Energy 365 fracture

Most fracture experiments are conducted under normal loading conditions (mode I) and the fracture properties are described in terms of the strain energy release rate, or crack extension force, Gj. If a steadily increasing load, P, is applied to a joint, a critical value. Pc will be reached at which crack extension will just begin. At this condition, Gi is referred to as the fracture energy, or fracture toughness, G. Various test specimen 

In this equation E is the modulus of the beam arms, b is the thickness of the beam, and m is a geometry factor, determined by the shape of the arms. 

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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. ... 

Table 3. Effect of Fiber Braiding on Fracture Energy of Alumina Fiber/Al—Li Composite ...

Material Initiation energy, f Propagation energy, f Total fracture energy, ... 

An acceptable reconciliation of inherent flaw and fracture energy concepts has not been achieved and provides an area of current study. The two theoretical concepts will be discussed, and several applications in fragment-size prediction will be described. We will make comparisons between the two fragmentation approaches and attempt to identify some conditions which determine when one or the other method applies. 

Note that this product of the spall stress and time is a constant provided F itself is constant. This relation is also useful for estimating fracture energy from dynamic spall data. Also, from (8.30) and (8.31) a relation for the fragment size... 

In the numerical calculations, an elastic-perfectly-plastic ductile rod stretching at a uniform strain rate of e = lO s was treated. A flow stress of 100 MPa and a density of 2700 kg/m were assumed. A one-millimeter square cross section and a fracture energy of = 0.02 J were used. These properties are consistent with the measured behavior of soft aluminim in experimental expanding ring studies of Grady and Benson (1983). Incipient fractures were introduced into the rod randomly in both position and time. Fractures grow... 

TEM has been used to demonstrate that the craze normally fails at the material interface [4-6], In addition the fracture energy calculated from the craze shape tends to agree well with the macroscopic measure of toughness. 

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... 

Usually tj/ is very much larger than Fq. This is why practical fracture energies for adhesive joints are almost always orders of magnitude greater than works of adhesion or cohesion. However, a modest increase in Fq may result in a large increase in adhesion as and Fo are usually coupled. For some mechanically simple systems where is largely associated with viscoelastic loss, a multiplicative relation has been found ... 

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]. 

In recent years there has been a renewed appreciation of potential beneficial effects of roughness on a macroscale. For example Morris and Shanahan worked with sintered steel substrates bonded with a polyurethane adhesive [61]. They observed much higher fracture energy for joints with sintered steel compared with those with fully dense steel, and ascribed this to the mechanical interlocking of polymer within the pores. Extra energy was required to extend and break these polymer fibrils. 

Intuitively the toughness of an interface would be expected to be related to the depth of interpenetration of the chains. Wool [32] argues that the fracture energy, r, for chain disentanglement at least, is proportional to the square of the interface thickness, which, via Eqs. 36 and 37, gives ... 

The coupling of Fg with the other loss terms ilr (cf. Eq. 10) means that even a modest absolute increase in Fg may lead to a much larger increase in fracture energy F. 

Fig. 1. The microscopic enlanglemenl slruciure, e.g, at an interface or in the bulk, is related to the measured macroscopic fracture energy G, via the VP theory of breaking connectivity in the embedded plastic zone (EPZ) at the crack tip. The VP theory determines

Fig. 10. Cantilever beams used to measure the fracture energy of nail pullout from wood. Top plan of beam showing nail heads. Bottom method of loading beams with a load P after [58].

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