Yield polycrystal

Example Approximate calculation of the hardness of solids. This concept of shear yielding - where we ignore the details of the grains in our polycrystal and treat the material as a continuum - is useful in many respects. For example, we can use it to calculate the loads that would make our material yield for all sorts of quite complicated geometries. 

Yield Stress The effect of hydrogen on the yield stress of iron and steels is unpredictable. For very pure iron single crystals and polycrystals the yield stress is frequently found to be decreased by hydrogen, but it may increase or stay the same, depending on the dislocation structure, crystal orientation and purity of the iron . Little information is available for steels. 

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,... 

T. N. Baker, Editor, Yield, Flow, and Ftacture of Polycrystals, Applied Science Publishers, London, UK (1983). See R. W. Armstrong, p. 1. 

A quantitative analysis of grain boundary impedances measured with macroscopic electrodes can be rather problematic if grain boundary properties vary from boundary to boundary (cf. Sec. 3.2). Hence, additional information on the distribution of grain boundary resistivities is often desired. Microelectrode measurements can yield such additional information (Sec. 4.2) and below a microcontact impedance spectroscopic study of grain boundaries in a polycrystal is exemplarily presented. The material of choice is again SrTiCE (0.2 mol % Fe-doped), which represents a model material for the technologically highly important class of perovskite-type titanates (see also above). 

If, however, one assumes uniform stress throughout the same nontextured polycrystal a similar averaging procedure can be performed over the elastic-compliance tensor using the corresponding nine elastic compliance constants Sn, S12, S33, S44, S55, Sss, S12, S23, and S31. This is known as the Reuss approximation (Reuss, 1929), after Endre Reuss (1900-1968), and it yields the theoretical minimum of the elastic modulus. 

Among numerous rare earth vanadate compounds, YV04 Eu has been investigated most for its value in practical use. Its bulk polycrystals could reach a quantum yield (QY) of ca. 70% as commercial red phosphor. Huignard et al. obtained 7-YV04 Eu " NPs with sizes around 15-30 nm... 

III. The third step of direct longitudinal transmission of strain onto connected crystalline blocks leads to a perfect stretching of these fibrils. Because of the alignment of the molecules the fibers in this condition should possess a strength about 1 to 2 orders of magnitude higher than the yield stress of randomly distributed folded polycrystals. As the fibrils are able to stabilize the enhanced micro-void volume between them, a lateral coalescence of these voids finally provides a local deformation zone in the shape of a craze as known from amorphous polymers. 

Our geometric model of the crystal is most appropriate for polycrystals since we have hypothesized that any and all planes and slip directions are available for slip (i.e. the discrete crystalline slip systems are smeared out) and hence that slip will commence once the maximum shear stresses have reached a critical value on any such plane. This provides a scheme for explicitly describing the yield surface that is known as the Tresca yield condition. In particular, we conclude that yield occurs when... 

For the type of polycrystal yield surfaces described above, the elementary treatments of hardening are highly intuitive. The fundamental physical idea behind such laws is the recognition that as plastic deformation proceeds, it becomes increasingly difficult to inspire subsequent yield. In chap. II, we will attempt to describe the origins of this phenomenon in the evolution of the distribution of dislocations, while here our aim will be to advance phenomenological approaches to this effect. 

Classical sputtering experiments with a mono-energetic ion beam in high vacuum show that the sputtering yield first increases with the mass of the incident ions and the pressure, but then decreases. For polycrystals, it is maximum at incident angle 30°. For single crystals, it is maximum in the direction perpendicular to a densely packed plane. 

Use the von Mises yield criterion to decide whether the material yields Can you decide which of the two results is correct Justify your answer In experiments on single crystals, the yield strength of the slip systems was determined as Tc- i = 60 MPa. Use the von Mises yield criterion to check whether a significant amount of slip systems in the polycrystal is activated at the stress value given The Taylor factor is M = 3.1. Calculate the stress deviator a for the given stress state ... 

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