Yield Stress Studies

In this section we discuss some recent combined SANS and yield stress studies of EVA fuel additives that have a widespread use in middle distillate fuels [58,59]. Other than the later discussed diblock copolymers or random crystalline-amorphous copolymers, relatively little has been done with respect to the microscopic evaluation of the polymeric aggregates nor on their interaction with wax by scattering techniques. These results nevertheless are presented first, in order to set the scene and to have a reference for the later... 

Since some earlier work based on anisotropic elasticity theory had not been successful in describing the observed mechanical behaviour of NiAl (for an overview see [11]), several studies have addressed dislocation processes on the atomic length scale [6, 7, 8]. Their findings are encouraging for the use of atomistic methods, since they could explain several of the experimental observations. Nevertheless, most of the quantitative data they obtained are somewhat suspicious. For example, the Peierls stresses of the (100) and (111) dislocations are rather similar [6] and far too low to explain the measured yield stresses in hard oriented crystals. 

The early study of brittle failures, notably those of the Liberty ships, indicated a temperature dependence. This can be illustrated by plotting both fracture stress (of) and yield stress (Oy) against temperature (Fig. 8.81). Below a certain temperature some materials exhibit a transition from ductile to brittle fracture mode. This temperature is known as the ductile-brittle transition temperature DBTT. 

Another approach to determining the contribution being made by each of the possible com-pression/decompression mechanisms involves monitoring the degree and rate of relaxation in tablets immediately after the point of maximum applied force has been reached. Once a powder bed exceeds a certain yield stress, it behaves as a fluid and exhibits plastic flow [121,122], Certain investigators [122] have studied plastic flow in terms of viscous and elastic elements and have derived the following equation ... 

Stresses can can be concentrated by various mechanisms. Perhaps the most simple of these is the one used by Zener (1946) to explain the grain size dependence of the yield stresses of polycrystals. This is the case of the shear crack which was studied by Inglis (1913). Consider a penny-shaped plane region in an elastic material of diameter, D, on which slip occurs freely and which has a radius of curvature, p at its edge. Then the shear stress concentration factor at its edge will be = (D/p)1/2.The shear stress needed to cause plastic shear is given by a proportionality constant, a times the elastic shear modulus,... 

A. Flores, F. J. Balta Calleja, G. E. Attenburrow, and D. C. Bassett, Microhardness Studies of Chain-extended PE III. Correlation with Yield Stress and Elastic Modulus, Polymer, 41, 5431 (2000). 

Many investigators 35 have reported experimental results on the necessary conditions for the static equilibrium of a sphere. The results of all such studies may be represented by a factor Z which is proportional to the ratio of the forces due to the yield stress xY and those due to gravity. 

Compression Test. Compression tests similar to that described in (5) were conducted for yield stress C and modulus E measurement. Rectangular neat resin specimens (1.27 cm x 1.27 cm x 2.54 cm) cut from the cast resin plates were tested under compression, as shown in Figure 1, in an universal testing machine at a loading rate of 0.05 cm/min. For each resin system studied, tests were conducted at several temperature levels between -60 and 60 degree C. All specimens were instrumented with strain gages for... 

The plastic deformation in several amine and anhydride cured epoxy resins has been studied. The experimental results have been reasonably interpreted by the Argon theory. The molecular parameters determined from the data based on the theory reflect the different molecular structures of the resins studied. However, these parameters are in similar enough range to also show the structural similarity in these DGEBA based systems. In general, the mechanisms of plastic deformation in epoxy resins below T are essentially identical to those in amorphouE thermoplastics. The yield stress level being related to the modulus that controls the intermolecular energy due to molecular deformation will, however, be affected by the crosslinks in the thermosets. 

The influence of fillers has been studied mostly at hl volume fractions (40-42). However, in addition, it is instructive to study low volume fractions in order to test conformity with theoretical predictions that certain mechanical properties should increase monotonlcally as the volume fraction of filler is Increased (43). For example, Einstein s treatment of fluids predicts a linear increase in viscosity with an increasing volume fraction of rigid spheres. For glassy materials related comparisons can be made by reference to properties which depend mainly on plastic deformation, such as yield stress or, more conveniently, indentation hardness. Measurements of Vickers hardness number were made after photopolymerization of the BIS-GMA recipe, detailed above, containing varying amounts of a sllanted silicate filler with particles of tens of microns. Contrary to expectation, a minimum value was obtained (44.45). for a volume fraction of 0.03-0.05 (Fig. 4). Subsequently, similar results (46) were obtained with all 5 other fillers tested (Table 1). 

A viscometer can be used to study the yield stress and viscosity of cement pastes (Section 1.3.1). This is carried out by plotting the shear rate against shear stress as shown in Fig. 2.4 for cement pastes of various water cement ratios. These cement pastes are generally considered to exhibit Bingham plastic behavior where the yield value is the intercept on the shear stress axis and is related to cohesion, and the slope of the line is the apparent viscosity which is related to the consistency or workability of the system. The following general observations can be made ... 

Pons et al. have studied the effects of temperature, volume fraction, oil-to-surfactant ratio and salt concentration of the aqueous phase of w/o HIPEs on a number of rheological properties. The yield stress [10] was found to increase with increasing NaCl concentration, at room temperature. This was attributed to an increase in rigidity of films between adjacent droplets. For salt-free emulsions, the yield stress increases with increasing temperature, due to the increase in interfacial tension. However, for emulsions containing salt, the yield stress more or less reaches a plateau at higher temperatures, after addition of only 1.5% NaCl. 

The non-aqueous HIPEs showed similar properties to their water-containing counterparts. Examination by optical microscopy revealed a polyhedral, poly-disperse microstructure. Rheological experiments indicated typical shear rate vs. shear stress behaviour for a pseudo-plastic material, with a yield stress in evidence. The yield value was seen to increase sharply with increasing dispersed phase volume fraction, above about 96%. Finally, addition of water to the continuous phase was studied. This caused a decrease in the rate of decay of the emulsion yield stress over a period of time, and an increase in stability. The added water increased the strength of the interfacial film, providing a more efficient barrier to coalescence. 

Z3. PMDA-ODA on MgO. PMDA-ODA peel force data shown in Fig. 7 exhibit a very interesting phenomenon as a function of T H exposure. The peel force is significantly increased as the time in T H is increased. This is somewhat unusual, but apparently repeatable. The exposure to APS has not made much difference in the results, which is understandable from the initial surface analyses after IPA cleaning and APS exposure. The XPS data show no detectable amount of APS on the thus exposed MgO surface. The reasons for the peel force increase as a function of T H exposure are not clear at this time. This is, however, due to increased interfacial strength, and not due to the polyimide mechanical properties (Young s modulus and yield stress) changes. If the latter were the case, then we should see similar effects also in the first two cases, which is not seen. However, more detailed analysis is essential to clarify the exact mechanism and this observation merits further study. 

The fracture properties of foods have been extensively studied and comprehensive reviews (64 and references therein) exist that address testing and application of fracture data in the food industry. As mentioned earlier, in the food industry compression tests are viewed also as fracture tests and the yield stress is often regarded as the fracture stress. However, in this review, the discussion is confined to only those types of fracture tests that lead to estimates of the fracture toughness and not the yield stress. The fracture toughness tests are relatively recent in the food industry. 

First, it is important to notice that the stress-strain curves and, consequently, the derived characteristics (yield stress, cry, plastic flow stress, crpf, and strain softening) have been studied in a temperature range extending to, typically, Ta - 20 K. Indeed, for temperatures closer to Ta, the experimental results are less reliable, as some creep behaviour can occur. 

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