Brittle behavior

An expression for the theoretical breaking strain aj], of a sohd with Young s modnlus E was proposed by Orowan (1949) [ORO 49] and Gilman (1959) [GIL 59], by modeling the interatomic separating force with a simple sinusoidal fimctioa The following result was obtained  

Although this result is corroborated by measurements obtained on fibers or whiskers, experimental values obtained are very clearly below In fact, in most cases, the fracture is initiated from a flaw located near an area where the stress attained is of the critical decoherence value. 

- when a, tends towards r, we get an expression close to that obtained by Orowan and Gilman. 

During sub-critical loading, the material stores up the potential energy Wg in the form of elastic energy  

Let us consider the closed system constituted by the cracked part (S surface area of the crack) and the forces which are applied, exchanging neither heat nor work with the outside. The conservation of total energy of this system is written  

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Oxygen, nitrogen, and carbon promote brittle behavior in all titanium alloys, and it is important to control the cumulative effect of these three elements during casting operations. 

Brittle fracture is probably the most insidious type of pressure-vessel failure. Without brittle fracture, a pressure vessel could be pressurized approximately to its ultimate strength before failure. With brittle behavior some vessels have failed well below their design pressures (which are about 25 percent of the theoretical bursting pressures). In order to reduce the possibility of brittle behavior. Division 2 and Sec. Ill require impac t tests. 

Orowan, E. (1952) Fundamentals of brittle behavior in metals, in Fatigue and Fracture of Metals, Symposium at MIT, ed. Murray, W.M. (MIT and Wiley, New York). 

Carpick, R.W., Enachescu, M., Ogletree, D.F. and Salmeron, M., Making, breaking, and sliding of nanometer-scale contacts. In Beltz, G.E., Selinger, R.L.B., Kim, K.-S. and Marder, M.P., (Eds.), Fracture and Ductile vs. Brittle Behavior-Theory, Modeling and Experiment. Materials Research Society, Warrendale, PA, 1999, pp. 93-103. 

Fig. 2-29 Typical creep-rupture ductile-to-brittle behavior of TPs.

Since blast-resistant design is based on structural response beyond elastic limits into the inelastic range, buildings should be carefully designed in a manner that minimizes stress concentrations, brittle behavior, and abrupt failures. Some of the significant design considerations for steel and reinforced concrete blast-resistant structures are briefly summarized in this section. 

Following this, attempts were made to remove a particle from the extruded plastic sheeting. When a particle was finally isolated, applying pressure with the ATR crystal resulted in cracking of the particle, so a representative spectrum could not be obtained. This brittle behavior usually indicates that the sample is inorganic in nature. 

The main considerations of mechanical properties of metals and alloys at low temperatures taken into account for safety reasons are the transition from ductile-to-brittle behavior, certain unconventional modes of plastic deformation, and mechanical and elastic properties changes due to phase transformations in the crystalline structure. 

We also note data from atomic force microscopy (AFM) versus depth, carried out by using a diamond tip for scratching patterns into the surface [12], Because of the 2° microtoming method reported, these authors were able to examine the depth profile of brittle behavior in weathered samples with excellent resolution. The data showed a very rapid decrease in the brittleness with depth into the sample which, of course, was a strong function of exposure time. The brittleness was more in line with the IR data (see above) versus depth than the molecular weight data, hence suggesting that some chain scission and branching can be tolerated in the system before it manifests brittle behavior. 

While solvent-modified epoxies show a considerable increase in toughness, a completely brittle behavior is observed after the drying procedure. Only those samples with volume fractions higher than 10% can be tested, because no natural cracks, which are necessary for correct SENB measurements, can be introduced into macroporous epoxies with porosities lower than 10% owing to their... 

The quantitative results of fracture energy, which are calculated from the total area under load-displacement curves, are presented in Fig. 50. It becomes obvious, that a brittle-tough transition exists at a volume fraction of around 10%. This brittle-tough transition is observed for solvent-modifled as well as semi-porous epoxies. A brittle behavior is observed in macroporous epoxies after complete solvent removal, thus giving low fracture energies similar to the neat epoxy for each porosity. 

There are several important things to note. The first is that elastic deformation is a reversible process, but plastic deformation and brittle fracture are not. More importantly, plastic deformation and viscoelastic behavior are kinetic phenomena time is important, and they can be affected by press speed. In reality, most materials exhibit both plastic and brittle behavior, but specific materials can be classified as primarily plastic or primarily brittle. For example, microcrystalUne cellulose defonns primarily by a plastic deformation mechanism calcium phosphate de-fonns primarily by a brittle fracture mechanism lactose is in the middle [8]. 

Time and energy can be saved if one recognizes that there is only one qualitative difference between a linear and a tridimensional polymer the existence in the former and the absence in the latter of a liquid state (at a macroscopic scale). For the rest, both families display the same type of boundaries in a time-temperature map (Fig. 10.1). Three domains are characterized by (I) a glassy/brittle behavior (I), (II), a glassy/ductile behavior, and (III) a rubbery behavior. The properties in domain I are practically... 

The location of Tp with respect to ambient temperature, Ta, in the timescale under consideration. In a first approach, one can distinguish between the cases where Tp < Ta (epoxy, phenolics) and Tp > Ta (UP, VE, PI). The networks belonging to the first family have relatively low moduli (E < 3 GPa, G < 1 GPa), and can display a ductile or semiductile behavior. The networks belonging to the second family have relatively high moduli (E > 3 GPa, G > 1 GPa), and generally exhibit a brittle behavior. 

Although a notable reduction of the phase size is reported for such compatibilized blends [64-67], the overall mechanical toughness remains unsatisfactorily low [64], As one reason, thermal stresses at the interface between PPE and SAN, occurring as a result of the different thermal coefficients of expansion during solidification following melt-processing, are identified as a crucial reason for the observed brittle behavior [68],... 

When solids deform almost to the breaking point, they exhibit brittle behavior the stress at fracture is several orders of magnitude lower than the computed strength. The loss is ascribed to the presence of minute cracks probably formed during solidification. Compressive stress can induce crack propagation the magnitude of the stress at... 

The general principles involved in the failure analysis of ceramic materials are similar to the failure analysis of metals and alloys. Because of the brittle behavior of ceramic materials, failure may result in many pieces of the sample, which have to be reassembled in order to obtain information on the form of loading and the point of fracture initiation. The utmost care should be exercised in the reassembly of the fractured pieces so that the features of the fracture are preserved. 

Fig. 4.1 Tensile creep curves for siliconized silicon carbide (Carborundum KX01). Over most of the data range, these data can be represented by a constant creep rate there is a short primary creep stage, and almost no tertiary creep. The rupture strain decreases with increasing creep rate. The strain to failure, =1.5%, indicates brittle behavior even at low rates of creep detormation. Figure from Ref. 28.

A brittle behavior. The force-displacement (F-d) curves are linear elastic. The crack propagates in an unstable way. The damage mechanisms have not been initiated before failure. The fracture surfaces are very smooth and mirror-like. At the microscopic scale, they are believed to be associated with the development of a single crack. 

The Transition from Ductile to Brittle Behavior of a Semicrystalline Polyester by Control of Morphology... 

Significant variation of the ultimate mechanical properties of poly(hexamethylene sehacate), HMS, is possible by con-trol of thermal history without significant variation of percent crystallinity. Both banded and unbanded spherulite morphology samples obtained by crystallization at 52°C and 60°C respectively fracture in a brittle fashion at a strain of r O.Ol in./in. An ice-water-quenched specimen does not fracture after a strain of 1.40 in./in. The difference in deformation behavior is interpreted as variation of the population of tie molecules or tie fibrils and variation of crystalline morphological dimensions. The deformation process transforms the appearance of the quenched sample from a creamy white opaque color to a translucent material. Additional experiments are suggested which should define the morphological characteristics that result in variation of the mechanical properties from ductile to brittle behavior. 

Recently Moore and Petrie (5) have demonstrated that control of sample thermal history can result in transition from ductile to brittle behavior for polyethylene terephthalate. This transition in behavior was related to volume relaxation of the glassy state. 

The effects of morphology (i.e., crystallization rate) (6,7, 8) on the mechanical properties of semicrystalline polymers has been studied without observation of a transition from ductile to brittle failure behavior in unoriented samples of similar crystallinity. Often variations in ductlity are observed as spherulite size is varied, but this is normally confounded with sizable changes in percent crystallinity. This report demonstrates that a semicrystalline polymer, poly(hexamethylene sebacate) (HMS) may exhibit either ductile or brittle behavior dependent upon thermal history in a manner not directly related to volume relaxation or percent crystallinity. 

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