Effective Fracture Surface Energy

For bulk specimens, Kic and Gic convey the same information. However, for adhesively bonded structures, such as the specimens described in this report, Kic and Gic differ. E in Equation 3 is the modulus of the adherend (the PMMA) rather than the adhesive, and so Kic is not characteristic solely of the PS layer but of the composite as a whole. The other expression for fracture behavior is the effective fracture surface energy, y. It is related to the fracture energy by... 

TABLE 3 Effective Fracture Surface Energies (in 10"1 N/m) Determined by Cleavage Experiments. Below 15 C the Effective Fracture Surface Energy is Close to y... 

The development of fractnre mechanics aimed at consideration of nonelastic and non-linear effects is of particnlar importance for applications in composite materials in which the internal strncture is actually designed to control the cracking and to increase the effective fracture surface energy. A few non-linear fracture approaches are described below. 

One of the purposes of this paper is to differentiate between surface free energy and fracture surface energy. Thus, several basic principles of fracture mechanics are discussed with reference to the Griffith s energy-b J nce concept and the Irwin-Orowan s plastic-zone concept. We also define several frequently misused terms, e.g., effective fracture surface energy, fracture energy and fracture toughness. Actual values of related parameters are presented to illustrate the applicability of fracture mechanics to the selection of polymers for structural materials. 

In the following sections, we shall discuss three modes of fracture and several fracture criteria. Later, we shall enumerate several major variables affecting effective fracture surface energy, fracture energy and fracture toughness of polymers. 

We now define the effective fracture surface energy, r, as the energy in creating two new surfaces and it s quantity becomes... 

Since the effective fracture surface energy includes chiefly the dissipative component, or the work of plastic deformation, Wj, and a minor component, surface free energy of a solid, 7 we may write... 

IV. PAKAMETERS AFFECTING EFFECTIVE FRACTURE SURFACE ENERGY, AND FRACTURE TOUGHNESS OF POLYMETHYL METHACRYLATE... 

Table I. Effect of Molecular Weight on Effective Fracture Surface Energy and Fracture Toughness of Polymethyl Methacrylate,...

The effect of molecular weight on fracture energy and fracture toughness of polymethyl methacrylate (PMMA) is illustrated with the data calculate< j from the effective fracture surface energy obtained by Berry ... 

The effect of crack speed on fractur to g of PMMA has been tabulated by Marshall and Williams." From their data, we calculated the effective fracture surface energy and the frac-ture2 nergy as shown in Table II. In Fig. 6, fracture toughness ia.shown to increase with the increase in crack speed, a. Williams used the analytic method to relate K and the strain rate at the tip of a propagating crack by the rollowing equa-... 

Effect of Molecular Orientation on Effective Fracture Surface Energy... 

For the study of the effect of orientation on fracture surface nergy, PMMA sheets were biaxially oriented in their planes. Effective fracture surface energies for three... 

The chief problem is that plastic deformation effects at the crack tip usually obscure the process of surface formation. The work needed to propagate a crack is utilized not only to form two surfaces and to bend the cleaved material elastically but also for plastic deformation around the crack tip [16]. The energy needed for this plastic deformation is dissipated as heat. Hence the measured quantity, which is called the effective fracture surface tension yntts- is numerically larger than y. Reliable results can only be obtained at temperatures below 150 K when plasticity practically disappears 121,55]. 

In a brittle polymer, Gjc measures the energy absorbed in forming unit area of fracture surface. Voids reduce the effective area of the fracture surface, and the effective area model predicts that the fracture surface energy G/c(0) of a foam should be related to the vcdume fraction 0 of voids and the fracture surface energy < ic(0) of the matrix by the equation ... 

Fracture Strength. The fracture strength, ac, of composites shows a range of results, but ac cannot exceed that of the matrix. The notch effects and residual stress concentration could lower it further. Whether or not the filler particles behave as precursors of cracks depends on the particle diameter, d. This can be qualitatively understood by the fact that the stored deformation energy, C/, is a function of whereas the fracture surface energy, y, is proportional to d. Applying the Griffith criterion of fracture initiation,... 

R. P. Kusy and M. J. Katz, Effect of molecular weight on the fracture surface energy of poly(meth-ylmethacrylate) in cleavage, 7. Mater. Sci. 11, 1475-1486 (1976). 

Polymer wear is not well understood and may be divided into abrasion, fatigue and roll formation. The effects of fracture surface energy and tearing energy instead of surface free energy on polymer wear are discussed. Surface free energy appears to influence only the polymer transfer. 

The changes in the fracture surface energy with the age of concrete are displayed in Fig. A. These changes resemble those in the compressive strength due to age of the material, an effect well-known in concrete technology. 

The fact that even the rapid deformation of a glassy polymer under concentrated stresses entails considerable local plastic deformation immediately suggests that the molecular properties, which influence yielding and flow, are also effecting Gc and thus the impact strength. The data compiled in Table 9-II reveal this dependency of Gc on temperature, rate of deformation, and molecular properties. A possible relation between molecular relaxation processes and fracture surface energy of polymers has been pointed out in many of the cited references (e.g. [14, 19, 22, 24, 25, 54,63,... 

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