Fracture mechanics ductile behaviour

The results above suggest that it may be possible to apply fracture mechanics data to determine failure loads of more complex structures, provided that (i) the adhesives used are not too ductile, (ii) bondline thickness is known and controlled, (iii) non-linear behaviour due to adherend and interface damage is limited, and (iv) the specimens employed to determine... 

P.A. Beaven, F. Appel, B. Dogan, R. Wagner Fracture and Ductilization of Gamma-Titanium Aluminides. In C. T. Liu, R. W. Cahn, and G. Sauthoff (eds.) Ordered Intermetallics - Physical Metallurgy and Mechanical Behaviour. Kluwer Acad. Publ. Dordrecht (1992) 413-432. 

Fig. 4. Load-extension curves for a typical polymer tested at four temperatures showing different regions of mechanical behaviour. 1. Brittle fracture. 2. Ductile failure. 3. Necking and cold drawing. 4. Rubber-like behaviour.

In every approach one finds a wide range of sophistication. In the continuum approach, the simplest (and most common) models are based on linear elastic fracture mechanics (LEFM), a well developed discipline that requires a linear elastic behaviour and brittle fracture, not always exhibited by fibres. Ductility and the presence of interfaces, not to mention hierarchical structures, make modelling much more involved. The same is true of the atomistic approach fracture models based on bond breaking of perfect crystals, using well established techniques of solid state physics, allow relatively simple predictions of theoretical tensile stresses, but as soon as real crystals, with defects and impurities, are considered, the problem becomes awkward. Nevertheless solutions provided by these simple models — LEFM or ideal crystals — are valuable upper or lower bounds to fibre tensile strength. 

As the name suggests, linear-elastic material behaviour is the precondition to allow applying the theory of linear-elastic fracture mechanics (lefm), discussed in this section. Strictly speaking, this precondition is fulfilled only in brittle materials like ceramics. In good approximation, it can also be used in ductile materials if the region of plastic deformation is restricted to the vicinity of the crack tip. Therefore, it can in many cases also be used to analyse metals. 

The fracture surface of an as-received sample is shown in Figure 2. The fracture surface exhibits the characteristic fiber pull-out typical of quasi-ductile glass matrix composite materials [13,15]. However, inspection of the fracture surfaces reveals that the average pull-out lengths are not uniform across the composite section but depend on the relative orientation of the fibre bundles and the fracture propagation plane. Areas exhibiting fewer fibres are observed when these were oriented parallel to the fracture surface. This behaviour explains qualitatively the lower Kic values determined in this material in comparison to unidirectional fibre reinforced composites, as mentioned above, where all fibres contribute equally to toughening by the pull-out mechanism [13,15]. 

Pressure on resources had materials science improving its products in leaps and bounds - not just metals but also the earlier polymers and natural fibres. The concept of fracture mechanics had been introduced during the First World War by the aeronautical engineer Alan Arnold Griffith (1893-1963) to explain brittle failures. The microscopic behaviour of materials, the way cracks propagated from surface flaws, led to the development of a particular palette of structural materials suited to severe conditions - elastic and ductile, with reserves of energy absorption when approaching failure point. 

Most of the theory developed to date has been concerned with the behaviour of cracks or crack-like defects produced by opening forces (Figures 2.12,2.13) applied to linear elastic brittle materials. More complex analyses have been developed for cracks induced by shearing or tearing, but these are beyond the scope of this text. On first consideration, the relevance of a fracture mechanics approach to plastics which are predominantly ductile may be questioned, but further reflection confirms that most unexpected failures are brittle in nature. 

The intermetallic alloy NiAl is discussed as a potential base alloy for high temperature structural materials. Its use is currently limited by low room temperature ductility and fracture toughness. Consequently, substantial research efforts have been directed towards understanding its mechanical behaviour [1, 2] so that detailed experimental [3, 4, 5] and theoretical [6, 7, 8] analyses of the deformation of NiAl are available today. 

Abstract The fracture properties and microdeformation behaviour and their correlation with structure in commercial bulk polyolefins are reviewed. Emphasis is on crack-tip deformation mechanisms and on regimes of direct practical interest, namely slow crack growth in polyethylene and high-speed ductile-brittle transitions in isotactic polypropylene. Recent fracture studies of reaction-bonded interfaces are also briefly considered, these representing promising model systems for the investigation of the relationship between the fundamental mechanisms of crack-tip deformation and fracture and molecular structure. 

As discussed in section 6.2.2, the values of Young s modulus for isotropic glassy and semicrystalline polymers are typically two orders of magnitude lower than those of metals. These materials can be either brittle, leading to fracture at strains of a few per cent, or ductile, leading to large but non-recoverable deformation (see chapter 8). In contrast, for rubbers. Young s moduli are typically of order 1 MPa for small strains (fig. 6.6 shows that the load-extension curve is non-linear) and elastic, i.e. recoverable, extensions up to about 1000% are often possible. This shows that the fundamental mechanism for the elastic behaviour of rubbers must be quite different from that for metals and other types of solids. 

---