Microstructure hysteresis

The properties of nanocomposite systems, whose microstructures aim at reproducing real systems, have been examined in various numerical modelling studies [127, 128], In general, the essential features of the hysteresis cycles may be satisfactory reproduced. In particular, soft layer reversal is quantitatively accounted for, which is expected for reversible phenomena. By contrast, the calculated high-field irreversible reversal of the hard phase magnetization is not reproduced in general. Such discrepancy illustrates the already mentioned difficulty to describe irreversible processes. 

There are a number of indicators of fatigue damage that have attracted interest in the literature. During the life of a component subjected to fatigue, the material can exhibit changes in modulus, permanent offset strain, shape of the hysteresis loops, and temperature rise of the specimen surface. Direct evidence of matrix crack density can be obtained by surface replication, while a more detailed analysis of microstructural damage requires scanning electron microscopy (SEM). 

Chu C.-H., Hysteresis and Microstructures A Study of Biaxial Loading on Compound Twins of Copper-Aluminum-Nickel Single Crystals, PhD Thesis, University of Minnesota, 1993. (unpublished)... 

The function h r, r ) accounts for the possibility that due to hysteresis effects, the interface does not advance completely to pores with capillary radius with increasing S, it depends on the detailed topology of the pore space and, thus, demands more detailed microstructure characterization. T is a factor of order 1, depending on pore geometry and wetting properties. 

Finally we can note that the ferroelectric state of relaxors is characterised by an extremely narrow hysteresis loop with a low value for the remanent polarisation (Figure 6.19a). This sort of hysteresis loop can be considered to fall into the continuum described previously (Figure 6.9) and suggests that the microsttucture of the phases is at an even more reduced scale than the fine-grained ceramic samples. Indeed, the behaviour when the materials are either cooled in or without an external electric field (FC or ZFC) is also taken as indicative of a complex microstructure. The strain versus applied electric field loop has a U shape, rather like the central portion of the strain curve for an antiferroelectric (Figure 6.19b). 

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