Energetics and Mechanics of Fracture

Because of the importance of failure phenomena in any consideration of multicomponent polymer systems, a brief review of the energetics and mechanics of fracture follows (Andrews, 1968, 1972 Berry, 1961 Broutman and Kobayashi, 1972 Eirich, 1965 Griffith, 1921 Halpin and Polley, 1967 Hertzberg et al, 1973 Johnson and Radon, 1972 Kambour and Robertson, 1972 Krauss, 1963 Lannon, 1967 Manson and Hertzberg, 1973u Mark, H., 1943,1971 Orowan, 1948 Prevorsek, 1971 Prevorsek and Lyons, 1964 Radon, 1972 Riddell et ai, 1966 Rivlin and Thomas, 1953 Rosen, 1964 Tobolsky and Mark, 1971 Williams, M. L., and DeVries, 1970 Zhurkhov and Tomashevskii, 1966). Specific cases are discussed in Sections 3.2 and 12.1.2. 

Even if the two criteria, energetic and mechanic, respectively, are based on different hypothesis, these ones describe the same phenomenon that of material fracture. Consequently, the following simple relations exist between G and K ... 

Since the first review on the effect of surface energetics on polymer friction and wear published in 197, (0 many new works have appeared. Some of these papers(2- ) are on fracture mechanics. In this paper we shall review our current knowledge about both fracture energetics and surface energetics of polymer wear. First, we discuss wear mechanisms and then emphasize these two aspects related to each wear mechanism. 

Abrasive Wear. Abrasive wear(18) is common for brittle, ductile and elastomeric polymers. Abrasion is the wear by displacement of materials from surfaces in relative motion caused by the presence of hard protruberanees or by the presence of hard particles either between the surfaces or embedded in one of them. As a result, microploughing, microshearing or microcutting can occur. Thus, fracture energetics and contact mechanics are involved in analyzing the wear results. We shall discuss briefly the wear rate with respect to different types of polymers. 

Landis, C.M. 2002b. Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics. Journal of the Mechanics and Physics of Solids 50, 127-152. [56 ] Landis, C M. 2004. Energetically consistent boundary conditions for electromechanical fracture. International Journal of Solids and Structures 41, 6291-6315. 

When fracture occurs out of the linear domain (fracture with yielding), e.g., for highly toughened thermosets or at high temperatures, it is still possible to apply fracture mechanics, with the energetic theory. For instance, the J-integral may be used for bulk materials (Williams, 1984) or Essential Work for Fracture for thin films (Mai and Powell, 1991 Liu and Nairn, 1998). 

Nevertheless, such a fracture-mechanics approach deals only with the initiation stage of the fracture process. In order to consider the whole fracture process (initiation and propagation, as described in the preceding discussion), an energetic approach is proposed here, which allows us to characterize the transitions in a precise and reproducible manner. 

In comparison with metals, most conventional polymers are low in wear resistance. For wear control, we need to understand various wear mechanisms for each polymer system (V). As discussed in a previous paper, for adhesive wear, surface energetics can determine the extent of surface wear. Thus, a low surface energy is preferred to minimize the surface attrition. In addition, a harder polymer is desired to lower the wear rate. For abrasive wear, fracture energetics become important a harder and tougher material should be more wear resistant. 

An electron emitted by either EE mechanism mentioned above can strike a surface and stimulate the emission of an ion. In surface physics, electron-stimulated desorption (ESD) is a widely studied phenomenon that has recently been extended to organic adsorbates (28). The energetics of this mechanism would demand that electrons strike the surface with a minimum energy of several eV, but this is conceivable considering the charging of the fracture surfaces that frequently occurs and the EE energy distributions observed. If this latter mechanism is correct, the flux of EE measured-i-the flux that... 

The energetic criterion, according to which the crack development into a mechanically solicited composite releases a certain amount of elastic energy that is stocked in material and can be evaluated. When its level attains a critical value, G, the cracks will propagate until the material s fracture. The critical energy of propagation represents an intricate characteristic of material, and in the case of brittle fracture, the Griffith criterion can be ex-... 

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