Brittle materials behaviour

Brittle Material Behaviour—Material deformation with negligible plastic deformation before fracture. 

Again because of the crosslinks, such brittle behaviour occurs whatever the temperature unlike brittle materials based on linear polymers, there is no temperature at which molecular motion is suddenly freed. In other words, the Tg, if there is one, does not produce dramahc changes in mechanical properties so that the material is changed from one that undergoes brittle behaviour to one that exhibits so-called tough behaviour. 

Evans (1975), Evans and Charles (1977), and Emery (1980) performed more refined fracture mechanics studies regarding the onset and arrest conditions Bahr et al. (1988) and Pompe (1993) extended this work and considered the propagation of multiple cracks while Swain (1990) found that materials showing non-linear deformation and A-curve behaviour have a better resistance to thermal shock. More specifically, the behaviour of a crack in the thermal shock-induced stress field was deduced from the dependence of the crack length on the stress intensity factor. Unstable propagation of a flaw in a brittle material under conditions of thermal shock was assumed to occur when the following criteria were satisfied ... 

Sheldon, G.L. and Finnie, I. (1966), On the ductile behaviour of nominally brittle materials during erosive cutting , Trans. ASME, 88B, 387-92. 

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... 

Non toughened semi-crystalline PET is a very brittle polymer whatever the loading conditions are i.e., un-notched and notched tensile tests, dart test (impact of a hemispherical striker against a clamped plaque) and izod test (Fig. 1. to Fig.4.). Amorphous PET exhibits a more ductile behaviour except when notched. In such a case even amorphous PET is a brittle material at room temperature (Fig. 3. and 5.). 

All experiments in this section were performed with a constant sample geometry of aAV = 0.5. As obvious from the section typical force-displacement curves", it was difficult to define unambiguously a single brittle-ductile transition four elementary materials behaviours involve three distinct ductile-brittle transitions ... 

In general, the predicted displacement using both LBNL s elastic and CEA s elasto-brittle (weakly inelastic) models are within the ranges of field measurements, except for very close to the drift wall. However, in a few individual anchors, displacement values are more than 50% larger than predicted by the elastic material behaviour. The increased displacement in these anchors may be explained by inelastic responses leading to a better agreement with the ubiquitous joint model (e.g. Anchor 4 in Figure 5a). 

Several researchers have argued in favour of strain rate dependant rock properties (eg., Prasad et al., 2000). They advise that the material model used for dynamic numerical modelling should contain provisions for strain rate dependant material properties. It is noteworthy that neither the material behaviour, which remains essentially elastic throughout the calculations nor the brittle failure law using element elimination is rate... 

Adhesives, as all plastics, are viscoelastic materials combining characteristics of both solid materials like metals and viscose substrates like liquids. Typically, the adhesive shear stress vs. shear strain curve is non-linear. This behaviour is characteristic especially for thermoplastic adhesives and modified thermosetting adhesives. Thermosetting adhesives are, by their basic nature, more brittle than thermoplastic adhesives but, as discussed earlier, are often modified for more ductile material behaviour. 

A statistical definition of brittleness can be formulated in terms of the Weibull distribution of fracture probability for a material (Derby et al., 1992). The Weibull modulus m (see Eq. 2) can range from zero (totally random fracture behaviour, where the failure probability is the same at all stresses, equivalent to an ideally brittle material) to infinity (representing a precisely unique, reproducible fracture stress, equivalent to an ideally non-brittle material). 

Figure 12 shows schematically the stress-strain curves of 1-D, 2-U, and 3-D reinforced C/C composites at room temperature. 1-D composites exhibit brittle fracture behaviour, the 2-D composites fail in a "semi-brittle" manner by a continuous step drop in load. °The mode of failure of 3-D composites, however, is not of a brittle type. One observes strain rates up to 5%. This nontypical fracture behaviour of 3-D composites is due to a continuous crac system inside the composite, as illustrated schematically in Fig. 13. This crack pattern depends on the weave pattern and originates during the processing of the carbon/carbon composite, as a result of the heating and cooling cycles. These cracks are able to annihilate fracture energy. If the cracks are closed at higher temperatures because of the thermal expansion of the material, the typical brittle fracture behaviour of C/C composites is found (see Fig. 13). ° ...

The processes in the range of ductile failure and in the intermediate range will now be briefly discussed to complete the description of the materials behaviour in the long-term tensile test. The branch of ductile failure in the stress versus time-to-failure diagram (or more precisely log crversus log tp) runs considerably flatter than the branch of brittle failure. Figure 3.18 shows typical stress versus time-to-failure curves. Within the range of high stresses ... 

While each material exhibits particular physical characteristics, they all follow a broad pattern of behaviour as shown in Figure 24.3. Where an item has a load applied to it, provided that the strain induced does not go beyond the elastic limit, then when the load is removed the item will return to its original size, i.e. there will have been no permanent deformation. However, if the elastic limit is exceeded permanent deformation occurs and the characteristic of the material will have changed. Typical stiff brittle materials are cast iron, glass and ceramics which have no ductility and will fracture at the elastic limit. Ductile materials include mild steel and copper, and elastic materials include plastics. 

Crosslinked polymers can be characterised conveniently by defining their crosslink density as branch points per unit volume or average molecular weight between crosslinks. This parameter in conjunction with the molecular nature of the polymer defines whether the material will behave as an elastomer or as a rigid material, which shows either ductile or brittle failure behaviour. Fillers can be used to modify properties further across the whole range of polymer behaviour. Because inorganic fillers are, compared to most polymers, much stiffer and less extensible materials, their incorporation into a polymer will usually produce a composite material of reduced strain to failure and increased stiffness relative to the polymer, i.e., the composite will be less elastomeric or less ductile. Nevertheless, large quantities of fillers are used in polymers that already have low strains to failure and show brittle failure behaviour. This chapter will confine itself to a discussion of the use of fillers in ductile and brittle crosslinked polymers. 

From the known behaviour of the 13 pol3maers shown in this diagram, two characteristic lines can be drawn. Line A divides the brittle materials on the right, which are brittle when notched, from those on the left, which are ductile even when notched. Both of these lines are approximations, but they do summarize the existing knowledge. 

Figure 8.6 Schematic diagrams representing the behaviour of a brittle material under uniaxial compression.

Investigations on the influence of fibres on the behaviour of advanced composite materials, where the fibre volume fraction is high and tends to be exploited mostly in an uncracked matrix, provided a system of reliable relations. In brittle matrix composites the situation is somewhat different the fibre volume fraction is usually low and their influence in an uncracked state is small and covered by a large scatter, which is characteristic for these materials properties. The fibres act on, and modify considerably, the brittle matrix behaviour only after the cracking. 

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