Ligament thickness

The modification of polymer deformation mechanisms in the localised area between mineral particles is another toughening contribution. In our case, the ligament thickness A, is about the same size as the mean particle diameter ... 

In practice, much of the literature still reports notched Izod numbers, but these can be deceptive, especially for materials close to a ductile-brittle transition. Better indicators of real toughness are obtained when samples of different thickness are considered. As one adds more rubber to a plastic, a critical concentration is often found where the toughness increases dramatically. In some cases, e.g., polymers that are capable of shear yielding, this correlates better with the interparticle distance or "ligament thickness" than with any other variable. 

The ductile-to-brittle transition in PA has been studied as a function of (1) materials parameters, including matrix molecular weight (4), type of polyamide (5, 6), and type of rubber (7), and interface (3), and (2) morphological parameters, including rubber concentration (9), particle size (9), ligament thickness (9, 10), use of very small particles (5, 11), and particle distribution (2). When one of these variables is studied, other variables are often changed too. Only in experiments with large series can some idea of the effect of a variable be obtained. 

Ligament Thickness. The ductile-to-brittle transition as measured in notched Izod, notched Charpy, and notched tensile impact tests is discontinuous and is dependent on both rubber concentration and particle size. These two parameters can be combined into a new morphological parameter that governs the ductile-to-brittle transition. The ligament thickness (interparticular distance), which is a function of rubber concentration and particle size,... 

The ligament thickness parameter in PA blends can therefore only apply to high-speed deformation. The meaning of ligament thickness as a parameter for toughening that is only applicable at high speeds is puzzling. 

Rubber particle size or ligament thickness has no effect on the onset of plastic deformation but may affect the extent of plastic deformation (i.e., the maximum draw ratio). A small change in draw ratio is of little consequence under isothermal conditions, but under adiabatic conditions it may result in enough heat generation for local melting and, hence, melt blunting. 

The smaller balls were machined together as one batch of 30 in one operation, while the larger balls were machined in sub-samples of 6-8, For the data evaluation the length of the notch (i.e. the ligament thickness) was determined for each specimen separately. The fillet radius at the notch base and the width of the notch were determined directly on separate specimens, the dimensions of which correspond directly with the thickness and condition of the grinding wheel. Because the fillet radius increases with progressive wear of the wheel requiring the wheel to be dressed after each cut, it was determined for each subsample separately. The relative fillet radius at the notch base was of the order of 0.25 for both types of balls. 

MLT matrix ligament thickness, LE PLLA-b- diblock copolymer, LP PLA-b-PEP diblock copolymer... 

First, that the toughness of polyamides was governed by an interpartiele matrix ligament thickness A defined by... 

Fig. 13.28 The dependence of the notched Izod impact energy of rubber-particle-modified Nylon-66 on matrix ligament thickness. A toughness jump occurs in blends with ligament thickness less than Ac of 3 pm (from Wu (1988) courtesy of Wiley Sons).

Fig. 13.29 A schematic representation of rubber particles surrounded by preferentially ordered crystalline layers of a critical thickness I — A /2 a) blends in which particles do not touch, the ligament thickness A > Ac, and the blends are brittle and (b) blends in which the ligament thicknesses A < Ac, where crystallographically ordered layers of low plastic resistance percolate through the volume, and blends are tough (from Bartczak et al. (1999a) courtesy of Elsevier).

Fig. 13.40 Toughness jumps in Izod fracture energy in CaCOs-particle-modified HOPE blends, at an interparticle ligament thickness A of 0.6 pm, which is again twice the thickness of films crystallized on the surfaces of CaCOs particles (from Bartczak et al. (1999b) courtesy of Elsevier).

Wu, S. (1988) A generalized criterion for rubber toughening the critical matrix ligament thickness, J. Appl. Polymer Sci., 35, 549-561. 

Curing agent (type and concentration) Concentration Matrix ligament thickness -... 

Wu [175-177] proposed that the MLT, i.e., surface-to-surface inter-particle distance is a fundamental parameter. For effective toughening, mean matrix ligament thickness (x) should be less than that of the critical value (xj where brittle-tough transition occurs. The x is independent of rubber volume fraction, particle size and characteristics of the matrix alone at a given test temperature and rate of deformation. For blends with dispersed spherical particles, the x can be related to the rubber particle size and rubber volume fraction < >) by the following equation [177] ... 

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