Micromechanical effects

Two examples of path-dependent micromechanical effects are models of Swegle and Grady [13] for thermal trapping in shear bands and Follansbee and Kocks [14] for path-dependent evolution of the mechanical threshold stress in copper. 

Wallace [15], [16] gives details on effects of nonlinear material behavior and compression-induced anisotropy in initially isotropic materials for weak shocks, and Johnson et ai. [17] give results for infinitesimal compression of initially anisotropic single crystals, but the forms of the equations are the same as for (7.10)-(7.11). From these results it is easy to see where the micromechanical effects of rate-dependent plastic flow are included in the analysis the micromechanics (through the mesoscale variables and n) is contained in the term y, as given by (7.1). 

Internal Stresses Micromechanical Effects upon Release from the Shocked State... 

Nevertheless, as response data have accumulated and the nature of the porous deformation problems has crystallized, it has become apparent that the study of such solids has forced overt attention to issues such as lack of thermodynamic equilibrium, heterogeneous deformation, anisotrophic deformation, and inhomogeneous composition—all processes that are present in micromechanical effects in solid density samples but are submerged due to continuum approaches to mechanical deformation models. 

We also want to point out the difference between simple rate-dependent phenomena and path-dependent effects. Simple rate dependence means that the internal micromechanical state (as possibly represented by some meso-scale variables) depends only on the current deformation and current rate of deformation the material has no memory of the past. In terms of dislocation dynamics and (7.1), a simple rate-dependent constitutive description would be one in which... 

The shock-induced micromechanical response of <100>-loaded single crystal copper is investigated [18] for values of (WohL) from 0 to 10. The latter value results in W 10 Wg at y = 0.01. No distinction is made between total and mobile dislocation densities. These calculations show that rapid dislocation multiplication behind the elastic shock front results in a decrease in longitudinal stress, which is communicated to the shock front by nonlinear elastic effects [pc,/po > V, (7.20)]. While this is an important result, later recovery experiments by Vorthman and Duvall [19] show that shock compression does not result in a significant increase in residual dislocation density in LiF. Hence, the micromechanical interpretation of precursor decay provided by Herrmann et al. [18] remains unresolved with existing recovery experiments. 

Asay et al. [24] investigate further the effects of nonlinear elasticity on micromechanical interpretation of decaying elastic shock fronts. Values of (Til, I, r/Cj, and which represent the highest Mg" " impurity concentration are shown in Table 7.1 for D = 0.1 GPa. 

Although the difference in final strength f, integrated through both the actual shock wave and the computational shock wave, will be mitigated by dynamic recovery (saturation) processes, this is still a substantial effect, and one that should not be left to chance. These are very important practical considerations in dealing with path-dependent, micromechanical constitutive models of all kinds. 

An important aspect of micromechanical evolution under conditions of shock-wave compression is the influence of shock-wave amplitude and pulse duration on residual strength. These effects are usually determined by shock-recovery experiments, a subject treated elsewhere in this book. Nevertheless, there are aspects of this subject that fit naturally into concepts associated with micromechanical constitutive behavior as discussed in this chapter. A brief discussion of shock-amplitude and pulse-duration hardening is presented here. 

That some enhancement of local temperature is required for explosive initiation on the time scale of shock-wave compression is obvious. Micromechanical considerations are important in establishing detailed cause-effect relationships. Johnson [51] gives an analysis of how thermal conduction and pressure variation also contribute to thermal explosion times. 

So, for given strain rate s and v (a function of the applied shear stress in the shock front), the rate of mixing that occurs is enhanced by the factor djhy due to strain localization and thermal trapping. This effect is in addition to the greater local temperatures achieved in the shear band (Fig. 7.14). Thus we see in a qualitative way how micromechanical defects can enhance solid-state reactivity. 

Micromechanics is the study of composite material behavior wherein the interaction of the constituent materials is examined on a microscopic scale to determine their effect on the properties of the composite material. 

The reader should be exposed to both micromechanics and macromechanics in order to function effectively in either material design or structurai design. The main thrust of this book is in iine with structurai design and analysis requirements. Thus, the point of our addressing micromechanics is to better understand how and why composite materials function. 

Shear-stress-shear-strain curves typical of fiber-reinforced epoxy resins are quite nonlinear, but all other stress-strain curves are essentially linear. Hahn and Tsai [6-48] analyzed lamina behavior with this nonlinear deformation behavior. Hahn [6-49] extended the analysis to laminate behavior. Inelastic effects in micromechanics analyses were examined by Adams [6-50]. Jones and Morgan [6-51] developed an approach to treat nonlinearities in all stress-strain curves for a lamina of a metal-matrix or carbon-carbon composite material. Morgan and Jones extended the lamina analysis to laminate deformation analysis [6-52] and then to buckling of laminated plates [6-53]. 

Anstice P. D. and Beaumont P.W.R. (1981). Hygrothermal aging effects on the micromechanisms of crack extension in glass fiber and carbon fiber composites. In Proc. ICF 5 (Francois D. et al.. eds.). Pergamon Press, Oxford, Vol. I, pp. 473-483. 

With respect to micromechanisms of failure, at low values of Ak, discontinuous growth bands whose spacings correspond to many cycles of loading were observed (26,32). Figure 10 shows the effect of composition on r, the spacing of the bands, the yield stress o (estimated from the Dugdale relationship, r ifK /80 ), and tlJe... 

In order to understand the effects of filler loading and filler-filler interaction strength on the viscoelastic behavior, Chabert et al. [25] proposed two micromechanical models (a self-consistent scheme and a discrete model) to account for the short-range interactions between fillers, which led to a good agreement with the experimental results. The effect of the filler-filler interactions on the viscoelasticity... 

The effect of polymer-filler interaction on solvent swelling and dynamic mechanical properties of the sol-gel-derived acrylic rubber (ACM)/silica, epoxi-dized natural rubber (ENR)/silica, and polyvinyl alcohol (PVA)/silica hybrid nanocomposites was described by Bandyopadhyay et al. [27]. Theoretical delineation of the reinforcing mechanism of polymer-layered silicate nanocomposites has been attempted by some authors while studying the micromechanics of the intercalated or exfoliated PNCs [28-31]. Wu et al. [32] verified the modulus reinforcement of rubber/clay nanocomposites using composite theories based on Guth, Halpin-Tsai, and the modified Halpin-Tsai equations. On introduction of a modulus reduction factor (MRF) for the platelet-like fillers, the predicted moduli were found to be closer to the experimental measurements. 

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