Fracture strain

Lastly, assuming that the rod fragments into pieces of nominal length given by (8.48), a dynamic fracture strain criterion, Sf = e , depending on the prob-... 

Note that as shown below, this must be the matrix stress at the fibre fracture strain. 

As shown in Fig. 3.4 stress-strain tests on uniaxially aligned fibre composites show that their behaviour lies somewhere between that of the fibres and that of the matrix. In regard to the strength of the composite, Ocu, the rule of mixtures has to be modified to relate to the matrix stress, o at the fracture strain of the fibres rather than the ultimate tensile strength, o u for the matrix. 

This is because, with brittle fibres, failure of the composite will occur when the fibres reach their fracture strain. At this point the matrix is subjected to the full applied load, which it is unable to sustain. 

By using diamide units, melt phasing can be avoided and at the same time the crystallization rate is rapid. Surprisingly, diese segmented copolymers widi diamide units not only crystallize quickly but also have a high fracture strain... 

Another measure is the true fracture strain which is expressed in terms of the true reduction in area at fracture and is given by, = q = In Aq/A(, where the subscript f refers to fracture. 

Impurities and flaws have a detrimental effect on the fibre strength. Due to shear stress concentrations at structural irregularities and impurities, the ultimate debonding stress r0 ( rm) or the critical fracture strain / may be exceeded locally far sooner than in perfectly ordered domains. Thus, during the fracture process of real fibres the debonding from neighbouring chains occurs preferably in the most disoriented domains and presumably near impurities. At the same time, however, the chains in the rest of the fibre are kept under strain but remain bonded together up to fracture. 

The strength of a fibre is not only a function of the test length, but also of the testing time and the temperature. It is shown that the introduction of a fracture criterion, which states that the total shear deformation in a creep experiment is bounded to a maximum value, explains the well-known Coleman relation as well as the relation between creep fracture stress and creep fracture strain. Moreover, it explains why highly oriented fibres have a longer lifetime than less oriented fibres of the same polymer, assuming that all other parameters stay the same. 

Brocklehurst [37] has written an exhaustive review of the early work (prior to 1977) on fracture in polycrystalline graphite. Much of this work focused on the fracture behavior of nuclear graphites. In most investigations considered, conventional fracture mechanics tests and analysis were performed for macroscopic cracks. LEFM provided an adequate criterion for failure. Additionally, results on work of fracture, strain energy release rate, and fatigue crack propagation were reported. 

AGS may be expressed as proportional to compressive yield stress), yt (fracture strain), the plastic zone size, and the square of the concentration factor, K. The influence of hydrostatic pressure was taken into account with a modified von Mises criterion (Chapter 12). 

Fig. 12. Dependence of zinc single-crystal fracture strain on temperature and environment (a) air,(b) mercury (after Rozhanskii et al. - ref. 15)...

Figure 11.9. Effect of fat content on fracture stress (A), fracture strain (B) and firmness (C) of Cheddar cheeses aged for 120 (O), 180 (A,) or 225 (A) days. Broken line indicates that the sample did not fracture on compression at the early ripening times (drawn from data of Fenelon and Guinee, 1999 Guinee et al., 2000a).

An alternative mechanism for the observed high fracture strain may be the reduction in surface imperfections for the gradient polymers. The surfaces of these materials must be more resistent to fracture because of the relatively high loading of rubbery phases. Thus, under stress they are likely to craze or crack, which would have initiated fracture for the sample as a whole. The validity of either mechanism, however, must await verification. 

In conclusion, we find that gradient polymers produced by diffusion polymerization generally show enhanced fracture strain, while retaining their plasticlike properties. This behavior appears to be a consequence... 

For brittle materials the stress-strain curves are almost linear up to the fracture point and the fracture strain is small, of the order of a few percentages. Figs. 13.74 and 13.75 show the tensile strain and flexural strength as functions of temperature for PMMA. At 10 °C the fracture strain increases, which points to a transition to ductile behaviour. The brittle... 

Representative stress-strain curves for the various materials, rates, and temperatures are shown in Figure 6. Tests were replicated from two to five times in general these replications had very high reproducibility in yield values. Values at fracture, especially fracture strain, showed much more scatter. Accordingly the yield values of the unmodified material, which are really fracture values, also contained more scatter. (In the plots of yield values to follow, the data symbols lie over all of the replication values unless the values are sufficiently spaced to permit another symbol.)... 

Consider now a polymer sample of current volume V responding by craze plasticity to an imposed current elongational strain rate e, developing a tensile (dilatational) flow resistance until a final fracture strain is achieved as shown in Fig. 1. The specific toughness W or the total deformational energy absorbed per unit volume for this polymer is the area under the stress strain curve, or... 

---