Ductile material behavior

Chip Formation (Abrasive Process), Fig. 2 Brittle material behavior versus ductile material behavior in grinding (based on Salje and Mohlen 1987 Klocke 2009)... 

Figure 8 from (Jochum 2013) shows the behavior in cutting of brittle hard materials, namely Circonium oxide and Yttrium oxide as it is used for dental implants. The picture shows ductile material behavior due to high compressive stresses and thus ploughing in the upper scratch. In the lower scratch an intercrystalline fracture is shown, which is due to the interaction between grain and material possibly as shear fracture, mechanism similar to the one pointed out by Kragelski in Fig. 6. 

Semi-crystalline thermoplastics can be assigned lower safety factors than amorphous thermoplastics, thermosets or fiber-reinforced plastics, owing to their ductile material behavior. 

Material behavior have many classifications. Examples are (1) creep, and relaxation behavior with a primary load environment of high or moderate temperatures (2) fatigue, viscoelastic, and elastic range vibration or impact (3) fluidlike flow, as a solid to a gas, which is a very high velocity or hypervelocity impact and (4) crack propagation and environmental embrittlement, as well as ductile and brittle fractures. 

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... 

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... 

This conclusion was only partly confirmed by scanning electron microscopy micrographs of RuC>4 stained surfaces taken at the crack tip of deformed specimens at 1ms-1, where the non-nucleated and /3-nucleated materials showed, respectively, a semi-brittle and semi-ductile fracture behavior. While some limited rubber cavitation was visible for both resins, crazes—and consequently matrix shearing—could not develop to a large extent whether in the PP or in the /1-PP matrix (although these structures were somewhat more pronounced in the latter case). Therefore, a question remains open was the rubber cavitation sufficient to boost the development of dissipative mechanisms in these resins ... 

A shortening in relaxation time in the critically strained region makes some materials tough. The shift of relaxation time is attributed to strain-induced dilatation and can reach as much as five decades. Thermal history, on the other hand, dictates the initial state from which this dilatation starts and may be expressed in terms of excess entropy and enthalpy. The excess enthalpy at Tg is measurable by differential scanning calorimetry. Brittle to ductile transition behavior is determined by the strain-induced reduction in relaxation time, the initial amount of excess entropy, and the maximum elastic strain that the material can undergo without fracturing or crazing. 

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. 

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). 

The deformation behavior of many pharmaceutical materials is time-dependent and the nature of this time dependency is often related to the mechanism of compaction for a given material. It is thought that time dependency or speed sensitivity arises from the viscoelastic or viscoplastic characteristics of a material. In contrast, studies have shown that brittle materials are much less speed dependent that ductile materials because yielding and fragmentation are not as dependent on the rate of compression. It is also believed that the particle size and size distribution of the powder or granules have an important role in the speed sensitivity due to the fact that this property affects the predominant mechanism of deformation (6,58-60). 

From studies of service behavior and from extensive laboratory investigations, the well-established terms stress-corrosion cracking (SCC) and corrosion fatigue have been shown to relate to a continuum of failure modes classified as environment-sensitive fracture. In many environments, the addition of stress, with associated strains, introduces a variable that can result in brittle failure in the sense of very limited plastic flow in otherwise ductile materials such as the stainless steels. Environment-sensitive fractures propagate at an advancing crack tip at which, simultaneously, the local stresses can influence the corrosion processes, and the corrosion can influence the crack-opening processes. Since these processes proceed by kinetic mechanisms, they are time and stress dependent with the result that the crack propagation rate can become very sensitive to the stress application rates. Conventional SCC usually has been associated with static stress, but this is seldom realized... 

To see how the fracture energy may be used in the initiation of chemical reactions, the concepts of fracture mechanics are introduced, including the strain rate and temperature dependence of the ductile-brittle behavior. The starting point is the Griffith theory which in its simplest form applies to perfectly brittle materials and states that for a crack to form, the elastic strain energy available must be at least sufficient to provide the energy of the new surfaces formed [74]. 

The characteristics of fracture surfaces of F-185 neat resin and those of F-185 matrix In the composites are similar to those reported In the literature ( ). The fact that the fracture surfaces of F-185 neat resin and F-185 matrix In the composites show typical ductile fracture behavior, while the unmodified HX-205 shows brittle fracture behavior, seems to Indicate the toughening effect of F-185 as a result of Incorporation of CTBN rubber. The fracture energies of these materials are being... 

Ductility is more commonly defined as the ability of a material to deform easily upon the application of a tensile force, or as the ability of a material to withstand plastic deformation without rupture. Ductility may also be thought of in terms of bendability and crushability. Ductile materials show large deformation before fracture. The lack of ductility is often termed brittleness. Usually, if two materials have the same strength and hardness, the one that has the higher ductility is more desirable. The ductility of many metals can change if conditions are altered. An increase in temperature will increase ductility. A decrease in temperature will cause a decrease in ductility and a change from ductile to brittle behavior. Irradiation will also decrease ductility, as discussed in Module 5. 

The equivalence of K and (7, which strictly holds for elastic materials with linear load-deflection characteristics, is referred to as linear-elastic fracture mechanics (LEFM). Subsequently this basic concept has been modified to describe also the behavior of ductile materials. For instance. Wells [3] considered the plastic strain at the crack tip as the crack... 

The introduction of small particles into a ductile material can substantially increase the yield strength, even if the volume fraction is low (< 10 vol.%). The particles can be introduced by precipitation (precipitation hardening) or by physical addition (dispersion strengthening). For example. Fig. 6.28 shows the effect of precipitation of Mg0.Fe203 on the stress-strain behavior of MgO. The extent of the strengthening is determined by several factors, including volume fraction. 

Derive an expression for the total energy required to fail, at constant strain rate, a ductile material exhibiting a stress-strain behavior described by Eq. (6.26). 

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