Fracture energy, interfacial

In both derivations of toughening behavior, increases in toughness for whisker-reinforced composites are dependent on the following parameters (1) whisker strength, (2) volume fraction of whiskers, (3) elastic modulus of the composite and whisker, (4) whisker diameter, and (5) interfacial fracture energies. 

Using fracture mechanics and the Griffith s energy criterion, Chow et al. have derived an analytical relation to determine the interfacial fracture energy between a brittle film and a polymeric substrate. 

For each system, the adhesion of the film to the substrate is characterized by an interfacial fracture energy value. The interfacial fracture energy term is calculated using an energetic approach which was proposed for analyzing the loss of adhesion of cracked films from the... 

The interfacial fracture energy associated with adhesion failure can then be calculated taking into account the elastic properties of the film and the defined critical strains. 

Table 4 presents, for each system, the average dimension of the de-adhered areas, the critical strains, and the corresponding interfacial fracture energy. 

Table 4. Decohesion Parameters Average Dimensions of the Decohered Areas (a X b), Critical Strains (e) and Corresponding Interfacial Fracture Energies (y)...

Even if the Al Oj interlayer accelerates the activation of the transverse cracking, it seems to have the opposite effect on adhesion failure. Indeed, we observe for both systems with an Al Oj interlayer (B and E) that the debonding and buckling are delayed. Therefore, the adhesion of the films is improved. The presence of this thermally grown Al Oj interlayer increases the interfacial fracture energy values to about 15 J.m in both systems. Two qualitative explanations can be proposed for the adhesion improvement. First, the Al Oj certainly permits an increase in the number of 0-Si bonds between the interlayer and the film. Second, prior to the... 

Interfacial fracture energy determination associated with the decohesion and buckling process. 

The interfacial fracture energy associated with the debonding of a layer. 

PA-6 / PP-MA interfacial fracture energies between molded plaques as function of temperature / video imaging, ESCA and SEM of fracture surfaces / DSC Bidaux etal., 1996... 

From the energy balance theory of fracture, four equations were produced to explain the failure force F in the different geometries given the same interfacial fracture energy R. The simplest equation was for peeling... 

The key to this discrepancy is that interfacial fracture takes place under conditions very far from thermodynamic reversibility. Associated with the propagation of an interfacial crack are processes that result in substantial energy dissipation and it is this that produces usefully large values of the interfacial fracture energy. This dissipation may be relatively localised, close to the crack tip it may in some cases, however, take place over macroscopic volumes. The latter situation is common for polymer melts and concentrated solutions, as anyone who has pulled their finger out of a pot of glue will attest. 

Figure 7.2. The double cantilever beam test for measuring interfacial fracture energy. Two welded polymer bars are driven apart by a razor blade of width 6 and the length of the crack ahead of the blade is measured.

The situation is more delicate when the two materials have different moduli. In this case, if the beams are of identical thickness the failure will no longer be purely mode I. In these circumstances the crack will deviate from the interface into the material with the lower deformation resistance, leading to additional energy dissipation. In these circumstances the measured values of the interfacial fracture energy will be larger than Gic- This problem can be overcome by using an asymmetrical test, in which the thicknesses of the two beams are unequal. At a particular ratio of thicknesses the measured fracture energy will be a minimum and this may be taken as the true value of G c. 

One might wonder whether it is possible to correlate the interfacial fracture energy of an incompatible polymer pair more precisely to the width of the interface. Such a correlation clearly exists at a qualitative level. For example, polystyrene is substantially less miscible with poly(2-vinyl pyridine) (PVP) than it is with PMMA. This is reflected via equation (4.2.4) in the width of the... 

Brown has shown (Brown 1991b), as will be discussed in much more detail below, that the fracture energy of an interface that fails by the formation and subsequent breakdown of a craze is proportional to the square of the number of effectively entangled chains crossing the interface. Thus we would expect the interfacial fracture energy to vary like... 

Figure 7.9. Interfacial reinforcement of a polystyrene/poly(vinyl pyridine) interface by a high relative molecular mass deuterated styrene-vinyl pyridine block copolymer, with degrees of polymerisation of each block 800 and 870, respectively. Circles (right-hand axis) show the measured interfacial fracture energy as a function of the areal chain density of the block copolymer 2, whereas crosses show the fraction of dPS found on the polystyrene side of the interface after fiacture. The discontinuity in the curves at 2 = 0.03 nm is believed to reflect a transition from failure by chain scission to failure by crazing. After Kramer et al. (1994).

Of maximum design stress of FRP laminate (N/mm ) Gf. interfacial fracture energy (N/mm )... 

Three- and four-point bending methods have been used to evaluate interfacial fracture energy quantitatively and to characterize the interfacial fracture between dissimilar... 

When the specimen is loaded, a crack is initiated from the notch and propagates to the interface as the bending moment increases. For a sufficiently weak interface bond, the crack deflects and propagates symmetrically along the interface at a constant load. The interfacial fracture energy (y) can be determined using ... 

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