Limiting draw ratios

The limiting draw ratio attained by stretching a polymer is determined, in terms of the rubbery high-elasticity theory, by the equality [124] ... 

More uniform thickness on the component and higher limiting drawing ratios (LDR) are achievable in the process. 

As the results of mechanical tension testing showed, limiting draw ratio of studied carbon plastics is decreased at the increase of carbon fibres volume content in interval 6.0-1.1. In order to obtain quantitative interrelation of X and D according to the equation (2), was made calculation D by the following method. The value of fractal (Hausdorft) dimension df of carbon plastics structure is determined according to the equation [5] ... 

Figure 1. The dependence of limiting draw ratio X on statistical segments number on chain part between clusters for carbon plastics at testing temperatures 293 (1), 313 (2), 333 (3) and 353 K (4)...

In Fig. 2 the comparison experimental 2, and ealculated aecording to the equation (2) TJ values of limiting draw ratio for studied carbon plastics at four testing temperatures are given. As can be seen, between and X enough close correspondence is received and observed scatter of data relationship 1 1 is symmetrical and due to well known statistical character of fracture process. 

Figure 2. The comparison of experimental X and calculated according to the equation (2) J values of limiting draw ratio for carbon plastics. The straight line give relation 1 1. The notation is than one, that in Fig. 1...

FIGURE 5.4 The dependences of limiting draw ratio in ZD on molecular weight of polymer chain par between nodes of cluster network A/j (1) and macromolecular binary hooking s network Af (2) for PAST films, prepared from various solvents [21],... 

There are several methods of limiting draw ratio theoretical estimation and the authors of Ref [21] use the two of them. Within the frameworks of rubber high-elasticity concept the limiting draw ratio is determined as follows [25] ... 

In Fig. 7.5, the experimental and theoretical dependences of limiting draw ratio X on testing temperature T were shown for PC and PAr. The Eq. (5.7) gives X = const, approximately equal to 6.5, that obviously does not correspond to the experimental data. The Eq. (7.8) gives the results, corresponding to experiment by both dependence c(7) course and X absolute values. Some systematic exceeding of X calculated values in comparison with the experimental ones is quite natural and reflects all sorts of defects availability in real samples [39]. 

The structure fractal dimension for B-PES can be calculated according to the Eq. (2.3). Besides, the combination of the Eqs. (2.16) and (7.9) allows to obtain one more formula for limiting draw ratio estimation [43] ... 

In the Ref [49] the two deformation-strength characteristics prediction was carried out strain up to fracture and fracture stress 0. For the value theoretical estimation two methods can be used. The first from them does not include in the calculation of molecular characteristics and, hence, does not take into account their change, in any case, directly [51], This method is based on the cluster model of polymers amorphous state structure notions [ 14], taking into account the order availability, and the limiting draw ratio value in this case is given as follows [51] ... 

In Fig. 14.8, the change of samples limiting draw ratio corresponding to their fracture in mechanical tests, as a function extrusion draw ratio X is shown. As one can seem the X,. increase at X growth is observed. Such behavior Xj is differed from traditionally observed one for oriented polymers, when X increasing decreases X,. owing to molecular chains mobility exhausting [19], Personally, it has been established, that for matrix UHMPE X enhancement from 3 up to 5 is accompanied by reduction from 1.18 uptol.l2[44]. 

FIGURE 14.8 The dependences of limiting draw ratio on extrusion draw ratio X for componors UHMPE-Al (1,3) and UHMPE-bauxite (2, S). - the theoretical dependence calculated according to the Eq. (14.16) [44],... 

The dependence p(A,) and mechanism of fracture knowledge allow to use the fractal analysis methods [47] for theoretical calculation of limiting draw ratio which is coimected with the value p according to the following relationship [47] ... 

The limiting draw ratio at fracture increase at extrusion draw ratio X growth is one from the most interesting features of the amorphous polymers extrudates [26,61]. Such effect was observed and in the case of DF-10 extrudates [2], Let us consider the value theoretical estimation... 

Limiting drawing ratio (LDR) for wall breakage of both quenched and tempered sheet (0.7 mm thick). Specimen numbers had the following average properties (see table on next page). 

Let us demonstrate the examples of dimension D usage for the applied problems settlement. The limiting draw ratio of polymer tension within the framework of high-elasticity theory is determined according to the formula [59] ... 

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