Surface energy fracture

The fracture toughness, a term defined by Irwin (1956, 1960) to characterize brittleness, provides a measure of the conditions required for catastrophic crack propagation in a material (see Section 1.6). One fracture toughness parameter is the surface fracture energy y, defined as one-half G, the critical strain energy release rate above which catastrophic failure occurs. In turn G is related to another convenient toughness parameter, the critical stress intensity factor a measure of the stress field at the crack tip. For fracture of an isotropic material in a plane strain modet (Baer, 1964, p. 946) ... 

Fig. 4.10. The variation of total potential energy and crack surface fracture energy with crack length is illustrated qualitatively for the configuration depicted in Figure 4.9 for the cases of (a) imposed boundary displacement 6 and (b) imposed boundary force P. The results illustrate the stability of crack advance under increasing displacement in case (a) and instability under increasing force in case (b). Adapted from Freund (1990).

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

Gilman [124] and Westwood and Hitch [135] have applied the cleavage technique to a variety of crystals. The salts studied (with cleavage plane and best surface tension value in parentheses) were LiF (100, 340), MgO (100, 1200), CaFa (111, 450), BaFj (111, 280), CaCOa (001, 230), Si (111, 1240), Zn (0001, 105), Fe (3% Si) (100, about 1360), and NaCl (100, 110). Both authors note that their values are in much better agreement with a very simple estimate of surface energy by Bom and Stem in 1919, which used only Coulomb terms and a hard-sphere repulsion. In more recent work, however, Becher and Freiman [126] have reported distinctly higher values of y, the critical fracture energy. ... 

Fig. 25.6. Fibres toughen by pulling out of the fracture surface, absorbing energy os the crock opens.

The practical adhesion, for example fracture energy T, will comprise a surface energy term Fq (VTa or VTcoh) lo vvhich must be added a term xf representing other... 

Surface energies are again important in determining the practical adhesion, F, in the breaking of an adhesive bond. Eqs. 7 to 10 show how the two are related. Emphasis was placed on the important contribution to fracture energy of which represents energy absorbing processes other than those (VTa and Wcoh) directly associated with the actual formation of new surfaces. It must be remembered that... 

If contact with a rough surface is poor, whether as a result of thermodynamic or kinetic factors, voids at the interface are likely to mean that practical adhesion is low. Voids can act as stress concentrators which, especially with a brittle adhesive, lead to low energy dissipation, i/f, and low fracture energy, F. However, it must be recognised that there are circumstances where the stress concentrations resulting from interfacial voids can lead to enhanced plastic deformation of a ductile adhesive and increase fracture energy by an increase in [44]. 

When comparing the nail solution with molecular systems, an additional surface energy term Go, term needs to be added to the fracture energy [1]... 

Wedge test fracture energy (from Eqs. 1 and 2) vs. adherend surface treatment (from ref. [3 )... 

Eqs. 1-5 hold whether failure is interfacial or cohesive within the adhesive. Furthermore, Eq. 5 shows that the reversible work of adhesion directly controls the fracture energy of an adhesive joint, even if failure occurs far from the interface. This is demonstrated in Table 5, which shows the static toughness of a series of wedge test specimens with a range of adherend surface treatments. All of these samples failed cohesively within the resin, yet show a range of static toughness values of over 600%. 

Fig. 21 The cross-section and fracture surface of SA-Tyrannohex. This shows relatively large fracture energy (-2000 J/m2), higher proportional limit (about 120 MPa) and high tensile strength (200 MPa)...

According to a newer theory83), see also84), the fracture energy 7 calculated from Eq. (43) or a similar relation has no connection with true surface energy. Energy is needed not to create a new surface but to deform the solid to its maximum strain. This rule is unquestionably correct for liquids. As was proved by Plateau (1869), a liquid cylinder can be extended by an external force until its length exceeds its circumference then it spontaneously splits into two spherical drops, and the combined area of the drops is smaller than that of the stretched cylinder. Thus, external work is required to stretch the cylinder, not to break it. 

These data, when compared with the surface tension 7S = 312, as determined by Khagabanov41, see Section III. 1, show that fracture energy in many instances is much greater that the energy determined by the shrinkage method. As stated above, an advantage of the new theory of 7 is, that it can account for the unexpectedly high values of this quantity. 

In many instances, 7 increases with temperature. The 7 of pure liquids always decreases when temperature T rises94. Thus the temperature coefficient of 7 is different from what would be expected from the true surface energy on the other hand, positive values oid y /dT agree with the new theory of fracture energy, because e0 of many materials is greater the higher the temperature. 

Many recent publications contain 7 values calculated from Eqs. (43), (52), etc., but this specific fracture energy is not identified with any energy residing in a surface rather it is treated as a material constant whose true nature is not specified. 

Additionally, the fracture energy for a zero extension rate can be defined as the bioadhesion work to the initial surface between the bioadhesive material (in a form of a tablet or disk) and the biological support of a surface Aq, which allows for calculation of the fracture energy (e) using Eq. (8). 

As for the samples prepared without catalyst, the ability for energy absorption after crack propagation decreases strongly as the solvent is removed. This is reflected in Fig. 49, where the load displacement curves of solvent-modifled, semi-porous, and macroporous epoxies prepared with initially 22 wt % cyclohexane (( )=18.5%) are shown. The crack length is the same in all three cases. Therefore the decrease in maximum load is directly proportional to the decrease in Kj. It is also clearly seen that the fracture behavior changes drastically and that the surface under the load-displacement curve, which is used to calculate the fracture energy is signiflcantly lowered. 

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