Yield behaviour, anisotropic

We will discuss here the anisotropic yield behaviour of oriented polymers but there is a need for a few preliminary remarks regarding the topic of yield in general. In describing the deformation of many crystalline materials, especially metals and ceramics, it is often convenient to introduce the idealisation of an elastic-plastic transition . The term elastic is used to describe the components of the strain which are proportional to the applied stresses, and which are completely recovered on removal of the stresses. Plastic strains are observed only for stresses greater than or equal to the yield stress and are not recovered on removal of the stress. The yield stress defines the elastic-plastic transition. 

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. 

For the odd electron systems, tf3 4Z andc 5 6Z+, measurements of the average susceptibility at very low temperatures are not likely to prove as informative as for the even electron, d 32 species. This is because whereas the latter yield a limiting value of 1 as T -+ 0, from which D/g2 can be directly estimated, the former lead only to a limiting value of the (x)-1 vs. T slope, which except for large values of D will be difficult to determine. Nevertheless calculation shows that even in cases for which only very small deviations from the spin-only behaviour are to be expected, e.g. V(Cp)2, the susceptibility may yet show very considerable anisotropy. Thus, with the parameters of Prim and Van Voorst (47), V(Cp)2 is predicted to show an anisotropy, (x — X )Kx of some 5% at liquid nitrogen temperatures, whilst Ni(Cp)2, with the much larger/) value, should show an anisotropy of about 30% at 77K, which is reduced only to some 12% even at room temperature. There is thus considerable scope for the measurement of anisotropic susceptibilities, and although this technique would probably not be applicable to the d8 bis-arenes (97,... 

These are essentially independent effects a polymer may exhibit all or any of them and they will all be temperature-dependent. Section 6.2 is concerned with the small-strain elasticity of polymers on time-scales short enough for the viscoelastic behaviour to be neglected. Sections 6.3 and 6.4 are concerned with materials that exhibit large strains and nonlinearity but (to a good approximation) none of the other departures from the behaviour of the ideal elastic solid. These are rubber-like materials or elastomers. Chapter 7 deals with materials that exhibit time-dependent effects at small strains but none of the other departures from the behaviour of the ideal elastic sohd. These are linear viscoelastic materials. Chapter 8 deals with yield, i.e. non-recoverable deformation, but this book does not deal with materials that exhibit non-linear viscoelasticity. Chapters 10 and 11 consider anisotropic materials. 

The 1030 keV resonance in the elastic scattering curve is also apparent in the yield of inelastically scattered protons and of 477 keV gamma radiation from the first excited state of Li produced in the reaction Li (/>/> ) Li . The inelastically scattered protons were found by Mozer et al. to be isotropically distributed at the resonance but become anisotropic at higher energies. The behaviour is that of an interference between two waves of opposite parity. In this experiment the inelastically scattered protons were selected magnetically from a thick target of natural... 

Interpretation of NMR relaxation data of macromolecules is based on the analysis of their dynamic behaviour in solution. For quasi rigid molecules, in addition to a minor, separable contribution from local mobility, the main contribution corresponds to the overall rotational diffusion of the complete molecule. Therefore, theoretical descriptions and computational methodologies for hydrodynamic calculations, which yield the full, anisotropic rotational... 

Peschl unconfined yield strength tester A sample is vertically compacted in a rectangular mould, and after the top lid and normal stress are removed one of the sidewalls of the tester is driven horizontally into the sample up to the point of failure. The stress applied to fail the powder is an estimate of the unconfined yield strength. If a bulk solid shows anisotropic behaviour, it might be expected that the described tester would produce... 

Since the publication of the second edition in 1983, the subject has advanced considerably in many respects, especially with regard to non-linear viscoelasticity, yield and fracture. We have altered some chapters very little, notably those dealing with viscoelastic behaviour and the earlier research on anisotropic mechanical behaviour and rubber elasticity, only adding sections to deal with the latest developments. 

The anisotropic behaviour of bulk solids mentioned in connection with Fig. 5 (procedure III) is of no influence in the design of silos for flow. With help of Fig. 5 and 6 it was explained that steady state flow was achieved with Oi (at steady state flow) acting in x-direction. The unconfmed yield strength was also measured with the major principal stress acting in x-direction. During steady state flow in a hopper the major principal stress is in the hopper-axis horizontal. In a stable dome above the aperture the unconfined yield strength also acts horizontally in the hopper axis. Therefore, the Flow Function reflects reality in the hopper area. 

The pipe was modelled assuming an elastic, perfectly plastic behaviour with a yield stress of 448 MPa. The material orientation for the anisotropic repair laminate is shown in Figure 11.1. The repair laminate through thickness modulus, Ett, and the axial modulus, Eaa, were orientated along the directions T and 2 , respectively, as shown in Figure 11.1(b). 

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