Fracture properties of polymers

It is dear that ductile failure occurs both at very short and at very long crack lengths, although the yield zone will be limited in extent in the latter case. The bar fails by brittle fracture at intermediate crack lengths. In this geometry. K increases with u, so there is no possibility that the crack will stop as a result of the tip becoming unloaded as it propagates fracture is catastrophic. 

The intersections of yield and fracture lines mark the transitions between modes.. Most usually, the crack length a is a small fraction of the width of the bar. I he critical crack length is then a (sec Fig. S. 14). As stress is increased from zero, the event which occurs first, depending on the size a of crack present, is 

F irst consider the elfects on Fig. 5.14 of varying the thickness of the bar. We have already noted that plane-strain conditions cause reduced crack-tip plasticity compared to plane stress, and hence ,j (/ and K. C onsequently. if bars of dilferent thicknesses are compared, with incretising B the point of intersection of yield and fracture lines (starred) moves to the left (i.e. li decreases), giving a greater tendency for brittle failure. A limiting value of ti is approached at large thicknesses, where plane strain conditions arc fully developed and the fracture stress is determined by 

Now consider the ell ccts of strain rate. Experiments show that K, - increases with increasing crack speed, as illustrated in Fig. 5.15 (5.N.8), but the resulting shift in fracture stress with increasing strain rate is usually smaller than the increa.se m yield stress. Consequently, u decreases. As a result impact and other forms of rapid loading tend to cause brittle failures. 

A particularly awkward feature of fracture in polymers, as in some other materials, is that under certain conditions small cracks grow very slowly under sub-critical stresses. As a crack grows, /C, increases. Finally, K, may reach its critical value. There is then a sudden brittle fracture, which may occur after the component has been carrying load apparently safely for a long period of lime (even several years). 

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The influence of solvents has been touched on in Sect. 2.3.2. In fact, the influence of environment on crazing and fracture properties of polymers is of major importance in the practical uses of these materials. There are many ways for the environment to induce fracture by means of stress cracking, stress crazing, chain scission, chain crosslinking, etc. Therefore, environmental fracture has been widely studied, specially from the experimental point of view. Reference is a review of environmental cracking of polymers. Most work on environmental crazing has been done in liquid environments - (solvents and non solvents of the material), or high pressure gas environment, near condensation pressure (liquid nitro-... 

Certain important physical properties of polymer glasses depend also on their nonequilibrium character (creep, yield stress, fracture properties). 

Figure 14.18 Shape of the time variation of a fracture property of an initially ductile (a) and initially brittle (b) polymer.

The macroscopic properties such as mechanical behavior of block copolymers or polymer blends depend directly on the relative concentrations of different constituents and their meso-structures. How to predict the exact macroscopic properties of polymer blends or block copolymers with meso-phase separation structures from pure component properties remains a big challenge. Some theoretical efforts have been explored. For example, Buxton et al. found that the deformations and fractures of polymer blends can be described by the... 

Ferry, J. D. Viscoelastic Properties of Polymers, 3rd Ed., John Wiley, New York, 1980, p. 366 Kausch, H. H. Polymer Fracture, Springer-Verlag, Heidelberg, 1978 Phoenix, S, L. Internat. J. Fracture 14, il I (1978)... 

One of the most important subjects of applied polymer science is the understanding of the deformation mechanisms and the fracture properties of semi-crystalline polymers. At the same time, it is one of the most diffictdt to study, and the amount of research in this area is high (see e.g. One of the complications experienced with semi-crystalline polymers stems from the fact that they are composed of crystalline and amorphous phases, arranged in a diversity of microstructures. These are generally... 

Previous work pursued the model analytically, for a linearly elastic [5] (or, later, non-linearly elastic [6]) material with constant thermal properties. The analytical model explained several measured fracture properties of thermoplastics the magnitude of impact fracture toughness and its dependence on impact speed [7] and the absolute magnitude of resistance to rapid crack propagation [8]. Recent results have shown that the impact fracture properties of some amorphous and crosslinked polymers show the same rate dependence [11],... 

It will be shown in Chapter 11 that the correlations developed in this monograph can be combined with other correlations that are found in the literature (preferably with the equations developed by Seitz in the case of thermoplastics, and with the equations of rubber elasticity theory with finite chain extensibility for elastomers), to predict many of the key mechanical properties of polymers. These properties include the elastic (bulk, shear and tensile) moduli as well as the shear yield stress and the brittle fracture stress. In addition, new correlations in terms of connectivity indices will be developed for the molar Rao function and the molar Hartmann function whose importance in our opinion is more of a historical nature. A large amount of the most reliable literature data on the mechanical properties of polymers will also be listed. The observed trends for the mechanical properties of thermosets will also be discussed. Finally, the important and challenging topic of the durability of polymers under mechanical deformation will be addressed, to review the state-of-the-art in this area where the existing modeling tools are of a correlative (rather than truly predictive) nature at this time. 

The effects of orientation on the mechanical properties of polymers at both small and large deformations depend on the mode of orientation, which determines the preferred average chain alignment. For example, the mechanical properties obtained after uniaxial orientation (which biases the chain end-to-end vectors in one favored direction) differ from those obtained by biaxial orientation (which biases these vectors in two favored direction). Furthermore, the mechanical properties obtained after simultaneous equibiaxial orientation (where orientation in the two favored directions is imposed simultaneously, at equal rates, and to equal extents) often differ from those obtained after sequential orientation in the two favored directions, as well as after orientation by different amounts and/or at different rates in those two directions. See Seitz [35] for a review of the effects of uniaxial and biaxial orientation on the fracture of polystyrene, which fails by brittle fracture or crazing, under uniaxial tension and impact. 

The third part of the book deals with the properties and applications of polymers. It starts with a discussion of polymer solution properties through the mechanical properties of polymers and concludes with an overview of the various applications of polymer materials solids. The viscoelastic nature of polymers is also treated. This section also includes a discussion of polymer fracture. The effects of various molecular and environmental factors on mechanical properties are examined. 

Attempts have been made to improve the mechanical properties of polymer-based materials, by adding a percentage of selected filler particles. There has been considerable improvement of properties such as elastic modulus, fracture toughness, flexural strength and hardness with the increase of the filler volume. 

Lohaus, L., Anders, S., 2004. Effects of polymer modification on the mechanical and fracture properties of high and ultra-high strength concrete. In ICPIC 04, 11. International Congress on Polymers in Concrete (2004), p. 183-190, Berlin BAM... 

Li, Y., The investigation of fracture properties of sisal textile reinforced polymers, Acta Mechanica Solida Sinica 17 (2) 95-103 (June 2004). 

Fejes-Kozma, Zs. Karger-Kocsis, J. (1994). Fracture Mechanical Characterization of a Glass Fiber Mat-reinforced Polypropylene by Instrumented Impact Bending. Journal of Reinforced Plastics and Composites, Vol.l3, No.9, pp. 822-834 ISSN 0731-6844 Ferry, J. D. (1980). Viscoelastic Properties of Polymers, 3rd Edition, Wiley Press, ISBN 978-0471048947, New York... 

Kar Karger-Kocsis, J., Gryshchuk, O. Morphology and fracture properties of modified bisphenol A and Novolac type vinyl ester resins. J. Appl. Polym. Sci. 100 (2006) 4012-4022. 

Han Han, Y.-G., Liao, G.-X., Xu, Y.-J., Yu, G.-P., Jian, X.-G. Cure kinetics, phase behaviors, and fracture properties of bismaleimide resin toughened by poly (phthalazinone ether ketone). Polym. Eng. Sci. 46 (2009) 2301-2308. 

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