Brittle and ductile materials

In the case of ceramics, ductility begins to become important at higher temperatures. As an 

The directions (arrows) along each of the edges are given, (b) The same (1 1 1) plane represented as a packing of atoms. One direction, [Oil], is marked 

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Most whiskers up to 1 micrometer in diameter obey Hooke s law to the point of fracture, regardless of their composition (Evans, 1972). Whiskers of brittle and ductile materials with larger diameters respond to stress differently. Metallic whiskers fail under tension by shear, whereas other compounds fail through fracture. 

Figure 8.12 illustrates a solid particle impinging on a surface. It has been found that the erosive wear rate depends upon the impingement angle, a, the particle velocity, vq, and the size and density of the particle, as well as the properties of the surface material. It has also been found that there is a difference in erosive wear properties of brittle and ductile materials. The maximum erosive wear of ductile materials occurs at a = 20°, whereas the maximum erosive wear for brittle materials occurs near a = 90°. Since the impingement angle is probably lower than 90° for these type of flow situations, we might consider only brittle materials, such as ceramics for this application. Let us examine brittle erosive wear in a little more detail first. 

II.1 In Section 8.2, we saw how erosive wear can be different for brittle and ductile materials. In reality, most materials exhibit behavior that is a combination of... 

FIGURE 13-19 Schematic plots of stress versus strain for brittle and ductile materials. 

Up to this point, the discussion has been mostly couched in macroscopic terms. Flaws were shown to concentrate the applied stress at their tip which ultimately led to failure. No distinction was made between brittle and ductile materials, and yet experience clearly indicates that the different classes of materials behave quite differently — after all, the consequences... 

Figure 2.3 Schematic representations of tensile stress-strain behavior for brittle and ductile materials loaded to fracture.

Kuhn, W.E., Milling of brittle and ductile materials, in Metals Handbook, 9th ed., American Society of Metals, Metals Park, Ohio, 1984, Vol. 7, pp. 56-70. 

While it is well established that the rupture stress of both brittle and ductile materials is increased significantly by the presence of compressive stress (known as the Mohr effect), it is generally believed that a similar relationship for flow stress does not hold. However, an explanation for this paradox with considerable supporting experimental data is presented below. The fact that this discussion is limited to steady-state chip formation rules out the possibility of periodic gross cracks being involved. However, the role of microcracks is a possibility consistent with steady-state chip formation and the influence of compressive stress on the flow stress in shear. A discussion of the role microcracks can play in steady-state chip formation will follow in the next section. Hydrostatic stress plays no role in the plastic flow of metals if they have no porosity. Yielding then occurs when the von Mises criterion reaches a critical value. Merchant [7, pp. 267-275] has indicated that Barrett [10]... 

The tensile test provides an insight into the stress/strain behaviour of a material under uniaxial tensile loading and makes it possible to distinguish between brittle and ductile materials. It is a useful tool for quality control and general comparison of properties, but it cannot be considered representative for applications with load/time scales widely different from those of the standard test. 

The double cantilever beam (DCB) is a widely used fracture test specimens for both brittle and ductile materials. Consider the DCB specimen schematically shown in Figure 4.9. From the discussion presented in Section 4.2.1, answer the following questions. 

Figure 2.2 Illustration of milling process, (a) Single-phase ductile materials, (b) Multiphase ductile materials, (c) Brittle materials, (d) Mixture of brittle and ductile materials (the SEM images were taken from Refs [5,7]).

When a mixture of brittle and ductile materials is miUed, both of the above-mentioned processes take place (Figure 2.2d). Plastic deformation of the ductile material absorbs the impact energy, resulting in much less fracture of the brittle material. Under the impact, the brittle particles can either penetrate into or sandwiched between two flattened ductile particles. Hence, repeated impacts lead to the dispersion of the brittle material within the ductile matrix. Metal matrix composites (MMC) could be synthesized in this way [8]. 

Typical stress-strain diagrams for brittle and ductile materials are shown in Fig, 2.7. For brittle materials such as cast iron, glass, some epoxy resins, etc., the stress strain diagram is linear from initial loading (point 0) nearly to rupture (point B) when average strains are measured. As will be discussed subsequently, stress and strain are point quantities if the correct mathematical definition of each is used. As a result, if the strain were actu-... 

TABLE 30.1 Fatigue Crack Propagation Characteristics of Brittle and Ductile Materials (UHMWPE meets the requirements to be considered an essentially brittle material from a fracture mechanics perspective.)... 

Typical stress versus strain curves for brittle and ductile materials, showing the areas under their respective curves they are measures of the toughness of the respective materials. 

The percent strain limits are arbitrary relative divisions defining the behavior. The above definitions of a brittle and ductile material assume that the reference temperature is room temperature. It is best to refer to ductile behavior and brittle behavior, rather than define materials as ductile or brittle. A material that is brittle at room temperature will be ductile at some elevated temperature, and a material that is ductile at room temperature will exhibit brittle behavior at a low-enough temperature. Ductile and brittle are relative terms. The point is that mechanical properties, particularly for polymers, are highly dependent on temperature. 

The other striking feature of nanotubes is their extreme stiffness and mechanical strength. Such tubes can be bent to small radii and eventually buckled into extreme shapes which in any other material would be irreversible, but here are still in the elastic domain. This phenomenon has been both imaged by electron microscopy and simulated by molecular dynamics by lijima et al. (1996). Brittle and ductile behaviour of nanotubes in tension is examined by simulation (because of the impossibility of testing directly) by Nardelli et al. (1998). Hopes of exploiting the remarkable strength of nanotubes may be defeated by the difficulty of joining them to each other and to any other material. 

More than 250 years ago it was observed that the strength of small-diameter wires increased proportionally as the diameter decreased (Musschen-broek, 1727). The inverse relationship between elastic strain and diameter has also been noted for whiskers of brittle or ductile materials of less than 20 micrometers in diameter (Evans, 1972). 

In terms of the mechanical behavior that has already been described in Sections 5.1 and Section 5.2, stress-strain diagrams for polymers can exhibit many of the same characteristics as brittle materials (Figure 5.58, curve A) and ductile materials (Figure 5.58, curve B). In general, highly crystalline polymers (curve A) behave in a brittle manner, whereas amorphous polymers can exhibit plastic deformation, as in... 

Despite the similarities in brittle and ductile behavior to ceramics and metals, respectively, the elastic and permanent deformation mechanisms in polymers are quite different, owing to the difference in structure and size scale of the entities undergoing movement. Whereas plastic deformation (or lack thereof) could be described in terms of dislocations and slip planes in metals and ceramics, the polymer chains that must be deformed are of a much larger size scale. Before discussing polymer mechanical properties in this context, however, we must first describe a phenomenon that is somewhat unique to polymers—one that imparts some astounding properties to these materials. That property is viscoelasticity, and it can be described in terms of fundamental processes that we have already introduced. 

The strength properties of solids are most simply illustrated by the stress-strain diagram, which describes the behaviour of homogeneous brittle and ductile specimens of uniform cross section subjected to uniaxial tension (see Fig. 13.60). Within the linear region the strain is proportional to the stress and the deformation is reversible. If the material fails and ruptures at a certain tension and a certain small elongation it is called brittle. If permanent or plastic deformation sets in after elastic deformation at some critical stress, the material is called ductile. 

The micromechanical deformation behavior of SAN copolymers and rubber-reinforced SAN copolymers have been examined in both compression [102] and in tension [103,104]. Both modes are important, as the geometry of the part in a given application and the nature of the deformation can create either stress state. However, the tensile mode is often viewed as more critical since these materials are more brittle in tension. The tensile properties also depend on temperature as illustrated in Figure 13.6 for a typical SAN copolymer [27]. This resin transforms from a brittle to ductile material under a tensile load between 40 and 60 C. 

By the first decade of this century it was established that material failures occur at such low stress levels, because real materials do not usually have a perfect crystalline structure and almost always some vacancies, interstitials, dislocations and different sizes of thin microcracks (having linear structure and sharp edges) are present within the sample. Since the local stress near a sharp notch may rise to a level several orders of magnitude higher than that of the applied stress, the thin cracks in solids reduce the theoretical strength of materials by similar orders, and cause the material to break at low stress levels. The failure of such (brittle or ductile) materials was first identified by Inglis (1913) to be the stress concentrations occurring near the tips of the microcracks present within the sample. 

The degree of fragmentation was found to diminish with smaller sieve fractions at the same compression load when several sieve fractions of unmilled crystalline a-lactose monohydrate was used. The authors concluded that particle fragmentation would reduce as porosity approached zero and elastic behavior would start to dominate the consolidation process (43). With a decrease in particle size, yield pressure decreased and the strain rate sensitivity index increased (44) which suggested a reduction in the extent of fragmentation. The transition from brittle to ductile material was thought to occur for a median particle size of around 20 pm (45). 

All materials tend to fracture if stressed severely enough. Some materials fracture more easily than others, and are thereby said to be brittle . Brittleness is the property of a material manifested by fracture without appreciable prior plastic deformation. In ductile fracture significant plastic flow occurs before fracture. Strain at fracture is more than a few per cent, unlike brittle fracture, and may be several hundred per cent. However, a sharp distinction cannot be made between brittle and ductile fracture since even in glassy materials some deformations take place. Further, a given material will fail in a brittle manner under some conditions and a ductile manner under other conditions. Thus, brittle fracture is favored by the low temperature, fast loading and when the state of stress approaches a uniform, i.e., triaxial or dUatational, state. Materials with low T are more... 

Superconducting materials can be divided into two general categories—brittle and ductile. The brittle superconductors consist of the intermetallic compounds such as columbium-tin (CbaSn) and vanadium-gallium (VsGa). The ductile superconductors consist of most of the elemental metals as well as alloys such as niobium-zirconium. 

The chip formation in abrasive processes defines the local interaction between abrasive grains and workpiece material in combination with the surrounding fluid media (cooling lubricant or air). It can mainly be distinguished between brittle and ductile removal mechanisms. 

Usually, grinding of hard and brittle materials causes microcracks which deteriorate surface quality. Thus, the transition from brittle-to-ductile material removal is considered to be of great importance for ultraprecision grinding. Much research effort has been spent to identify this transition and to understand the removal mechanism. 

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