Description Of Hysteresis Loops Research Articles

Advantages of Dual Hyperbolic Tangent Function Over Single Hyperbolic Tangent Function in Description of Hysteresis Loops

If the mathematical description of the magnetic hysteresis loop branches should be simple, easy to use and should credibly describe the waveform magnetic hysteresis loop with a minimum number of parameters, then it inevitably leads to the description of magnetic hysteresis loop branches with a hyperbolic tangent function. This paper presents the advantages in description of magnetic hysteresis loop branches with a hyperbolic tangent function over other functions. The advantages in description of magnetic hysteresis loop branches with dual hyperbolic tangent function versus description with a single hyperbolic tangent function when the magnetic hysteresis loop has a very pronounced saturation region are provided. Also, this paper presents numerical difficulties in describing of magnetic hysteresis loop branches with a hyperbolic tangent function. Using soft magnetic material, as an example, a numerical procedure for determining parameters in description of magnetic hysteresis loop branches with a single and two hyperbolic tangent functions is shown. The numerical results are analyzed and discussed.

Magnetic bubbles and stripe domains in nanostructured FePd elements

The analysis of the magnetization process in rectangular thin dots exhibiting a canted anisotropy is reported. The studied dots with quality factor Q≈0.4 are large enough to sustain at least a bi-domain pattern at the remnant state. The various magnetic patterns observed in modeling hysteresis with the external field applied along one of the edges of the dot, moving from one saturated state to the opposite one, are described according to the length of the dots. The facts that the easy axis is tilted with respect to the normal of the dot surface, associated with the limited size of the dots, impose a double flux-closure scheme for the magnetization distribution. The reversal occurs via bubbles nucleation inside the dots followed by the transition to a stripe pattern. Furthermore, it is shown in the description of hysteresis loop that the full magnetization reversal needs successive injections of two sets of Bloch-points. Special attention is paid to topological problems associated with the injection and expulsion of these singularities.

Inversion of Ramberg–Osgood equation and description of hysteresis loops

The Ramberg–Osgood equation has been approximately inverted. Four orders of approximations providing progressively more accurate inversions are considered. The second order inversion is used to develop closed-form relations for stress in terms of strain and for cyclic stress in terms of cyclic strain. Explicit relations between the cyclic-strength coefficient and the cyclic strain-hardening exponent and between the cyclic strain-hardening exponent and the elastic modulus are developed. Application to nine different engineering metals shows that the proposed approximate inversion provides a powerful tool for describing stress–strain relations. Examples of hysteresis loops for a number of strain time-histories are presented. Also, it is shown that augmenting the strain time-history with fictitious strain segments to close all the hysteresis loops yields the same stress–strain relation as that obtained through the rain-flow counting method.

Stress Rate Effect on the Pseudoelastic Behaviour of CuZnAl Single Crystals

Tensile pseudoelastic tests performed on elaborated single crystals show that the width of hysteresis loops and the slope of the stress-strain curves during phase transformation increase as the applied stress rate increases. In the first elementary model without mechanical dissipation, the integration of heat equation permits the qualitative description of hysteresis loop. The second model with a non-convex free energy and mechanical dissipation allows us a quantitatively good modeling of loading rate effects.

Hystérésis d'alliages thermoélastiques, étude comparative de quelques modèles de comportement des alliages à mémoire de forme

The hysteretic behaviour of shape memory alloys (SMA) needs a more and more thin analysis because of its importance for technological applications. The comparison between different approaches allows to explicite the specifity of every model (macroscopic approach, micro-macro level, local description, phenomenological approach) and their points of convergence. On one hand, a thermodynamic treatment with a free energy expression as a mixing rule of each phase (parent or austenite phase and martensite) by adding a coupling term: the configurational energy, allowes modelling of material hysteresis loops. On the other hand, a phenomenological treatment based on a local investigation of two single crystals with a visualisation of microscopic parameters allows to perceive the phase transition mechanisms (nucleation, growth). All the obtained results show the importance of entropy production (or of the definition of the configurational energy term) for the correct description of hysteresis loops (subloops or external)

Cyclic plasticity under nonproportional loading. (1st report. A new description of hysteresis loops).

Thin-walled tubes of a carbon steel were subjected to nonproportional cyclic loading. A new expression for describing the cyclic deformation under multiaxial stresses was demonstrated for examining the propriety of the constitutive equation in cyclic plasticity presented in a previous paper, based on the random barriers theory. With this expression, the cyclic deformation, both under the proportional loading and under the nonproportional loading, could be discussed inclusively in the same category. The experimental results proved that the plastic potential function used in the equation and its change characteristics depending on the cyclic history, induced from the experiments on the uniaxial stress cycling, were applicable to the case of the multiaxial stress cycling. Moreover, it was suggested that an effect of anisotropy produced by cyclic deformation might be reflected in the internal structure variable which was one of the fundamental components in the constitutive equation.