Deformation history

Here r(t) is the stress at a fluid particle given by an integral of deformation history along the fluid particle trajectory between a deformed configuration at time f and the current reference time t. 

The energy which drives the fragmentation process (elastic plus kinetic) is determined by the dynamic loading conditions and does not directly depend on the properties of the material at issue. The fragmentation energy, on the other hand, is an intimate property of the material and can depend in a complex way on the thermal and dynamic conditions at spall, as well as on the deformation history of the material leading to spall. 

A substantial portion ( 15%) of the magnetite was found to be converted to hematite. As prior work showed small conversion (1%) of hematite to magnetite, the data indicate that the conversion can proceed in either direction depending upon the local microscopic deformation history of the powder particles. 

The function iKt-t ) may be interpreted as a memory function having a form as shown in Figure 3.14. For an elastic solid, iff has the value unity at all times, while for a purely viscous liquid iff has the value unity at thfe current time but zero at all other times. Thus, a solid behaves as if it remembers the whole of its deformation history, while a purely viscous liquid responds only to its instantaneous deformation rate and is uninfluenced by its history. The viscoelastic fluid is intermediate, behaving as if it had a memory that fades exponentially with time. The purely elastic solid and the purely viscous fluid are just extreme cases of viscoelastic behaviour. 

These two mathematical Equations (4.59) and (4.60) illustrate an important feature about linear viscoelastic measurements, i.e. the central role played by the relaxation function and the compliance. These terms can be used to describe the response of a material to any deformation history. If these can be modelled in terms of the chemistry of the system the complete linear rheological response of our material can be obtained. 

Mair, J.L, Hart, C.J.R., Stephens, J.R. 2006. Deformation history of the northwestern Selwyn Basin, Yukon, Canada implications for orogen evolution and mid-Cretaceous magmatism. GSA Bulletin, 118, 304-323. 

The promise of luminescent methodology is based on many types of information that can be derived from mineralogical samples. These include RE from Ce to Yb, identities down to the ppb range, the valence states of the RE, the nature of the sites at which RE reside and the ways of compensating the charge, and features related to the presence of other ions (donors, activators). All this information can be used to determine the chemical, thermal, and deformational history of the material. 

An overview of the origins of yield stress and parameters which can lead to variations in behaviour with highly filled polymer dispersions is given by Malkin [1]. Much of the following literature, describing experimental work undertaken, demonstrates that yield phenomena can be correlated with the extent of interaction between the filler particles and the formation of a network structure. However, the actual behaviour observed during experimentation may also depend on the deformation history of the material, or the time and temperature of imposed deformation, especially if the material exhibits thixotropic properties. 

This section summarizes results of the phenomenological theory of viscoelasticity as they apply to homogeneous polymer liquids. The theory of incompressible simple fluids (76, 77) is based on a very general set of ideas about the nature of mechanical response. According to this theory the flow-induced stress at any point in a substance at time t depends only on the deformations experienced by material in an arbitrarily small neighborhood of that point in all times prior to t. The relationship between stress at the current time and deformation history is the constitutive equation for the substance. 

The response of simple fluids to certain classes of deformation history can be analyzed. That is, a limited number of material functions can be identified which contain all the information necessary to describe the behavior of a substance in any member of that class of deformations. Examples are the viscometric or steady shear flows which require, at most, three independent functions of the shear rate (79), and linear viscoelastic behavior (80,81) which requires only a single function, in this case a relaxation function. The functions themselves must be determined experimentally for each substance. 

For steady shear flow, the shear rate y is constant for all past time. Since deformation history now depends only on the parameter y, the stress components become functions of y alone ... 

Viscoelastic behavior is classified as linear or non-linear according to the manner by which the stress depends upon the imposed deformation history (SO). Insteady shear flows, for example, the shear rate dependence of viscosity and the normal stress functions are non-linear properties. Linear viscoelastic behavior is obtained for simple fluids if the deformation is sufficiently small for all past times (infinitesimal deformations) or if it is imposed sufficiently slowly (infinitesimal rate of deformation) (80,83). In shear flow under these circumstances, the normal stress differences are small compared to the shear stress, and the expression for the shear stress reduces to a statement of the Boltzmann superposition principle (15,81) ... 

Unfortunately, the energy dissipation method upon which these calculations are based is only applicable to the evaluation of viscosity in steady deformations. The method does not lend itself to an extension of the disentanglement model to other components of the stress or to other types of deformation history. 

Still, sophisticated, exact, numerical, non-Newtonian and nonisothermal models are essential in order to reach the goal of accurately predicting final product properties from the total thermomechanical and deformation history of each fluid element passing through the extruder. A great deal more research remains to be done in order to accomplish this goal. 

The deformational history of the Sy element is coupled to the chemical reaction and mass transfer "problem through the D term in Eq. 2. From a physical standpoint, n is the relative stretch undergone by a material interface in its passage through the extruder (see Figure 3). 

The filler network break-down with increasing deformation amplitude and the decrease of moduli level with increasing temperature at constant deformation amplitude are sometimes referred to as a thixotropic change of the material. In order to represent the thixotropic effects in a continuum mechanical formulation of the material behavior the viscosities are assumed to depend on temperature and the deformation history [31]. The history-dependence is implied by an internal variable which is a measure for the deformation amplitude and has a relaxation property as realized in the constitutive theory of Lion [31]. More qualitatively, this relaxation property is sometimes termed viscous coupling1 [26] which means that the filler structure is viscously coupled to the elastomeric matrix, instead of being elastically coupled. This phenomenological picture has... 

Since then, TEM has been used to study dislocation microstructures in a wide range of naturally and experimentally deformed minerals and rocks. In general, the aim of the experimental studies is to determine the deformation mechanisms by relating the evolution of the observed mi-crostructures to the macroscopic deformational behavior observed under varying conditions of temperature, confining pressure, chemical environment, strain-rate, stress, and total strain, and then to use this knowledge to interpret the microstructures observed in naturally deformed specimens and hence to determine their deformational history. 

Stress estimates based on measurements of p, d, and D in naturally deformed crystals also assume (i) steady-state deformation, at the cessation of which the evolved microstructure is frozen in, (ii) a simple deformation history, and (iii) experimental data that can be extrapolated to geological conditions. 

The accuracy with which we calculate closure temperatures depends on having high-quality diffusion data. For some systems (e.g., Lu/Hf in garnet), reliable diffusion data do not exist. For many others, we have no good understanding of the effects of natural compositional variability or deformational history on dififusivity. The experiments necessary to improve this situation are difficult and time-consuming, but they are of cmcial importance. 

Reddy S. M., Kelley S. P., and Wheeler J. (1996) A AtP At laser probe study of micas from the Sesia zone, Italian Alps implications for metamorphic and deformational histories. J. Metamorph. Geol. 14, 493-508. 

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