the unfilled system. is, of course, true in the medium to high shear-rate region. In the low-shear-rate region, however, the effects of yield stress would dominate and the uniqueness of the curve will be... 

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