Anisotropy planar

Substitution for Fe has a drastic effect on intrinsic magnetic properties. Partial substitution by or decreases J) without affecting seriously, resulting in larger and values. Substitution by Ti and Co causes a considerable decrease in K , the uniaxial anisotropy (if j > 0) may even change into planar anisotropy (if < 0). Intermediate magnetic stmctures are also possible. For example, preferred directions on a conical surface around the i -axis are observed for substitution (72). For a few substitutions the value is increased whereas the J) value is hardly affected, eg, substitution of Fe byRu (73) or by Fe compensated by at Ba-sites (65). 

Single-ion bound excitations in S= 1 Heisenberg antiferromagnetic chains with strong planar anisotropy. 

Fig. 2. Anisotropy in low-dimensional materials a) axial anisotropy in 1D b) planar anisotropy in 2D...

For the case of an isotropic metallic material, the well-known von Mises yield criterion is often sufficient to describe yielding. This is, however, not true for anisotropic materials, especially aluminium sheet metals. In order to take into account anisotropy, the classical yield criterion proposed by von Mises should be modified by introducing additional parameters. A simple approximation for the case of planar anisotropy is given by the quadratic criterion of (Hill 1948) ... 

The rocks with planar anisotropy exhibit the highest strength in the direction perpendicular to the anisotropy and the lowest at an inclination of 30°-45° with the plane of anisotropy in jointed samples. The anisotropy of the specimen influences the dynamic elastic modulus more than the static elastic modulus... 

In this paper the compressive strength/elastic modulus of the jointed rock mass was estimated as a function of intact rock strength/modulus and joint factor. The joint factor reflects the combined effect of joint frequency, joint inclination and joint strength. Therefore, having known the intact rock properties and the joint factor, jointed rock properties can be estimated. The test results indicated that the rock mass strength decreases with an increase in the joint frequency and a sharp transition was observed from brittle to ductile behaviour with an increase in the number of joints. It was also found that the rocks with planar anisotropy exhibit the highest strength in the direction perpendicular to the anisotropy and the lowest at an inclination of 30o-45o in jointed samples. The anisotropy of the specimen influences the dynamic elastic modulus more than the static elastic modulus. The results were also compared well with the published works of different authors for different type of rocks. 

Material Young s modulus, E GPa 10 psi Yield strength MPa ksi Tensile strength MPa ksi Uniform elongation (%) Total elongation (%) Strain hardening exponent in) Average normal anisotropy (r, ) Planar anisotropy (Ar) Strain rate sensitivity (m)... 

The planar anisotropy which is responsible for the magnitude and position of ears in a deep-drawn cylindrical cup and to undesirable metal flow in the blank holder, in the general case, is usually defined by... 

In steels, moderate plastic deformation and low annealing temperature are beneficial in developing the recrystallization texture. Planar anisotropy increases with increasing deformation and higher annealing temperature in copper sheets, whereas the inverse is found in brass sheets [28]. 

We can observe a fairly good agreement between the numerical prediction and the experimental observation. However, the current model does not consider the planar anisotropy in SMC/BMC rheology which is developed by flow-induced anisotropic fiber orientation in the planar direction. This issue should be addressed in the forthcoming work to improve the model. 

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