Viscoplasticity of Ferromagnetics
The principal objective of this chapter is to give a rational thermodynamic ap- proach to inelasticity of ferromagnetic materials in a simplified version which should serve primarily for subsequent nondestructive electromagnetic examination of inelastic behaviour of reactor steels (cf. [MSC87, ZH-88, Ruu88]). Due to limited space, however, some second-order effects have to be omitted from the consideration.
In this chapter, like in [Mic86a, Mic87a, MM-89], the associativity of flow rule (the normality of the plastic stretching tensor onto a yield surface) has not been taken as granted even if such an approach is accepted in the majority of the papers dealing with the subject. Such normality is seriously questioned not only by the theoretical but by experimental results as well.1 For these reasons the normality is at first abandoned and instead of such an assumption, evolution equations (exposed in the second section of this chapter) are based on the appropriate geometry of deformation and tensor representation. This geometry is founded on the continuum theory of dislocations (compare to [Kro60, Mic74b, FFP91]) and is shortly reviewed in the next section. As already mentioned in the chapter devoted to thermodynamics a very attractive approach to the extended thermodynamics has been proposed in [Mul71] with a rational analysis of thermodynamic processes leading to the desired thermodynamic restrictions of general constitutive equations. This approach with Liu’s theorem ([Liu72]) was applied to viscoplastic materials in [Mic86a] and to inelastic composite materials in [Mic87a]. However, despite its originality an inherent coldness function (which is not quite clear from the experimental point of view) is inevitable. The method with its advantages and drawbacks was discussed in detail in Section 4.2.4.
KeywordsPlastic Strain Plastic Strain Rate Thermodynamic Process Residual Magnetization Accumulate Plastic Strain
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