Micromechanism

One of the more recent advances in XPS is the development of photoelectron microscopy [ ]. By either focusing the incident x-ray beam, or by using electrostatic lenses to image a small spot on the sample, spatially-resolved XPS has become feasible. The limits to the spatial resolution are currently of the order of 1 pm, but are expected to improve. This teclmique has many teclmological applications. For example, the chemical makeup of micromechanical and microelectronic devices can be monitored on the scale of the device dimensions. 

The advantages of miniaturization are now being exploited in areas beyond microelectronics. Adaptation of materials and processes originally devised for semiconductor manufacture has allowed fabrication of sensors (for example, pressure meters and accelerometers used in the automotive industry) (6,7), complex optical (8) and micromechanical (6,7,9) assembHes, and devices for medical diagnostics (6,7,10) using Hthographic resists. 

D. Cho, R. Warrington Jr., A. Pisano, H. Bau, C. Friedrich,. ara-Almonte, and. Liburdy, eds.. Micromechanical Sensors, Mctuators and Systems, American Society of Mechanical Engineers, New York, 1991. 

Packaging (paper and plastic) packaging adhesives release coatings barrier coatings Photochemical machining (89) micromechanical parts optical waveguides... 

The characteristic features of a cord—mbber composite have produced the netting theory (67—70), the cord—iaextensible theory (71—80), the classical lamination theory, and the three-dimensional theory (67,81—83). From stmctural considerations, the fundamental element of cord—mbber composite is unidirectionaHy reinforced cord—mbber lamina as shown in Figure 5. From the principles of micromechanics and orthotropic elasticity laws, engineering constants of tire T cord composites in terms of constitutive material properties have been expressed (72—79,84). The most commonly used Halpin-Tsai equations (75,76) for cord—mbber single-ply lamina L, are expressed in equation 5 ... 

Fig. 12. Micromechanics of ductile reinforcement particles yielding within process 2one and particles bridging in crack wake.

Fig. 13. Micromechanics of whisker toughening (a) schematic diagram depicting frictional bridging, whisker fracture and pullout and (b) electron...

The use of PB modeling by practitioners has been hmited for two reasons. First, in many cases the kinetic parameters for the models have been difficult to predict and are veiy sensitive to operating conditions. Second, the PB equations are complex and difficult to solve. However, recent advances in understanding of granulation micromechanics, as well as better numerical solution techniques and faster computers, means that the use of PB models by practitioners should expand. 

As with any constitutive theory, the particular forms of the constitutive functions must be constructed, and their parameters (material properties) must be evaluated for the particular materials whose response is to be predicted. In principle, they are to be evaluated from experimental data. Even when experimental data are available, it is often difficult to determine the functional forms of the constitutive functions, because data may be sparse or unavailable in important portions of the parameter space of interest. Micromechanical models of material deformation may be helpful in suggesting functional forms. Internal state variables are particularly useful in this regard, since they may often be connected directly to averages of micromechanical quantities. Often, forms of the constitutive functions are chosen for their mathematical or computational simplicity. When deformations are large, extrapolation of functions borrowed from small deformation theories can produce surprising and sometimes unfortunate results, due to the strong nonlinearities inherent in the kinematics of large deformations. The construction of adequate constitutive functions and their evaluation for particular... 

An example of research in the micromechanics of shock compression of solids is the study of rate-dependent plasticity and its relationship to crystal structure, crystal orientation, and the fundamental unit of plasticity, the dislocation. The majority of data on high-rate plastic flow in shock-compressed solids is in the form of ... 

Unfortunately, in many cases, one or more of the above three components are unavailable, and we resort to substantial subjective guesswork in establishing underlying micromechanical causes of a particular macroscale observation. 

We will attempt to address a number of these phenomena in terms of their micromechanical origins, and to give the essential quantitative ideas that connect the macroscale (continuum description) with the microscale. We also will discuss the importance of direct observations, wherever possible, in establishing uniqueness of scientific interpretation. 

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... 

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. 

Much of what we currently understand about the micromechanics of shock-induced plastic flow comes from macroscale measurement of wave profiles (sometimes) combined with pre- and post-shock microscopic investigation. This combination obviously results in nonuniqueness of interpretation. By this we mean that more than one micromechanical model can be consistent with all observations. In spite of these shortcomings, wave profile measurements can tell us much about the underlying micromechanics, and we describe here the relationship between the mesoscale and macroscale. 

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). 

A typical shock-compression wave-profile measurement consists of particle velocity as a function of time at some material point within or on the surface of the sample. These measurements are commonly made by means of laser interferometry as discussed in Chapter 3 of this book. A typical wave profile as a function of position in the sample is shown in Fig. 7.2. Each portion of the wave profile contains information about the microstructure in the form of the product of and v. The decaying elastic wave has been an important source of indirect information on micromechanics of shock-induced plastic deformation. Taylor [9] used measurements of the decaying elastic precursor to determine parameters for polycrystalline Armco iron. He showed that the rate of decay of the elastic precursor in Fig. 7.2 is given by (Appendix)... 

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. 

Steady-propagating plastic waves [20]-[22] also give some useful information on the micromechanics of high-rate plastic deformation. Of particular interest is the universality of the dependence of total strain rate on peak longitudinal stress [21]. This can also be expressed in terms of a relationship between maximum shear stress and average plastic shear strain rate in the plastic wave... 

By far, the most thoroughly studied material regarding the relationship of micromechanical behavior to macroscale response is LiF [23]-[35]. These data, taken as a whole, remain an important resource from which we are able to develop further understanding of dynamic micromechanical response to shock compression. 

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. 

In summary, it is clear that the micromechanical shock response of single crystal LiF is extremely complex. These results certainly temper the initial enthusiasm associated with Taylor s [9] study of Armco iron as a eomplete explanation for the relationship between the microscale and the macroscale in shock-loaded solids. 

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