Heterogeneous Micromechanics

That this is not always the case should be expected. In fact, if it was not for heterogeneous localization of some flow phenomena, it would be very diflicult to initiate secondary explosives, or to effect shock-induced chemical reactions in solids. Heterogeneous shear deformation in metals has also been invoked as an explanation for a reduction in shear strength in shock compression as compared to quasi-isentropic loading. We present here a brief discussion of some aspects of heterogeneous deformation in shock-loaded solids. 

Bai [48] presents a linear stability analysis of plastic shear deformation. This involves the relationship between competing effects of work hardening, thermal softening, and thermal conduction. If the flow stress is given by Tq, and work hardening and thermal softening in the initial state are represented 

Grady and Asay [49] estimate the actual local heating that may occur in shocked 6061-T6 Al. In the work of Hayes and Grady [50], slip planes are assumed to be separated by the characteristic distance d. Plastic deformation in the shock front is assumed to dissipate heat (per unit area) at a constant rate S.QdJt, where AQ is the dissipative component of internal energy change and is the shock risetime. The local slip-band temperature behind the shock front, 7), is obtained as a solution to the heat conduction equation with y as the thermal diffusivity 

In place of a complete evolutionary expression of normal softening and yield-strength recovery, Swegle and Grady [13] propose a temperature-dependent yield strength F(7]) in qualitative agreement with expected behavior 

The evolution of T, is just an exercise in mesoscale thermodynamics [13]. These expressions, in combination with (7.54), incorporate concepts of heterogeneous deformation into a eonsistent mierostruetural model. Aspects of local material response under extremely rapid heating and cooling rates are still open to question. An important contribution to the micromechanical basis for heterogeneous deformation would certainly be to establish appropriate laws of flow-stress evolution due to rapid thermal cycling that would provide a physical basis for (7.54). 

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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. 

Because of the inherently heterogeneous nature of composite materials, they are conveniently studied from two points of view micromechanics and macromechanics ... 

Micromechanics — The study of composite material behavior wherein the interaction of the constituent materials is examined in detail as part of the definition of the behavior of the heterogeneous composite material. 

Thus the study of surfaces has emerged as an important focus in the chemical sciences, and the relationship between surfaces of small systems and their performance has emerged as a major technological issue. Flow in microfluidic systems—for example, in micromechanical systems with potential problems of stiction (sticking and adhesion) and for chemistry on gene chips—depends on the properties of system surfaces. Complex heterogeneous phases with high surface areas—suspensions of colloids and liquid crystals—have developed substantial... 

Low, B.Y., Gardener, S.D., Pittman, C.U. and Hackell, R.M. (1994), A micromechanical characterization of graphite fiber/epoxy composites containing a heterogeneous interphase region. Composites Sci. Technol. 52, 589-606. 

Micromechanical experiments made so far can be roughly divided into two parts (i) design of special techniques to measure and evaluate separately different contributions in the net force, such as adhesion, friction, deformation, and (ii) imaging of various heterogeneous surfaces such as blends, composites and microphase separated structures by conventional SFM s to collect statistical information and understand the origin of the mechanical contrast. Many of the micromechanical experiments were discussed elsewhere [58, 67, 68, 381, 412-414]. Here we will focus on recent advances in analytical applications of the active probe SFM. 

Nemat-Nasser, S. Hori, M. (eds.) Micromechanics, Part 1 Overall Properties of Heterogeneous Materials, Second Revised Edition (Elsevier Amsterdam, 1998). 

Based on a local dissolution law, the micromechanical approach is able to discuss the effects of the local heterogeneity of the mechanical affinity on the dissolution process and to predict the evolution of the pore space morphology. Whenever it is possible to describe the latter by a scalar parameter , (22) yields its evolution (t) which captures the chemomechanical coupling in so far as it controls the evolution of the poroelastic coefficients in (13). Nevertheless, the implementation of this modelling requires to be able to determine the microscopic strain state along the fluid-solid interface by appropriate micromechanical techniques. 

S. Nemat-Nasser, M. Lori Micromechanics Overall properties of heterogeneous materials. J. App. Mech 63, 561 (1996)... 

S. Nemat-Nasser and M. Hori, Micromechanics Overall Properties of Heterogeneous Materials, North-Holland, New York (1993). 

The microstinctural configuration of heterogeneous materials can be correlated to the macroscopic constimtive relations within the micromechanics framework. In this approach the representative volume element (RVE) represents a specific arrangement of subphases, each of which has a specific geometry and mechanical properties. Selection of an RVE is extremely... 

Hori, M. and Nemat-Nasser, S. (1999) On two micromechanics theories for determining micro-macro relations in heterogeneous solids. Mechanics of Materials, 31, 667-682. 

Abstract This chapter describes the elastic qualities of advanced fibre-reinforced composites, in terms of characterization, measurement and prediction from the basic constituents, i.e. the fibre and matrix. The elastic analysis comprises applying micromechanics approaches to predict the lamina elastic properties from the basic constituents, and using classical lamination theory to predict the elastic properties of composite materials composed of several laminae stacked at different orientations. Examples are given to illustrate the theoretical analysis and give a full apprehension of its prediction capability. The last section provides an overview on identification methods for elastic proprieties based on full-field measurements. It is shown that these methodologies are very convenient for elastic characterization of anisotropic and heterogeneous materials. 

Nanjangud, S. C. Brezny, R. Green, D. J. J. Am. Ceram. Soc. 1995, 78, 266-268. Nemat-Nasser, S. Hori M. Micromechanics - Overall Properties of Heterogeneous Materials North-Holland / Elsevier Amsterdam, The Netherlands, 1999 (second edition) pp 1-786. 

Analytical models are mathematical models that have a closed form solution to the equations used for describing changes in a system. Some analytical models are developed for highly specific applications, whereas others for general applications. In material science, micromechanical models are developed to analyze the composite or heterogeneous materials on the level of individual constituents. They can predict the properties of the composite materials and account for interfaces between constituents, discontinuities, and coupled mechanical and nonmechanical properties. 

Tobias Schuller - Institute of Polymer Research Dresden. Dr. Schuller received his Master degree in Physics from the TU Dresden in 1997. He went to the IPF in 1998 to work in the fields of micromechanics, fracture mechanics, interface cracks in heterogeneous materials and of finite element simulation. He received his PhD in Engineering Science from the University of Kaiserslautern in 2004. He is currently senior developer of Micro-Optronic Messtechnik GmbH. 

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